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U nive I'Sity dissertation entitled

An Abundance Study of IC 418 Using High Resolution, Signal-
to-Noise Emission Spectra

presented by

Brian David Sharpee

has been accepted towards fulfillment
of the requirements for the

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6/01 cJCIRC/DateDuepGS-p. 15

AN ABUNDANCE STUDY OF 10 418 USING HIGH
RESOLUTION, SIGNAL-TO-NOISE EMISSION SPECTRA

By

Brian David Sharpee

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Physics and Astronomy

2003

ABSTRACT
AN ABUNDANCE STUDY OF 10 418 USING HIGH RESOLUTION,
SIGNAL-TO-NOISE EMISSION SPECTRA
By

Brian David Sharpee

An on-going problem in astrophysics involves the large and varying disagreement
between abundances measurements made in planetary nebulae (PNe), determined
from the strengths Of emission lines arising from the same source ion, but excited by
differing mechanisms (recombination and collisional excitation) in planetary nebulae
(PNe).

We investigate the extent of this problem in IC 418, a PN chosen for its great
surface brightness and perceived visually uncomplicated geometry, through the use of
high resolution (Rm 30000 = 10 km sec“1 at 6500A) echelle emission spectroscopy in
the optical regime (3500-9850A). These observations allow us to construct the most
detailed list of atomic emission lines ever compiled for IC 418, and among the most
detailed from among all PNe. Ionic abundances are calculated from the fluxes Of
numerous weak (1 X 10"5 H5) atomic emission lines from the ions of C,N,O, and Ne,
using the most recent and accurate atomic transition information presently available.

The high resolution of these Spectra provides well-defined line profiles, which, coupled

with the perceived simplicity of the object’s expansion velocity distribution, allows
us to better determine where in the nebula lines are formed, and where the ions
that produce them are concentrated. Evidence for “non-conventional” line excita-
tion mechanisms, such as continuum fluorescence from the ground state or enhanced
dielectronic recombination, is sought in the profile morphologies and relative line
strengths. Non-conventional excitation processes may influence the strengths of lines
enough to significantly alter abundances calculated from them.

Our calculations Show that recombination line-derived abundances exceed those
derived from collisionally excited lines, for those ions for which we observed lines of
both types: 0+, 0”, and Ne+2 by real and varying amounts. We find that both
continuum fluorescence and dielectronic recombination excites numerous lines in IC
418, but that there is no evidence in our data that either process is responsible for the
observed overabundances in all recombination lines as opposed to their collisionally
excited counterparts. The calculated levels of temperature fluctuations in the zones
in which these ion reside are dubious, and significantly exceed model predicted values.
In summary, no satisfactory, single universally applicable answer to the abundance
discrepancy problem shown to exist by us in IC 418, is revealed by our observations.

We developed several new techniques to analyze these data. Of particular in-
terest is EMILI (Emission Line Identifier), a public-domain program that utilizes a
comprehensive atomic transition list and a set of Simple tests and criteria, to quickly
provide its user with a list of rank ordered IDS for unidentified emission lines found
in deep, high resolution spectra. Presented here are the results of applying EMILI to

the identification of weak emission lines in the spectra of IC 418 and other PNe.

T0 Tanya

iv

ACKNOWLEDGMENTS

It is said that the journey of a thousand miles begins with a Single step. I am
most greatful to my advisor, Professor Jack Baldwin, for guiding my first steps down
that road, then provisioning me for the long haul. When the road forked along
the way I was glad for the presence Of my guidance committee: Professors Robert
Williams, Eugene Capriotti, James Linnemann, and Hendrik Schatz who provided
caring and sound advice. Thanks also to Professors Horace Smith and Peter van
Hoof for providing me essential tools for completing this thesis.

I cannot forgot the many folks who Shared the road with me, my fellow grads and
travelers: Andrew Schnepp, Chris Hanley, Barton Pritzl, Robert Slater, Wayne and
Marguerite Tonjes, Jason and Viki Grenya, Zach Constan, James Armstrong, Alexan-
der Volya, Michael Davis, Dali Georgobiani, Regner Trampedach, Aaron Lacluyze,
Karen Kinemuchi, Mark Watry, all in PA 318, and later BMPS 3245/ 3248/ 3265.

To those there where the road began: my parents, Jerry and Boni Sharpee, thanks
for your never-ending encouragement and faith in me. Finally, this thesis would not
have been possible without the compassion and caring Of my wife, Tatyana Sharpee,

who has always kept me steering in the right direction!

TABLE OF CONTENTS

LIST OF TABLES
List of Figures

1 Introduction

1.1 The Emission Line Spectra of PNe .................
1.2 Abundance Determinations .....................
1.3 Nature and History of Abundance Discrepancies ..........
1.4 Proposed Solutions ..........................
1.5 IC 418 .................................
1.6 Goals .................................

2 Observations and Reductions

2.1 Observations .............................
2.2 Reductions ..............................
2.3 Error Analysis .............................
2.3.1 Internal Agreement .........................
2.3.2 Systemic Disagreements Between Spectra ............
2.3.3 Obtaining a Total Error Estimate for Final Line Values .....
2.4 Comparisons With Other Spectra ..................

3 A Semi-Automated Emission Line Identifier - EMILI

3.1 Introduction ..............................
3.2 Overview ...............................
3.3 Modeling the Nebula .........................
3.3.1 Velocity Structure Modeling ....................
3.3.2 Abundances .............................
3.4 Template Flux ............................
3.5 Multiplet Check ............................
3.6 Ranking the Transitions .......................
3.7 Output ................................
3.8 Application to Other Spectra ....................
3.9 Application to Current Dataset ...................
3.10 Future Directions of the Code ....................
3.11 Conclusions ..............................

4 Results

4.1 Plasma Diagnostics ..........................

vi

ix
xi

1
3
7
11
12
18
21

23
23
28
44
44
48
51
61

65
65
66
69
70
72
78
83
88
88
93
95
99
102

104
104

4.1.1 Temperature and Density Diagnostics .................. 104

4.1.2 Balmer Jump Temperature ........................ 110
4. 2 Abundances .................................. 113
4.2.1 Ionic Abundances from Collisionally Excited Lines ........... 113
4.2.2 Ionic Abundances from Recombination Lines ............... 120
4.2.3 New/H+ .................................. 158
4.2.4 Other Ions ................................. 160
4.2.5 Comparative Ionic Abundances ...................... 161
4.3 Sources of Abundance Discrepancy ..................... 163
4.3.1 Continuum Fluorescence .......................... 163
4.3.2 Enhanced Dielectronic Recombination .................. 180
4.3.3 Temperature Fluctuations ......................... 187
5 Conclusions 194
APPENDICES 206
A Mechanics of Data Reduction Steps 207
A1 Bias Correction and Image TTimming .................... 207
A2 Flat Fielding ................................. 208
A3 Scattered Light and Sky Background Corrections ............. 211
B RDGEN 213
B] Inputs ..................................... 213
8.2 Method .................................... 214
83 Operation ................................... 218
BA Code Benefits and Limitations ........................ 223
C Profile Fitter 225
C1 Introduction .................................. 225
C2 Method .................................... 226
C3 Operation ................................... 232
C4 Benefits and Limitations of the Code .................... 238
C5 Future Work ................................. 241
D EMILI User’s Manual 242
DJ Introduction and Purpose .......................... 242
D2 User Inputs .................................. 243
D.2.1 Input Line List ............................... 244
D.2.2 Matched Line List ............................. 245
D.2.3 Abundance Table .............................. 250
D.2.4 Command/ Parameter List ......................... 251
D3 Installing and Running the Code ...................... 256
DA The EMILI Process .............................. 258
D5 Outputs .................................... 261
D.5.1 Full Output List .............................. 261

vii

D.5.2 Sample Line Identification ......................... 264

D.5.3 Summary List ................................ 268
D.5.4 Reader .................................... 269
D6 Future Improvements ............................. 271
D7 Contact Information ............................. 272
E IC 418 Line List 273
Bibliography 305

viii

LIST OF TABLES

2.1 Observing journal for IC 418 observations. ................
2.2 Effective total integration times of co-added object Spectra (in hours).
2.3 Lines saturated in the long spectra. ....................
2.4 Observed versus laboratory wavelengths for Balmer and Paschen lines.
2.5 Reddening parameters ............................
2.6 Statistics of matched line measurements within blue, intermediate, and
red set-ups, and in their overlap regions ................

2.7 Wavelengths of strong lines, and ionization potentials of their parent ions.

2.8 Estimated wavelength uncertainty budget for each line, depending upon
it’s 8/ N and final wavelength. The numbers N indicate the numbers
of lines which were used to calculate the error within the particular
8/ N or wavelength bin ...........................

2.9 Comparisons lines (135 = 100). .......................

2.10 Relative flux in line ratios ..........................

3.1 The ionization potential energy bins and Signature lines used to calculate
the ICF values ..............................
3.2 The IDI assignment breakdown for a putative IDs for a given unidentified
line. A lower IDI value means a better ID in general. .........
3.3 Manual IDs versus EMILI IDS for emission lines in the Orion Nebula
as Observed by Baldwin et a1. (2000). The second column lists the
number of times within each EMILI rank, that a particular manual
line identifications matched the EMILI identification of that rank for
that line. The bottom row without a rank entry indicates the number
of lines for which the manual ID was not ranked by EMILI, or for which
the transition was not present in the EMILI transition database. The
third column Shows the percentage of all 388 lines that fall in each
category. .................................
3.4 The same as Table 3.3 for the spectrum of the PN N GC 7009 by Walsh et
al. (2001). ................................
3.5 The same as Table 3.3 for the Spectrum of IC 418 as observed by HAF.

These statistics include only lines assigned Single distinct IDS by HAF.

ix

26
34
38
41
43

47
54

57
62
64

69

89

94

94

94

3.6

4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.12
4.13
4.15
4.16

4.17
4.18
4.19

4.20
4.21

CI
D1

D2

D3

E.1

Numbers and percentage of EMILI IDS chosen as final IDS for each EMILI
IDI rank, out of the total number of IDS used from EMILI. The average,
minmum, and maximum IDI values among IDS chosen within each
rank are also listed. These numbers includes all transitions from lines
thought to be blends, or which otherwise had multiple EMILI selected
for them. “Total” equals the total number of EMILI IDs selected, not
the number of individual emission lines. ................

References for Atomic Data for Collisionally Excited Lines. .......
Plasma Diagnostics and Their Uncertainties for IC 418. .........
Ionic abundances from collisionally excited lines ..............
References for atomic data for recombination excited lines. .......
Temperatures used for recombination line abundance calculations.
Recombination line He+ /H+ abundances. .................
Recombination line C+2/H+ abundances. .................
High excitation C II recombination lines. .................
Recombination line NJr/H+ abundances. ..................
Recombination line N‘FZ/H+ abundances. .................
Recombination line O+/H+ abundances. ..................
Recombination line OH/H+ abundances. .................
Recombination line Ne+2/H+ abundances. .................
Comparative ionic abundances for IC 418 from collisional/ recombination
lines, in units such that log (H+)=12.0, for present and other surveys.
Measured IC 418 expansion velocity from line profiles. ..........
C II dielectronic lines. ............................
N II dielectronic lines. ............................
C II dielectronic lines and abundances. ..................
Temperature fluctuation t2 and T o values and corrected abundances,
N +,- / H+, using different Balmer jump temperatures Te(H+) and Model
value of t2 = 0.005. ...........................

Legend for entries in final column Of the profile fitter output. ......

The ionization energy bins used to determine ICF values and velocity cor-
rections to the Observed line as a function of putative ID ion’s ionization
energy. ..................................

The lines specifically used to calculate the ICF values, and their defaults
in each bin. ................................

For each observed unidentified line, all putative IDS are ranked, by defining
a “score” or IDI value for each transition. The IDI is awarded on the
basis of the putative ID meeting the main criteria listed below. A lower
score generally means a better ID. ...................

IC 418 Line List ...............................

97

105
106
117
122
123
125
131
132
134
139
146
151
159

162
170
181
182
183

190
239

246

246

LIST OF FIGURES

2.1 Approximate Slit posistion with respect to an HST image of IC 418 (Cia-
rdullo et a1. 1999). The width of the Slit is 1” and the length shown
here corresponds to the 11.9” long decker employed in the blue and
intermediate set-ups. ........................... 24
2.2 An excerpt from a typical 2-D intermediate Spectrum. Each rougly horr-
izontal dark strip is an echelle order, with wavelength increasing from
left to right within an order, and from top to bottom across adjacent
orders. Nebular and night sky emission lines, represented as “blobs”
and more narrow strips respectively, can be seen superimposed within
the orders. Atmospheric absorption bands appear as “bright” bands
within an order (see 7 orders from the bottom). Scattered light ob-
jects and ghosts (objects between and intruding into orders) can also
be seen. Flares eminated from the bright saturated lines of Ha and the
flanking [N 11] doublet AA6538,6584A at the rough center right of the
image. Cosmic rays appear as small pin prick strikes across the entire
spectrum. ................................. 27
2.3 Segment from the co—added blue l—D flux calibrated spectra. Numerous
weak emission lines can be seen. Steps for reducing 2-D spectra to 1-D
spectra are given in the text. ...................... 28
2.4 A blown-up portion of the 2-D blue spectrum, showing emission lines of
differing profile morphology depending upon the ionization energy of
the line’s parentage. The “central cavity” in the [N 1] lines is created
by the diflerential expansion of the nebula, its ionization stratification,
and the effect of looking through the nebula to intercept the same
spherically expanding shell. At the center of the slit, most of the
expansion velocity is in the direction of the observer, leading to a larger
Doppler shift in the line profile, whereas at the edges, the expansion
velocity is more perpendicular to the line of sight, hence the “donut”
shape of the lines on the 2-D spectrum. The dashed lines Show the
extraction windows over which the order was summed at each column
in the CCD. ............................... 29

xi

2.5 A comparision between the extracted Spectrum, calibrated with the fit to
the sensitivity function used to calibrate the nebular Spectra, and a
tabulated low resolution spectrum (Humay et al. 1994) for the flux
standard star {2 Cet (HR 718). The smooth curve is the tabulated
spectrum, whereas the somewhat more broken curve is the flux cal-
ibrated spectrum. Over most of the orders the two Spectra nearly
overlap, typically to better than 5%. There is some deviation on the
edges of orders as indicated by the “spikes” sticking out above the
smooth curve. ..............................

2.6 A portion of the full Slit blue spectrum extracted from the order shown
in Figure 2.4. This demonstrates the differing profile morphologies
exhibited by lines whose parents ions are of different ionization poten-
tials. Higher ionization lines, such as [Ar III] A5191.8A on the left have
more Gaussian-like profiles, while low ionization lines, such as the [N I]
doublet on the right have double peaked Gaussian-like profiles, as in-
fluenced by the differential expansion velocity of the nebula exceeding
the thermally generated width of the line. ...............

2.7 A portion of the 2-D red spectrum which depicts an obvious night Sky
emission line near the center of the image. Note that it fills the entire
slit rather than just the portion superimposed on the nebula, as the
adjacent nebular line does. Both lines sit on the wing of the broad
nebular emission line blend of O I A8446A on the left edge of the
picture. From Osterbock et al. (1996) the night sky line is most
likely 6-2 P2(3.5) A8452.250A, a vibration-rotational transition of the
terestrial OH molecule, and has a FWHM of z 9 km 8‘1 which is the
instrumental resolution. The adjacent nebular line we believe is He I
A8451.158. ................................

2.8 The absolute value of the wavelength difference (in km sec"1 ) between the
reddest and bluest measures (A 1am E reddest - bluest) among those
used to compute the final line wavelength values, versus the minimum
8/ N among all the measures. Similarly, the ratio of the reddest to
bluest measurements’ fluxes (Flux Ratio : reddest/bluest). .....

2. 9 Flux and Wavelenght Agreement as a Function of Wavelength in Blue,
Intermediate, and Red Spectra. .....................

2.10 Statistics of Multiple Line Measurements In the Intermediate-Blue Overlap
Region ..................................

2.11 Left: The 10 scatter from individual measurements of the wavelength and
flux of a particular line used to calculate that line’s wavelength and
flux, for all lines as a function of S/ N . Right: The same information
plotted against wavelength (A) for all lines S / N 220. .........

2.12 Top: laboratory minus observed wavelength (AA) for lines from Table 2.7
as a function of Observed wavelength. Bottom: same versus ionization
potential (x) of parent ion. An obvious trend towards smaller wave-
length difference between observed wavelenght and laboratory wave-
length with increasing ionization potential is evidenced. .......

xii

33

37

39

2.13 The percentage flux error (10 measurement scatter) as a function of

3.1

3.2

3.3

3.4

3.5

3.6

3.7

4.1

4.2

— log(I(/\)/I(Hfl)). ............................

A segment of the Matched Line List for the IC 418 data. Listed in columns
from left to right are: A. observed wavelength (A) B. laboratory wave-
length of transition (A), C. Spectroscopic notation for the transition’s
source ion D. flux with respect to H5 .................

A subset of the Input Line List for the IC 418 dataset. Listed in columns
from left to right are: A. observed wavelength (A) B.,C. errors in
measurement (A), D. flux with respect to H5 E. FWHM (km/sec) F.
Signal to noise. ..............................

The velocity correction, vm, in km s‘1 for all bins “A”-” E”, calculated
from the Matched Line List from the EMILI run on the present IC 418
dataset. ..................................

A typical multiplet of Fe 11 showing all allowed transitions under LS cou-
pling. The position of the energy levels is not to any scale. Fraction
beside of the levels are the j total angular momentum values of the
each of the upper and lower levels. The numbers indicate the transi-
tions and their laboratory wavelengths. ................

The header for the EMILI output file generated by its run on IC
418 databaset. The header includes information regarding the in-
put/output files, specified temperature, density, instrumental resolu-
tion, and the calculated ICF (labeled here as ”ix 1” — ”ix 5”) and vac,
(lableled here as ”irvcor 1” — ”irvcor 5”) values for the five ionization
energy bins. ...............................

The EMILI output for a line observed at 5179.52A in our IC 418 spectrum.
Column legend is provided in the text. .................

The distribution of flux: —log(I(/\)/I(HB)) versus S/N for remaining
unidentified lines. Small triangles at S/N=150 indicate unidentified
lines with indeterminate S / N. ......................

Diagnostic diagram for IC 418. In the diagram “D” adjacent to the ion
denotes a density diagnostic for that ion, while “T” denotes a temper-
ature diagnostic. .............................

The blue spectrum in the vicinity of the Balmer series limit, including
all regions that were fit to establish the continuum levels. The jump
is at 3648A, indicated by the vertical line. We used two fits to the
continuum redward of the jump. The solid horizontal line indicates
a fit over the large region of the continuum away from the jump and
yields a temp of 5300 K . The dashed line is a fit in immediate vicinity
of the jump, and yields a temp of 6600 K . The same fit blueward of
the jump, indicated by another horizontal solid line, was used in both
temperature determinations. ......................

xiii

59

67

68

72

84

90

91

99

107

4.3

4.4
4.5

4.6
4.7
4.8
4.9
4.10

C1

C2

C3

D1

D2

D3
D4

Representative line profiles for ions of differing ionization potential with a
comparative sample of the instrumental resolution element. The “INS”
profile, of the night sky emission line [O I] A5577, demonstrates the
limits of our instrumental resolution. The level of ionization increases
clockwise from the instrumental profile. ................

Line profiles from C II lines. ........................

FWHM versus ionization potential x for non-blended lines from various
ions. Small circles are recombination lines; stars are collisionally ex-
cited lines for the same ion. The dashed line is the instrumental reso-
lution limit. ...............................

Line profiles from N I, [N I], and [N 11] lines. ...............

Line profiles from [N II] and N 11 lines. ..................

Line profiles from [O I], [C II], and O I lines. ...............

Line profiles from [0 II], [C III], and 0 II lines. ..............

Lines profiles from [Ne III] and Ne II lines. ................

A sample line detection input file “lzblue418x.6”, with columns entries
explained in the text. ..........................
A segment from the output file “res” to the profile fitter. A legend for the
various columns is given in the text. The entry for the line fitted in
Figure C3 is listed at the bottom. ...................
The fitted profile of a line from the full slit, long exposure, blue Spectrum.
The actual data are the dotted line, superimposed upon the solid line
which is the fit. .............................

A subset of the Input Line List from ic418.in. Listed in columns from left
to right are: A. Observed wavelength (A) B.,C. errors in measurement

238

(A), D. flux with respect to H3 E. FWHM (km/sec) F. signal to noise. 245

A Matched Line List (ic418.match). Listed in columns from left to right
are: A. observed wavelength (A) B. laboratory wavelength of transi-
tion (A), C. Spectroscopic notation for the transition’s source ion D.
flux with respect to H5 .........................

A Command/Parameter List (ic418.cmd). ................

The header for the EMILI output file generated by its run on the included
data. Information regarding the input/output files, specified temper-
ature, density, and instrumental resolution, is contained here, as are
the values for the ICFs (labeled here as “ix 1” — “i1: 5”) and the ve-
locity corrections (labeled here as “irvcor‘ 1” — “irvcor 5”) for the five
ionization energy bins. NO elements were depleted in this run.

xiv

263

D.5 An example of EMILI output from the Full Output List (ic418.out). This
is an identification of a line observed at 6347.19A (after correction to
the nebular rest frame as established by the Balmer and Paschen series
of H5. EMILI suggests that Si 11 A6347.100A is the most likely ID.
This ID has a small residual wavelength difference (indicated by small
value in km/sec in column G). It also has a Template Flux (column F)
nearly the same value as what was observed (top line, second numeric
value). An additional multiplet line, Si II 6371.370A (column J), was
found to correspond with another line in the Input Line List and indeed
the code found the only other multiplet line it expected to find (column
H). Thus, this putative ID did well (column I) with a low score and a
primary (“A”) ranking. ......................... 265
D6 A segment from a Summary List (ic418.dat). From left to right the
columns are: A. a unidentified line’s observed wavelength B. that
line’s measured flux with respect to H5 C. the EMILI primary IDS
(labeled “A” in the Full Output List) associated with the line. . . . . 269

XV

Chapter 1

Introduction

Planetary Nebulae (hereafter PNe, singular PN) are the remains of stars which began
their existence with anywhere from a tenth to ten times the present mass of our sun.
Near the end of their lives, such stars bloat, becoming large giant and supergiant stars,
the result of rapid burning of nuclear fuel in Shells around an inert electron- degenerate
core. The burning iS erratic, and in concert with the star’s outer distended layer’s
low surface gravity and strong radiation pressure, pulsational instability begins to set
in and eventually strip the star of its outer skin. The core is exposed and becomes
the “central star” of the PN, whereas the giant star’s former outer layers continue to
expand to sizes of a light year or more, becoming the Shell or ring commonly seen in
PNe. While nuclear fusion in the system has ceased with the departure of the outer
layers, the still white-hot core is capable of ionizing and exciting the former stellar
envelope with its copious UV photons, leading to the emission Spectra observed for
PNe. Our own sun is predicted to be destined for just such a fate in approximately

4.5-5.0 billion years.

PNe provide a set of universally “old” (at least several billion years, approaching
the characteristic age of our galaxy) objects, from whose spectra elemental abun-
dances can be determined. It is thought that the precusors of PNe, asymptotic red
giant branch stars, can produce iron-peak and trans-iron elements in the S-proceSS in
their distended envelopes, and there is some evidence that elements normally associ-
ated with the r-process can also be synthesized there as well (Balteau et a1. 1995).
However, PNe precursors do not generally process any elements both lighter than iron
and heavier than oxygen in their interiors, and their outer shells preserve a record
of the level of enrichment of the gas in those elements at the time and place they
formed. The Spatial and kinematic distribution of PNe, along with the abundances
determined from their spectra, provide a means to gauge the chemical composition of
the gas throughout our galaxy at a much earlier epoch. Such information provides an
important constraint on the chemical enrichment models and mechanisms proposed
for galaxies. Thus PNe are important on two levels, as a test of both stellar and
galactic evolution.

Emission lines are the chief means of determining the physical attributes of PNe
and H II regions such as the Orion Nebula. Indeed almost everything known about
PNe properties, including temperature, density, and composition, is derived from
understanding and interpreting the strengths and ratios of the strengths of the various
emission lines which dominate their spectra. AS such, it is important to understand
the mechanisms that give rise to individual lines. A Significant effort has been invested
over the years to do precisely that, and methods of interpreting the strengths of

such lines based upon our understanding of their formation mechanisms have been

developed (Osterbrock 1989). These methods have been considered among the most
reliable in all of astronomy.

However, the advent of significant improvements in the calculation of important
components of line strength equations, the opening of the UV frontier via Space-
borne instruments, and improving observational techniques, have brought to light a
significant aberration in the results Obtained with these methods. This casts into
doubt the level of our understanding of emission line formation mechanisms which
underpin this work.

We begin with a discussion of the components of emission line Spectra and the
mechanisms which dominate the creation of lines in these Spectra. This is followed by
a discussion of how abundances and other physical attributes of emission-line regions
are determined from the strengths of these lines. The history of the abundance

determination problem and the merits of proposed solutions conclude this chapter.

1.1 The Emission Line Spectra of PNe

PNe and H II regions have spectra dominated by two types of emission lines which
overlie a weaker continuum. The two types of emission lines are recombination lines
(RL) and collisionally-excited (CL) so—called “forbidden” lines. Each has a different
formation mechanism.

Recombination lines (RL) are as advertised: lines created from the cascade of an
electron recaptured to an excited level en-route to the ground state of an ion. The

strongest examples of such lines in the visible part Of the Spectrum are the Balmer

 

series of neutral hydrogen. Line strengths for RL are directly proportional to the
number density of the source ion. Their value is two-fold.

First, because the lines form during cascades, their strengths depend mainly upon
the transition probabilities (i.e. Einstein coefficients) between the initial and final
levels along the cascade path, which do not depend on temperature. The strength also
depends upon the recombination cross section of the ion, and therefore the thermal
properties (temperature) of the free electrons, but the overall temperature dependence
is generally very weak. For example for H5 the temperature dependence takes the
form z T""8 (Osterbrock 1989). Thus RL are mostly free of the effects of any
temperature fluctuations along the observational line of sight. N ebular temperatures
can be determined by comparing the strength of strong recombination lines with the
continuum difference around the Balmer jump. However, until recently using this
method has been difficult due to the confusion of the continuum level in the vicinity
of the jump caused by line crowding at the limit, as well as other effects.

Secondly, RL are mostly free of Optical depth effects (with the only exception being
recaptures into the ground state) and intensities are thought to suffer only minimally
from resonance absorption or scattering along the line of sight. This is due primarily
to the extremely short (z 10"8 S) lifetimes of excited levels relative to the lifetime of
ions against ionization. This may not hold, however, for ions with meta-stable excited
states (such as the 28 38 term in neutral helium for example), for which absorption
of line photons or the continuum from the central star can be a factor.

Thus RL are ideally suited for abundance determinations of PNe. However only
very abundant species, such as hydrogen and helium, have RL that are strong enough

4

to be easily separable from the continuum.

Collisionally excited lines (CL) arise from collisions between free electrons,
stripped from abundant elements by the central star’s photoionizing radiation, and
plentiful ions. The Boltzman factor at typical nebular temperatures limits the exci-
tations from the ground state to only low-lying energy levels. However, in the case of
multi-electron ions with energy levels within only a few eV of the ground state, such
as exists for 0+2, collisional excitation is the chief populator of such levels, with re—
combination and cascade to the excited levels providing only a minimal contribution
at typical nebular temperatures. Transitions between these levels, so called forbidden
transitions, are normally prohibited by electric dipole selection rules and cannot be
excited directly by line photons or by those in the continuum provided by the diffuse
gas or the central star. Such transitions can only occur in a diffuse enviornment where
the time scale of collisonal de-ercitation of such levels becomes as long as the lifetime
of the collisionally excited level against spontaneous decay and release of a photon. In
the diffuse gas of a PN, where the electron density N, % 103/cm3, electron collisions
are most certainly rare, but collisional de-excitation is even rarer. The emission of
a line photon during decay iS more likely to occur before collisional de-excitation.
Indeed CL are often the strongest and in many cases the only lines observed in the
visible region of the spectrum for many ions of less abundant heavy elements. The [0
III] lines at AA4959,5007 are often the strongest emission lines observed in PNe and
H II regions.

CL are used to gauge electron properties of PNe, since they arise from electron

collisions, and because of their easy observability. The electron temperature is most

 

often measured by comparing the sum of intensities of [0 III] A4959 + A5007 which
originate from the same level, with the intensity [O III] A4363, which terminates at the
same level the others begin at. Although these [0 III] lines are the most commonly
employed, similar temperature measures can be made with other ions with strong
CL, such as those of N+. Since this ion is of lower ionization energy, and because
nebulae have ionization stratification, such diagnostics measure the temperature from
different parts of an emission line region. Electron densities can also be measured by
comparing the ratios of CL of the same ion, the ratios of [O II] A3729/ A3726 and [S
II] A6716/ A6731 being the most commonly used.

However, the Maxwell-Boltzman equilibrium distribution established by the
rapidly colliding electrons introduces an exponential temperature dependence as well
as a T’l/2 factor in the collisional rates. Thus, CL intensities are susceptible to
temperature fluctuations within the region where they form. Because of this strong
dependence on temperature in general, CL are not ideally suited for abundance de—
terminations.

Together RL and CL form the emission line spectrum. The underlying contin-
uum radiatively derives from several sources. These include recombination to various
abundant ions, such as H+, He+ (first ionized hydrogen and helium), and He”,
Bremsstrahlung between free electron states through interactions of free electrons
with these ions, the continuum from the central star, and the continuum formed by
the two-photon process which dominates the transition from the 28 level of neutral
hydrogen to the ls level of the ground state, a transition ruled out by electric dipole

selection rules for single photon emission.

1.2 Abundance Determinations

The intensity of a line, regardless of the mechanism which led to the excitation of
its source level, is directly proportional to the population of the level within the ion
from which it arises, n,, the rate at which the transition occurs Aij, and the photon
energy, huij:
Ioc /n,;A,-th,-j, (1.1)
For recombination lines, among levels with energy high energy that collisional
excitation from the ground state plays no significant role, the processes which populate
and de—populate a particular level must be in equilibrium, Since the line strengths are
not time varying. In the absence Of photoionization from an excited level (a good
assumption given the short lifetimes of the excited levels versus the ionization rate
under nebular conditions) the population of a level depends upon direct recombination
to that level and cascades to and from that level. The population of a level i may

determined from:

00 2—1
NNea,-(Te) + Z nkAk, = ”12 Aik, (1.2)
k>i k<i

where N is the overall ionic abundance, N, is the electron density, A“, and Ak,
are the spontaneous transition coefficients (Einstein coefficients), and a, the rate of
recombination directly to a level i.

However each level nk is in turn itself populated by direct recombination and cas-
cades from above, and de-populated by cascades to lower energy states, and so forth
for next higher level, and the next, until it = 00 at which point only recombinations
to that level can populate a level. In essence one can specify a recombination coeffi-

7

cient which tells the rate of the recombinations to all levels that ultimately lead to a

population in the i state via cascades:

00 1—1
NNeZak(T)Cki = ”1:24am (13)
k=i k<i

where Ck, is a probability matrix, made up of combinations and ratios of transition
probabilities, and defined as the probability that a recombination to the k level ulti-
mately follows a cascade path that leads to a population in the i state, among all such
cascade paths available from that level. Selecting a particular downward transition

i —> 3', the intensity of a particular line can then be expressed:

 

I = NN.af,-”(T.)hu.j. (1.4)
where
e ooziak(Te)Cki
aijff(Te) = 2k ,-_1 Aij- (1.5)
k<i Aik

A?! f
l]

The parameter Or is called the effective recombination coefiicient of that particu-
lar transition. This coefficient is dependent primarily on atomic parameters, such as
the coupling scheme employed to establish the source and destination level, and the
associated branching ratios governing the probability of departure from a particular

level to other levels (involving ratios and combination of spontaneous transition co-

‘3”
1]

efficients). Therefore a is only weakly dependent on temperature, often varying
with Te’(0'8'1‘3). This parameter is therefore insensative to temperature fluctuations
along the line of sight through the nebula, and ideal for abundance determination,
provided optical depth effects (such as self-absorption from meta-stable low levels, or

H-Lyman series photons) do not complicate the contributions from pure cascades.

8

With an observed intensity for a particular line, rough knowledge of the nebular
temperature and density, and an effective recombination coefficient for that emission
line under those temperature and density conditions, one may solve for N to get the

ionic abundance of the line’s parent ion. The of,”

are generally expressed as tables
of values at particular temperatures and densities, and fitted with interpolation func-
tions of temperature, often a power law, at specific densities (Storey 1994, Kisielius
& Storey 2002). However, calculations of as”, are complicated by unknown Einstein
coefficients for many transitions, and departures from LS coupling among higher an-
gular momentum 1 levels, which can lead to larger numbers of escape routes from
a particular excited level. Thus, at present, effective recombination coefficients for
individual lines, or for the multiplets to which they belong, exist for only a few ions.
Collisionally excited lines generally originate only from energy levels within a
few eV of the ground state. The time scale of collisional excitation exceeds the
recombination rate, so collisional excitation dominates the populations of these levels,
hence the relative weakness of recombination lines as compared to forbidden lines of
many ionic species. The formalism for obtaining abundance is the same as with
recombination lines, in that the population of the level responsible for a particular
line must be determined by employing equations of statistical equilibrium for every
involved level:
anNeri + 27171431 = ZniNeQij + ZniAij- (1-6)
j¢i j>i 1751' j<i
Here n, and n, are the fractions in levels i and j respectively for that ion, and q,,

and q,-,- are the collisional excitation and de-excitation rates to and from a particular

 

level. The collisional excitation rate is defined as:

8.629 x 10‘6 Q,-
——————T 1,, E." (1.7)

:9
k).
Ill

where u),- iS the statistical weight of the beginning level of the transition, and Q,- is the
collision strength of the transition, a parameter arising from quantum calculations in-
volving the wave functions of the final and initial states. The collisional de-excitation

rate iS related to the excitation rate for the same pair of levels by:

wt
qji = $427 exp(—x/kTe) (1-8)
J

where X is the energy difference between levels i and j.

The resulting system of equations for a particular ion can then be solved for either
the temperature and density of the region from which the line originates, if only the
line intensities are provided; or the abundance of the particular ion, if the temperature
and density are Specified in addition to the observed line strengths.

For the ions with the strongest optical forbidden lines, generally only five levels
are involved: the 3P2“), 1D2, and 150 levels (for ions with ground state valance
electron configuration of p2 or p4), and the 433/2, 2D5/2,3/2, and 2P3/2,1/2 levels of the
p3 configuration. Notable exceptions include iron and nickel which have many low

lying energy levels which may be collisionally excited.

10

 

1.3 Nature and History of Abundance Discrepan-
cies

The advent of precise calculations of the recombination coefficients has made mean-
ingful theoretical calculations of the intensities of RL possible, while the opening of
the UV via space-borne observatories has made observable CL (for ions with few
other strong RL or CL in the visible). Improved Spectral resolution, allows weak RL
to be both resolved and detected amid the noise of the continuum. Thus, abundance
determinations can now be made and compared via the measured strengths of both

RL and CL produced by the same ion. Two major problem areas have emerged:

1. The observed strengths of RL and CL Show both a large scatter, and disagree
with model calculated values. Esteban et al. (1998) showed that ratios for [Fe
II] CL disagreed by up to a factor of 13. Peimbert et al. (1993) found that the
observed Cid/H+ RL ratio exceeds the calculated ratio by a factor of 2 in the
Orion Nebula (an H II region), while more recently Esteban et al. (1998) found

that the discrepancy is closer to 1.5.

2. Ionic abundances from RL intensity measurements do not agree with abun-
dances determined from CL for the same source ion. While some PNe Show no
discrepancy, for others it differs by more than an order of magnitude. Barker
(1991) noticed in N GC 2392 that the UV collisionally excited inter-combination
line C III] A1909 yields an abundance of C+2 that is an order of magnitude lower

than that found from the C III A4367 recombination line, but found no such

11

discrepancy for ions of either 0 or N. However Liu et al. (1995a) found that
total C, N, and O abundances derived from averages of their constituent ions’
RL, differ by a remarkably constant factor of five from the abundances for the
same ions same derived from CL in the PN NGC 7009. Liu et al. (2000) sur-
veyed NGC 6153, and found the abundance discrepancies to be nearly tenfold.
Dinerstein et al. (1998) surveyed fourteen PNe and found that the discrepancy
for O+2 varied from nebula to nebula, from no difference to well over an order

of magnitude of difference.

Where the discrepancies occur, the recombination-line derived abundances always

exceed those from collisionally-excited lines from the same parent ion.

1 .4 Proposed Solutions

Many explanations have been advanced to explain these problems, all with attractive
features, as well as distinct drawbacks:

Temperature Fluctuations:

The most commonly invoked explanation is temperature fluctuations within the
PN, confusing the temperature derivations and driving down the abundance derived
from the highly temperature sensitive optical CL. Early on Peimbert (1967) char-
acterized these fluctuations with the factor t2, representing the rms fluctuation of
temperature in the region producing the line. Rubin (1969) used the t2 formalism
to characterize their effect on the determination of abundances. Another perceived

manifestation, is the usually lower Balmer jump temperature, with respect to optical

12

CL-determined temps (Peimbert 1971).

In some cases the measured t2 is sufficient to explain the abundance discrepancy
(Peimbert et al. 1993), but not in all cases (Liu et al. 1995a, 2000, Garnett & Diner-
stein 2001a). It has also proven difficult to construct a physically meaningful photo-
ionization model of smooth un-clumped gas incorporating t2 values large enough to
bring abundances into alignment (Viegas & Clegg 1994, Kingdon & Ferland 1995b).
The agreements in abundances between those calculated from relatively temperature
insensitive fine structure lines (collisionally excited transitions between the individual
total angular momentum j states within the terms of the ground state configurations
of many ions) and from their more temperature sensitive optical counterparts, also
argues for a minimal effect of temperature fluctuations (Liu et al. 2000).

Density Perturbations:

Numerous PN e have obvious, visually discernible structure: dark knots, filaments,
and “comet trails” as seen in HST images of PNe. The Helix Nebula is a prime
example. In such structures both the electron and ionic densities might be fluctuat-
ing and locally concentrated. It stands to reason that many of these condensations
may be small enough to remain unresolved (Viegas & Clegg 1994 and see below).
Condensations with large electron densities in addition to ionic concentrations could
be sufficiently dense to make collisional de-excitation of the nebular CL Significant
enough to affect temperature determinations from their intensity ratios, influence
density determinations, and consequently affect abundances determined using other
RL and CL which utilize those temperatures and densities. Furthermore, density
condensations would provide a safe harbor for lower ionization Species in the higher

13

 

ionization environment closer to the central star, as the cores would be sufficiently
Shielded from the ionizing flux (Grandi 1975b) to allow low ionization ions to exist and
accumulate. Emission in RL arising from condensations, could add to the emission
from lower temperature regions where the RL parent species dominates. If one’s line
of Sight intersected both regions, the result would be large difl'erences in determined
abundances from place to place in the PN. Viegas & Clegg (1994) made use of an n2
parameter characterizing the filling factor (the amount of volume of a PN taken up by
high ne condensations). This successfully accounted for the abundance discrepancy
exhibited in the CL and RL O+2/H+ ratios in NGC 6572. Liu et al. (2000) invoked
a model cooler metal rich (hydrogen deficient) condensations begetting stronger RL
than in the surrounding “normal” abundance gas from which the CL arise.
Nevertheless even the proponents of this explanation acknowledge its weaknesses.
Viegas & Clegg (1994) noted that the chief constraint on their scenario is the neces-
sity of these clumps to have 0”, the origin Species of the [O III] CL, as a major
component. This limits the placement of such condensations to a narrow region of
most PNe, unless the central star happens to be unusually hot (T > 105K) or the
nebula small (thereby expanding the fractional volume over which 0+2 could exist).
It would also not affect temperature determinations made from CL of other lower
ionization ions located in other parts of the emission-line object. Liu et al. (2000)
found that while the abundances of elements as derived from their CL were almost a
factor of ten smaller than those derived from their RL, the ratios of CL abundances
of one ion to another are nearly equal to ratios of RL abundances of the same two
ions, a finding that they cannot reconcile with their own two component models of RL

14

 

 

and CL sources. Garnett & Dinerstein (2001b) question both the origin of metal-rich
condensations, as proposed by Liu et al. (2001), and why they Should appear only
in the most evolved PNe, which they claim Show the biggest abundance discrepancy
in 0+2. Finally such condensations might be to small to directly observe. Viegas
& Clegg (1994) predict that the condensations would be of 0.1 ” in angular extent,
barely resolvable by the HST.

Shock Waves:

It has also been proposed that an additional energy source within a nebula, such
as shock waves, may act to contribute additional excitation of both forbidden lines
([8 II] A4069,4076 Esteban et al. 1998) and recombination lines (e.g. Multiplet 15
lines in 0+2). Garnett & Dinerstein (2001b) suggest that dielectronic recombination,
enhanced by such additional energy input, may totally explain the abundance dis-
crepancy seen in this particular ion. Evidence for shocks in nebulae is not direct,
but their existence is widely suspected and indirectly inferred (see Liu et al. 1995a,
Esteban et al. 1999 and references therein). These shocks may arise as a consequence
of interactions between stellar winds arising in different phases of the PNe evolution
and the progenitor’s outer envelop gas, or in the case of H II regions, from winds
flowing off the ionizing star or stars. The difference seen in the magnitude of the
abundance discrepancy from PN to PN would then arise from the propagation time
of the shock through the nebular gas. Garnett & Dinerstein (2001a) saw an anti-
correlation between surface brightness, a proxy for nebular age, and the level of 0+2
abundance discrepancy. They interpreted this as the shock not having propogated as
far in the younger PNe.

15

However as pointed out by Liu et al. (1995a) such processes can only selectively
excite certain lines in certain elements. It’s difficult to see how processes affecting only
certain lines can influence abundance determinations enough to obtain the abundance
discrepancies seen in overall elemental abundances from multiple Species, as they are
observed in NGC 7009. Liu et al. (2000) saw no correlation between ionic abundance
discrepancy and ionization potential in NGC 6153, suggesting that the discrepancy
may have nothing to do with the temperature structure or local temperature-driven
phenomenon such as di-electronic recombination induced by shocks. The constancy
of ratio of collisionally-excited Species seen by Liu et al. (2000) also argues for some
sort of global problem.

Continuum Fluorescence:

Excitation from the ground state via the continuum radiation from the central star
of a PN or the exciting star of a H II region may play a large role in the excitation
of certain levels. Even for forbidden lines, an increased population of their source
levels (induced by cascades following excitations to higher permitted levels) may be
Significant, at low nebular temperatures.

Grandi (1975a) Showed that the intensity of the O I permitted line A8446, observed
in the Orion Nebula, could not be produced entirely by either pure recombination
or any other standard mechanism. His calculations failed to reproduce the observed
intensity ratio with respect to Ha by any Single or combination of methods by over
two orders of magnitude, although calculations utilizing continuum fluorescence could
explain its strength. Evidence for a strong continuum fluorescence influence on certain

lines of N I was advanced in Grandi (1975b), and Grandi (1976) Spectulated on the

16

large role it may have in the excitation of numerous other lines in PNe.

More recently, Esteban et al. (1999) saw excessive line strengths for [Fe II] lines
of multiplet 7F, as compared to other [Fe 11] lines from other multiplets, that may
indicate the presence of a large continuum fluorescence contribution. Lucy (1995)
invoked starlight continuum fluorescence to explain the apparent super—solar Ni/ Fe
ratio observed in the Orion Nebula. Both Liu et al. (1995b) and Bautista (1999)
saw the potential for continuum fluorescence contributions to the intensity of neutral
species forbidden lines. Ferland (1992) suggested that his models (incorporating an
attenuated continuum flux) can explain the anomalous difference in intensities seen
between two strong lines of N+2 which cannot be explained by the action of the Bowen1
mechanism alone. Peimbert et al. (1993) confirmed that the starlight continuum may
account for the unusual strength of the N+2 permitted line A4641 in M17, which is
one of the products of the above Bowen mechanism. Finally Esteban et al. (1998)
identified a variety of permitted lines potentially Significantly driven by continuum
fluorescence in the Orion Nebula.

As with the other mechanisms, this one too has problems. Often only levels with
energy below 1 Ryd can be excited in nebular environments, due to large optical
depths for A _<_ 912A, the result of absorption by abundant hydrogen. Stellar contin-
uum radiation also diminishes severally with distance away from the central star. As
with di-electronic recombination and Bowen fluorescence, it is a selective exciter.

In summary, several different mechanisms and conditions have been advanced to

 

1The Bowen Mechanism is the excitation of a specific transition by line photons emitted at a
nearly identical wavelength in a strong resonance line of an abundant ion (Bowen 1924).

17

 

explain the unusual abundance discrepancy, each Showing problems as well as promise.
The effects of each mechanism on RL and CL needs to be better understood, so our
understanding of line formation mechanisms as a whole may be improved, and our

interpretations made more physically meaningful.

1.5 IC 418

We choose for observation the bright southern PN IC 418 (PN G# 215.2-24.2) located
at RA 5:27:28.3 and Dec -12:41:48.22 (J2000). This PN has attributes which makes

it a good target for high resolution spectroscopy, and subsequent abundance analysis.

1. Simple Geometry. Visual inspection of images of IC 418 in wide band filters

 

indicate that the nebula appears visually uncomplicated, consisting of co-centric
Spherical Shells, uncomplicated by large-scale turbulent velocity flows. This view
is consistent with early models of IC 418 by Flower ( 1969) and Reay & Worswick
(1979). Thus, line profiles will be dominated by the local thermal properties and
the expansion velocity distribution of the nebular gas, making them easier to fit
with confidence (in many cases by a simple Gaussian functions). Narrow band,
emission line images of IC 418, also suggest a simple ionization stratification.
Lines from ions with low ionization potentials are further away from the center,
and lines from ions with higher ionization potentials further in. Given the
expansion velocity gradient present in the nebula, in which the outer portions
of the nebula expand faster than the inner portions, lines from the same ion

or from ions with nearly the same ionization potential Should Show the same

18

profiles if they are produced by the same excitation mechanism, or differing

profiles if they are not.

2. Extremely Bright Nebulosity and Central Star IC 418 has the largest surface

 

brightness (measured in terms of the flux of radiation in the H5 line per unit

1 2

area: 2.33 x 10“12 erg sec‘ cm’ arcsec‘2) of any PNe available at the time
and location of our observations. Thus a small Slit area, necessary for high
dispersion echelle spectroscopy, can capture a Significant amount of flux from
the nebula. The bright central star of this nebula, with a V band magnitude

of 10.17, makes it easier to detect resonance absorption lines (Williams et al.

2003)

3. Large Proper/LSR velocity The helio-centric velocity of IC418 is quite large,

 

moving night Sky emission lines away from their nebular counterparts. More
importantly, the velocity of IC 418 with respect to the local standard or rest
(LSR) iS also quite large (61 km /S) Since the interstellar medium (ISM) is the
primary source of absorption lines, any nebular gas absorption is separated and
distinct from the ISM produced absorption components, simplifying their use

in abundance analysis.

The only drawback to the choice of IC 418 is its low ionization, meaning lines
from ions with high ionization potentials will not be readily observable. However,
low ionization generally indicates a young PN. Thus, we should be able to test the
theories of Garnett & Dinerstein (2001a,b) that younger PNe Should not Show a large
discrepancy in O+2 abundance due to the absence of Shock-enhanced di-electronic

19

 

—

recombination, since our spectra Span the richest area of 0+2 optical RL.

Finally, IC 418 has seldom been subjected previously to high resolution spec-
troscopy, Hyung, Aller, & Feibelman (1994) (hereafter HAF) are one of only a hand-
ful of known examples, and never to an extensive abundance analysis with as many
lines as are expected to be revealed by the depth of the Spectroscopy employed here.
HAF used a combination of echelle spectroscopy and IUE observations to compare
the intensities of the C III] AA1907,1909 collisionally excited intercombination lines
with the strong C II A4267 recombination line. They found that the recombination
derived abundance exceeded the collisionally excited value by a factor of three. How-
ever, they computed abundances for other ions only from collisionally excited lines,
deeming the recombinations present in the spectra too weak to make meaningful
abundance determinations. Henry, Kwitter, & Bates (2000) (hereafter HKB) also
used IUE Observations in the UV and optical spectroscopy to make abundance de-
terminations in IC 418. However the Spectra sampled different regions in the nebula,
the Spectroscopy was of much lower resolution than that employed here, and again
only collisionally excited lines were used to measure abundances.

Preliminary comparisons between these data and an archival HST STIS absorp-
tion Spectrum we have obtained of the IC 418 central star, Show a disagreement
between the ratio of abundances of Fe+ to Ni+ derived from absorption line analysis
as compared to the same ratio derived from collisionally excited lines (Williams et
al. 2003). This despite the Similarities in low level ionization potentials, recombina-
tion coefficients, and condensation temperatures. Also, the STIS spectrum shows a

distinct C+4 absorption feature, whereas the strongest predicted C+3 recombination

20

emission lines, which Share the same ionic parentage as the absorption feature, are
barely visible in our emission Spectrum.

So while previous studies have suggested that the abundance problem exists in
this object, the full extent of the abundance discrepancy problem if any, has not been

determined, and warrants further study.

1.6 Goals

The goal of these observations are to gauge the abundance discrepancy problem in
IC 418, and to carry out simple tests that can help us to understand the potential
origins of the problem, by making use of the advantages of deep (long exposure time),
high resolution echelle Spectroscopy, which provides here well defined line profiles,
minimization of line blending, and continuous coverage over a large bandpass spanning
3500A to 9850A. The high resolution will allow us to examine recombination line
profiles for consistency within and between multiplets of the same ion, and to compare
them with profiles of collisionally excited forbidden lines arising from the same ion.
Differences in profiles may indicate differing excitation ionic parentage, and invalidate
comparisons in abundance made between such lines. The large bandpass and depth
of the observations will allow the Simultaneous calculation of abundances from many
different ionic species and elements, at the same place within the nebula, including
calculations from the strengths of weak recombination lines only revealed in Spectra
of this depth and quality.

We will also take this opportunity to develop tools to help automate and improve

21

 

the processes of line detection, measurement, and identification. The wealth of in-
formation provided by spectra of a quality similar to our own, which are now readily
available from today’s generation of instruments, demands software tools to improve

the accuracy and efficiency of the data reduction and analysis.

22

 

Chapter 2

Observations and Reductions

Here I summarize the equipment used and steps employed to obtain and reduce the
observed Spectra and to obtain a list of flux-calibrated emission lines for analysis. The
accuracy of line measurements post-reduction is provided, and the process utilized
to identify the lines concludes this section. Supplemental material may be found in

Appendix A, B, and C.

2. 1 Observations

Spectra were obtained with the echelle Spectrograph on the Cassegrain focus of the
Blanco 4 m telescope at Cerro-Tololo Inter-American Observatory during the course
of five consecutive photometric nights, UT 26-31 December 2001. The spectra were
imaged on a SITe 2048x2048 CCD, set to a gain of 1.1 e‘/ADU and with a read
noise of 3 e‘ per pixel. To improve the signal to noise, CCD pixels in the direction

of the slit were binned by a factor of two.

23

 

 

Figure 2.1 Approximate slit posistion with respect to an HST image of IC 418 (Ciar-
dullo et al. 1999). The width of the slit is 1” and the length shown here corresponds
to the 11.9” long decker employed in the blue and intermediate set-ups.

The slit was first centered on the IC 418 at (12000 = 5"27’"28.33, 62000 2 —12°41’48”,
rotated to a position angle of 180 degrees, then offset #4” west, to a final position with
respect to the nebula as depicted in Fig. 2.1. The slit was nominally aligned with the
same portion of the nebula throughout an observing night. As a consequence there
was some spatial smearing at blue wavelengths due to the changing direction of the
atmospheric dispersion as the night progressed. The position of the slit avoided the
central star, and intersects bright regions of the nebula as seen in emission line HST
WFPC2 images (Ciardullo et al. 1999). To reach the desired resolution of 9 km/sec
(z 0.2A at 6500A), a 1” width slit was used. To cover as wide a wavelength range as

possible at this resolution, three instrumental set-ups were utilized, designated here

24

 

as blue, intermediate, and red. Two observing nights were dedicated to both the blue
and red set-ups, with the final night assigned to the intermediate set-up.

The blue Spectra were taken using a 79.1 grooves mrn‘1 echelle grating and a 316
grooves mm‘1 cross disperser (grating KPGL2), with no order separator filter. This
set-up utilized the long blue camera and blue collimator, to yield a plate scale of 0.27”
per pixel at the CCD (0.56” per binned pixel). The grating tilt was set to allow full
coverage of the wavelength range 3500-5950A. A 11.9” Slit length (decker length) was
used, the longest length possible under this set-up to avoid order overlap in the 2-D
images. The nebula filled nearly the entire slit (as seen in Figure 2.1). The total area
imaged by the Slit from the nebula was 1” x 11.9”.

The intermediate red Spectra were taken using a 31.6 grooves mm"1 echelle grat-

1 cross disperser (grating G181), and an order sep-

ing, a different 316 grooves mm"
arator filter (GC495). This set-up utilized the long red camera and red collimator,
with focal ratios identical to their blue counterparts, yielding the same plate scale at
the CCD. The grating tilt (1207) was set to allow continuous wavelength coverage
5090-7425A which overlaps some of the regions covered by the other two set-ups. The
11.9” decker length was again utilized, with the Slit imaging the same 1” x 11.9” area
of the nebula as was imaged under the blue set-up.

The red Spectra were taken with the same Optical set-up as the intermediate red
Spectra, but with a different order separator filter (RG610), and with a different
grating tilt (560), to allow continuous coverage of the wavelength region 7350-9865A.

Spectral orders under this set-up were Spaced further apart on the CCD, allowing the

use of a slightly larger decker length, which we employed to maximize the observed

25

Table 2.1 Observing journal for IC 418 observations.

 

 

Date Setup Exposures
(UT) (number x sec)
27/12/01 blue 6x1800
2 x 120
28/12/01 blue 6x1800
2x 1000
6x120
29/12/01 red 8x1800
3x300
30/12/01 red 9x1800
3 x300
31 / 12 / 01 intemediate 10 x1800
3x120
3x30

 

flux from the nebula. An area of 1” x 19.6” centered at the same position as the other
set-ups, was imaged under this set-up. The nebula filled roughly two-thirds of the
length of the Slit at this decker size.

A series of short (30-300 sec) and longer (1000—1800 sec) duration exposures were
taken throughout each of the observing nights, yielding 2-D spectra, an example of
which is shown in Figure 2.2. Table 2.1 lists the numbers and duration of exposures
for each observing night, as well as associated instrumental set-ups. The Short ex-
posures were used to accurately measure the fluxes of strong emission lines which
quickly saturated the CCD. Repeated longer exposures were taken for eventual co-
addition to improve signal—to-noise and enhance the detection of weak lines against
the continuum. Spectra of flux standard stars and calibration frames were also taken

each night.

26

’\\M\\\Mlbilfimhmhmll‘mll .. ‘illhl'l‘ . l
- 1M\\I\\M\M\\\ll\\ll\\l\lm\M‘lillllhllll
\ t\lll\\lM\\ll\l\li\‘i\

\\

,\\. M '\. [W l,» "‘ \ ‘,\\ ill
.Illllnll’..l\‘\Alltlillllll"‘nlll’ll‘l’ ll)\\\.l\\.\\’. ll \\ \l~'\\\ A. .I)‘ . . fl)’-\‘\ll\\l\\lll’\\ill\\l

l) , it
will” Ill“ it”

i
n‘
‘l
[l

.l i .ll‘ .ll .Lt

 

Figure 2.2 An excerpt from a typical 2-D intermediate spectrum. Each rougly hor-
rizontal dark strip is an echelle order, with wavelength increasing from left to right
within an order, and from top to bottom across adjacent orders. Nebular and night sky
emission lines, represented as “blobs” and more narrow strips respectively, can be seen
superimposed within the orders. Atmospheric absorption bands appear as “bright”
bands within an order (see 7 orders from the bottom). Scattered light objects and
ghosts (objects between and intruding into orders) can also be seen. Flares eminated
from the bright saturated lines of Ha and the flanking [N II] doublet AA6538,6584A
at the rough center right of the image. Cosmic rays appear as small pin prick strikes
across the entire spectrum.

27

 

NOAO/IRAF’ V2.113XPOR'I‘ sharpeeflhowardmmmsmedu Thu 15:06:14 06-Mar-20
[blue418cx.ec[‘.7]]: ic418 4.3“ w 1800. ap:7 beam:58

 

 

 

 

 

 

 

 

 

 

1.00E-13 - T l I ' J4
8.008-14 —- —
6.00E—14 — —
4.003-14 —- —
2.003-14 — [J U a
l l l l L l

3830 3340 3050 3860 3870 3000

Wavelength (angstroms)

Figure 2.3 Segment from the co-added blue 1-D flux calibrated spectra. Numerous
weak emission lines can be seen. Steps for reducing 2-D spectra to 1-D spectra are
given in the text.

2.2 Reductions

Individual nights were reduced separately to flux calibrated 1-D Spectra (see Fig-
ure 2.3). Initial processing of the raw 2-D Spectra, namely image trimming, bias
correction, flat fielding, and scattered light correction were carried out using stan-
dard techniques (see Appendix A) as implemented in IRAF1 tasks. Dark current

appeared negligible in our exposures and no attempt was made to correct for it.

 

1IRAF is distributed by National Optical Astronomical Observatories, which is operated by Asso-
ciation of Universities for Research in Astronomy, Inc., under cooperative agreement with National
Science Foundation.

28

 

 

[Ar [11] 5191.3 [N [15197.9 [N I] 5200.3

   
 

IIII
IIIIIIII

- IIIIII III-l.

IIIIIIIIIIIIII ,U_,_ ,

w
3 La. 0.! “In: 1.1. ._|‘ -..-- .' tun-.4 1

 

. .
i I.

.. I II

I.....l!'ll!l&l II

 

.. ... . ........_._.._.....L.A...., .
,. . , A.‘ .‘m . mu ... A , ' . . r. A
.
' ‘ Q n - '11}. ‘- t..-n .1 I ,., I 4 ' . . t . . .
.. .x . . . .
u [
.‘ .
, . - , q a .fi
I - r n p; ‘Ilg‘n, “1.3: g...~,.\ _.-~a."1 lu‘ ‘wu - .. ~ x
i , "'7 Irp- .“ “ 'EN‘IH :‘IW'W n . gun-gum. . . u . W :
5 'l. | I . A I. U' Ir ' ’ ‘
.2... ..

Figure 2.4 A blown-up portion of the 2-D blue spectrum, showing emission lines of
differing profile morphology depending upon the ionization energy of the line’s parent-
age. The “central cavity” in the [N 1] lines is created by the differential expansion of
the nebula, its ionization stratification, and the effect of looking through the nebula
to intercept the same spherically expanding shell. At the center of the Slit, most of the
expansion velocity is in the direction of the observer, leading to a larger Doppler Shift
in the line profile, whereas at the edges, the expansion velocity is more perpendicular
to the line of sight, hence the “donut” shape of the lines on the 2-D spectrum. The
dashed lines Show the extraction windows over which the order was summed at each
column in the CCD.

1-D spectra were extracted from processed images (the 2-D spectra), using a
combination of the standard IRAF echelle package task apall for all flux standard
star and calibration spectra, and a modified version of the Spectral extraction program
employed by Rauch et al. (1990) for all nebular Spectra. Both routines sum the counts
along a specified fraction of the Slit length at each position along the path of each

order. The Ranch et al. routines allowed the simultaneous creation of a companion

error array, during the extraction process, for each extracted 1-D Spectrum. The

29

errors (10 uncertainties) were calculated incorporating both the CCD read noise and
photon shot noise added in quadrature along the specified extraction length. Spectra
were extracted over both the full slit length (11.9” for the blue and intermediate
setup, 19.8” in the red), and over a smaller length of 6.5” corresponding to the limits
of the ”central cavity region” exhibited by many lines of low ionization species (see
Figure 2.4). The modified Ranch et al. extraction routines also flagged individual
isolated pixels that exceeded a Specified flux threshold as probable cosmic rays, by
assigning the total flux extracted along the column containing the pixel with a large
variance. During later variance weighted co-addition, the positions in each spectrum
where these artifacts occurred were given lower weights in the sum. The full slit
length spectra were used to detect extremely weak lines more efficiently, while the
smaller Slit length spectra were used to provide a uniform set of emission line fluxes
sampled from the same area of the nebula under each instrumental set-up. Since
the nebula completely filled the slit length in two of the instrumental set-ups, no sky
subtraction was done during the nebular extraction. The scattered light subtraction,
obtained from fits to the regions of the spectra between the orders, was utilized to
establish the zero point of the flux scale.

Wavelength calibration was accomplished through the use of ThAr comparison
lamp spectra taken periodically throughout the night, using the IRAF task ecidentify.
The RMS errors of the final fits to the dispersion solution were generally on the order
of 0.5—1.0 km sec‘1 for the blue and intermediate set-ups, and 1.0-1.5 km sec‘1 for
the red set-up. The smaller number of non-saturated ThAr reference lines in the red

spectra, is primarily responsible for the increased scatter in the red spectra solutions.

30

However the error is well below the individual pixel size of about 3 km sec‘1 in all
Spectra. Each extracted 1-D standard star and nebular Spectrum was re-binned to a
linear wavelength scale from the ThAr comparison 1-D Spectra taken nearest in time
to that spectrum.

The nebular Spectra were flux calibrated by employing spectra of the standard
stars 62 Cet, 29-Psc, and 0 Crt, taken with a 6.6” slit oriented parallel to the parallactic
angle, obtained at the beginning and end of each night. The Spectra of the flux
standard stars were extracted, wavelength calibrated, and compared to tabulated, low
resolution flux calibrated spectra of the same star taken at contiguous 16A intervals
(Hamuy et al. 1994). A “sensitivity” function that converts total counts within a pixel
in the extracted Spectra to units of flux was then established by fitting a multiplicative
function whose efiects bring the two standard star spectra into alignment, using in
the IRAF task sensfunc.

Prior to wavelength calibrattion, to improve the quality of the fit, each spectra
was divided by a spectrum representing the combined signature of the blaze function
and a black body. The continuum was strongly non-linear on the edges of the orders,
where the blaze function was at its minimum, and in the vicinity of broad stellar
and atmospheric absorption features. This division has the effect of flattening the
standard star spectra, making it more tractable to fit the sensitivity function with a
lower order function. This was necessary in order to constrain the sensitivity function
fits which were based upon only a dozen or so calibration points across each echelle
order. A flat field spectrum of a quartz-iodide continuum source, taken through the

narrowest possible decker (1”), was obtained each night for the purpose of flattening

31

the spectra. This spectrum was extracted in the same manner as the standard star
Spectra, and divided into each standard star and object Spectrum prior to wavelength
calibration. The resultant sensitivity functions were then applied to all other object
Spectra taken within that night. A comparison between a flux calibrated standard star
spectrum employing this sensitivity function and the original low-resolution spectrum
is shown in Figure 2.5. The two spectra essentially overlap, with only 1-5% difference
between continuum levels except along the extreme edges of orders where the echelle
blaze yields a minimum intensity.

Individual flux calibrated object spectra within an instrumental set-up, with Sim-
ilar exposure times and extraction widths, were then co-added. A correction for
instrumental flexure afl'ecting wavelength alignment between individual spectra was
made beforehand. This was accomplished by choosing a fiducial spectrum within an
object group, calculating the average shift in wavelength of a series of strong lines
observed in each of the other spectra relative to the fiducial’s values, then adding an
additional shift equal to the amount necessary to bring the fiducial’s measure of a
strong night Sky line wavelength into alignment with the laboratory value. This put
each individual Spectrum onto an absolute wavelength scale exhibiting an average

1 within each group. To account for the possibility of

scatter of about :El km sec"
variable cloud obscuration of the object in between individual exposures, or between
those taken on differing nights, the individual Spectra were scaled in flux to another
chosen fiducial exhibiting the strongest average flux value for a series of strong emis-
sion lines. This assumes that the brightest Spectra was the one least likely to have

been obscured by clouds. Spectra were then added together using the average value at

32

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cc; "x80 c :2 NNVE

33

Table 2.2 Effective total integration times of co-added object spectra (in hours).

 

 

Set-Up Exp. Length Extraction Width: (full, cavity)
Blue short 0.5 0.5

long 6.6 6.6
Intermediate short 0.3 0.3

long 5.0 5.0
Red short 0.5 0.5

long 8.5 8.5

 

each pixel, weighted by the previously mentioned error array, excluding those pixels
whose value deviated by more than 30 from the average at that position. Cosmic
rays were effectively rejected from the calculated average at each pixel, due to the
large sigma assigned to the pixels in which they were located during the extraction
process, and the use of sigma clipping. Final spectra derived from individual spec-
tra of both short and long duration and of differing extraction widths along the slit
were constructed for all three instrumental set-ups in this manner. Spectra created
from from individual short duration exposure spectra (30 sec, 120 sec, 300 sec) are
denoted short, those from long duration exposure (1000 sec, 1800 sec) labeled long.
Those Spectra extracted from the full length of the slit are called full, while those
from the extracted over the position of the slit corresponding to the central cavity
region are called cavity. Table 2.2 includes the total effective integration times of each
extracted spectra.

The blue spectra exhibited artifacts known as Rowland ghosts, which arise from
beat frequencies due to periodic ruling errors from the 79 grooves cm‘1 echelle grating

used in the blue set-up, and are a commonly known anomaly of spectra obtained with

34

this class of grating. These ghosts manifest themselves as two pairs of symmetrically
positioned emission lines flanking real, strong emission lines in the extracted spectra.
The position and strength of these ghost lines is related to the position and strength
of the line they flank. The method of Baldwin et a1. (2000) was followed in modeling
the ghosts with a kernel, convolving it with the spectra, then subtracting off the
convolved spectra from the original spectra. No Rowland ghosts were evident in the
intermediate and red set-up spectra, which were taken with a different echelle grating.

Emission line detection was carried out on the long, full object spectra using the
program RDGEN (Carswell et al. 2001). This program automatically finds emission
lines above a specified threshold related to signal-to-noise (S / N). Details of its oper-
ation may be found in Appendix B. RDGEN provided estimates of the center wave-
length, full width at half maximum (FWHM), and S/ N for each detected line. The
original 2-D spectra were then examined to remove spurious line detections caused
by residual scattered light artifacts, specifically cross-CCD flares which arise from a
combination of the nature of the echelle grating and reflection of strong lines off the
optics of the spectrograph. These appeared as roughly horizontal or vertical streaks
across the CCD, centered on strong emission lines, and can mimic or blend with
real emission lines at the locations of the orders they intersect. Residual cosmic ray
strikes were also identified and removed at this stage. Remaining line detections were
confirmed by looking for evidence of true nebular origin, i.e. similar line morphology,
exclusive filling of the nebular portion of the image slit, and repeated detection within
orders with overlapping wavelength coverage. The statistics of the remaining lines

detections, as a percentage of those retained versus the total number of lines detected

35

in particular S / N and FWHM bins suggest that lines with a S / N 2 7 were at the noise
limit, and those above S/ N = 20 were clearly detected. Similarly, lines with F WHM
in a range bounded by the instrumental resolution at it: 9 km sec‘1 and an upper

1 were considered probable detections when the same statistics

limit of 50 km sec’
were considered. In general only line detections having a S / N Z 7 and with FWHM
in the above range were retained as probable detections of genuine lines. However,
exceptions were made for some line detections outside these limits, such as when the
lines were clearly evident in the extracted spectra and in the 2-D image, or for line
blends detected by the software as a single lines, but having FWHM that exceeded
the upper bound.

A portion of the full, long blue spectrum is depicted in Figure 2.6. In general, emis-
sion line profiles fell into 3 categories: Gaussian, double peaked, or blends. Any line
of sight penetrates through the nebula and intersects both the forward and backward
edge of the expanding gas shell, as well any intervening more highly ionized region in
between. The double peaks arise from the large change in the radial component of
the expansion velocity between the front and back components of the shell (on the
order of 12 km sec'1 for [N II] in IC 418, as determined by Acker et al. (1992), and
quoted in Hyung, Aller, & Feibelman (1994) (hereafter HAF)). Thus double peaks
generally denote a line originating from the outer, more rapidly expanding portion
of the nebula. In contrast, a Gaussian line profile signifies confinement of its parent
species to the slower moving inner regions of the nebula, where the differential ex-

pansion velocity is either unresolved at our resolution or below the intrinsic profile

FHWM of the emitting gas itself (about 20 km sec‘1 for hydrogen). Blended lines

36

NOAO/IRAF' V2.11EXPORT sharpeeGhoward.pa.mau.edu Thu 14:43:55 OG-Iar-ZO
[blue418x.ec[".22]]: ic418 4.3“ w 1800. ap:22 beam:43

 

 

 

l l l I l l
8.00E-14 '— '-
6.00E-l4 — "*
4.00E-14 — —
2.00E-14 — —

l l I J l l

 

 

 

5192.5 5195 5197.5 5200 5202.5 5205

Wavelength (angstroms)

Figure 2.6 A portion of the full slit blue spectrum extracted from the order shown
in Figure 2.4. This demonstrates the differing profile morphologies exhibited by lines
whose parents ions are of different ionization potentials. Higher ionization lines, such
as [Ar III] A5191.8A on the left have more Gaussian-like profiles, while low ionization
lines, such as the [N I] doublet on the right have double peaked Gaussian-like pro-
files, as influenced by the differential expansion velocity of the nebula exceeding the
thermally generated width of the line.

take on a variety of appearances, depending upon the particular morphology, number,
and difference in wavelength of its constituents.

For every line detection made by RDGEN in the full, long spectra, deemed genuine
by the above standards, a fit to the local continuum and line profile in the cor-
responding long, cavity spectrum for the same instrumental set—up was made at the
wavelength of the detection. For lines saturated in the long exposures (see Table 2.3),

the fit was applied to the short, cavity spectrum. The fitting function was the combi-

37

Table 2.3 Lines saturated in the long spectra.

 

Set-Up Lines (Ion/ Wavelength (A))
Blue H6, [0 III] 4959,5007
[0 II] 3727,3729

 

Intermediate Ha, [N II] 6548,6583
[0 II] 7320,7330
[Ar III] 7137, He I 5876,7067

Red [3 III] 9072,9520

 

nation of a single Gaussian and linear function representing the line profile shape and
the local continuum. Such a function was fit to all lines regardless of a priori knowl-
edge of actual line profile morphology, using a standard X2 minimization software
routine, the details of which may be found in Appendix C. The wavelength measure
in this case was the center of Gaussian function that best fit the line profile. In cases
where the profiles were clearly non—Gaussian, the flux was calculated by fitting the
local continuum with a low order polynomial around the line and simply summing
the flux contained within the region where the line clearly extends beyond the con-
tinuum. The wavelength measure here was the first moment of the line profile, the
flux averaged wavelength over the entire line profile. Where line blends were clearly
separable by multiple Gaussian, they were fitted using multiple Gaussian functions
by the “d-d” (de-blend) option in the IRAF task splat. Otherwise the simple sum was
retained.

Night sky emission lines from the Earth’s atmosphere also appear in these spectra,
particularly in the red spectrum. These lines are narrower than the PN lines in

general, and have uniform surface brightness along the slit (see Figure 2.7). With the

38

 

Figure 2.7 A portion of the 2-D red spectrum which depicts an obvious night sky
emission line near the center of the image. Note that it fills the entire slit rather
than just the portion superimposed on the nebula, as the adjacent nebular line does.
Both lines sit on the wing of the broad nebular emission line blend of O I A8446A on
the left edge of the picture. From Osterbock et al. ( 1996) the night sky line is most
likely 6-2 P2(3.5) A8452.250A, a vibration-rotational transition of the terestrial OH
molecule, and has a FWHM of z 9 km s"1 which is the instrumental resolution. The
adjacent nebular line we believe is He I A8451.158.

aid of the Osterbrock (1996,1997) atlases of night sky lines, plus careful examination
of the 2D images, it was possible to identify most of these and eliminate them from
the line list. However a few such lines in blends may have survived this screening
process.

To account for differing photometric conditions on the observing nights, for er-
rors in positioning the slit in exactly the same place between nights, and differences

in the wavelength dispersion solutions used in the individual spectra, all line mea-

39

surements were normalized to a chosen fiducial, the long intermediate spectra. This
was accomplished using the procedure described in Sect 2.3.2, and involved making
comparisons between measurements for the same line present in the overlap regions
between spectra. Similarly, the line measurements from the short exposure spectra
were normalized to their longer exposure counterparts, by taking the average ratio
of fluxes for ten well defined intermediate strength lines, measured in both the long
and short exposure spectra. Scale factors of 0.900, 0.925, and 1.060, derived from the
average ratio of the ten lines, were applied multiplicatively to the line measurements
from the short exposures spectra of the blue, intermediate, and red, respectively, in
order to align them with the fiducial.

Finally, line measurements were considered arbitrarily to represent the same line if

1 . Only those measurements

the difl'erence in wavelengths did not exceed 15 km sec’
possessing a S / N within a factor of two of the largest value, among all measurements
considered to represent the same line, were included in the final sum. Also rejected
were line measurements corresponding to line profiles with obviously poor morphol-
ogy, such as those on the edges of orders, or in regions were the flux calibration was
suspect, such as near strong absorption features in the standard stars. Line measure-
ments meeting the above criteria were averaged together, with the largest S/ N among
the group of measurements and its FWHM adopted as the S/ N and FWHM of the
individual line. '
The wavelengths for all lines were corrected to the air wavelength in the nebular

rest frame by using the median difference between the accepted and observed wave-

lengths for 47 Balmer and Paschen lines (see Table 2.4). The resultant correction

40

Table 2.4 Observed versus laboratory wavelengths for Balmer and Paschen lines.

 

 

Line Lab Observed Vel
(A) (A) (km sec‘1 )

Balmer

H30 3662.256 3663.100 -69.1
H29 3663.404 3664.244 -68.8
H28 3664.676 3665.521 -69.2
H27 3666.095 3666.937 -68.9
H26 3667.681 3668.521 -68.7
H25 3669.464 3670.302 -68.5
H24 3671.475 3672.315 -68.6
H23 3673.758 3674.597 -68.5
H22 3676.362 3677.202 -68.5
H21 3679.352 3680.191 -68.4
H20 3682.808 3683.648 -68.4
H19 3686.830 3687.673 -68.6
H18 3691.554 3692.400 -68.8
H17 3697.152 3698.002 -69.0
H16 3703.852 3704.699 -68.6
Hl5 3711.971 3712.817 -68.4
H14 3721.938 3722.746 -65.1
H13 3734.368 3735.218 -68.3
Hl2 3750.151 3751.007 -68.5
H11 3770.630 3771.493 -68.7
H10 3797.898 3798.766 -68.6
H9 3835.384 3836.264 -68.8
H7 3970.072 3970.982 -68.8
H6 4101.734 4102.682 -69.3
H5 4340.464 4341.460 -68.8
H3 4861.325 4862.439 -68.7
Ha 6562.800 6564.305 -68.8
Paschen

P28 8298.834 8300.780 -70.3
P27 8306.112 8307.964 -66.9
P26 8314.260 8316.135 -67.7
P25 8323.424 8325.322 -68.4
P24 8333.783 8335.679 -68.3
P23 8345.552 8347.465 -68.6
P22 8359.003 8360.887 -67.6
P21 8374.475 8376.402 -69.0
P20 8392.396 8394.317 -68.7
P19 8413.317 8415.241 -68.6
P18 8437.955 8439.838 -66.9
P17 8467.253 8469.188 -68.6
P16 8502.483 8504.427 -68.6
P15 8545.382 8547.343 -68.8
P14 8598.392 8600.346 -68.2
P13 8665.018 8667.004 -68.8
P12 8750.473 8752.464 -68.3
P11 8862.783 8864.779 676
P9 9229.014 9231.107 -68.0
P8 9545.972 9548.037 -64.9
Median -68.6
Standard Dev. 0.9

 

41

of +68.6 km sec“l corresponds to a heliocentric velocity of +61.3 km sec‘1 which
agrees well with published values of +61.0 km sec‘1 (Acker et al. 1992) and +62.0
km sec‘1 (Wilson 1953).

Intervening nebular and interstellar dust act to preferentially scatter out the blue
component of, or “redden”, the inbound flux. To correct for this effect, final line fluxes
were de-reddened through the application of the reddening curve of Cardelli, Clayton,
& Mathis (1989), with a standard RV value of 3.1. The de-reddened intensity of any
emission line can be related to the de-reddened intensity of HB through the following

relationship:

 

1A0 = Ammauoknnml (2.1)
[H60 1H5 ,

where I A is the measured flux of a line, [AD the measured flux corrected for reddening,
[H5 and [H50 the same for the H5, CH5 is the log extinction at HB, and the quantities
f (A) and f (H6) are the relative extinction curve values of Cardelli, Clayton, & Mathis
normalized to H6 at the wavelengths of the lines. The value for CH5 was established
by comparing the final relative flux values between 20 pairs of Balmer and Paschen
lines beginning from the same level. Since these lines arise from the same upper level,
their relative intensities should be the simple ratio of the products of their Einstein
transition coefficients and photon frequencies. Since the intrinsic intensity ratio is

known, the equation:

IP11,O _ {Fl—110CH3[f(P11)+f(H11)] (2.2)
IHII,O [H11 ,

may be solved for cm for any pair of Paschen (P11) or Balmer (H11) lines.

Carried out for 20 pairs of lines (see Table 2.5), a median value of CH5 2 0.34 :l:0.5

42

Table 2.5 Reddening parameters

 

Line Ratio c113
P28/H28 0.29
P27/H27 0.40
P26/H26 0.34
P25/H25 0.35
P24/H24 0.34
P23/H23 0.36
P22/H22 0.39
P21/H21 0.30
P20/H20 0.33
P19/H19 0.34
P18/H18 0.32
P17/H17 0.33
P16/H16 0.35
P15/H15 0.33
P14/H14 0.24
P13/H13 0.35
P12/H12 0.37
P11/H11 0.38
P10/H10 0.19

P9/H9 0.32

 

Median 635 0.34
ACHB (Stdev) 0.05

 

was determined where the error refers to the standard deviation about the average.
This value exceeds the published values of 0.21 from HAF and 0.14 from HKB, but
agrees well with the value of 0.34 determined by the Shaw & Dufour (1995) re-analysis
of the HAF data, as well as with the value of 0.29 from Mendez (1989). It is likely
that the amount of reddening varies with position in the nebula, so some variance
in the coefficient is expected when comparing studies looking at different parts of
the nebula. De-reddened using eq. 2.1 above and our determined extinction value at

HB, the Balmer to Paschen line intensity ratios show a 6% scatter from the expected

43

values.

2.3 Error Analysis

Here we assess the degree of uncertainty in the wavelength and flux measurements by
studying the consistency, within and between each spectrum of repeated measures of
the same lines in differing spectral orders and in spectra from different observational
set-ups. In addition, we gauge the degree of accuracy of our reduction steps by
comparing to theoretical values and previously observed values of the wavelength and

flux for a selected group of lines.

2.3.1 Internal Agreement

In Figure 2.8, the wavelength difference between the reddest and bluest individual
measurements (in the sense of reddest minus bluest) of the same line measured from
diflerent orders of the same echelle spectrum, are plotted against the minimal S/ N
of those measures. Comparison against the minimal S/N, emphasizes the poorest
quality measurements, such as those closest to the edges of spectral orders, where
the S/ N is generally lower, profiles less distinct, and calibration generally the worst.
Similarly, we plot the ratio of the fluxes of the reddest and bluest measurements for
the same line. The 1 a scatter in the wavelength differences (in km sec‘1 ) and flux
ratios, and the median values of all such measures in both parameters from different
ranges of minimal S / N are compiled in Table 2.6. We include night sky line detections

in the wavelength analysis that follows, but not in the flux analysis, since night sky

44

line intensities vary with time and position in the sky.

The scatter in both wavelength and flux generally falls in all three spectra as
one goes beyond the S/N=20 value established for lines “clearly separated” from the
continuum. For higher S/N measurements, the median wavelength difference and
the scatter about the average wavelength difference declines down to the level of the
individual dispersion solution fits (about 0.5-1.0 km sec‘1 in the blue and intermedi-
ate red, and 1.0-1.5 km sec’1 in the red). Flux agreement also improves across the
S/N>20 threshold for all three spectra, again on a par with the 5% uncertainties
in the individual sensitivity function fits used to flux calibrate the individual con-
stituent spectra. If the five strongest lines with multiple measurements are chosen
from each spectrum, the average velocity difference and ratio of flux between measures
is 0.4:l:0.4 km sec"1 and 0.95:1:0.05, 0.23:1:0.08 km sec‘1 and 1.04:1:004, and 1.4:l:1.0
km sec"1 and 1.03:}:002 for the blue, intermediate, and red spectra respectively. The
somewhat larger wavelength difference in the red arises directly from the larger resid-
ual in the red dispersion solutions. An obvious small shift is seen upon inspection of
their respective profiles, but is still well within the uncertainty expected from that
source. It is also small compared with the instrumental resolution of 10 km sec‘l .
The scatter in wavelength and flux ratio matches the expected uncertainty from cali-
bration for line detections above S / N220, suggesting that errors from the calibration
steps dominate the total error in the measured parameters for those detections. The
increasing amount of scatter below the S/N=20 cutofl, indicates that measurement
errors contribute dominate in weaker lines. Since these measurements are made at the

edge of each echelle order and thus represet the worst case comparisons, we judged

45

 

 

 

 

 

 

 

 

 

 

 

 

w)
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T T l f I ' I I Y
BMe 4
° 8
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A L l A A l J L A A i A A A A 1 L L A A
100 200 300 400 500
Min RDGEN S/N
V I I V V I r Y T V V I fffi'fi r Y Y Y Y
Inter a
O
46 4
O O
O O
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L A LA 1 A A l A A A 1 l L A A A l A A A A
100 200 300 400 500
MkiRDGEN S/N
Y W TW' I I V V I V I I Y I fi' 1'
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o ‘1
fiaaflb ‘GP_' 0Q>oo ——°—— —- e— —- <
44 l A 4 L41. 1 A A 4 L l L A L A l A
100 200 300 400 500

Min RDGEN S/N

Figure 2.8 The absolute value of the wavelength difference (in km sec‘1 ) between
the reddest and bluest measures (A lam E reddest - bluest) among those used to
compute the final line wavelength values, versus the minimum S/N among all the
measures. Similarly, the ratio of the reddest to bluest measurements’ fluxes (Flux

Ratio E reddest/bluest).

46

Table 2.6 Statistics of matched line measurements within blue, intermediate, and red
set-ups, and in their overlap regions

 

 

Setup/ Stat S/ N Range N Med(“) 0

Blue

Wavelength > 7 41 0.974 2.457
> 20 26 0.259 1.260

Flux > 7 41 0.950 0.284
> 20 26 0.947 0.199

Intermediate

Wavelength > 7 79 0.759 2.641
> 20 35 0.456 0.750

Flux > 7 63 1.014 0.405
> 20 29 1.015 0.089

Red

Wavelength > 7 103 0.755 1.768
> 20 74 0.627 1.480

Flux > 7 54 1.002 0.151
> 20 37 1.015 0.089

Intermediate-Blue

Wavelength“) > 20 40 1.257 2.290

* 0.211 3.468
Flux“) > 20 39 1.138 0.233
* 0.997 0.205

Intermediate-Red

Wavelength“) > 20 4 1.424 1.185

Flux“) > 20 3 0.972 0.048

 

(a)
(b)
(C)

median and 0 for wavelength in km s‘
Intermediate — Other Spectra A

1

Other Spectra Flux / Intermediate Flux

after correction for systemic shift (see text Sect 2.3.2)

47

both the flux and wavelength values to be in tolerable agreement, and the spectra to
be self consistent.

In Figure 2.9, the same flux ratios and wavelength differences are plotted as a
function of wavelength for all three spectra, including only stronger (S / N 2 20) lines.
This is done to look for any gross systemic errors in dispersion solutions or in the
sensitivity functions that trend with wavelength (which acts as a proxy for position on
the CCD). The general wavelength difference scatter does increase on the edges of all
spectra. This is expected from the declining instrumental sensitivity at the edges of
spectra, which makes line profiles less distinct, and measures from order to order less
certain. Apart from the systemic trend in the red spectrum past 9400A, due to the
previously mentioned deterioration of the dispersion solution fits in this undersampled
region, no other apparent trends are evident. No evidence for a wavelength dependent

flux ratio is present in any of the three spectra.

2.3.2 Systemic Disagreements Between Spectra

Systemic differences between the three difl'erent instrumental setups are determined
by comparing measurements for lines with at least one measurement in each overlap-
ping spectrum which had suflicient S / N to be included in the final average values for
that line.

In Figure 2.10 the wavelength difference (the average of the intermediate spectrum
measurements minus the blue spectrum measurement) and the flux ratio (the blue

spectrum measurement divided by the average of the intermediate spectrum mea-

48

 

 

 

 

 

 

flux Rofio

 

 

 

 

 

 

l!)
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Blue
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ALAAAAJEJEAAALAALAJAAIAELAJ
3500 4000 4500 5000 5500
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7500 8000 8500 9000 9500
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flux Rofio

Flux Rotio

 

VTV’VTrff‘TTVV'I'VVVY

V V I I

8

O
O
p—oyog—oe—O—O'O—QO’V‘O————‘

 

A PA A l A AAAAL l A LA A l A A A 1 LA A A

 

 

o
3500

 

 

 

 

 

4000 4500 5000 5500
lam
' mic l l ' 1 I 'v r
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lam
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o o
Lg£°$§§$0qpfi§§¢44 3. Q5. 0.,
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41. IAAAAIAAAI 1A4.

 

 

 

7500 8000 8500 9000 9500

lorn

Figure 2.9 Flux and Wavelenght Agreement as a Function of Wavelength in Blue,

Intermediate,

and Red Spectra.

49

 

 

 

 

 

 

 

 

r ' I , w I I I
o _ Inter—Blue 4‘ Inter—Blue
'- . , ¢ — -
’0? L O O
\ ' Q
E . 9%) o 00 o 0 +5
VO—o-o——o£°—o oo——-—————cr
E F O 0 g N r- '1
2 L:
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0 ° & O 0— 09002. _ ______
.- _ d F0? ‘00 o 0—8 ‘50
l l- o
. 1 . 1 ‘ O . l . L
0 200 400 0 200 400
RDGEN S/N RDGEN S/N

Figure 2.10 Statistics of Multiple Line Measurements in the Intermediate—Blue Over—
lap Region

surements) are plotted as functions of the final S/N of the line, for all lines with a
S / N> 20. The median values of the ratios and differences and the 10 scatter in those
values about the mean for all such lines are listed in Table 2.6. The median wave-

1 was added to the blue measurements

length difference of approximately 1.2 km sec—
to bring the two spectra into alignment. Similarly, a scale factor of 1.138 was divided
into every blue measurement to align the two spectra (we arbitrarily chose to use the
intermediate spectra as the fiducial for both wavelength and flux). These corrections
were applied to the blue measurements prior to collation of the measures to determine
the line’s wavelength and flux. The asterisked rows in Table 2.6 show the significant
improvement in the median value of wavelength difference and flux ratio with blue
measurements corrected in this manner. The flux agreement seems tolerable, in light
of the expected 5% errors in the flux calibration for each spectrum.

Unfortunately, in the intermediate-red spectra overlap region, similar comparisons

are difficult to interpret, because the size of the overlap was small, and due to the lack

50

of S / N _>_ 20 measurements in the portion of the intermediate spectrum correspoding
to the overlap with the red. The scatter here is also expected to be somewhat larger
given that more individual measurements can contribute to the final line attribute
calculations, sometimes as many as four, two from each of the spectra. The results in
Table 2.6 suggest that a small offset exists in wavelength between the intermediate
and red spectra wavelength measurements. Because the overlap region covers only
the extreme end of the intermediate spectrum and the beginning of the red spectrum,
covering only about two orders in each setup, it was decided not to adjust all red values
based upon results from one or two orders alone. The flux values show the same level
of agreement, despite the small number and mostly lower S/ N measurements, as in
the blue-intermediate region, again within the expected 5% flux calibrations errors
from each spectrum. Increasing our confidence in the match between the red and
intermediate measurements, is the agreement between the Balmer (from the blue)
and Paschen (from the red) line wavelengths (Table 2.4), and the low scatter in the
de-reddened fluxes (Table 2.5). Since the blue and intermediate measures are both
fairly close, we infer that the intermediate and red measurements are within 95% or

1

better agreement in flux, and are apart by no more than 1 km sec“ in wavelength.

2.3.3 Obtaining a Total Error Estimate for Final Line Values

Consistency has been shown both within and between the spectra, and a reasonable
idea of what sources of error dominate particular classes of lines has been determined.

Now we attempt to decouple the various sources of error to arrive at a crude estimate

51

 

 

 

 

 

   

 

 

LO LO
‘— I I I I r «— I I I T
-1 l- 1
1 " I
4 4
1? E - ”a? F3 — 1
\ r \ r
E r E r
:‘5 « 5, .
7; LO ' — E) LO
0 ‘ .4 b
o .
o
O 333‘ @- QL_O __ _—l__ __ Q...l _ .— —1 O
O 200 400 600 800 1000 4000 6000 8000 10000
Min RDGEN S/N A (A)

Figure 2.11 Left: The 10 scatter from individual measurements of the wavelength
and flux of a particular line used to calculate that line’s wavelength and flux, for all
lines as a function of S / N. Right: The same information plotted against wavelength
(A) for all lines S/NZ20.

of the total error in the final wavelengths and fluxes for the lines.
Wavelength Uncertainty

One source of wavelength error is poorly defined line profiles, or measurements in
the vicinity of scattered light features or flares, problems to which weak lines are more
vulnerable. For lines below S / N<20, this measurement error dominates. To obtain a
value for the likely error due to this eflect, we first plot the 10 scatter (in km sec“1 ) in
the individual wavelength measurements for each particular line, for all measurements
that went into calculating that line’s final wavelength, against the S/ N of those lines
(left panel Figure 2.11). The average amount of that 10 scatter among those lines
above and below the S/N=20 cutoff is then calculated. We make the assumption
that these average values of individual measurement’s scatter are characteristic of the

measurement errors for all lines within each S/ N regime even though, as has been

shown, it is more likely the residuals in the wavelength calibration dominate for lines

52

with S/N> 20.

To obtain an estimate of the error due to wavelength calibration problems alone,
we plot the same 10 scatter in individual measurements as was done before, as a
function of wavelength for only those lines with a S/N> 20 (right panel Figure 2.11).
Then we calculate the average of the lascatter within 500A bins, and adopt this value
as the error arising from the calibration steps for all lines with wavelengths within
a specific bin. For the most part these values fall within the expected 0.5 — 1.5 km
sec"1 errors in the dispersion solutions, and including this factor takes into account
the deterioration of the dispersion solution in the red spectrum seen in Figure 2.9.

Finally, to look for any absolute systemic bias in the final wavelength values, we
determined the difference between the final values of wavelength (corrected to the
rest frame of the nebula as established for ionized hydrogen) for several well known
un-blended emission lines (Table 2.7) with indisputable identifications, against their
accepted wavelengths as drawn from the NIST database 2. The results are shown in
the upper panel of Figure 2.12.

The lower panel of the same figure, shows the wavelength difference plotted as a
function of the ionization potential of the lines’ parent ions. There is a definite trend
towards a higher velocity difference for lower ionization potential ions. This might
be reflective of a legitimate differential expansion velocity with ionization potential
energy along our line of sight to the neubla, like that predicted by Gesicki, Acker,
& Szczerba (1996) for IC 418. It might also simply indicate uncertainties in the

accepted wavelengths (indicated by the error bars in the plot) or may be the result

 

thtp: //physics.nist.gov/cgi-bin/AtData/linesiorm

53

Table 2.7 Wavelengths of strong lines, and ionization potentials of their parent ions.

 

 

Line Obs A Lab A AA I.P. (x)
Ion/MA) (A) (.4) (km sec“l ) (eV)
[0 II] 3727 3726.035 3726.032 -0.24 35.12
[0 II] 3729 3728.785 3728.815 2.41 35.12
[Ne III] 3869 3868.745 3868.75 0.39 63.45
[Ne III] 3968 3967.457 3967.46 0.23 63.45
[S H] 4068 4068.668 4068.6 -5.01 23.34
[S 11] 4076 4076.374 4076.35 -1.77 23.34
[0111] 4363 4363.191 4363.209 1.24 54.94
[Ar IV] 4711 4711.352 4711.37 1.15 59.81
[Ar IV] 4740 4740.205 4740.17 -2.22 59.81
[0 III] 4959 4958.915 4958.911 -0.24 54.94
[0 III] 5007 5006.845 5006.843 -0.12 54.94
[Ar III] 5192 5191.702 5191.816 6.59 40.74
[N I] 5198 5198.012 5197.902 -6.35 14.53
[N I] 5200 5200.329 5200.257 -4.15 14.53
[Cl III] 5517 5517.686 5517.66 -l.41 39.61
[Cl III] 5537 5537.853 5537.7 -8.29 39.61
[0 I] 5577 5577.389 5577.339 -2.69 13.62
[N 11] 5755 5754.629 5754.59 -203 29.60
[0 I] 6300 6300.405 6300.304 -4.81 13.62
[s III] 6312 6312.107 6312.06 -223 34.79
Si 11 6347 6347.193 6347.11 -3.92 33.49
[0 I] 6363 6363.886 6363.776 -5.19 13.62
Si II 6371 6371.418 6371.37 -2.26 33.49
[N 11] 6548 6548.096 6548.05 -211 29.60
[N H] 6583 6583.467 6583.45 -0.77 29.60
[S H] 6717 6716.523 6716.44 —3.71 23.34
[S H] 6730 6730.893 6730.816 -3.43 23.34
[Ar III] 7135 7135.744 7135.79 1.93 40.74
[0 II] 7320 7320.135 7319.99 -5.94 35.12
[011] 7330 7329.679 7329.67 -037 35.12
[Ar III] 7751 7751.074 7751.11 1.39 40.74
[Cl 11] 8579 8578.795 8578.7 -3.32 23.81
[S III] 9068 9068.905 9068.6 -10.09 34.79
[Cl II] 9123 9123.737 9123.6 —4.50 23.81
[S III] 9531 9530.929 9531.1 5.38 34.79
Mean -1.90

 

54

 

10

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A r
3: ’ l 9 9 w 8
éOPH¢--—l+—l‘:+j——— .-—-+--r-——;-—~---l—
J l' I
:5 . + f .
1 g l .
o 0 *
.. <> ‘
l
4000 5000 6000 7000 8000 9000
4(3)
O.- .4

 

AA (km/s)
0
l

 

—10
3

 

 

 

 

 

 

o 20 40 60 80
x (60

Figure 2.12 Top: laboratory minus observed wavelength (AA) for lines from Table 2.7
as a function of observed wavelength. Bottom: same versus ionization potential
(x) of parent ion. An obvious trend towards smaller wavelength difference between
observed wavelenght and laboratory wavelength with increasing ionization potential
is evidenced.

55

of the use of the first moment of the line profile in the wavelength measurements of
non-symmetric profile emission lines. As no particular source can be ruled out, we
assume the worst, that the difference is purely due to the wavelength measurement
technique, and adopt a value of 1.9 km sec"1 (indicated as a straight line in the upper
panel of Figure 2.12), as a systemic wavelength uncertainty for all lines. An additional
:l:0.9 km sec‘1 uncertainty can be added directly to this to represent an additional
systemic error arising from the radial velocity correction (see Table 2.4) for a total of
2.8 km sec‘1 for all lines regardless of S/ N .

The measurement and calibration errors could conceivably cancel out each other,
but the 2.8 km sec‘1 total potential systemic error cannot be added in quadrature
with the other errors. We express the total approximated uncertainty in line wave-

lengths as:

0tot = V UM2 + 002 + 0’5, (2-3)

Where OM is the error due to measurement problems, 00 is the error to wavelength
calibration problems, and as is the 2.8 km sec“1 total systemic error described above.
A summary of the components of the estimated total wavelength uncertainty is shown
in Table 2.8.

We compared this error, at“, calculated for each line, against the original 10 scat-
ter shown among those individual measurement used to calculate that line’s wave-
length, and adopted the greater of the two for the total wavelength uncertainty for
that line. The error calculated in eq. 2.3 was adOpted for all lines with single con-

tributing measurements. We believe this gives a reasonable upper limit to wavelength

56

Table 2.8 Estimated wavelength uncertainty budget for each line, depending upon it’s
S / N and final wavelength. The numbers N indicate the numbers of lines which were
used to calculate the error within the particular S/ N or wavelength bin.

 

 

N (km sec“1 )
Measurement Error (0M)
S/N < 20 104 2.016
S/N Z 20 160 0.749
Calibration Error (00)
AA (A)

3500-4000 11 0.901
4000-4500 7 0.321
4500-5000 5 0.328
5000-5500 16 0.807
5500-6000 23 0.735
6500-6500 6 0.290
6500-7000 7 0.410
7000-7500 12 0.837
7500-8000 14 0.802
8000-8500 24 0.911
8500-9000 23 0.523
9000-9500 10 1.592
Systemic Error (05)

(a) 35 1.899

(b) —- 0.900

 

(a) For Wavelength: Lab.Obs A, see Figure 2.11
For Flux: Lab vs. Obs Ratios, see text Sect. 2.3.3
(b) For Wavelength: Radial Velocity Corr. See Table 2.5

57

uncertainty for each line.
Flux Uncertainty

Contributing to the uncertainty in flux measurements, are errors in the flux cal-
ibration, systemic errors arising from the peculiarities of observing equipment and
variability in observing conditions, and measurement errors due to poorly defined
profiles of weak lines. The distinct contributions from these sources are difficult to
de—correlate from one another.

Comparisons between previously obtained flux standard star spectra, and spectra
of those same stars calibrated in the same way as our object spectra, in all observing
set-ups, show that over the majority of most orders, the flux calibration is better than
95% accurate (see for example Figure 2.5). However, on the edges of orders where the
echelle blaze function rapidly falls off, the accuracy of the calibration declines. The
accuracy also falls in the vicinity of places with problematic calibrations. Specific
problems exist at wavelengths near the broad hydrogen absorption features in the
standard stars. Nevertheless, since these locations also correspond to places where
the S/ N is relatively smaller, and the locations in the nebular spectra corresponding
to strong absorption lines in the standard stars were carefully screened, the influence
of individual measurements from these locations is somewhat mitigated by our mea-
surement selection criteria. Therefore, we simply adopt a value of 5% as the likely
error due to errors in flux calibration.

We tested for any bulk systemic errors by comparing observed, reddening cor-
rected, line flux ratios with their theoretically calculated values for several un-blended,

un-ambiguous, close pairs of lines, such as those used to calculate electron density.

58

 

UFlux (7°)

 

 

 

 

—|og (lx/le)

Figure 2.13 The percentage flux error (10 measurement scatter) as a function of

-108(1(/\)/1(Hfi))-

These pairs were chosen because of their large flux, the fact that their intrinsic flux
ratios depend only upon atomic parameters (i.e. spontaneous transition coefficient
and wavelengths), and their relative closeness in wavelength which minimize redden-
ing correction problems. For the following pairs of lines: [Ne III] AA3869/396SA, [O
111] AA5007/4959A, [N II] AA6548/6583A, and [o 11] AA 6300/6363A, the theoretical
ratios exceed the observed ratios by 1.4%. Such a small departure was judged not to
be statistically significant.

It is traditional in nebular astrophysics to estimate the errors attributable to
measurement problems by determining the scatter in individual flux measurements
for those lines having multiple individual contributing measurements, as a function
of the fluxes of those lines. In Figure 2.13 we plot the measurement scatter (10)

as a percentage of individual flux, against the log of the line fluxes normalized to

59

the de—reddened flux of H73. We then calculated the average scatter within decadal
bins. We find that the average scatter plus systemic error for lines of flux I(A) to be:
I(A)/I(HB) < 10‘4 = 20%, 10‘4 < I(A)/I(Hfi) < 10‘3 = 10%, and for all higher bins
I(A)/I(HB) > 10‘3 = 5%, the level of the expected uncertainty in the flux calibration
alone. While some individual lines exhibit a larger amount of scatter, the general
level of uncertainty for the strongest lines compares quite favorably with those levels
given by HAF, HKB, Baldwin et al. (2000), and Esteban et al. (1998), to which this
work is compared.

To obtain an estimate of the intrinsic uncertainty of the line flux measurements,
we adopted the values determined for the measurement uncertainty above, and added
in quadrature a potential 5% error due to flux calibration. This yields for lines of
differing flux a AI of: I(A)/I(Hfi) < 10‘4 = 21%, 10‘4 < I(A)/I(Hfi) < 10‘3 = 11%,
and for all higher bins I(A) /I(Hfl) > 10‘3 = 7%. In those cases where lines had higher
flux measurement scatter than the value appropriate for its flux under this criteria,
the actual measurement scatter was adopted as the flux uncertainty for that line.

Lines fluxes may also be susceptible to uncertainty in the reddening correction.

The flux of any reddening corrected line may be represented by the following equation:
10 = Iec”BD(’\), (2.4)

where Io is the reddening-corrected flux, 1 the observed flux, CH5 the log extinction
of H5, and D(A) = f (A) / In 10) the rescaled extinction function curve at wavelength

A. Assuming that the reddening error is a systemic error, the flux of a reddening

60

corrected line and its error may be represented:

 

 

I, = IeCHBDW,
a], 31,,
A10 — (BI) AI+ (aCHBACHB),
= 1, [ATI- + 000mm,] , (2.5)

where the Acme is the uncertainty in the log extinction at H5, CH5 listed in Table 2.5.

2.4 Comparisons With Other Spectra

HAF and HKB have previously observed emission lines in IC 418. General compar-
isons of our final flux values may be made to both studies in order to look for gross
problems with the flux calibrations, even though their slits were positioned at difler-
ent locations within the nebula. In Table 2.9, comparisons between fluxes are made
between a wide variety of strong lines with un-ambiguous identifications from the
three studies, where the columns (2),(3),(4) are the reddened line strengths, normal-
ized to H6, for the lines listed in column (1). The ratio of each studies’ line strengths
relative to each other follow in columns (5),(6), and (7). The spectra of HKB was of
insufficient resolution to resolve many close line pairs (e.g. [O II] AA3737,3729A) and
thus comparison are made between the sum of the flux in the pair, which is indicated
by a dashed line in the row of the line with the redmost wavelength in the pair. The
average of the ratios of intensities between each pair of studies is relatively constant
around unity, even if the scatter about that average is fairly large. Some individual

lines approach a factor of two difference in flux between studies (see for example the

61

Table 2.9 Comparisons lines (I 3,3 = 100).

 

 

Line (Ion/A (73.)) Obs HAF HKB HKB/HAF HAF/Obs HKB/Obs
[011] 3727 96.183 79.62 105 0.93 0.83 0.77
[0 II] 3729 40.687 33.19 — - -— 0.82 _-
[Ne III] 3869 2.461 1.84 2 1.09 0.73 0.80
[Ne 111] 3968 0.791 0.58 0.72

[s11] 4068 1.482 2.24 3 0.98 1.48 1.39
[8 II] 4076 0.636 0.81 — —- 1.25 ——
H7 39.638 44.16 40 0.91 0.98 0.89
[0111] 4363 0.832 0.49 0 1.02 0.64 0.66
H0 I 4471 4.105 3.43 3 0.87 0.82 0.72
H6 100.000 100.00 100 1.00 1.00 1.00
[0111] 4959 74.199 29.85 37 1.24 0.40 0.50
[0111] 5007 221.374 87.30 125 1.43 0.40 0.57
[Ar III] 5192 0.041 0.03 0.77

[N I] 5198 0.215 0.44 0.5 0.74 2.37 1.66
[N I] 5200 0.125 0.24 -— —~ 2.09 -—
[Cl 111] 5517 0.204 0.20 0.2 1.00 1.11 1.11
[C1111] 5537 0.400 0.41 1.17

[01] 5577 0.030 0.05 1.85

[N 11] 5755 3.191 4.29 4 0.93 1.55 1.45
He I 5876 16.031 12.05 11 0.91 0.79 0.72
[OI] 6300 2.672 4.45 4 0.90 1.86 1.67
[s III] 6312 1.053 1.08 1 0.93 1.14 1.06
Si 11 6347 0.063 0.17 2.98

[o I] 6363 0.939 1.57 1 0.64 1.86 1.19
Si 11 6371 0.054 0.06 1.25

[N 11] 6548 67.557 83.18 66 0.79 1.27 1.01
Ha 393.893 409.26 321 0.78 1.07 0.84
[N 11] 6584 206.107 242.10 197 0.81 1.21 0.99
He I 6678 4.947 3.01 3 1.00 0.68 0.68
[s 11] 6717 2.672 4.24 3 0.71 1.77 1.25
[s 11] 6731 5.679 8.02 6 0.75 1.57 1.18
He I 7065 9.389 6.47 8 1.24 0.72 0.88
[Ar 111] 7135 11.069 7.46 9 1.21 0.69 0.84
[011] 732001) 18.779 19.11 42 1.19 1.05 1.25
[011] 7330(0) 15.725 16.32 — — , 1.07 ~—
[Ar 111] 7751 3.137 0.97 2 2.06 0.34 0.71
He I 8361 0.185 0.07 0.42

o I 8446 1.741 1.92 1.23

[Cl 11] 8579 0.438 0.35 0.89

[8111] 9068 28.321 19.50 34 1.74 0.81 1.42
H 1 P8 9228 4.512 3.36 6 1.79 0.83 1.48
[s III] 9532 68.931 51.40 102 1.98 0.88 1.75
Mean 1.09 1.05 0.98
Standard Dev. 0.38 0.49 0.29

 

l“) Sum of doublet

62

ratio “HAF/ Obs” for [O III] AA4959,5007A which may have some significance). Nev-
ertheless, if there were any large overall systemic problem with the flux calibration,
it might be expected that the average of the ratios would be further skewed in a par-
ticular direction from unity. We concluded that the present survey’s flux calibration
is at least as accurate as the previous surveys it is being compared against here.

Comparisons can also be made to the between observed and theoretical ratio of
lines whose relative fluxes depend either only on atomic parameters, as in the case
of forbidden lines arising from the same upper level; or only weakly upon nebular
physical conditions, such as recombination lines from the same ion. Theoretical ratios
were calculated for the list from Table 2.7 and several other line pairs. The inputs
included spontaneous transition coefficients and wavelengths drawn from the NIST
database, line emisstivity ratios for H I recombination lines (Balmer and Paschen
series) from Storey & Hummer (1995), typical IC 418 electron temperature (10000 K )
and density of 10000 cm'3 (HAF and here see Section 4.1.1), and the emissivity ratios
of Brocklehurst (1972) for He I recombination lines. These flux ratios are compared
to observed values from our data, HAF, and HKB in Table 2.10, where column (1)
lists the line pair, (2) the theoretical ratio of the line strengths, and (3),(4),and (5)
the observed flux ratios of these lines from this study, HAF, and HKB.

As can be seen, good agreement between the theoretical and observed flux ratio
values in this study and the close agreement with the observed ratios in the other
studies suggest that the present survey’s flux calibration is at least as accurate as
previous studies. HKB suggest that their strongest lines are in the neighborhood of

10% flux accuracy. Given the better agreement between our ratios and theory with

63

Table 2.10 Relative flux in line ratios

 

 

Line Pair Flux Ratios

Ion (A (21)) Theory Obs HAF HKB
[Ne 111] 3869/3968 3.27 3.17 3.20 (a)
He I 5876/4471 2.76 3.04 3.02 3.33
[0111] 5007/4959 2.90 2.96 2.91 3.42
[N 11] 6583/6548 2.96 3.04 2.90 2.97
He I 6678/4922 2.89 3.18 2.77 3.00
[Ar 111] 7135/7751 4.14 3.76 7.92 4.00
P8/H6 0.04 0.04 0.03 0.05
[011] 6300/6363 3.09 2.86 2.85 4.
[SIII]9532/9069 2.58 2.37 2.62 3.00

 

(a) [Ne III] 3968A blended with He

respect to HKB, we would estimate the true accuracy of the strongest lines within
the present survey to be closer to the 5% accuracy estimated for the strongest lines,
as calculated previously.

In summary, we have attempted to calculate and quantify the legitimate sources
of error that could contribute to the final wavelength and flux values of each emission
line. Our data set has been shown to be both internally consistent and comparable to
previous data, with a reasonable degree of confidence. Adjustments have been made
to remove systemic sources of error, whenever such adjustments did not introduce
additional spurious noise. The remaining errors are most likely a product of the
limitations of the instrumentation and reduction techniques, although we believe that
their magnitude, approximately equivalent to other nebular abundance studies, should
be sufficient for obtaining decent information regarding the physical attributes of IC

418.

64

Chapter 3

A Semi-Automated Emission Line

Identifier - EMILI

3. 1 Introduction

Deep, high-resolution emission spectra of planetary nebulae (PNe) and H 11 regions
obtained with modern instrumentation (Esteban et al. 1999, Baldwin et al. 2000, and
this study) reveal hundreds of emission lines, including numerous weak recombina-
tion and collisionally excited lines, which have not been routinely identified. The
traditional approach for identifying such lines is a manual one. For each observed
line, an atlas of known lines is consulted, and candidate lines at about the observed
wavelengths are then ruled either in or out on the basis of being from ions in plausible
ionization states with plausibly high chemical abundances, on the presence or absence
of other member of the same multiplet, and so forth. This procedure is extremely

time consuming, demanding, and subject to observer bias.

65

EMILI, for Emission Line Identifier, is code designed to automate these steps,
making use of a portion (3000-11000A) of a large atomic transition database (Atomic
Line List v2.04, van Hoof 1999), which includes r4:200,000 transitions from all ele-
ments Z s 30, from which more possible IDs than could reasonably be considered
manually can be tested for suitability. To assist in the identification process, the
code models nebular ionic abundances, adjusts for any ionization energy dependent
wavelength shifts among the observed lines (nebular velocity structure), and makes
order of magnitude estimates of each transition’s possible flux under assumed nebular
physical conditions. The latter overcomes a limitation of spectral modeling in which
exact atomic parameters, i.e. eflective recombination coefficients and collisional cross
sections and strengths, need to be known, but are often in short supply. Likely iden-
tifications are ranked, with the results presented in a straightforward manner to the
end-user.

We present here the basic framework by which EMILI makes its identifications,
and provide comparisons between manually and EMILI- derived identifications for
high resolution nebular spectra as a gauge of its accuracy. For the actual operation
and utilization of the code, the reader is referred to Appendix D, the“EMILI User’s

Manual” .

3.2 Overview

The steps EMILI utilizes in determining possible IDs for each line can be summarized

as:

66

5006.845 5006.843 [0 III] 2.15e+00
6583.467 6583.450 [N II] 1.63e+00
3726.035 3726.032 [0 II] 1.24e+00
4958.915 4958.911 [0 III] 7.27e-01
6548.088 6548.050 [N II] 5.36e-01
3728.785 3728.815 [0 II] 5.23e-01
9530.929 9530.600 [S III] 4.23e-01
9068.905 9068.600 [S III] 1.78e-01
7319.087 7318.920 [0 II] 3.69e-02
7320.135 7319.990 [0 II] 1.01e-01
7329.679 7329.66 [0 II] 5.86e-02
7330.754 7330.73 [0 II] 5.63e-02
5875.650 5875.640 He I 1.37e-01
7135.744 7135.773 [AI III] 8.26e-02
4471.499 4471.486 Ha I 4.49e-02
6730.893 6730.816 [S II] 4.42e-02
6678.153 6678.152 He I 3.87e-02
3868.745 3868.750 [Ne III] 3.09e-02

A B C D

Figure 3.1 A segment of the Matched Line List for the IC 418 data. Listed in columns
from left to right are: A. observed wavelength (A) B. laboratory wavelength of
transition (A), C. spectroscopic notation for the transition’s source ion D. flux with
respect to H5

1. Model the observed object’s velocity structure and determine ionic abundances
from information supplied in a Matched Line List (Figure 3.1), a list of observed
and pre—identified lines supplied by the user from the same spectrum in which

the user wishes to identify other lines.

2. For each observed line the user wishes to identify in the spectra, contained in
an Input Line List (Figure 3.2), draw from the transition database all transi-

tions within a set number of measurement uncertainty sigma of the observed

67

6363.89 -0.08 .08 7.58e-03 56.70 485.20

6371.42 -0.08 .08 4.33e-04 31.00 198.30
6379.65 -0.11 .11 8.62e-06 25.50 10.70
6382.99 -0.11 .11 1.95e-05 44.10 16.10
6392.50 -0.11 .11 9.28e-06 17.60 6.20
6402.27 -0.08 .08 1.07e-04 21.90 75.50
6454.39 -0.11 .11 1.01e-05 22.40 5.40
6456.00 -0.11 .11 1.25e-05 19.30 8.70
6461.85 -0.08 .08 5.83e-04 18.60 93.50
6527.26 -0.08 .08 2.84e-04 29.30 70.60

.08 5.35e-01 39.80 10430.00
.08 3.12e+00 31. 30 14100.00

6548.10 -0.08
6562.80 -0.08

ODODOOOOOOOOOOO

6578.05 -0.08 .08 5.37e-03 18.30 870.50
6583.47 --0.08 .08 1.63e+00 40.20 11370.00
6610.65 -0.11 .11 2.79e-05 25.00 11.70

A BC D E F

Figure 3.2 A subset of the Input Line List for the IC 418 dataset. Listed in columns
from left to right are: A. observed wavelength (A) B.,C. errors in measurement (A),
D. flux with respect to H5 E. FWHM (km/sec) F. signal to noise.

wavelength for that line. Correct the observed wavelength with the value ap-
propriate from the velocity structure model for each transition’s parent ion’s

ionization potential.

3. Calculate a template flux, the predicted intensity of a line corresponding to a
specific transition, for all transitions selected in the previous step. Retain the

transitions with the strongest predicted lines.

4. For each surviving transition, look for the presence of additional lines in the

Input Line List which could correspond to transitions from the same multiplet,

68

Table 3.1 The ionization potential energy bins and signature lines used to calculate
the ICF values

 

Bin Energy Range (eV) Signature Lines

A 0-13.6 Mg I] A4571, Na I A5890, 5896,
[s I] A7775, [0 I] A8727
Ca II (H&K) A3934, 3968

 

B 13624.7 H5

C 24.7-54.5 He I A5876, 4471

D 54.5-1000 He II A4686

E > 100 [Fe X] A6375, [Ne V] A3426,

[Fe v11] A6087, [Ar X] A5533

 

by meeting certain relative wavelength agreement and flux criteria.

5. Rate each transition’s likelihood of being the possible ID for a line, based upon
the agreement between laboratory and observed wavelengths, the predicted
strength of transition relative to all other possible IDs for that line, and re-
sults of the multiplet check, to arrive at a rank-ordered set of possible IDs for

presentation to the user.

3.3 Modeling the Nebula

EMILI models the observed object as consisting of five distinct zones or bins, each
representative of a different range of ionization potential energy. The bounds of each
bin are listed in Table 3.1. EMILI utilizes the information provided in the Matched
Line List to determine the properties of all transitions whose parent ions reside in one
of those bins. Specifically, EMILI calculates a correction to the observed wavelength

of each unidentified emission line, depending upon the parent ion for the transition

69

being tested as its possible ID, appropriate to that’s ion’s residence within one of the
energy bins. EMILI also determines the parent ion’s abundance, based upon which

bin it resides in.

3.3.1 Velocity Structure Modeling

Baldwin et al. (2000) showed in their spectrum of the Orion Nebula that among their
observed emission lines, the magnitude of the residual wavelength difference between
the observed and laboratory values (after correction to the rest frame of the nebula)
correlated with the ionization potential of the lines’ source ions. They attributed this
to a foreground matter flow having a component parallel to the line of sight, with a
differential flow velocity. PNe have been shown to have a radially differential expan-
sion velocity (see for example Gesicki, Acker, & Szczerba (1996) for IC 418), with
increasing velocity correlated with increasing distance away from the central star. As
ionization stratification means higher ionization potential ions concentrated towards
the central star, the result is to anti-correlate ionization potential with velocity. This
effect, coupled with hypothetical flows and geometric effects, can produce a pattern
of velocity residuals similar to that seen among the Orion emission lines.

EMILI calculates a correction to be applied to the observed wavelength of any
unidentified line, based upon the ionization potential of a possible ID transition’s
parent ion. For each line listed in the Matched Line List, the bin to which its parent

ion belongs is determined, and the velocity difference between the laboratory and

70

observed wavelength (Am), and Aobs respectively) is calculated according to the formula:

(am

where um, is the velocity difference in km sec‘1 for that transition and c the speed of
light. For each bin the average um, is determined from all lines in the Matched Line
List belonging to that bin, to arrive at a correction for all potential ID transitions
whose parent ion falls within it. When a particular transition is being tested as a
possible ID, the observed wavelength of the unidentified line is corrected to the “rest”

wavelength of that transition (Am, according to the formula:

 

hszm0+flfU, (33

where here um, is the average wavelength correction (in km sec‘1 ) for ions belonging
to the bin in which the parent ion of the transition resides.

The number and extent of these bins were established to match the ionization
potentials of the ions producing the most well-observed nebular emission lines, in order
to maximize the chance that each bin would be equally and adequately represented
in constructing the velocity model. Matched Line List has no entry for a bin, the bin
adopts the correction value of the nearest bin with a non-zero um.

In Figure 3.3, the correction value, um for each bin for the present IC 418 dataset,
as calculated by EMILI, is plotted, indicating that a real ionization energy dependent

velocity field attributable to some source is evidenced in the line wavelengths.

71

 

   

 

 

 

‘0 I I I I I
For IC 418 Matched Line List
to
w
8 rt) L
(I)
\
E
35
3 N l. C
)0
O~——— _7- _-—"—"_————'_‘
D E
'— l l l L I
' o- 136— 247— 545—
13.6 24.7 54.5 100.0 >100.0

Ionization Potential (ev)

Figure 3.3 The velocity correction, user, in km s‘1 for all bins “A”-” E”, calculated
from the Matched Line List from the EMILI run on the present IC 418 dataset.

3.3.2 Abundances

The second use of the Matched Line List is to establish rough estimates of the expected
ionic abundances for all ions Z _<_ 30. The overall elemental abundances with respect
to hydrogen are read in from the default solar (or user-supplied) abundance table,
and are modified by ionization correction factors (ICFs). ICFs are calculated using
the strengths of certain “signature” lines (again see Table 3.1) listed by the user in
the Matched Line List. Each ICF value acts as the fraction of the total elemental
abundance present in ions in each of the ionization energy bins. Multiplying the

elemental abundance by a combination of these ICF values, as described below, yields

72

ionic abundances for all ions of that element present in the nebula.

For the first ionization energy bin “A”, the code looks for strong, collisionally
excited, forbidden transitions for neutral ions such as [C I] A8727A; or for strong,
collisionally excited permitted resonance lines like the Na I AA5890,5896A and the Ca
II H&K AA3934,3968A doublets. EMILI arbitrarily assigns a value for $4, the ICF
for bin “A”, based on the flux, I ,\ / 1H3, of the strongest observed signature line listed
in the Matched Line List for the bin. If the strongest line has a flux IA/IHB < 10‘4
then 17,; = 0.001; if 10‘4 S IA/Iug < 10“2 then 1174 = 0.01, and if 10'2 S [A/Ifig
then 23.4 =2 0.1. A minimum value 27., = 0.001 is assigned if no lines are observed or
included from bin “A” in the Matched Line List.

In a similar manner, the code looks for lines belonging to ions with large (>100
eV) ionization potentials (the population of bin “E”). Depending upon the strength
of the strongest signature line that is found for bin “E” in the Matched Line List,

EMILI will assign a value:
173 = 10‘3 + IA/Infi, (3.3)

where I ,\ / [H5 is the flux of that indicator line with respect to H5, up to a maximum
23E 2 0.5. Again, a minimum value of x3 = 0.001 is assumed if no lines are present
from this bin in the Matched Line List.

The ratio of ICFs for the “B” and “C” ionization bins is determined by the code by
comparing the ratio of the observed fluxes with the theoretical value. The calculation
uses a pair of particularly strong lines: H5 from bin “B”, and He I A5876A and

A4471A from bin “C”. The theoretical ratio is related to the observed ratio of the

73

lines, IHe+ /IH5, by:

I”... _ NH..N,a*;{j,A,,B

‘— 1 3.4
[He NpNea‘gfif A ”8+ ( )

 

 

where NH8+, Np, and N, are the densities of ionized helium, ionized hydrogen, and
electrons respectively. The are” factors refer to the effective recombination coefficients
for the transitions (cr‘lzifef.r for He I A5876 or A4471 etc...), and the A values are the
wavelengths. Some fraction, 51:0, of the helium atoms along the line of sight are singly
ionized, and similarly, a fraction, :63, of hydrogen atoms are also ionized. These
are equivalent to the ICF values :33 and 2:0. Calling y the elemental abundance
ratio between hydrogen and helium, and assuming completely ionized hydrogen in
the ground state at the location of He++ production, the ratio of the fraction are to

:33 may be expressed as:

5170 _ _1_IHe+ 02ft; /\He+

5178 _ 11 1H6 /\H5 (12%. '

 

(3.5)

We assume (Osterbrock 1989) an intrinsic intensity ratio of [15876 / 114471 2 2.76, and
standard values for the eflective recombination coefficients for H5 , c135! , and for He I
A4471, “144711 of 3.03 x 10“14 and 1.37 x 10"14 cm3 sec“1 respectively at an electron
temperature of 10000K and density of 10000 cm‘3 (Osterbrock 1989). These values
of the effective recombination coefficients vary less than an order of magnitude over
all typical nebular temperatures and densities.

The value of 230/233 is calculated from the intensity, with respect to H5 , of either

He I line. For He I A5876:

x—C 0.7415173, (3.6)
51313 y 1H5

74

and for He I A4471:

£9 = 2.03124471 . (3.7)
$3 y 1116

 

The average of the two :60 / :1: 3 ratios is used if both lines are observed and present in
the Matched Line List.
The ratio of the ICFs $0 to 3:0 is computed using the observed fluxes of the same

two He I lines, and the observed flux of He II A4686A:

 

f2 : ’\He+ aifiégs IA4686 (3 8)
SEC ail)"; /\(4686) IHC+ , '

where the H e+ subscript refers to the use of one or the other of the He I lines. Using
dig“ = 1.37 x 10‘13 cm3 sec”1 for the effective recombination coefficient of He II

A4686A, and the same assumptions used in calculating :rC / 133, the ratio of 2:0 to me

can be expressed in terms of the intensity ratios:

 

 

I
x—" = 0.11 “686 , (3.9)
113C IA5876
01‘:
I
£9 = 0.04 “686. (3.10)
1170 IA4471

The average arc/2:1) is used if both He I lines are observed and listed in the Matched
Line List.

The values for 23,, and 333 are then used with the ratios from eqs. 3.6-3.7 and
eqs. 3.9-3.10, and all the ICF values normalized to sum to unity, providing a system
of equations from which EMILI solves for .133, (cc, and 2:0.

Where signature lines are not present in any bin “B”-” D”, EMILI assumes the
following in its calculations for the remaining ICFs:

75

o If no signature lines are present in either bins “C” or “D”, the object is assumed
to be of extremely low ionization, in which case most of the ions reside in
bins “A” or “B”: are and :30 are assigned values of 0.001 and 2:3 assumes the
remainder of unity after subtraction of all other ICFs. Alternatively, the object
may instead be of extremely high ionization, with most of the ions in bin “E”,
indicated by .735 assigned its maximum value. In this case 1:3 through 1:0 receive

minimum values of 0.001.

c If no signature lines are present in bin “D”, but bin “C” is p0pulated, it is
assumed that the object is in fairly low ionization. In this case 330 takes a
minimum value of 0.001, and x3 and are share the remaining portion of unity

according to the value of ate/3:3.

o If signature lines are present from all bins “B” -” D”, then the ionization is as-
sumed to be moderate, and the values of $3, 3:0, and 3:0 split the remaining
portion of unity (after subtraction of 117.4 and mg), with 2:3 and 2:0 getting the

majority, and all factors proportioned according to the ratios of 330/233 and

30/303

1133 =(1—$A—$E)/(1+—+——),

5130
170 = 173—,
$3
$1)
1131) = 5130—.
1130

0 Finally, if signature lines are absent from bin “B” but present in bins “C” and

“D”, the object is considered to be highly ionized. Then 2:3 assumes a minimum

76

value of 0.001, and 2:0 and :60 share the remainder according to 1130/5150.

It is important to note that while the ICFs act as percentages of a particular
element present as a specific ion in the nebula, the sum of the products of the ICFs
multiplied by the overall elemental abundance for each of its ions need not sum to
the elemental abundance. This is the case where elements may have multiple ions
within a particular ionization bin. The goal of these calculations are rough estimates
of the ionic abundances only.

To smooth out the abundance model, for ions with ionization potentials near the
edges of the bins, and a next lower stage of ionization in a different bin, the average
of the ICF values for those bins is multiplicatively applied to the overall elemental
abundance. For example, O++ has an ionization potential of 54.94 eV, while O+ has
an ionization potential of 35.12 eV. Since these energies lie within different bins the

abundance of 0+2 is calculated as:
= _(O). (3-11)

since the ionization potential of singly and doubly ionized oxygen reside in bins “B”
and “C” respectively; “O” is the elemental abundance with respect to hydrogen.

If the ionization potentials for an ion and its predecessor are both in the same bin
however, then just the ICF value for that bin is used. For example, the ionization
energy of N +2 is 47.45 eV, and for N+ is 29.60 eV, both in bin “C”. Therefore, the
abundance of N +2 is calculated by EMILI, from the elemental abundance of nitrogen,

as:

N+2 = :60 (N), (3.12)

77

For neutral ions, the “next lower” ionization bin is the lowest energy bin. Special
cases are established for completely ionized hydrogen and helium: HJr = 2:3 and
He+2 = :00. In this manner ionic abundances are calculated for all ions for which line

information is stored in the line database.

3.4 Template Flux

EMILI draws, from its transition database, dozens of transitions within a few mea-
surement uncertainty sigma of each unidentified line in the Input Line List. For each
of these possible IDs, EMILI calculates an expected strength, or template flux of the
emission line produced by such a transition, under the user-specified nebular temper-
ature and density conditions. Only the transitions producing the strongest predicted
lines (those within 1/1000 of the strongest predicted transition among all possible
IDs for that line) are retained for further analysis, on the assumption that these are
the most likely to be observable.

The template flux calculation is meant to be only an order of magnitude estimate
of the relative flux (with respect to H5) that could be observed in such a line. It
is not a calculation of absolute flux, something better accomplished by emission-line
region spectral modeling codes such as CLOUDY (Ferland et al. 1998). In any event,
an exact calculation of the absolute flux for every transition in the Atomic Line List
v2.04 would fail due to lack of atomic parameters for all but a few ions. What
the code does attempt, however, is to compare transitions by their relative strengths,

calculated and normalized uniformly, so that we may judge those most likely to be the

78

correct identification because they are the strongest, relative to all other transitions
in the unidentified line’s immediate vicinity.

When calculating the template flux for a transition, EMILI assumes that a line
arising from it may have contributions from both standard recombination and colli-
sional excitation. Only H5, the line to which all template fluxes are normalized, is
assumed to be entirely created by recombination-cascade. The template flux equa-
tion, then, has two distinct components: collisional excitation and recombination
excitation. The specified nebular temperature and density, the ionic abundances,
and the attributes of the transition, determine their relative contributions.

The template flux equation is based upon a few simplifying assumptions:

1. The nebula has a single electron temperature and density. This is appropriate,
given the approximations made for atomic parameters, and the fact that such
parameters are unlikely to vary by an order of magnitude except in the most

extreme conditions.

2. In the collisional contribution, each ion is modeled as a two level atom, of mul-
tiplicity unity on both levels. The upper level may be collisionally excited/de-

excited.

3. Only direct recombination and cascade is assumed in the recombination contri-

bution. No allowance is made for possible dielectronic recombination.

4. The vast majority of the parent ion of the transition is assumed to be in the

ground state. No levels are considered to be meta-stable, to have sufliciently

79

small spontaneous emission coefficients to allow self-absorption, or resonance

scattering.

The collisional portion of the template flux equation is derived from the equation
of statistical equilibrium for the collisionally-excitable upper level of an ion of interest
with net nuclear charge Z. The intensity of a line arising from this level, I ,\, divided by

an estimate of the intensity of H5, 1H5, can be shown to be equivalent to (Osterbrock

 

1989)
1*— ~ 10 x 1014NZ q” (313)
[He 1 + Ne‘Izl/Am

An approximate value of afiffif z 1.0 x 10‘14 cm3 sec“1 , the nearly constant eflective

recombination coefficient for H5, has been used. N z is the overall ionic abundance
with respect to hydrogen; Q12 and q21 are the rates of collisional excitation and de-
excitation of the ground and excited states respectively, and A21 is the spontaneous
emission coefficient of the transition.

The rate of collisional de-excitation has the functional form:

 

(3.14)

where 012 a dimensionless collision strength for the transition, a factor arising from
quantum mechanics that is defined as the overlap between the initial and final wave-
functions of the excited electron. The collision strength generally has a value between
0.1 and 10 for a wide range of collisionally excited lines. Assuming a typical value of

1, and an average nebular temperature of 10000 K, q21 can be expressed as a simple

constant equal to 10‘7 cm3 sec‘1 .

80

The collisional excitation rate is related to the de-excitation rate by the Boltzmann

factor:

~ 1 3 —1
912 ~ 2421 exp (kT) cm s . (3.15)

Z, the net nuclear charge, is included here to scale the collisional cross-section which
enters into the derivation of the collisional excitation rate for non-hydrogenic ions. x is
the energy difference between the ground and excited levels. Assuming that the main
temperature dependence is in the exponential factor, and scaling the temperature to

units of 104 K, T4 E T/104, q12 can be expressed simply as
71,2 x 1.0 x 10'7 Z exp(—0.8x/T4) cmas‘l. (3.16)

Making these substitutions, the collisional portion of template flux equation yields:

_Ii ___ 1 X 1.07sz exp(—O'8X/T4)

1H,, 1+ 1.0 x 10-7N..,/.421 '

 

(3.17)

1 , while

For a typical allowed, electric dipole, recombination line, A21 z 1.0 x 107 sec—
A21 z 100 sec‘1 for intercombination lines, and A21 z 1.0 x 10‘1 sec’1 for magnetic

dipole and electric quadrupole forbidden lines. These values for A21 are substituted

into the final form of the template flux collisional excitation contribution:

IA 5 exp(-0.8x/T4)
—— = 1.0 10 N Z .
I... X Z 1+ 1.0 x 10-7N../A21

 

(3.18)

The constant pre-factor is scaled down to yield better agreement with the observed
strengths of actual well-known nebular lines. The pre—factor is further diluted by
a factor of 10 for transitions arising from neutral ions to account for the greater
difficulty in collisionally exciting such ions (in the absence of the Coulomb focusing
effect induced by the net nuclear charge of a non-neutral ion).

81

For the recombination portion of the template flux we start with a generalized
version of the effective recombination coefficient interpolation formula of Pequignot
et al. (1991), who fitted effective recombination coefficients to numerous C,N,O ions’
levels. We divide this by the same approximate value of the effective recombination

coefficient of H5 (afffif z 1.0 x 10’”) to yield:

 

aeff T4 —0.7
——z1 Z 1 .1
at? 0( + )((2+1)) ’ (3 9)

where Z is the net nuclear charge, equal to the ionic charge used in Pequignot et
al. (1991) minus one. To convert to an intensity ratio we must multiply through by
a branching ratio and by the numeric ionic abundance with respect to hydrogen for
the ion NZ“, where this ion is in the next higher stage than the one used in the
collisional portion. Assuming recombination to a non-metastable level, the branching
ratios take the form of 1421/ (1.0 x 107 sec“1 ) where the denominator is an order of
magnitude estimate of the typical sum of spontaneous emission coefficients for all
permitted transitions off the level, which will dominate the de-population of such a
level. A21 is the order of magnitude estimate of the spontaneous emission coefficient
for the various types of transitions defined earlier. After simplification we are left
with:

£— _ N A21 (Z+1)1'7
1H,. _ “11.0 x 106 T."-7

 

(3.20)

We dilute the above equation by a factor of ten for electric dipole permitted transitions
to again attempt to get better agreement with actually observed line strengths.

For each transition being tested as a possible ID for a particular line in the Input
Line List, a value for the template flux of that transition is calculated according to

82

the sum of eqs. 3.18 and 3.20. The template flux is then normalized by the calculated

template flux for H5.

3.5 Multiplet Check

An important component of EMILI is the automatic checking for additional lines
belonging to the same multiplet as a predicted strong transition being tested as a
potential ID for an unidentified observed line. Multiplet transitions are those that
are between different pairs of j states in the same upper and lower levels. A typical
multiplet, and all of its associated permitted transitions, is depicted in Figure 3.4.
The validity of a particular transition as a potential ID is enhanced by evidence of
other observed lines which could sensibly correspond to transitions from the same
multiplet.

Lines from the same multiplet of the same transition type (electric or magnetic
dipole or quadrupole) should exhibit similar wavelength agreement between their
matches in the Input Line List and the transition’s tabulated “laboratory” wave-
lengths, since the parent ion is the same, and any errors in the laboratory wavelengths
should presumably be of the same magnitude and direction given a common source
of measurements.

These lines should also have fluxes within an order of magnitude of each other:
they should differ only by the product of the relative occupation of the relevant levels
(roughly proportional to their statistical weights), and their Einstein spontaneous

emission coefficients (generally also within an order of magnitude of each other). The

83

Fe II e4D - u4Fo Multiplet Transitions
1. 7116.40 A

 

9’2 2. 7117.95A

 

 

 

 

 

772 772 3. 7163.46A
5,2 5,2 4. 7349.76A
. 9.

3,2 3,2 5 739 96A
9 6. 7436.77.41

172
7. 7563.71 A
8. 7602.18 A
9. 7700.58 A

Figure 3.4 A typical multiplet of Fe 11 showing all allowed transitions under LS cou—
pling. The position of the energy levels is not to any scale. Fraction beside of the
levels are the j total angular momentum values of the each of the upper and lower
levels. The numbers indicate the transitions and their laboratory wavelengths.

ratio of strengths of two typical recombination lines from the same multiplet can then

be expressed approximately as:

5 ~ (2.71 +1)/11

~—:—-—-——, 3.21
I. (2.2+1142 ( l

where (2 jl +1) and (2 j2+1) are the statistical weights of the 3' states of the upper level
of the multiplet from which the lines originate, and A1 and A2 are the spontaneous
emission coefficients of the two transitions.

For each surviving ID transition, EMILI searches for all multiplet transitions
within the wavelength bounds of the Input Line List with upper and lower j val-
ues , jzower and jam," respectively, which meet the criteria of jzower > jl’owe, — 1 and

jumper > jam," — 1, where jLPPe, and flower are the values of the upper and lower states

84

of the transition being tested as an ID. As an example, in Figure 3.4, if the Fe II
A7399.96A line was being tested as a possible ID, all those other transitions in the
multiplet other than line “9”, A7700.58, would be searched for. This is done to avoid
biasing the total detection statistics, by looking for lines that might be weaker than
the transition being tested and potentially undetectable in the spectra because of
their smaller statistical weights. Lines from a level with large j are usually strong
given the large statistical weight, while transitions between low j states are generally
weak (Williams, private communication). For the same reason, EMILI will draw only
those lines of the same or stronger transition type, electric dipole, magnetic dipole,
or electric quadrupole in order of decreasing strength, as the transition being tested.
If testing a particular collisionally excited, magnetic dipole, transition, such as the
nebular [O III] A4959A line, EMILI would not look for the A4923, electric quadrupole
A j = 2 line arising in the same multiplet, because the quadrupole transition is ex-
pected to be generally weaker. However if the A4923 line were being tested, the code
would look for the A4959 line.

In the list below 11 and A1 correspond to the observed intensity and wavelength
of the candidate line EMILI is presently attempting to identify. A1 and jl are the
spontaneous emission coefficient and j value of the upper level of the transition EMILI
is testing as a possible ID to that un-identified line. 12 and A2 are the observed
intensity and wavelength for another un-identified line from the Input Line List to
which a transition of the same multiplet is thought to correspond. A2 and jg are this
transition’s spontaneous emission coefficient and upper level j value. In this example

the j values of the upper and lower levels of the “2” line satisfy the EMILI criteria

85

for potential detection in the nebula (i.e. jg 2 jl — 1 for both the upper and lower
levels). To be accepted as a detected multiplet line, the following criteria must be

satisfied:

1. F luz Criteria: If both transitions have A values in the transition database, then

following eq. 3.21,

0.333 < . ‘-
A2(2]2 +1.) 12

< 3, (3.22)

must be true. If either or both A values are not known, then a somewhat looser

tolerance is allowed:

1
0.1 < —’ < 10, (3.23)
12

If the transition being tested is of lower expected strength than the other multi-
plet member, (because of weaker transition type), the upper bound is expanded

and the lower bound is dropped when the A values don’t exist.
— < 104, (3.24)

or eq. 3.22 applies if the A values are known. This reduces the possibility of
the code mistaking a much stronger line, relative to the line being ID’d, as a
multiplet member. The generous limits are used to accommodate the possibility

of errors in the flux measurements of either lines.

2. Wavelength Criteria: Since both lines belong to the same ion and multiplet,
they each should arise from exactly the same region of the nebula. Thus, the
differences between the observed wavelengths, after correction for the multi-

plet’s ionic parentage, and the corresponding laboratory wavelengths of the

86

transitions, should be nearly the same, assuming that lines of similar strength
have similar uncertainties in their wavelength measurements and laboratory-

determined values. Velocity difl'erences, 111,2, are calculated from:

A1 - Alab,1 /\2 - Alab,2
c———— ' - c—————

ul = , 112 — , (3.25)

A100,]. Alaba2
where Alab,1 and Alab,2 are the laboratory wavelengths of the multiplet transitions.

In order for EMILI to accept the line “2” as a detected multiplet member the

relative difference in velocities should satisfy:
[01 — 112' _<_ 02 , (3.26)

where 02 is the uncertainty in measured velocity of line “2” in units of km

sec‘1 .

If all the lines from a multiplet fall within the larger of the user-specified instru-
mental resolution or natural line width, it is assumed that the lines are blended.
A statistical weight-weighted average wavelength replaces the transition’s laboratory
wavelength, all the multiplet lines are considered to form a single line at that wave-
length, and the multiplet check is not carried out.

Currently, EMILI carries out the multiplet check for only pure LS-coupled tran-
sitions. Future incarnations of the code will include the check for transitions from
the three other coupling schemes employed in constructing the current and other

transition database.

87

3.6 Ranking the Transitions

EMILI calculates an “Identification Index” or IDI value for each transition consid-
ered as an ID for an observed line, assigning an integer value based upon a three
part scheme outlined in Table 3.2. The scheme gives equal weight to the relative
template fluxes for all possible IDs for a line, the degree of wavelength agreement,
and the multiplet check results, to calculate a numeric “score” for each competing
ID transition. The relative IDI values within a particular line can be used to judge
the most likely ID, while the absolute values may be used to judge the quality of a
particular ID. A lower value of IDI indicates a better identification.

As an aid in visual inspection of the output, in addition to the numeric IDI value,
EMILI assigns a alphabetic “rank”: “A”’, “B”, “C”, or “D” based upon the relative
IDI values for all potential ID transitions within a particular line, with rank “A”
being the “best” ID for that line, “B” the second best and so on, with ties in IDI

value receiving equal ranks.

3.7 Output

EMILI’s output consists of a large ASCII file (referred to as the Full Output List).
The list begins with a header contains information about the run’s parameters, names
of input and output files, the user-specified temperature, density and instrumental
resolution, and the calculated velocity corrections, um, and ICF values (174 -zE). The
header from the output for the EMILI run on the present IC 418 dataset is shown in

Figure 3.5.

88

Table 3.2 The IDI assignment breakdown for a putative IDs for a given unidentified
line. A lower IDI value means a better ID in general.

1. Flux Basis (F)
A putative ID template flux among all other putative IDs for the same line satisfies
the following condition:
F Condition
0 Exceeds computed fluxes of all other putative IDs by factor 2 10.
1 Within a factor of 10 of the largest putative ID template flux.
2 Within a factor of 100 of the largest putative ID template flux.
3 Within a factor of 1000 of the largest putative ID template flux.

 

 

2. Wavelength Basis (W)

The residual wavelength difference (in km/s) between the observed line’s corrected
wavelength and that for the putative ID is within a number of measurement sigmas
(a) of the observed line’s corrected value:

 

 

W Conditions
0 S 0.50
1 S 1.00
2 S 1.50
3 S 2.00

 

3. Multiplet Basis (M)

For a putative ID, the number of detected multiplet members, D, out of P possibly
observable members satisfy:

 

 

M Conditions

0 P/D =1/1,D > 2
1 P/D = 0/0,2/1

2 P/D=1/0,(> 2/1)
3 P/D =(>1)/0

 

IDIvalue=F+W+M

89

EMILI Output File
Input Line List: ic418.in
Input Matched List: ic418.match
Results List: ic418.out
Short Results List: ic418.dat
Abundance Table: abun.dat
Electron TEmp: 10000.
Electron Density: 10000.
Inst. Resolution: 10.

ICF Values: Bin/8

ix 1: 0.00999999978
ix 2: 0.498415828
ix 3: 0.489584208
ix 4: 0.00100000005
ix 5: 0.00100000005

Velocity Structure: Bin/Veltkm/s)

irvcor 1: 4.26208973
irvcor 2: 4.08970976
irvcor 3: 1.74469769
irvcor 4: -0.0550202653
irvcor 5: -0.0550202653

Figure 3.5 The header for the EMILI output file generated by its run on IC 418
databaset. The header includes information regarding the input / output files, specified
temperature, density, instrumental resolution, and the calculated ICF (labeled here
as ”in: 1” — ”i3: 5”) and 1100,. (lableled here as ”irvcor 1” — ”irucor 5”) values for the
five ionization energy bins.

The header is followed by an entry for every unidentified line, similar to that
seen in Figure 3.6, containing information regarding possible IDs for that line. In
each entry, the top row indicates the observed wavelength of the particular line,
its flux, (normalized to the observed H5 line strength), and the S/N and FWHM
of the line. Each succeeding row is a potential ID for the line, listed in order of
increasing velocity difl'erence between laboratory and observed, corrected wavelength.
The columns indicate: ( 1) The observed wavelength of the line, corrected by the 000,

appropriate for the transition. (2) The laboratory wavelength of the transition. (3)

90

Observed Line: 5179.52 3.33-05 8111: 18.40 FWHM: 18.5
5179.45 | 5179.000* 5 I 1073985643 4 8.38-06 26.0 0/0 8

5179.52 5179.178 Fe III 1747436964 263 1.18-04 19.9 */0 9
5179.49 5179.172$ Fe II 1746398483 7 1.78-04 18.4 0/0 60
5179.49 5179.256 Fe II 1746167982 8 4.78-04 13.5 7/0 8
5179.49 5179.262 AI II 1209154620 265 1.18-05 13.2 6/0 9
5179.49 5179.344 II II 471096463 263 3.58-04 8.4 2/0 7

|
l
l
l
l
+ 5179.49l 5179.420 N I 469938193 262 1.18-04 4.07/0 5C
I
I
l
|
l

+ 5179.49 5179.432S III II 1209296995 9 1.18-05 3.3 0/0 48

+ 5179.49 5179.520 N II 471088267 263 3.58-04 -1.8 2/1 24 5175.889 -3.4
5179.52 5179.738$ Ne II 672424011 7 1.98-04 -12.6 0/0 60
5179.49 5179.831 II I 469933071 264 1.28-04 -19.8 7/0 8
5179.52 5179.900 C III 404892760 5 1.18-03 -22.0 0/0 60

5179.52 | 5179.900 C III 404893785 5 1.18-03 -22.0 0/0 60
5179.49 | > 5180.310 [Fe III] 1746959383 4.78-02 -47.5 2/0 0<

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

Figure 3.6 The EMILI output for a line observed at 5179.52A in our IC 418 spectrum.
Column legend is provided in the text.

The parent ion of the transition. (4) and (5) are internal reference numbers for the
transition, employed in the transition database. (6) The template flux. (7) The
velocity difference between the observed line, post-correction, and the transition’s
laboratory wavelength. (8) The multiplet statistics with format “X/ Y”, where out of
“X” other multiplet lines expected to be observed, “Y” were actually detected. (9)
The IDI value and rank. (10) If additional multiplet lines are found by the code, they
are listed along the same row in decreasing observed flux order. The velocity difference
between the multiplet transition’s laboratory wavelength and the corrected, observed

wavelength from its corresponding line are listed for each multiplet line found. Up to

91

three such lines at maximum are displayed.

Additional marks in the individual line identification entries include a “+” be-
fore column (1) which indicates that the laboratory wavelength is within 1.50 of the
observed, corrected wavelength, where a is the observed wavelength’s measurement
uncertainty. An “*” after column (3) indicates that all the lines from the multiplet
were within the instrumental resolution or natural line width, and the listed wave-
length is a statistical weight-weighted blend wavelength. A “8” in transition was
not a pure LS coupling. The multiplet check is not currently carried out for such
transitions, indicated by a “0/0” entry in column (8). Finally the last row in each
identification, with a “>” preceding column (3) and a “<” in column (9), indicates
the strongest predicted transition in the velocity region between the initial search ra-
dius from the transition database, and twice that radius. This allows strong lines with
poor theoretically calculated or laboratory observed wavelengths to be considered as
possible ID. The multiplet check is carried out for these lines, but the transition is
not ranked and no IDI value is calculated.

EMILI suggests that for the weak line (3.3 x 10’5 times the flux of H5) whose
EMILI output is depicted in Figure 3.6, N II A5179.52A is the most likely ID. This is
based upon its relatively strong template flux, actually within an order of magnitude
of the observed value, close wavelength agreement, post-velocity model correction,
and the detection of a second line, out of a possible two, from the same multiplet.
It is significant that this line, N II A5179A 3p 5?” - 3d 5F, must arise from di-
electronic recombination, as it belongs to a multiplet with spin multiplicity of 5, a

level incapable of being excited by standard one-body recombination between N ++

92

and a free electron. Such a line, unusual among nebular lines, may not have even been
considered as a possible ID using “conventional” manual identification procedures, nor
have been included in a model spectrum.

A second output file, called the Summary List, simply states the observed wave-
length and all “A” rank EMILI identification for all unidentified lines. An example,
generated by a run on the IC 418 dataset, may be seen in the EMILI User’s Manual

(Appendix D)

3.8 Application to Other Spectra

EMILI has been applied to several nebular spectra, including the Orion Nebula (Bald-
win et al. 2000) and NGC 7027 (Walsh et al. 2001), in addition to the present dataset
on IC 418. Manual IDs were available for the Orion and NGC 7027 datasets, which
allowed a comparison with the IDs suggested by EMILI. Comparing EMILI primary
rank “A” IDs against manual IDs in the two datasets (Tables 3.3 and 3.4) shows
that at least 75% of the time, the EMILI primary ID corresponds to the manual ID.
Including cases where EMILI secondary and tertiary IDs correspond to the manual
IDs are included, the matching statistics improve to about 90% or better in both
objects. In these examples where individual lines were listed with multiple IDs, the
matches include only the highest ranked EMILI ID among those manual IDs.
Running the present incarnation of EMILI with the IC 418 data of Hyung, Aller,
& F iebelman (1994) (HAF) (at a Te 2 10000 and N8 = 11500), yields the results in

Table 3.5, where EMILI IDs are compared to manual ones for lines in which HAF

93

Table 3.3 Manual IDs versus EMILI IDs for emission lines in the Orion Nebula as
observed by Baldwin et a1. (2000). The second column lists the number of times
within each EMILI rank, that a particular manual line identifications matched the
EMILI identification of that rank for that line. The bottom row without a rank entry
indicates the number of lines for which the manual ID was not ranked by EMILI, or
for which the transition was not present in the EMILI transition database. The third
column shows the percentage of all 388 lines that fall in each category.

 

Rank N %

 

 

A 329 85%
B 34 9%
C 12 3%
D 5 1%
8 2%
TOTAL 388

Table 3.4 The same as Table 3.3 for the spectrum of the PN N GC 7009 by Walsh et
al. (2001).

 

Rank N %

 

 

A 258 73%
B 31 9%
C 23 7%
D 7 2%
33 10%
TOTAL 352

Table 3.5 The same as Table 3.3 for the spectrum of IC 418 as observed by HAF.
These statistics include only lines assigned single distinct IDs by HAF.

 

Rank N %
A 178 88%

 

 

B 4 2%
C 5 2%
D 0 0%
16 8%
TOTAL 203

94

had a distinct single transition as an ID. Good agreement, on a par with the earlier
works, is shown between the manual and EMILI-derived IDs. In addition, EMILI
provides possible IDs for lines left unidentified in this work. For twenty or so lines,
the transitions corresponding to the manual IDs could not be found in the EMILI
transition database. In some of these cases HAF did not provide a corresponding
multiplet member from which to confirm the wavelengths and transition types, nor
did the listed wavelength match any nearby transition for the same ion and transition
type in the database. If these lines are thrown out, the EMILI matching statistics
improve to nearly 95% for primary rank “A” IDs against manual IDs.

It should be noted that the manual IDs are unlikely always to be correct, so that

some EMILI primary IDs may be better than their manual counterparts.

3.9 Application to Current Dataset

A list of 805 probable nebular lines were submitted to EMILI for identification. For
each line, the observed wavelength was assigned a measurement uncertainty based
upon a statistical analysis of agreement between multiple measurements of the same
line in differing orders and spectra, and agreement between the observed and labo-
ratory wavelengths of several well know emission lines (see Sect 2.3.3). A subset of
this list, including 40 emission lines with unambiguous identification and no obvious
blending, were used by the code to establish the velocity model and ionic abundances
in the manners described previously. The distribution of velocity corrections and ICF

factors for each ionization energy bin are listed in the EMILI output header shown

95

in Figure 3.5. EMILI was run with T8210000 and ne=10000, composite values es-
tablished from various forbidden line diagnostics (see Sect 4.1.1). The instrumental
resolution was set to 10 km sec"1 .

For each unidentified line, the code searched the transition database for all tran-
sitions within 50, where a is the assigned wavelength measurement uncertainty, then
computed template fluxes for emission lines corresponding to them. The multiplet
check was carried out for the transitions with the strongest template fluxes in this
region, and for the transition with the strongest template flux in the 5-100 halo re-
gion. The boundary condition on the left hand side of eq. 3.22 was removed in an
effort to improve multiplet member detection chances, but there appeared to be no
significant difference in this regard in comparison with a previous run using both
boundary conditions.

Based upon the wavelength agreement between observed, corrected line wave-
lengths and the laboratory wavelengths of potential ID transitions, the relative
strength of their template fluxes, and the results of the multiplet check, an IDI value
was calculated and a rank awarded to each possible ID for a particular observed line.
A sample of the EMILI output for an individual line in this dataset may be found in
Figure 3.6.

The EMILI output was compared to the line identifications from high resolution
PN and H II region spectra, including HAF (1C 418), Liu et al. (2000) (PN NGC 6153),
Baldwin et al. (2000) (Orion Nebula), and Esteban et al. (1999) (H II region M8).

The strongest recombination lines expected from a variety of ions were determined

by referencing Williams (1995, and private communication), Liu et al. (2000), Moore

96

Table 3.6 Numbers and percentage of EMILI IDs chosen as final IDs for each EMILI
IDI rank, out of the total number of IDs used from EMILI. The average, minmum,
and maximum IDI values among IDs chosen within each rank are also listed. These
numbers includes all transitions from lines thought to be blends, or which otherwise
had multiple EMILI selected for them. “Total” equals the total number of EMILI
IDs selected, not the number of individual emission lines.

 

 

 

Rank N % Avg IDI Min IDI Max IDI
A 543 67.5 2.7 0 7
B 91 11.3 5.1 2 9
C 56 7.0 6.3 2 >9
D 38 4.7 6.8 4 9
None 77 9.6 7.8 5 >9
TOTAL 805

(1945), and Osterbrock, Tran, & Veilleux (1992). These were used to establish likely
upper flux limits for lines ID’d as belonging to those ions, and to judge the credibility
of identifications made by EMILI of transition arising from ions of comparable and
higher ionization potentials. Choices for individual line identifications were then made
based upon the EMILI output, and the above information, and incorporated into the
final line list (Appendix E).

Table 3.6 lists the numbers of different EMILI ranked IDs which were chosen
manually from the output as actual line IDs. Some lines had multiple IDs selected,
where it was suspected that the line might be a blend of two or more individual
transitions of similar strength, or where two or more IDs were thought to be equally
likely. Table 3.6 includes every individually selected ID transition from these lines.
On a whole, it appears that EMILI provided reliable IDs (confirmed primarily by
previous literature or via the multiplet check) for about 69% (555 lines) of the total

number of individual lines originally submitted for identification (805 lines). When

97

including cases where it was thought that EMILI provided at least a possible ID (624
lines) the estimated success rate rises to 78%.

EMILI was unable to provide any convincing IDs for the remaining unidentified
lines. However, a significant number of these lines, 250 or so, were found in the re-
gion 86700-8800A. Some of these lines are fairly strong (> 10'4 H5) and inspection
of the original 2-D images established that many are real, but obvious transitions
responsible for them were apparently not included in the EMILI transition database.
An inspection of Osterbrock, Tran, 86 Veilleux (1992) and the Kurucz atomic tran-
sition database (Kurucz & Bell 1995) suggested that most of these lines correspond
remarkably well to higher (n > 15) transitions from He I singlet and triplet states
whose upper levels were not included in calculating the transitions in the Atomic
Line List v2.04. Several Balmer and Paschen lines for transitions originating above
n = 40, as well as for a handful of iron forbidden lines observed in the spectra, were
also not present in the EMILI database. These identifications were made manually
using information from the Kurucz database for the hydrogen lines; and Moore (1945)
and the N IST database for the iron forbidden lines. These lists also provided quality
identifications for a handful of additional lines in this region, with only a possible
EMILI-provided ID.

The remaining 120 unidentified lines had no EMILI IDs that were in any way
distinguishable from each other in the EMILI output, or had IDs for ions thought not
to be abundant enough to be able to produce lines of any observable strength. Many
of them are on the extreme edges of the original 2-D spectra, where the signal-to-noise

was not as good due to the declining illumination of the spectra at these locations. In

98

 

D»).

 

 

200 300
S / N
Figure 3.7 The distribution of flux: —log(I(A)/I(H5)) versus S/N for remaining

unidentified lines. Small triangles at S/N=150 indicate unidentified lines with in-
determinate S/ N.

addition, most of these lines were not observed in any of the comparison spectra we
used to confirm our IDs. However, the distribution of the S/ N and observed fluxes
of these lines, as seen in Figure 3.7, shows that some relatively strong lines remain
un-identified. Many of these are probably real lines, although some of them may
be scattered light artifacts, ghosts, cosmic rays, or night-sky lines that survived the

various screening processes.

3.10 Future Directions of the Code

The greatest limitation of the present code is the fact that there is no cross corre-
lation between individual line identifications, beyond the multiplet check. For in-
stance, there is no check to see if lines ID’d from a particular ion all exhibit the

same wavelength agreement between observed and laboratory values, or all have the

99

same FWHM. Such a check could further enhance the believability of whole sets of
identifications, and might reveal the existence of unresolved blends.

Another limitation of the code is the confinement of the multiplet check to pure
LS-coupled level transitions. The current incarnation of the code works extremely well
isolating those lines that have pure LS coupling, but is incapable of defining what a
multiplet is in the intermediate coupling schemes which apply to many nebular lines
(especially to lines from levels with excited electrons of higher angular momentum
quantum number 6 such as the strong 3d-4f lines of the abundant species O II and N
II). It would be advantageous to include additional code making the multiplet check
available for these important nebular lines.

It is desirable that the template flux values more accurately reflect true observed
line fluxes. The template flux equation makes no allowance for dielectronic recombina-
tion, Bowen-like fluorescence, charge transfer, or continuum fluorescence by starlight
from the central star. It addition, no provision is made for the difference in observed
flux. between lines in the same multiplet, but of diflerent transition type. For in-
stance, the [0 III] 3P0 - 1D2 A4923 transition (an electric quadrupole transition) has
the same template flux as the [O III] 3P1 - 1D2 A4959 magnetic dipole transition, but
is observed to be nearly four orders of magnitude stronger in our IC 418 spectrum.
This occurs because the branching ratios and spontaneous emission coefficients of
individual transitions are not incorporated into the collisional part of the template
flux equation.

Finally, the results obtained from using EMILI with PN spectra have shown that

the code is somewhat too reliant on good wavelength agreement between the observed

100

and laboratory wavelengths of an observed line and that of its potential ID. This al-
lows transitions of iron, nickel, and less abundant species to often times be ranked
higher than other more obvious IDs, because of a coincidence of one of their innumer-
able transitions with an observed wavelength. Furthermore, laboratory transitions,
although called “laboratory”, are more often calculated from theoretical levels, rather
than actually observed in an are or in some other fashion, and their wavelengths are
sometimes not as accurately determined as the actual observed wavelengths of nebu-
lar emission lines. A poignant example of this from the Atomic Line List v2.04 is the
strong [Ne III] doublet AA3869,3968, with both lines’ laboratory wavelengths differing

1 more than twice the instrumental

from their observed wavelengths by > 20 km sec‘
resolution.

In future releases we will address these problems, by adding additional logic to
further cross-correlate line identifications, to carry out the multiplet check for all
transitions regardless of coupling scheme, and to improve the accuracy of the template
flux equations with respect to actually observed relative line strengths. Furthermore,
our wish is to eventually make the code iterative. For example, a user would interpret
the output from an initial run and make decisions as to possible identifications for
each of the lines. The user could then adjust nebular physical parameters or initial
elemental abundances and re-run the code, using the chosen IDs from the previous
run to re-calculate the velocity model and ionic abundances, and refine the quality of
the line identifications.

The detection of He I lines in our spectra which were not present in the transition

database, as well as Balmer and Paschen lines above n = 40, demonstrates the need

101

to link, broader transition databases to the program. Presently, the Atomic Line List
v2.04 is virtually meshed into the code, making updating to a more expansive database
difficult. However, plans are in the works to incorporate its successor, the Atomic
Line List v2.05, into EMILI. This line list expands the available ion list to Z S 36,
and includes He I out to n = 50. Because of the similarity to the presently utilized
transition database, its incorporation into EMILI should not require extraordinary
effort.

A longer-range goal is the establishment of an EMILI “standard” to which any
transition database can be converted and utilized, and to allow multiple databases to
be accessed simultaneously. Not only would this allow rapid upgradability, it would
also allow EMILI to utilize transition lists more appropriate to specific classes of
emission-line objects such as PN, quasars, or novae, or to incorporate molecular lines,

or even to make EMILI applicable to stellar absorption spectra.

3.1 1 Conclusions

We have presented a software package called EMILI, which is specifically designed
to take advantage of the vast amount of information available in modern atomic
transition databases, to aid in the identification of atomic emission lines in PN, H II
regions, and other emission-line region objects. EMILI overcomes some limitations
present in model spectra by using generic values of scarce atomic parameters. EMILI
is a tool specifically tailored to PN and H II region emission line identification, by

employing techniques to model the expansion velocity distribution along the line

102

of sight to a such an object, and to calculate rough ionic abundances. The code
minimizes the observer bias that could go into the line identification by providing a
uniform set of criteria by which individual potential identifications can be judged.
The code automates a time consuming and tedious process. Finally EMILI provides
good agreement between manual and code-derived IDs. We believe that EMILI is
an invaluable tool for those studying emission line regions and their spectra, which
should only improve with further work.

The code is publically available at:

www.pa.msu.edu/people/sharpee/emili.html

103

Chapter 4

Results

4. 1 Plasma Diagnostics

4.1.1 Temperature and Density Diagnostics

Electron temperature and density estimates were established from the relative
strengths of various collisionally excited lines in particular combinations (diagnos-
tic line ratios). Tasks from the IRAF nebular package (Shaw & Dufour 1995), which
solve the statistical equilibrium equations for the collisionally-excitable levels of the
involved ions, using a five or greater level ion, were used along with the observed
values of the diagnostic ratios to make the density and temperature determinations.

We used the most recent version (2.0) of nebular. However, it was found that the
default transition probabilities and collision strengths that came with the package
produced unlikely results. The densities and temperatures that were found using

different ions did not agree well with each other, and when we ran the test cases

104

Table 4.1 References for Atomic Data for Collisionally Excited Lines.

 

Ion Transition Probabilities

Collision Strengths

 

C I Froesc-Fischer & Saha (1985)

N I Mendoza (1983)

N11 Mendoza (1983) (1-5)“)
Weise, Fuhr, &. Deters (1995) (6)

O I Mendoza (1983)

O 11 Mendoza (1983) (1-5)
Weise, Fuhr, & Deters (1995) (6)

Ne III Butler & Mendoza (1984)

S 11 Cai & Pradhan (1993) (1-5)
Verner, Verner, & Ferland (1996) (AMA-(1,7431)
Keenan, Hibbert tha, & Caylon (1994)
(remaining for 6)

S III Mendoza (1983) (1-5)
Heise, Smith, & Calamai (1995) (A62,A63)
LaJohn & Luke (1993) (A64)
Kaufman & Sugar (1986) (.465)

C1 II Wilson & Bell (2002)

Cl 111 Butler & Zeippen (1987)

Ar III Mendoza (1983)

Ar IV Butler, Zeippen, & Le Bourlot (1987) (1-5)
Kaufman & Sugar (1986) (6-8)

Johnson, Burke, & Kingston (1987)
(921 $131,932

Pequignot 83 Aldrovandi (1976) (remaining)
Mendoza (1983)

Mendoza (1983) (1-5)

Dopita, Mason, & Robb (1976) (6)
Mendoza (1983)

Mendoza (1983) (1—5)

Dopita, Mason, & Robb (1976) (6)
Butler & Mendoza (1984)

Cal & Pradhan (1993) (1-5)
Ramsbottom, Bell, & Stafford (1996)

Mendoza (1983) (1-5)
Galavis, Mendoza, & Zeippen (1995) (6)

Wilson & Bell (2002)

Butler & Zeippen (1987)

Mendoza (1983)

Butler, Zeippen, & Le Bourlot (1987)

 

9’) Indicates levels/parameters used from reference.

Note: References not listed in bibliography are referenced in the nebular package help

file: at-data.hlp distributed with the package.

given with the package task temden, substantially different results were obtained.

Further investigation showed that the atomic parameters had been updated since the

original thorough testing that led up to the release of the package. After considerable

investigation, it was decided to go back to the original atomic parameters for most

ions, which came from the sources that still are the most widely used. Table 4.1 lists

the references for the atomic data that were eventually adopted.

Calculated temperatures and densities can be found in Table 4.2. To solve for

the electron temperature and density, a density and temperature diagnostic from

the same ion, or from ions with similar ionization potential energies of the previous

105

Table 4.2 Plasma Diagnostics and Their Uncertainties for IC 418.

 

 

Ref Diagnostic Energy“7 X—Ref
Density 716 (cm—3)
(1) [N I] A5200/A5198 0.0 9000 --- -6000 (1)
(2) [8 II] A6716/A6730 10.4 17000 --- -9000 (2)
18000 - - . -10000 (3)
(3) [011] A3726/A3729 13.6 10000 +20000 -5000 (3)
10000 +1 7000 -4000 (4)
10000 +20000 -5000 (5)
(4) [Cl 111] A5517/A5537 23.8 11000 +3000 -2000 (6)
. 10000 +3000 -2000 (7)
(5) [Ar IV] A4711 /A4740 40.9 6000 +10000 -4000 (8)
Temperature T. (K)
(1) [01] (A6300 + A6363)/A5577 0.0 9400 +600 (1)
(2) [s11] (A6716 + A6731)/(A4068 + A4076) 10.4 7000 +5000 (2)
(3) [Cl 11] (A8579 + A9124)/A6162 13.0 10100 +700 -500 (2)
10200 +700 -500 (3)
(4) [0 II] (A3726 + A3729) /(A7320 + A7330) 13.6 10000 +4000 -3000 (3)
(5) [N 11] (A6548 + A6583)/A5755 14.5 9400 +500 -1100 (3)
(6) [s III] (A9069 + A9532) /A6312 23.4 9500 +600 -500 (4)
(7) [Ar III] (A7136 + A7751) /A5192 27.6 9000 +500 -400 (4)
(8) [0111] (A4959 + A5007)/A4363 35.1 8900 +300 -300 (5)
Balmer Jump 5300 6600 i500

 

(“I Ionization potential of previous stage of ionization for ion
(b) Upper density uncertainty / lower temp uncertainly unavailable for combinations with
[N I] and [S 11] density diagnostics, see not in text

stage of ionization, were paired off (see “X-Ptef” numbers in the Table). The nebular
task temden was used iteratively between the two diagnostics, taking the output
from the density diagnostic as the assumed density for the temperature diagnostic,
and vice-versa, until both diagnostics returned the same temperature and density.
These intersection points between diagnostics may also be directly inferred from the
diagnostic diagram shown in Figure 4.1.

Errors for each diagnostic line intensity and the reddening uncertainties, were

propagated through the ratio calculation to yield the errors in the listed temperatures

106

-... -U .-v

 

  
  

 

 

   

   

 

 

 

[- I I I I I; I I I I l I I I '1' ‘ l I T I I T I I I I I I I I I ;
13000 - ' [CI [1110] [5 Inn 8
:[Ar IV] D ] ,l j
' d
I [ '1' -
12000 +— g . _
[— 1 _
L i ..
:4 : .7 :
E 11000 [— ] —
g - ," [s 1111‘ 1
=1 :2. .....l ......[Cl [1] T -
E 10000 _ I ...................... ... ... “a;
8 - [N [I] T .
:3 "“":‘-“-~- [01] T '1
- 1' [s m] T [Ar {1111‘ 7"“ “-
9000 n:::t::::::::::::: [11:1 _- -------------
: l [0 III] 1 . ~- _
I
: l . :
_ l ‘ —1
800° 1- ,l [0 ml) 1’ [8 II] T .1
I If I l 1 l l 1 l I l 4‘ l l I I l l J l I J L L . L l
5000 7500 10000 12500 15000 17500 20000

Electron Density

Figure 4.1 Diagnostic diagram for IC 418. In the diagram “D” adjacent to the ion
denotes a density diagnostic for that ion, while “T” denotes a temperature diagnostic.

and densities. These errors may be overestimates, as the measurement scatter for all
the diagnostic lines with repeated measurements was smaller than the tabulated error
value. Since diagnostic ratios match lines of neighboring wavelength, the effects of flux
calibration and reddening errors are minimized when their strengths are compared in
ratio.

As seen in the figure, nearly all the diagnostics seem to converge in the vicinity
of 10000 cm‘3 and 9600 K (the average values excluding the [8 II] temperature, and
[S II] and [Ar IV] densities). There is a general trend in increasing temperature

with decreasing energy of ionization. This is in line with the notion of the general

107

hardening of the central star radiation with increasing distance from the central star,
assuming that decreasing ionization potential energy also correlates with increasing
distance from the star. The lower [0 III] (source ion 0”) temperature with respect
to [0 II] value is also in line with the probable effects of efficient cooling by strong
0“2 IR fine structure lines, to which 0+ has no analog (Garnett 1992). The lower
[S II] temp is a direct consequence of its pairing with the (probably saturated) [S
11] density diagnostic, and its curve does pass through the region where many of the
other diagnostics intersect. The composite temperature from the diagnostics is about
1000 K less than that observed in Hyung, Aller, & Feibelman (1994) (HAF), but
our data show greater internal consistency than the various temperature diagnostics
calculated by HAF and Henry, Kwitter, & Bates (2000) (HKB) for IC 418.

The [N I] and [S II] diagnostic ratios are most likely saturated: observed values
place them at the high density limit of their theoretical intensity ratio versus density
curves (Stanghellini & Kaler 1989). [In the high density limit the theoretical ratios
become essentially constant with respect to density. Small observational errors in
the observed ratio can lead to large uncertainties in the calculated densities. This
is reflected in the tabulated null uncertainties recorded for the upper [N I] and [S
II] uncertainties and their matched temperature diagnostic lower bound uncertain-
ties. Interestingly, both HAF and HKB determined [S 11] densities, 5600 cm‘1 and
3300 cm‘3 respectively, that were much lower than the value determined here, and
in the case of HAF, lower than those from any of their other observed density di-
agnostics. However, a compilation of previous IC 418 [S 11] density determinations

made by Stanghellini & Kaler show a wide range of observed values, 4300-25000 cm‘3.

108

Furthermore, Copetti & Writzl (2002) have shown that [S 11] densities are statisti-
cally higher than [0 II] densities for the densest nebulae from a compendium of PN
observations.

The [Ar IV] density diagnostic, observed in IC418 for the first time here and
the highest ionization diagnostic we observed, yields the lowest density value. This
lends credence to the notion that these lines arise from the central cavity observed
often in other PNe (Stanghellini & Kaler 1989). For IC 418, such a cavity has been
previously conjectured to be of lower density then the surrounding nebular shell in
order to explain the deficit of Ha emission observed spectra-photometrically in the
central region of the nebula (Reay & Worswick 1979). However, the location of the
slit (see Figure 2.1) doesn’t appear to correspond to the obvious visual location of
the central cavity. The atomic data may also be incorrect for this ion; the use of
the Ar+3 atomic parameters used presently in nebular (Kaufman & Sugar 1986) at
the [0 III] temp of 8900 K, returns a somewhat higher value of 7800 cm'3, even
though other diagnostic Show tighter agreement when the previous atomic data is
used. Alternatively, these lines are also the weakest of our observed diagnostic lines
with uncertainties which would bring it into alignment with the other diagnostics.
However, since both diagnostic lines are distinct in profile and free of blending in our
spectra, we assume that lower density is not an observational artifact.

We conclude that the agreement among the diagnostics is very good. The dis-
agreements are attributable to expected observational errors in the line intensities,
real effects such as diagnostic line ratio saturation, or inaccuracies in atomic parame-

ters, and a (probably) non-homogeneous, stratified ionization structure, even though

109

IC 418 appears to be a uncomplicated system.

4.1.2 Balmer Jump Temperature

The difference in the continuum levels across the Balmer jump (at 364697131), com-
pared to the strength of a Balmer line, may also be used to measure the nebular
temperature. From the Milne relation, the emission coefficient of the continuum due

to recombinations to the first excited state alone, jg, can be written as (Kwok 2000):

, _ 2.16 x 10-38 NpNe 0.8761

4.1
.72 47f T43/2 8 a ( )

 

where all other symbols are defined as before. Dividing by the emission coefficient
for H5, incorporating the weakly temperature dependent formula for agfln) from

Pequignot et al. (1991) leaves

12. = C
jug agg(T4)T43/2 ’

 

(4.2)

where C is a constant. Since the intensity of a line is directly proportional to the
integral of the emission coefficient along the line of sight, the observed intensity
difference in the continuum across the jump divided by the observed H5 intensity can
be equated to eq. 4.2, and the equation solved for temperature.

To obtain the value of the jump, a linear least squares fit to the continuum ex-
cluding obvious emission lines and scattered light features, was made blueward (3500-
364591) and redward (3775-4065A) of the discontinuity. The jump values was then
determined by extrapolating the fits on both ends to the Balmer series-limit wave-

length (364697A). These fits sampled wavelengths in overlapping orders twice. The

110

continuum values were weighted by the associated spectrum error array, and sub-
jected to three cycles of sigma clipping to reduce the effects of remaining weak lines
and artifacts within the fitted regions. The resulting fits are displayed in Figure 4.2.
The He I recombination discontinuity at 3680A wasn’t accounted for as it wasn’t
clearly evident in the spectrum. The redward fit value was then subtracted from the
blueward fit value to yield a jump intensity.

The jump intensity was then corrected for reddening, and divided by the dered-
dened intensity of H5. The observed ratio was equated to eq. 4.2, and the relation
solved for temperature. A temperature of 5300 Kzlz500 K was determined, where the
error is derived from the formal errors in the fit coefficients and reddening correction,
propagated through the temperature calculation. The region immediate redward of
the jump was not originally included in the fit due to the confusion of the contin-
uum level by crowded lines at the series limit, and an overlaying contribution to
the continuum by a broad flare from the [0 II] /\/\3727,3729 doublet in an adjacent
order. Carefully selecting only a narrow region of relatively flat continuum nearer
to the jump than the previous fit (3673-3686A) yields a somewhat higher value of
6600 Ki600 K.

The resultant temperatures agree with the standard observation of lower Balmer
jump temperatures with respect to the forbidden line measures. This is attributed
to recombination-derived temperatures giving a large weight to cooler regions where
recombination is the most efficient, while collisionally excited line-derived tempera-
tures tend to weight more strongly the warmer regions where collisional excitation is

most efficient (Liu & Danziger 1993). However, as seen in Figure 4.2, scattered light

111

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112

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artifacts, the inaccuracy of the scattered light correction, lingering intensity profiles
inherited from the echelle blaze even after correction by quartz lamp division, and the
weakness of the continuum level itself, all contribute to making this determination
somewhat dubious. Finally, the choice of where to fit the continuum redward of the
jump also plays a significant role in the determined temperature.

A similar temperature calculation in the Paschen continuum is complicated by
the presence of numerous broad and deep atmospheric absorption bands, which con-
trive, along with the problems described above, to confuse the true continuum level.

Therefore, this calculation was not carried out.

4.2 Abundances

4.2.1 Ionic Abundances from Collisionally Excited Lines

We calculated abundances for C,N,O,Ne,S,Ar,and Cl ions, with respect to ionized
hydrogen (NH/H1"), where is the ionization state of the particular ion, from the
intensities of their collisionally excited lines, using the abundance and ionic tasks
from the IRAF nebular package (Shaw & Dufour 1995). This task solves for the
populations of the affected levels of these ion and returns an abundance, given the
intensity or intensities of observed lines corresponding to transitions between these
levels, and a temperature and density value. In the case where multiple lines from
the same ion are observed, the task returns an abundance value that is average of

the abundances determined from each transition, weighted by their relative intrinsic

113

strengths. The atomic information used in these tasks is derived from the references
in Table 4.1.

For each ion’s abundance calculation we used the temperature and density deter-
mined from its forbidden line diagnostics (an “ion-specific” temperature and density),
or those from the ion with the closest previous stage ionization potential. This ap-
proach, in the absence of an explicit ionization model, is superior to using a single
temperature and density: the different ionization zones in the gas are expected to
have different temperatures due to differing cooling mechanisms (Garnett 1992) and
characteristics of the local radiation field (Osterbrock 1989). Our observations sug-
gest a real scatter in the nebular diagnostics that goes beyond observational errors,
where the application of a single set of parameters could be un-physical. However, we
also repeated our calculations using a single set of temperature and density values:
9600 K and 10000 cm”3 which represent an average of our diagnostics except those
from the [S II] and [Ar IV] lines. This allows a direct comparison with the results of
Liu et al. (2000) in NGC 6153, who employed a single set of temperature and density
values for most of their own abundance calculations.

Calculations were carried out for individual lines in ionic and for line groups and
ionic averages in abundance. The matrix of results from various combinations of lines
within each ion is listed in Table 4.3. The entry for each ion in this table concludes
with the weighted average of the abundances from multiple collisional lines, calculated
at the ion specific parameters, as determined by abundance.

In general, the abundances of individual lines within an ion show as good or better

internal agreement when calculated at the ion specific parameters, than they do when

114

the average temperature and density are used. This is not surprising since the same
lines were employed to calculate the density and abundance in the first place. However
for three ions, N+, 0+2, and S+2 an additional non-diagnostic collisional line yields
an abundance that closely matches those calculated from the diagnostic lines. The
large scatter in the Co/H+ ratio is the result of the A9824 line being on the extreme
edge of the final order of the red spectrum, where the flux calibration is dubious. The
calculated S+ abundances are probably overestimates, given the artificially low ion
diagnostic temperature employed. The slightly better internal abundance agreement
for this ion using the average as opposed to ion specific parameters, suggests that
the S+ temperature is probably closer to those values determined from the other
diagnostics coming from ions with similar ionization potential.

We note that the auroral line [N 11] A5755, and the trans-auroral lines [0 II]
AA7320,7330 do not exhibit a noticeable departure in abundance from the other lines
from the same ion. It has been conjectured that these lines could have significant
contributions to their strengths from recombination cascade, roughly proportional to
the ionic abundances of their parent ions (Liu et al. 2000). Because these lines give
similar abundances, and because the ionic abundances determined from the recom-
bination lines of their parent ions are at least two orders of magnitude below their
measured intensities, we don’t believe recombination plays a significant role in their
excitation.

We adopted for all ions the abundance determined from the weighted average
of the ion’s diagnostic lines calculated at ion specific diagnostic parameters, except

for C" and 8“, where we used the [C I] A8728 abundance and the weighted value

115

at the average nebular diagnostic parameters, respectively. Temperature uncertainty
dominates collisional abundances determinations, incorporating the uncertainties in
the intensities of the individual diagnostic lines. We determined the uncertainties
in collisional abundances by taking the extreme temperature and densities values,
determining the abundances again, then using the extremes in the abundances as
the uncertainty limits of the abundance. For ions of particular interest (those with
directly comparable recombination lines) the final abundances and their uncertainties

are:

N+/H+ 4.124(+3.204, —0.556) x 10-5,

o+/H+ = 1.663(+19.687, —1-308) >< 104’
0+2/H+ = 1.201(+0.188, —0-142) >< 10”,

Ne+2/H+ = 4.344(+0.761, —0.616) x 10-6.

The larger relative uncertainty in the O+/H+ value is due to the large temperature
errors from the [0 II] temperature diagnostic ratio. These propagate into large errors
in abundance when those errors are calculated using the method described above.
However, given the relative agreement of the [0 II] diagnostic temperature with other
temperature diagnostics of similar ionization potential, and the realistic trend in
temperature with ionization potential among the diagnostics (see Figure 4.1), the
actual uncertainty in the [0 II] temperature is probably smaller than than our best
determination of the formal error from line intensities and the reddening correction.
Thus, while we quote here and will continue to quote the formal error in the O+

abundance as a manner of form, we believe it to be too large.

116

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4.2.2 Ionic Abundances from Recombination Lines

We calculated the ionic abundances from the relative strengths of the numerous re-
combination lines of the following ions: C+, C”, N+, N+2, 0+, 0”, and Ne”. The
abundance of a particular ionic species of ionization state i with respect to ionized
hydrogen (N H / H+), as determined from a specific recombination line of that ion, can

be expressed as:

_A: _ AHB aeff(AiTe)_I;
H+ MA) awe) IHB’

 

(4.3)

where A is the air wavelength of the recombination line, AM is the air wavelength of
the H8 line (4861325150, as” (A, Tc) and dig are the weakly temperature dependent
effective recombination coefficients of the ionic transition corresponding to the line
and H8 respectively, and I ,\ / 1H5 is the de-reddened intensity of the line with respect
to H5.

We used the emissivity interpolation formula of Aller (1984) to calculate 0:35], as
this was the formula employed by the IRAF tasks nebular and ionic which were used
to calculate the ionic abundances from collisionally excited lines.

Table 4.4 lists the references for the atomic data we used in our recombination
line abundance calculations. Most of the references do not list values for effective
recombination coefficients for individual transitions, only for the entire multiplet to
which a transition belongs. The multiplet values must be multiplied by a branching
ratio to get an individual transition’s effective recombination coefficient. This ratio

accounts for the likely population among the multiplet’s fine-structure states and

the relative contribution of each multiplet transition to the multiplet’s total intrinsic

120

intensity.
To obtain unknown branching ratios, we adopted a technique described in the
NIST database 1. The branching ratio, B, for a particular transition is derived from

the ratio of its atomic parameters to those from all transitions in the multiplet:

2(j+1)AA

B = ,
Z: 20:“ + 1)Ai)\i

 

(4.4)

where A is the spontaneous emission coefficient for the transition of interest, 2( j + 1)
is the statistical weight of the level from which the transition originates within the
multiplet, and A is the air wavelength of the transition. The denominator is the same
for all z' permitted transitions of the multiplet.

The above scheme assumes that all levels in the multiplet are populated according
to the their relative statistical weights, a common assumption for all but metastable
levels. Eq. 4.4 assumes that all transitions follow LS coupling selection rules, which
falls short for transitions from levels generated by a valance orbital of angular mo-
mentum quantum number 8 > 2 (i.e. 3d-4f transitions in N+2,O+2, and Ne”).

Calculations were carried out for the following opacity cases for which atomic data

was available. Specifically...
0 Case A: All transitions are optically thin.

0 Case B: All transitions which terminate on the term of the ground electron con-
figuration with the lowest energy are considered Optically thick. As an example,

for 0 II recombination lines, this would mean that all transitions ending on the

 

1 Equation 23, http: / / physics.nist. gov / Pubs / AtSpec / nodel 7.html#nodel75.

121

Table 4.4 References for atomic data for recombination excited lines.

 

Ion Source Transitions / Case“)
Effective recombination coefficients / emmisivities

 

H I Aller (1984)

He I Smits (1996)

C I Victor & Escalante (1990)
Pequignot et al. (1991)

C II Davey et al. (1999)

N I Pequignot et al. (1991)

N II Victor & Escalante (1990)
Kisielius & Storey (2002) (3-3)

0 I Pequignot et al. (1991)

0 II Storey (1994) (3s—3p)

Liu et al. (1995) (3p—3d,3d—4f)
Ne 11 Kisielius et al. (1998) (3-3)

Liu et al. (2000)“) (3d-4f)

Spontaneous emission coefficients

Atomic Line List v2.04

(van Hoof 2001)
(a) No entry indicates same source for all transitions.
(b) From unpublished calculations by Storey.

 

2s22p3 48" term of 0+ would be considered optically thick, and no radiative

decays would be allowed to this term.

0 Case C: (0 II recombination lines only) All transitions which terminate on the
0+ 2822p3 4S" and 2D" (the term with the next highest energy) terms, are

considered optically thick and no radiative decays to these terms are allowed.

For each ionic abundance calculation, the ion specific temperature or that from a
ion with a similar ionization potential, as determined from the diagnostic line ratios,
was utilized. Table 4.5 lists the temperatures used for each ion. The same temper-

122

Table 4.5 Temperatures used for recombination line abundance calculations.

 

Ion Te ( K) / Source
He I 9600

C I 10100([Cl 11])
C II 9500([S III])
N I 9400([N II])
N II 9000([Ar III])
0 I 10000([O II])
0 11 8900([0 111])
Ne 11 8900([0 111])

 

 

atures were used in the emissivity formula for HB. Recombination line abundances
are mostly insensitive to density and all calculations were carried out using the mean
density of 10000 cm“3.

Within each multiplet of an ion, abundances from individual lines, as well as a
complete “summed” multiplet abundance, were calculated. In the summed multiplet
abundance, the numerator of eq. 4.4 is replaced with the sum of the atomic parameters
for all lines observed from the same multiplet, and the intensity used in eq. 4.3 is the
sum of their observed intensities. This approach is superior to averaging individual
line abundances, because large deviations arising from poorly observed individual lines
are smoothed out. In the following abundance tables, summed multiplet abundances
are referred to as “Sum”, while a colon after the intensities of lines indicate that
the line intensity is suspect, due to poor measurement, uncertain identification, or
suspected blending. Multiplets with at least two lines observed and included, will
have a summed abundance, set off by bold typeface.

Finally, for recombination lines the main source of error is the uncertainty in

the intensity measurement. Abundance is linearly proportion to intensity, as seen in

123

eq. 4.3, so the errors in abundance may be determined directly from the intensity
errors for individual lines. Calculating a summed multiplet abundance reduces the

influence of intensity uncertainties.

He+ /H+ and He+2 /H+

We follow Liu et al. (2000) in obtaining the He“L abundance from the arithmetic aver-
age of the He+/H+ values determined from He I A4471, A5876, and A6678, weighting
by their rough intrinsic uncertainty ratio, 1:3:1, respectively. Prior to the abundance
calculations, the line intensities were corrected for electron collisional excitations from
the He" 25 3S metastable level. These excitations alter the populations of the lines’
origin levels, according to the formalism of Kingdon & Ferland (1995b) at the mean
temperature and density (9600K and 10000 cm'3). The emissivities2 and intrinsic
intensity ratios of Smits (1996) tabulated at 10000K and 10000 cm"3, the closest
to our mean diagnostic temperature and density, were used to make the abundance
calculations for the individual lines. Emissivities were only available for hydrogen
case A for the He I triplet lines AA4471,5876, while both case A and B were used for
A6678. The resultant abundances are listed in Table 4.6.

The line abundances show a systematic increase with wavelength which could be
indicative of an error in the reddening correction, or an effect of the flux calibra-
tion disagreement between the blue (A4471) and intermediate spectra (A5876,6678).
Corrections for the collisional excitation from the 28 3S level are sizable: 5% for

AA4471,6678 and 11% for A5876. However, the disagreement only gets worse if these

 

2Ernissivity E hc/A x ae”(/\, Te)

124

Table 4.6 Recombination line He’r/H+ abundances.

 

 

 

Line A A0 S/N FWHM I(A)/I(Hfi) Value (He+/H+) Notes
(A) (A) (km/S) I(Hfl=100)) (X102)
Case A Case B
Singlet
4471.474 4471.499 1935.0 23.7 4.4921 9.027
5875.615 5875.650 5395.0 25.9 13.6746 9.452
Triplet
6678.152 6678.153 2346.0 21.6 3.8721 10.300 10.073
Average 9.537 9.491 (1)
(1) Case B average includes case A AA4471,5876.

corrections are ignored. Examining Smits (1996) Table 4 shows that for two surveyed
PN, the ratio of observed to theoretically calculated flux of A6678 is consistently less
than 1.0, while the same ratio for A4471 was unity. Decreasing the emissivity of A6678
with respect to A4471 would bring the A6678 abundance in closer agreement with the
A4471 value. However, A5876 shows a neutral or opposite trend in those same PNe,
and Liu et al. (2000) found the opposite trend from ours in their A6678 abundance.
Alternatively, since the emissivity ratios of AA5876,6678 to A4471 decrease with
temperature, a lower temperature could also bring their abundances into alignment.
Using Smits (1996) at 5000K and 10000 cm“3 reduces the scatter in the line abun-
dances from 12% to about 3%, and simultaneously removes the wavelength trend. The
line abundances also decline 5, 6, and 13%, for A4471, A5876, and A6678 respectively,
from their higher temperature values. This suggests that the He+ ion is more accu-
rately described by a temperature characterizing a larger portion of the nebula, such

as the Balmer jump temperature, than by temperatures determined from relatively

125

smaller zones.

For the final He+ abundance, we adopted the 9600K case B average, which uses
the case A AA4471,5876 and case B A6678 abundances. We caution, however, that the
actual abundance may likely be somewhat smaller, for the reason described above.
Errors in reddening, the collisional excitation correction, and the flux calibration,
may also play a role.

Our deep spectra exhibit a rich He I recombination spectrum, with some triplet
sequences observable out to principal quantum number n = 27. However, no observ—
able He II lines, even the intrinsically strongest A4686 line, were observed by us or by
Hyung, Aller, & Feibelman (1994) (HAF). Interestingly, three of the remaining un-
identified lines in our IC 418 line list correspond in wavelength to He II recombination
lines identified in N GC 6153 by Liu et al. (2000). However the lack of an observable
A4686 line suggest that these are probably just a coincidence. We conclude that the

value of He+2/H+ is probably negligible.

C+/H+

N o C I recombination lines were observed in IC 418 by HAF. This is probably because
the expected strongest C I multiplets are either located in the near-IR (multiplet 1 at
@10695A) and beyond their wavelength coverage, or correspond to possibly optically
thick resonance lines in the UV (Pequignot et a1. 1991).

We observe only one C I line with a credible ID, A9094.830 (S/ N = 127.4,
FWHM=80.8 km sec"l , flux=0.0103) from multiplet 3. According to eq. 4.4, this

transition has the highest branching ratio among all transitions of the multiplet, so

126

its appearance, coupled with the reasonably large multiplet effective recombination
coefficient, appears genuine. Other transitions of this multiplet have branching ratios
a factor of four lower, so their absence among our detected lines is not necessarily
significant.

Using the effective recombination coefficient for the multiplet from Pequignot et
al. (1991), the ionic abundances are C"/H+ = 2.274 x10"4 and C+/H+ = 0.673X10‘4
for cases A and B respectively. Given that the resonance C I recombination lines3
in the UV were not detected by HAF or Henry, Kwitter, & Bates (2000) (HKB) in
their UV surveys of IC 418, we assume that case B prevails for this ion and adopt
the A9094.830 abundance for this case as the ionic abundance.

Additional C I recombination lines were identified in the vicinity of 6000-6020A.
Examination of the spectrum show that most are probably real lines. Effective re-
combination coefficients for their multiplets are available only for case B in Escalante
& Victor (1990). Abundances calculations from un-blended lines are two orders of
magnitude greater than for the A9094.380 line. The lines seem inordinately strong
if they are true C I recombination lines. The line ID’d as C I A5990.980 3p 3D - 5d
3D° could conceivably be pumped from the ground state by starlight fluorescence or
a unknown Bowen-like mechanism. However, the line ID’d as C I A6019.890 3D - 5d
3F" is unlikely to be pumped, given its large angular momentum difference with the
ground 2522p2 3P. The more likely explanation is that these lines are mis-identified,

and we do not use them to calculate abundances.

 

3Resonance lines are transitions from the ground state directly to an excited level. Most often
the lines leading to levels from which permitted transitions can occur are in the UV.

127

C+2/H+

Many strong C II recombination line multiplets are observed in our spectra. How-
ever, effective recombination coefficients are available only for doublets. Calculated
individual line and summed multiplet abundance values for our observed doublets are
listed in Table 4.7.

Multiplets 3 and 6 are in excellent agreement. The latter includes the A4267
lines often used to determine ionic abundance due to their strength and lack of con-
tributions from continuum fluorescence and dielectronic recombination. Since it is
also case-insensitive, a comparison with the extremely case-sensitive multiplet 3 lines
argues that case B prevails for the ion.

The overabundance in multiplets 2, 4, and 5, with respect to A4267 is probably not
due to incorrect atomic parameters, since the same reference was used by Liu et al.
(2000) and their results show much better agreement than that seen here. Enhanced
dielectronic recombination is also probably not to blame, as effective recombination
coefficients (Davey et a1. 2000) exceed by at least two orders of magnitude coefficients
measuring dielectronic recombination alone (Nussbaumer & Storey 1984) for all the
upper levels of the multiplets considered here.

Grandi (1976) has shown that continuum fluorescence by starlight in the Orion
Nebula is extremely important in feeding the levels from which many of the lines
observed here. Continuum fluorescence from the the 2p 2P0 ground state of C+ by
central star radiation can populate higher 2S and 2P terms directly (e.g. the upper

levels of multiplets 3 and 4), or indirectly following cascades from those levels (mul-

128

tiplets 2 and 5). The sense of the abundance enhancements observed here suggest
a similar mechanism here: lines from levels that could be directly populated by this
mechanism show strongly enhanced intensities, whereas lines from levels one step
down the cascade chain show lesser degrees of enhancement. Angular momentum
states further removed from the ground state (the upper level of multiplet 6) are
affected much less, as enhanced populations are diluted by longer cascade changes
distributing the excess. The close agreement between multiplets 3 and 6 suggest that
the population of the upper level of multiplet 3 is dominated by contributions follow-
ing strong A4267, fluorescence-immune emission, despite the fact that the upper level
of multiplet 3 can also be directly populated by continuum fluorescence.

There are flaws to the above argument. Recombination occurs at the boundary
between the C+ and C+2 zones in the nebula, whereas continuum emission should
take place only where C+ is most abundant. These locations should have different
physical conditions, temperatures and expansion velocities, which should affect the
line profiles and their FWHM. However we note no difference in FWHM between
lines enhanced by or immune to this mechanism. We will examine the actual line
profiles in § 4.3.1. Also, a large population of C+ is not suggested by the strength
or number of observed C I recombination lines, although the strongest C I multiplets
are outside our observing bandwidth. Finally resonance transitions for these levels
are all blueward of the Lyman limit. If fluorescence fuels these lines, significant C+
should exist behind the ionization front, where such lines are not optically thick due
to ionizing hydrogen.

Nevertheless, we follow Liu et al. (2000) in simply using the case B A4267 abun-

129

dance as the final C‘Lz/H+ value. Our deep spectra allow the observation of high
excitation C II recombination lines, whose intensities can be predicted using this
abundance and recombination theory. The resulting calculated intensities (Table 4.8)
show excellent agreement.

A number of quintet multiplets and C+ 232p (3P0) n6 series lines are present in
our spectrum (see § refdielec). The former are most likely created by dielectronic
recombination, since the alternative: recombination directly onto the C+2 232p (3P0)
state, is unlikely given significant populations of this level are not expected at nebular
temperatures (Davey et al. 2000). The quartet lines are generally less intense, by an
order of magnitude or more, than their singly excited doublet counterparts. Since,
they are weak, and because interactions with doublets may only proceed via inter-
combination lines which are not seen in our spectra, we don’t believe they contribute
significantly to level populations in the doublet states. The good agreement between
predicted and observed intensities of several higher excitation lines, suggests that we

are safe using the A4267 abundance as the final value for this ion.

130

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Table 4.8 High excitation C II recombination lines.

 

 

 

Line(s) A A0 S / N FWHM Observed Predicted

(A) (A) (km/S) I(Al/I(Hfi) I(Al/101B)
I(H5)=100 I(HB)=100

4d-6f 6151.270,.540 6151.336 127.3 26.7 0.0306 0.0242
4d-8f 4620.185 4620.348 41.7 18.0 0.0107 0.0103
4d-9f 4329.675 4329.876 20.7 21.4 0.0070 0.0074
4f-6g 6461.950 6461.848 93.5 18.6 0.0584 0.0587
4f-7g 5342.370 5342.392 153.2 18.4 0.0277 0.0303
4f-8g 4802.740 4802.454 72.8 19.5 0.0183 0.0179
4f-10g 4292.250 4292.406 35.2 21.2 0.0089 0.0080

N+/H+

We observed four multiplets for which effective recombination coefficients are available
in Pequignot et al. (1991). The calculated abundances, listed in Table 4.9, scatter
considerably both among the multiplets, and within the individual lines comprising
the multiplets. Multiplet 1 is case-insensitive, but the derived abundances from other
multiplets do not show better agreement under either case.

Grandi (1975a) predicted that the 3d 4P and 45 4P levels are strongly enhanced
by continuum fluorescence from the ground 2p3 48" ground state through particu-
larly strong resonance transitions in the UV near or redward of the Lyman limit.
Subsequent cascades in the IR from these terms can then feed the upper levels of
multiplets 1, 2, and 3, leading to an enhancement of their line strengths. Our ob-
served intensities concur with this scenario. The upper level of multiplet 19, 3d 4D,
is also connected to the ground state, albeit by a multiplet of strictly LS-forbidden
UV transition around A953A, and is also possibly excited by continuum fluorescence

since its energy is close to the 3d 4P term. The lower transition probability (a.k.a.

132

lower stimulated absorption coefficient) in the 3d 4D resonance lines, about a factor
of ten less than the resonance lines feeding the 3d 4P and 48 4P levels, is probably
compensated for in the multiplet 19 line strengths, because those lines arise directly
from the excited level, as opposed to falling through a cascade chain to the origin
levels of multiplets 1, 2, and 3.

It is obvious that the individual lines within the multiplets are not populated
according to _LS coupling, given their large scatter; Esteban et al. (1999) reached a
similar conclusion for the N I lines of the Orion Nebula. The lack of an exact estimate
of the continuum fluorescence contribution to the line strengths (for which an explicit
radiation model of the nebula is necessary), suggests that abundances determined
from this ion are not reliable. We assume that the lowest summed multiplet abun-
dance is most likely the closest to the actual abundance due to recombination alone,
and take it as an “upper” limit for comparison purposes with the collisionally excited
lines. The profiles of these lines should provide an important test of where the lines
arise within the nebula. If continuum fluorescence dominates these lines, they should
have identical profiles and FWHM to collisionally excited [N II] ”6548,6583. We

will examine this in § 4.3.1.

133

Table 4.9: Recombination line N + / H“L abundances.

 

 

Line(s) A A0 S/N FWHM I(A)/I(Hfi) Value (N+/H+) Notes
(A) (A) (km/s) I(HB)=1OO (x104)

Case A Case B
Multiplet 1 (3s 4P - 3p 4D")
8680.282 8680.370 396.1 56.8 0.0385 11.741 11.389
8683.403 8683.525 382.0 57.6 0.0417 24.373 23.644
8686.149 8686.267 - - - 52.3 0.0220 32.358 31.389
8703.247 8703.334 254.2 54.0 0.0268 39.573 38.389
8711.703 8711.778 234.7 52.8 0.0273 31.617 30.671
8718.837 8718.959 143.9 53.4 0.0135 18.566 18.011
Sum: 0.1698 21.395 20.755
Multiplet 2 (33 4P - 3p 4P")
8184.862 8185.270 168.0 20.8 0.0152 29.273 24.898 (1)
8188.012 8188.451 152.9 51.1 0.0381 79.391 67.527 (2)
8200.357 8200.503 138.6 51.5 0.0131 137.038 116.559 - - -
8210.715 8210.965 92.0 45.4 0.0198 130.193 110.737 - - ’
8216.336 8216.298 304.1 62.2 0.0598 50.045 42.566 (3)
8223.128 8223.205 347.8 50.4 0.0623 131.673 111.996 ° - °
8242.389 8242.508 - - - 53.9 0.0551 108.692 92.449
Sum: 0.2634 76.979 65.475
Multiplet 3 (38 4P - 3p 4S")
7423.641 7423.733 119.4 58.3 0.0156 157.648 52.104
7442.298 7442.351 219.9 57.7 0.0363 185.041 61.157
7468.312 7468.457 59.2 0.0583 200.919 66.405
Sum: 0.1102 188.280 62.228
Multiplet 19 (3p 4D° - 3d 4D)
9810.010 9809.767 40.5 57.5 0.0082 247.988
9822.750 9822.279 40.6 0.0076 66.698
9834.610 9834.627 14.7 51.5 0.0082 178.536
Sum: 0.0240 124.461

 

(1)

(2)
(3)

Irregular profile complicated by adjacent absorption fea-

ture.

Blend with 0 II A8188.520?
High FWHM, Blend?

134

N+2/H+

We observed numerous N II recombination lines, including lines from ten triplets, a
singlet line, and numerous 3d-4f transition lines. For the singlet and triplets’ lines, ef-
fective recombination coefficients were available from both Escalante & Victor (1990)
(EV) and more recently from Kisielius & Storey (2002) (KS). However, effective re-
combination coefficients for the 3d-4f transition were not published by KS due to de-
partures from LS coupling. Instead we worked backwards from the results of Liu et al.
(2000) to obtain coefficients for individual lines, for a temperature of 9100 K . Using
these coefficients at our assigned N+2 temperature of 9000 K increases the abundance
artificially by 1-2%. A density of 10000 cm“3 was used with the KS fitting function
for the coefficients. Abundances were calculated under both opacity cases, where the
relevant atomic data was available. The results are listed in Table 4.10.

For nearly all the triplets, the KS values, resulted in lower abundances, than those
calculated using EV values. The general scatter does not favor either opacity case A
or B, though the case B values yield more realistic abundances. Comparing summed
multiplet abundances for triplets, our abundances show a larger scatter (a: 38%)
than the Liu et al. (2000) abundances (022970) for multiplets observed in common
(3, 5, 20, 28), calculated using EV case B coefficients. Our abundances calculated
using KS case B coefficients have less scatter (a=25%). We therefore adopt for all
triplets the KS derived case B abundances, acknowledging that not all multiplets may
adhere to it strictly. For the lone singlet line observed, A4437.030 3p 1P - 3d 1D",

the EV coefficient greatly exceeded the KS value, resulting in a higher abundance.

135

We arbitrarily chose to use the case A EV values, as was done for singlets in Liu
et al. (2000). A second ID’d N II singlet line, A6610.560 (3p 1D - 3d 1F"), yields
an abundance 5 times higher than for A4447.030 under case A EV, and is likely a
mis-identification.

The overabundance exhibited by multiplet 30 could be explained by a highly
efficient Bowen-like fluorescence arising from the near coincidence between the He I ls2
1S - 1s8p1P° A505.68A line and the resonance transition N II 2p 3P - 4s 3P")\508.608A
from the ground state (Grandi 1976). Given the 3A wavelength difference, however, it
seems unlikely that this mechanism will work here, and it is more likely that the level
is pumped via continuum fluorescence. Liu et al. (2002) reached the same conclusion
based on the greater relative strength of the 3s-3p and 3p-3d lines compared to the
3p—4s lines of this multiplet in several of their PNe spectra. However, our observations
show that the lines are of nearly comparable strength. We conclude only that some
sort of ground state fluorescence is exciting this level, whether Bowen, continuum, or
a combination of the two.

Transitions in the cascade path are similarly enhanced (multiplets 3 and 5).
Grandi (1976) also suggests that the intensity of multiplet 20 can be explained by
a combination of continuum fluorescence through the resonance transition to the 3d
3D" level, and standard recombination-cascade from levels above. Since multiplet 28
shares the same upper level, presumably it too can be enhanced. Resonance transi-
tions also connect the ground state with the 3d 3P0 state, which in turn can enhance
the strengths of multiplets 21, 24, and 29. Only multiplet 36 is probably not en-

hanced, since no resonance transition exists to its upper 4p 3D level, and because it

136

is far removed any of the previously described cascade paths. It is not surprising that
this multiplet, apart from the 3d-4f states, yields the smallest abundance.

For the 3d-4f transitions, the abundances were smaller still. This isn’t necessarily
due to measurement error from the weakness of the 3d-4f lines, since the abundance
from the 3d-4f A4447.030 line, which has a strength comparable to some of the 3-3
transition lines, exhibits yields a small abundance. The general decrease in abundance
with increasing level energy or multiplet number might naively suggest the importance
of the continuum fluorescence in the exciting the lower levels of the ion. However,
the true explanation is unclear. The effective recombination coefficients may also be
in error, being inferred from other data rather than drawn from a tabulated source.
For these reasons we did not include these transitions in the final ionic abundance.

We confirm the observations of Esteban et al. (1999) in the Orion Nebula: multi-
plets 3 and 5 abundances agree well, “middle” multiplets 20, 24, and 28 less well, but
multiplets 30 and 36 again agree well. It is unclear why the middle four 3d multiplets,
show such large scatter, and why the agreement gets better again for levels of still
higher energy. The 3d multiplets’ fine—structure states are apparently not p0pulated
according to relative statistical weights. If the problem were due to continuum or
Bowen-like fluorescence, it seems odd that multiplet 30, the upper level of which can
be excited by either process, shows relatively good agreement. LS coupling may fail
for the 3d multiplets, or the scatter among the lines of the 3d multiplets might be
due in part to their lower S / N, while multiplet 30 lines are generally stronger.

In addition to the N 11 singlet and triplet lines, members of at least two quin—

tet multiplets are present in our spectra. These lines appear genuine: most ID’d by

137

EMILI as primary “A” IDs. Some of these lines have been tentatively observed in
the Orion Nebula (Baldwin et al. 2000). They all have an intensity of approximately
0.60 — 5.0 x 10“5 H6, which is an order of magnitude less than the average value from
the standard N 11 recombination lines. These lines must be created by a mechanism
that preserves total angular momentum. While Grandi (1976) suggests that dielec-
tronic recombination is unlikely to populate the levels from which these lines arise,
it remains a possible excitation mechanism for them. As with the 0+ quartet lines,
their strengths, and the lack of distinct inter-combination (spin changing) transitions
observed in our spectrum, suggest that if dielectronic recombination or some other
process is responsible for their existence, they contribute little to the populations of
the levels from which one-body recombination lines arise. We will list all of these
lines in § 4.3.2.

A few other, mostly weak, N II recombination lines were observed in our spectrum,
but generally only single members of a multiplet; some with no effective recombination
coefficients. We chose not to calculate abundances from these lines.

With the great uncertainty in the excitation source for the lower term multiplets,
we will adopt the summed multiplet 36 abundance for N"2 based this multiplet’s
apparent independence from opacity case and and immunity from continuum fluores-
cence. Abundances from the 3d-4f lines, however, suggest that this estimate may still

be a factor of two too high.

138

 

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143

O+/H+

We observed numerous O I recombination lines, including all of the triplet series of
transitions 3p 3P - ns3S° and 3p 3P - nd 3D", up to order n=8 and n=9 respectively,
and nearly all of the quintet series 3p 5P - ns 5D” transitions out to order n=8.

The O I line A8446 line is predominantly excited by continuum fluorescence from
starlight, in which resonance transitions excite upper 3S" and 3D" terms, which are
then followed by cascades to the A8446 origin level(Grandi 1975a). Grandi (1975a)
has shown that continuum fluorescence by starlight is 9 times more effective than
fluorescence via Lfl photons directly through the resonance transition at A1012A for
the 3d 3D° level followed by cascade to the 3p 3P A8446 origin level.

All of the levels of the ns 3S” and nd 3D” sequences have resonance transitions
to the ground state, but only some have coincidences with a specific Lyman series
photon energy. Though the 3p 3P - 7s 38" A5555 transitions lacks this coincidence, its
observed intensity fits well with the rest of the sequence. These sequences were still
readily detectable at the highest excitation upper levels observed in our spectrum,
yet both abruptly terminated when their upper levels exceeded exactly 13.40 eV.
If these lines are continuum fluorescence lines, the source ion, neutral oxygen, would
reside outside the ionization front beyond which the continuum radiation is truncated
blueward of the Lyman limit. The Lyman limits corresponds roughly to that 13.40
eV “cut-ofl"’ energy. Thus, it is likely the same process excites all of the excited levels
which feed the A8446 line.

Recombination is also ruled out in dominating the excitation of the triplet lines

144

we observed based upon the comparative intensities of the A8446 line (multiplet 4)
to its quintet counterpart, 33 58° - 3p 5P, at A7773 (multiplet 1). If recombination
dominated both spin multiplicity groups, then the relative strengths of comparative
lines, such as A8446 and A7773 should be roughly proportional to their statistical
weights. However, A8446 is observed to be stronger than A7773 by roughly 20 times,
exceeding the ratio of statistical weights which is unity. Fluorescence process from
the ground state can’t strengthen quintet lines, but it can strengthen triplet lines.
Our abundances are listed in Table 4.12. The excellent abundances agreement
of the quintet multiplets indicates strict LS coupling with little additional excitation
mechanism contribution beyond recombination. The much larger calculated abun-
dance of A8446 attests to the efficiency of continuum fluorescence in its excitation as
compared to recombination. For the quintets, effective recombination coefficients were
available only for case A. Therefore we adopt the average of the case A abundances

from the quintet multiplets as our final value.

145

 

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146

0+2/H+

Our IC 418 spectra reveals a rich 0 II recombination line spectrum. We followed
Liu et a1. (2000) in using for the 3s-3p transitions the LS-coupling based effective
recombination coefficients from Storey (1994). For 3p-3d and 3d-4f transitions we
used Liu et al. (1995a) who calculated effective recombination coeflicients based on
an intermediate coupling scheme. Abundances calculated from both individual lines,
and from the sum of those lines observed within each multiplet are listed in Table 4.13.
Calculations were carried out under all opacity case for which atomic data existed (no
case C calculations were available for the 3p-3s transitions from Storey (1994)). Blank
entries under each case in the table indicate missing coefficients. Comments regarding
individual lines and multiplets can be found immediately following the table.

The most striking thing is the excellent agreement shown between summed abun-
dances from nearly all multiplets, under the opacity case C. The large population of
the 2p4 2D” that this would entail would require electron densities in the vicinity of
the 0+ to be near that level’s critical density, so that a more Boltzmann-like pop-
ulation distribution is set up between the collisionally-excitable levels. Our electron
density, determined directly from 0+ forbidden lines, is 10000 cm‘3, which exceeds
the critical density of 34000 cm“3 at the assigned ionic temperature of 8900 K. Thus
it is conceivable that a significant pOpulation could be present in the 2p4 2D° state,
to allow transitions terminating at the state to become optically thick, establishing
case C conditions. This argues against the choice of case A for doublets, as was done

by Liu et al. (2000) in their study of NGC 6153. But their density was only 3500

147

cm‘3 so our choice for case C is more valid in IC 418 than it would be in NGC 6153.
The idea that IC 418 might be in case C has been previously proposed by Harrington
et al. (1980). We adopted case C for all doublets, where atomic information for this
case was available.

For the quartets, Liu et al. (2000) chose case B, which gave better agreement
between case-sensitive and case-insensitive multiplet abundances. Our data also sug-
gests that either case B or C prevails for quartets. Abundances for case insensitive
multiplets, such as from multiplets 1 and 2, agree much better with case B and C
abundance from case-sensitive multiplets 19, 20, and 28. Case C does yields more
consistent results between the doublet and quartet multiplets, for those multiplets
with atomic data available to allow a calculation of case C conditions. Though case
C would seem only to affect doublets, non LS-coupling schemes relax selection rules,
allowing interplay between doublet and quartet states that is not allowed in strict-LS
coupling. Because the 3p state was calculated here in LS coupling, adopting case
C will not have a significant effect upon its level populations. So, case C values for
multiplets 1 and 2 should be fairly close to case B values.

The origin of the large abundance for multiplet 11 is not clear. This was not seen
by Liu et al. (2000) for this multiplet. Hyung, Aller, & Feibelman (1994) speculate
that several 0 II recombination lines in IC 418 could be strengthened by continuum
fluorescence by starlight. The upper level of multiplet 11, 3d 4F, is connected to
the ground state by a resonance transition at A430A. However, Grandi (1976) has
calculated that continuum fluorescence can at most make a 20% contribution to the

lines of multiplet 2, and much less to other quartet multiplets, under the physical

148

conditions prevailing in the Orion Nebula, or IC 418. Multiplet 2 does not exhibit a
distinct overabundance in our data. O+ lies near the interface region where hydrogen
is changing from ionized to neutral, so the Optical depth of radiation capable of
exciting its resonance transitions is extremely large. We note that Storey (1984)
predicts zero intensity in this multiplet under case A conditions, and the effective
recombination coefficient for the multiplet for case B is eight times smaller than that
determined by Liu et al. (1995a), so we might conclude that in this particular case
the atomic data might truly be uncertain.

Within the multiplets, individual line abundances seem to show good agreement.
Much of the scatter here can be attributed to individual measurement uncertainties
and blends with other lines. However, in multiplet 12 several additional lines should
have been detected (AA3847.893,3864.667) according to the relative branching ratios
provided by Liu et al. (2000). For multiplet 20, the LS-coupled values for abundances,
using Storey (1994) effective recombination coefficients and branching ratios defined
as in eq. 4.4, seem to show less scatter than the abundances calculated using Liu et
al. values.

The 3d-4f transitions show excellent agreement among themselves, and with abun-
dances determined from other multiplets under case B or C conditions. These transi-
tions are immune to fluorescence excitation and are case insensitive. Although weak,
they seem to serve as excellent abundance indicators. Because of the greater consis-
tency of case C abundances across all types of multiplets, we will use the average of
the summed abundances from each multiplet (except multiplet 11) using the highest

opacity case available (using case C when available, else case B). Included in this

149

average is the sum of the 3d-4f values.

We observed enhanced abundances from multiplets 15, 16, and 36, all of which
are have large low-temperature dielectronic recombination coefficients (Nussbaumer
& Storey 1984). This agrees with the trend seen by Garnett & Dinerstein (2001a)
in other PNe. However the abundances of these lines cannot be reconciled with
other 0 II recombination line abundances, within the temperature range for which
the Nussbaumer & Storey formalism is valid (to 60000K ). This may indicate that
high-temperature, “enhanced” dielectronic recombination is occurring as is argued
by Garnett & Dinerstein (2001a). We also observe several 0 II sextet lines, which
must be formed exclusively by dielectronic recombination. The lines appear to be
genuine detections according to EMILI. Their strengths are generally an order of
magnitude less than recombination lines. As with the N II quintets, dielectronic
effective recombination coefficients are not available. Since sextet line can not directly
interact with levels from which standard recombination lines occur, and because they
are extremely weak, we assume they do not affect the abundances determined from
the conventional recombination lines. All of these multiplets are discussed further in

§ 4.3.2.

150

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157

4.2.3 Ne+2/H+

Only a handful of Ne 11 lines were definitively detected in our spectra. Our calculated
abundances from them are listed in Table 4.15. We again deduced the unpublished in-
termediate coupling-calculated effective recombination coefficients for individual lines
that were used by Liu et a1. (2000) for their 3d-4f transition abundance calculations,
which we determined by working backwards from their tabulated intensities and abun-
dances. We assumed that the calculations were carried out in case A, as was used for
their 3-3 transition quartets, but it is not explicitly stated there. However, it is likely
that they are case insensitive anyway.

Unfortunately, the positions of many of the strongest predicted lines coincide with
a region of the relevant spectrum which is particularly noisy due to nearby saturated
lines and crowding at the Balmer limit confusing the continuum level. The Ne 11
lines aren’t strong enough to be clearly separable from the continuum in the short
duration spectrum either. Many other lines observed by Liu et al. (2000) are outside
our bandpass. The sole detected 35-3p line, Ne II A3777.134, was marginal ID’d,
due to its amorphous line profile and its small theoretical strength with respect to
the other lines of the same multiplet which were not clearly visible. Some of the
strongest 3d-4f transitions observed by Liu et al. (2000), such as Ne 11 3d 4F - 4f 2[5]°
A4409.298 and a complex of lines featuring Ne II A4428.634 3d 2D - 4f 2[3]° are clearly
not present in our spectrum. None of the strongest optical recombination lines of Ne

II were seen by HAF, so it may simply be that IC 418 is neon poor.

158

Table 4.15: Recombination line New/H+ abundances.

 

Line(s) A A0 S/N FWHM I(A)/I(Hfi) Value (Ne+/H+) Notes
(A) (A) (km/s) I(Hfi)=100 (x105)
Case A Case B

 

Multiplet 1 (35 4P - 3p 4P")
3777.134 3777.164 9.4 41.5 0.0050 4.143 4.114

3d - 4f Transitions

 

4219.745 4219.753 8.0 19.9 0.0015 2.796

4391.991 4391.963 7.4 15.8 0.0022 2.276

4457.050 4457.091 59.4 26.0 0.0134 140.834 - - - - - -
Average: - - - 2.536 - - - (1)
( 1) Does not include A4457.050.

The data of Liu et al. (2000) and Luo, Liu, & Barlow (2001) showed that abun-
dances from 3d-4f transitions are consistently a factor of two larger than from 3-3
transitions. Our data actually show the opposite trend. This casts further doubt on
our A3777.134 ID. However, the effective recombination coefficients for the 3d-4f may
themselves be in error by a factor of 2 (Liu et al. 2001). The higher abundance from
Ne II A4457.050 does not arise from this effect, but probably from the existence of
an unknown blend. However an obvious alternate candidate does not exist in our the
EMILI output. The 3d-4f transitions.

Despite the uncertainty of the effective recombination coefficients of the two prob-
able 3d-4f transitions IDs, their IDs were simply deemed more trustworthy than the
A3777.134 line. The final adopted ionic abundance was the average of their abun-

dances.

159

4.2.4 Other Ions

Besides the ions listed here, effective recombination coefficients exist for only a handful
of additional ions.

We observed numerous S 11 lines whose excitation is most likely recombination.
While effective recombination coefficients exist for the upper levels of the transitions
(N ahar 1995), specific branching ratios for multiplets don’t as yet exist. We welcome
future calculations of S II effective recombination coefficients, as their recombination
lines in conjunction with the strong [S III] AA9072,9530 collisionally-excited lines, can
provide another excellent test of relative abundances.

We also observed numerous Si, Fe, and Ni permitted and forbidden lines. As our
analysis concentrates upon the C,N,O,Ne ions which have previously shown a history
of the forbidden line/ recombination line abundances discrepancy problem, we chose
not to calculate abundances from these lines.

Finally, the strongest transitions of C III, N III, and 0 III, as determined from
Williams (1995) are simply not present in our spectra. Many lines of these ions are
excited either by continuum fluorescence, or a resonance fluorescence with a He II line
photon (Grandi 1976). Given the lack of He II photons for excitation to allow weaker
transitions to manifest themselves, and the low level of ionization in IC 418, we chose

not to calculate abundances for these ions from the small number of measured lines.

160

4.2.5 Comparative Ionic Abundances

Listed in Table 4.16 are the final ionic abundances determined in this study, and in
other recent studies of IC 418. Bold items in this table indicate ionic abundances for
the same ion derived from both recombination and collisionally excited lines observed

in the present study.

161

Table 4.16 Comparative ionic abundances for IC 418 from collisional/ recombination
lines, in units such that log (H+)=12.0, for present and other surveys.

 

 

Ion Line Type Present HAF HKB Notes
He+ Recombination 10.973 10.844 10.839 (1 )
C" Collision 5.217
C+ Recombination 7.828 - - - - - -
Collision - . - 8.230 (2)
C+2 Recombination 8.744 - - - . . -
Collision - - ' 7.968 8.446
N0 Collision 5.934 6.484
N+ Recombination (9.317 - - - - - -
Collision 7.615 7.713 7.567
N+2 Recombination 38.030 7.491 (3)
Collision . . . . . . . . .
00 Collision 6.765 6.954 (4)
0+ Recombination 8.543 - . . ~ - '
Collision 8.221 8.246 7.792
O+2 Recombination 8.172 - - ' - - .
Collision 8.080 7.540 7.886
\‘e+2 Recombination 7.404 - - - - - ~
Collision 6.637 6.281 6.623
S+ Collision 6.247 5.903 (5)
8+2 Collision 6.372 6.276
Cl+ Collision 4.128 4.439
Cl+2 Collision 4.742 4.696
Ar+2 Collision 6.005 5.703
Ar+3 Collision 2.955

 

HAF = Hyung, Aller, & Feibelman (1994)

HKB = Henry, Kwitter, & Bates (2000)

 

(1)
(2)

(3)
(4)
(5)

In HAF, average of tabulated He I AA4471,5876 values.
In HAF, tabulated value at Ne=11500 cm’3. Decreases
to 8.133 at N¢=S6OO cm’3.

In HAF, calculated from an unknown recombination line,

using coefficiets of Pequignot et al. (1991)

In HAF, tabulated value at NC=11500 cm‘3. Decreases
to 6.687 at Nc=5600 cm‘3.
In HAF, average of tabulated S 11 ”4068,4076 and

AA6716,6713 values calculated at Ne=5600 cm'3.

162

4.3 Sources of Abundance Discrepancy

4.3.1 Continuum Fluorescence

Continuum fluorescence from the ground state, due to radiation from the central star
exciting levels through resonance transitions, has been suggested to explain the excess
emission from several multiplets belonging to C+, N+, N”, and 0+.

We will seek confirmation of this process, as well as other additional information,
through an examination of the detailed line profiles from this study’s high level of
resolution (10 km sec‘1 ). Line profiles, in velocity space, are the product of the
emissivity of the source ion and the thermal width of the line, as functions of radial
velocity (i.e. position in the nebula), and the radial velocity distribution, convolved
with the instrumental profile. We will make use of a fundamental property of line
profiles: lines belonging to the same parent ion should have nearly identical profiles.
Specifically, we will compare recombination line profiles with collisionally excited lines
from the same source ion, or from an ion in the next lower ionization stage. Profile
agreement with the same source ion favors recombination as the dominant excitation
process, while profile agreement with the differing ions favors continuum fluorescence
as a large contributor to a line’s strength.

As seen in Figure 4.3, lines belonging to ions of increasing ionization potential,
have generally narrower profiles (clockwise around the figure starting with “INS”).
At low ionization, the ion is distributed further away from the central star, where
the expansion velocity is the largest. Our line of sight intercepts both the front and

back edges of expanding, roughly spherical shells. At our instrumental resolution

163

 

  

 

1
l '

[om]

  
 
 

I
15.6 [on] 3726

  

5007

Relative Intensity

 

 

 

 

 

Figure 4.3 Representative line profiles for ions of differing ionization potential with
a comparative sample of the instrumental resolution element. The “INS” profile, of
the night sky emission line [0 I] A5577, demonstrates the limits of our instrumental
resolution. The level of ionization increases clockwise from the instrumental profile.

the individual components of emission from both edges are separated in the profile,
as in [O I] A6300 above in Figure 4.3. At higher ionization potentials, the ions are
concentrated nearer the central star where the expansion velocities are less, and it
become increasingly more difficult to separate “forward” and “rearward” nebular
emission components (see [0 II] A3726, Figure 4.3). Eventually the intrinsic full
width half maximum of the nebular lines due to thermal motions (about 20 km
sec“1 ) prohibits separation at our resolution as the components merge together ([0
III] A5007, Figure 4.3). This clear sequence of profile width with ionization energy
is a consequence of the comparatively simple expansion geometry of IC 418, and is a
primary reason why this PN was chosen for observation.

In the following plots we show, the profiles of representative lines from each multi-

plet from which abundances were determined, choosing the strongest line most likely

164

not to be part of a blend. The abscissa of each plot is line intensity normalized to
the largest intensity within the line, while the ordinate is the wavelength spread of
the profile in velocity space, centered on the line ID’s tabulated wavelength. In each
profile box are listed the ID (upper left hand corner, with wavelength rounded to
nearest A), the FWHM (in km sec’l , upper right corner), and if applicable, the

multiplet to which the line belongs (below the FWHM).

CII

In addition to the strongest lines, the profiles of the high-excitation lines from Ta-
ble 4.8 are also included for comparison purposes. The C II A4267 line includes all
of multiplet 6. This line is a blend, as are the high-excitation lines. Line profiles are
shown in Figure 4.4.

As mentioned earlier, the pattern of abundance enhancement shown by the other
C 11 lines with respect to A4267 is in general agreement with potential continuum
fluorescence excitation of some of the upper levels of the observed multiplets (mul-
tiplets 3 and 4) followed by cascade through additional observed multiplets (2 and
5), as proposed by Grandi (1976). Multiplet 6, A4267, being of higher orbital angu-
lar momentum, is removed from both direct excitation of its upper level, as well as
cascade from higher energy levels which could be so excited.

Unfortunately, no collisionally excited lines of either C+ or C+2 are present in our
observed bandpass, nor is the FWHM listed in HAF or HKB for UV lines of those
ions. However, C II, N II, and 0 II “recombination” lines have similar FWHM (see

Figure 4.5). The C II lines here are narrow, and show negligible evidence of the type

165

 

 

 

 

  
 
  

 

 

 

 
  
 
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Velocity (km/sec) Velocity (km/sec)

Figure 4.4 Line profiles from C II lines.

166

 

Cll

 

1r-

Cll

 

 

 

Relative Intensity

 

Cll

   

Cll

      
 

4267

 

 

 

 

Figure 4.4 Line profiles from C II lines.

-20 O 20 4O
Velocity (km/ sec)

166

Relative Intensity

 

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x (eV)

Figure 4.5 FWHM versus ionization potential x for non-blended lines from various
ions. Small circles are recombination lines; stars are collisionally excited lines for the
same ion. The dashed line is the instrumental resolution limit.

of double lobe profile indicative of lines of lower ionization.

The proposal of continuum fluorescence of multiplets 4 is challenged by the sim-
ilarity of their line profiles with the high—excitation C II lines, which would not be
excited by this mechanism. Nor do multiplets 2 and 5 exhibit larger FWHM than
other multiplets’ lines as would be expected from cascades following fluorescence.
Only the lines of multiplet 3, whose upper level has the possibility of being directly
excited by continuum fluorescence, show a slight increase in FWHM. However the
agreement between A4267 and the summed abundance of multiplet 3, would seem to
confirm that the population of the upper level of multiplet 3 is dominated by strong
recombination and cascade from A4267, rather than continuum fluorescence.

Therefore, we conclude that the line profiles do not support a large contribution

from continuum fluorescence. These lines appear to be most strongly excited by

167

recombination. Since the contribution of continuum fluorescence can not be exactly
quantified without a model of the central star radiation and radiative transfer through
the nebula, it is unknown what ratio of C+ to C+2 would give a small enhancement
to line strengths, but leave the profiles relatively unchanged, from the straight re-
combination case. The effects of continuum fluorescence over recombination are more

clearly demonstrated in the N I profiles.

NI

Recall from Table 4.9 that each observed multiplet returned a vastly different abun-
dance, when calculated on the basis of pure recombination excitation. The over-
abundance was attributed to strong continuum fluorescence and subsequent cascade
through the upper levels of multiplets 1, 2, 3. As can be seen in Figure 4.6, the
profiles of the strongest non-blend member of the each of these multiplets resemble
the [N I] AA5198,5200 lines more than any of the [N II] lines. These lines FWHM
also agree well with those for the [N 1] lines. The A9810.010 line from multiplet 19,
was theorized here to be strengthened directly by continuum fluorescence excitation
of its 3d 4D upper level. Although the profile is less distinct, and perhaps affected
by its location on the extreme edge of the red spectrum, it is again more indicative
of [N I] rather than [N II]. We conclude that all of these lines are powered primarily
by continuum fluorescence, and that the abundances determined from these lines’
strengths under pure recombination are untrustworthy.

Splitting the two lobes of the emission in each profile yields an expansion velocity

of the object. All lines (except A9810.010 of multiplet 19) were split with the “d-

168

 

 

  
    
   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I ' I I I
[NII] 6548 39.8
I
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[Nll] 6583 40.2
3‘ 3‘
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C C
0 0
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j ' I ' I ' I VI
A A 1 1 1 l L 1 L l L I
-40 -20 0 20 40 -4O -20 O 20 4O
Velocity (km/sec) Velocity (km/sec)

Figure 4.6 Line profiles from N I, [N I], and [N II] lines.

(1” function of the IRAF task splat which fits multiple Gaussians. The expansion
velocities of N" and N+, as well for as other ions as determined from their profiles,
is listed in Table 4.17. The [N II] expansion velocity agrees well with the 12.0 km
sec‘1 given in Acker et al. (1992).

We note that each profile exhibits a velocity dependent structure which is not
symmetric about the line center, indicating that forward component emission is not

as strong as the rearward component. This is a common feature of many PNe lines at

169

Table 4.17 Measured IC 418 expansion velocity from line profiles.

 

 

Ion Line Velocity
(A) (km/sec)
N0 [N I] A5198 15.3
[N I] A5200 14.9

N I A8683.525 14.8
N I A8223.128 13.7
N I A7468.312 14.5

N+ [N 11] A6527 11.7
0° [0 I] A5577 14.5
[01] A6300 16.0
[o I] A6363 15.9

 

high resolution (Osterbrock 1989), and indicates a departure from spherical symmetry
for the real object. It may also indicate a slit location off-center from an axis through
the central star. However, a comparison of the [N I] A5198,5200 density diagnostic
line profiles shows that the rearward component of [N I] A5200 exceeds that of [N I]
A5198 even when the relative differences in scaling are taken into account. This would
indicate differing densities in the forward and rear components of the shell occupied
by N".

For the [N 11] lines a similar determination of temperature is complicated by the
“filling in” of the line profile centers by emission from the strong [N II] A5755 and
nearly saturated [N II] AA6548,6583 lines bleeding over to adjacent pixels. The much
weaker [N II] A6527 possesses the two lobe pattern characterizing foreground and
background emission from the same expanding shell, but in a symmetric profile. While
the difference in FWHM between the A6527 and other [N 1] lines can be explained by
broad non-Gaussian wings in their near-saturated profiles, it is not immediately clear

why the intensity ratio between [N II] A6527 and AA6548,6583 appears to be velocity

170

dependent. Since all three lines originate from the same upper level, their intrinsic
intensity ratios should be equal to a ratio of their spontaneous emission coefficients.
However, since the line profiles are drawn from different spectra (AA6548,6583 from
the short duration intermediate spectrum, A6527 from the long duration intermediate
spectrum) we believe it is likely that the extraction windows used for the two spectra

were mis-aligned, giving rise to the different profile for A6527.

NII

In addition to the strongest non-blended lines, we include the strongest of the 3d-4f
transitions we observed, as well as the strongest quintet line (multiplet 66 A5173.385)
in Figure 4.7.

Our earlier conclusion was that there was no consensus on the large scatter in
abundance exhibited from the various multiplets. Grandi (1976) specifically names
multiplet 30 to be excited by pumping via the He I A505.68 photons. However, Liu et
al. (2002) concluded that it is more likely that this multiplet is excited by continuum
fluorescence from the ground state. In either case the possibility exists for enhance-
ment of lines in multiplets down the cascade path. The profile of A3829.795 (multiplet
30) is somewhat broader than A6167.75O (multiplet 36), the latter thought here to
be less likely affected by any fluorescence process. The profile of A5679.558 (multi-
plet 3), on the cascade path, also appears slightly broader than other lines. However,
A4601.478 (multiplet 5), also on the cascade path does not appear noticeably different
or broader than other lines. Grandi (1976) also suggests that lines of multiplet 20

may be excited by a mix of continuum fluorescence and standard recombination. The

171

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idea that other lines may also have a similar mix of contributions from both processes
is reinforced by the similarity of profile and FWHM of A4803.286 (multiplet 20) with
other lines outside of multiplets 20 and 26. The broad profile of A4478.682 (multiplet
21) is more likely due to the irregular profile of a comparatively weaker line with
respect to the other lines, than to broadening due to significant fluorescence contri-
bution. Unfortunately the A5173.385 line is weak, from which no real conclusions can
be drawn. The strongest 3d-4f transition, A4041.310, has a profile that agrees well
with other N 11 lines, despite a slightly higher FWHM.

As with C II, no collisionally excited lines of N‘L2 were observed in our spectra,
nor are statistics for IC 418 available elsewhere for comparison. However, it is clear
from a comparison with the N+ collisionally excited line profiles, that this ion is not
the majority parent ion of these lines. This is evident not only in FWHM, but also
in the lack of a two-lobe structure characterizing lines of lower ionization potential.
The asymmetry in the profiles are also not evident in the N 11 lines.

We conclude therefore that these lines’ strengths are most likely not dominated by
fluorescence. Nevertheless, a small contribution from continuum fluorescence cannot

be ruled out on the basis of the relative line profiles alone.

OI

Confirmation of A8446 (multiplet 4) being strongly fluorescent-enhanced is clear by
comparing its line profile, with that of the 0" collisionally excited lines [0 I] A6300,
A6363, and A5577, in Figure 4.8. The two lobe signature of lower ionization is present

despite the fact the A8446 is a blend of several transitions.

173

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 4.8 Line profiles from [O I], [0 II], and O I lines.

Velocity (km/soc)

The profiles of the line A7771.944 (multiplet 8) and the blend at A9266 (multi-
plet 8), show excellent agreement with one another, and align fairly well with the
profiles of 0+2 collisionally excited lines [0 II] AA3726,3729. However both lines lack
the two lobe signature and / or asymmetric profile indicative of lower ionization that
[0 II] AA3726,3729 posses. The difference in profile may be due to a slight differ-
ence in the position of the slit from the blue (AA3726,3729) to the red spectrum
(AA7771.944,9266). The O I lines might also arise from a slightly different portion
of the nebula than do the [0 II] lines. Recombination lines will tend to form in the
portion of a particular zone occupied by an ion where recombination is most effective

(cooler temperature), while collisional lines favor regions where collisional excitation

174

is the highest (warmer temperatures). This is the notion of temperature fluctuations
within the region in which O+ resides. We will test for this in § 4.3.3.

Given the excellent agreement between abundances determined from the
A7771.944 line and the A9266 blend, based on pure recombination theory alone, re-
inforced by the obvious disagreement between their profiles and those of [O I] colli-
sionally excited lines, we rule out fluorescence processes as major contributors to the

O I line strengths.

011

In addition to the strongest lines from those multiplets which were used for abundance
determination, we plot the strongest 3d-4f transition at A4089.288, and the strongest
lines from multiplet 15, 16, and 36 in Figure 4.9. Lines from the latter multiplets are
thought to be excited primarily through dielectronic recombination and they yield
larger abundances than most of the other 0 II lines (see § 4.3.2).

The line profiles generally confirm what our abundance measurements told us:
all lines strengths appear to be well-described by recombination alone. The profiles
of the representative lines agree extremely well with those of the 0+2 collisionally-
excited lines, and do not conform to the 0+ collisionally-excited lines. There is no
evidence for the double lobe/ asymmetric structure in the 0 II lines that is evidence
in [0 II] AA3726,3729. Specifically, we don’t see any obvious signature of fluores-
cence activity in the profiles of the representatives from the “dielectronic” multiplets
A4590.974 (multiplet 15), A4351.260 (multiplet 16; actually a blend of two transi-

tions), and A4185 (multiplet 36), which could be acting to enhance their respective

175

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176

lines’ strengths. The profile from the representative of the multiplet which yielded
the most discrepant abundance (A3907.455, multiplet 11) is somewhat broader than
the other 0 II lines. However, this is also among the weakest lines in the group, so
its irregularly shaped profile could be a function of marginal detectability. Nor are
there even vague traits that could cause us to think it might be similar to the [0 II]
lines. Finally, the profile of A3883.137 (multiplet 12) is extremely irregular, since it’s
the weakest among non 3d-4f 0 II transitions. It was included here because the other
two observed multiplet members are parts of blends.

We conclude that if any continuum fluorescence is acting to strengthen the lines,
it is at a level that is even less pronounced than in C II or N II, and certainly not at

the level of N I or O 1.

Ne II

We plot in Figure 4.10 the profiles of all the lines we used to determine the Ne+2
abundance.

All the Ne II lines, except Ne II A4457.050, are extremely weak. Unfortunately the
profiles are not distinct enough to draw many conclusions. However it does appear
that A3777.134 (multiplet 1), the only non 3d-4f transition of Ne II we observed,
appears to have a similar profile, in its primary peak, to those exhibited by the Ne+2
collisionally excited lines [Ne III] AA3869,3968. The secondary peak may be indicative
of a second blended line or a noise spike from the continuum; it is difficult to tell.
Even if it was a second line, its inclusion into the summed flux for this line (the

reason for the large FWHM was the inclusion of the secondary smaller peak in the

177

Relative Intensity

 

  

 

 

      

 

 

I ' I I I
[Nelll] 3869 13.6
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Velocity (km/ sec)

Relative Intensity

 

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3d-4f
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Figure 4.10 Lines profiles from [Ne III] and Ne II lines.

FWHM measurement) would be insufficient to explain the factor of six difference in

the abundances derived for recombination versus collisionally excited lines.

For the 3d-4f transitions, A4219.745 is somewhat broader than the [Ne III] lines,

but this could again be contributed to noise. The A4391.991 line, which is somewhat

stronger, shows good agreement with the [Ne III] lines in its profile. For A4457.050,

we note that the profile is distinctly broader than any of the other Ne II or [Ne III]

lines. It is not clear why this 3d-4f transition should be strengthened when others are

not. The 3d-4f transitions should be immune to ground state fluorescence processes.

This leads us to believe that this is a line from a different ion, with Ne II A4457.050

at most part of a blend with that line.

178

Conclusions

0 Where continuum fluorescence is predicted or shown to dominate the contribu-
tion to a line strength, such as for the N I lines of the same multiplicity as the
ground state, or the O I A8446 lines, it is readily apparent from the profiles that
this is the case. Their profiles clearly resemble those of collisionally excited lines
of the same ionization state, as opposed to those of the next higher ionization

state.

0 Where continuum or Bowen-like fluorescences are thought to contribute a signif-
icant amount to a line’s strength, there are hints of larger F WHM and broader
profiles. However these subtle differences may be masked by irregularly shaped
profiles from weaker lines. There is no distinct signature for enhancement on a
lower level than that shown for the O I A8446. The dependence of a profile’s
morphology on the degree of continuum fluorescence enhancement is not clearly

demonstrated in our dataset.

e The profiles of [N I] AA5198,5200 suggest that electron densities may vary be-
tween the forward and rearward portions of the shell, evidence not seen in the

[O I] temperature diagnostic lines’ profiles.

0 O I recombination lines lack the asymmetric profile of the [0 II] collisionally
excited lines. This suggests that these 0 I recombination lines may be formed
interior to [0 11] lines, or that temperature fluctuations may be present in the

region of the nebula occupied by 0+. Alternatively, this may also be due to

179

observational diflerences between the individual spectra.

4.3.2 Enhanced Dielectronic Recombination

Our long duration exposure spectra reveal numerous lines which, according to both LS
selection rules and the effective recombination coefficients of Nussbaumer & Storey
(1984), are either primarily or solely produced by dielectronic recombination. We
list some of the brightest of these lines, and the ones with the most certain IDs,
for C+2 in Table 4.18, N+2 in Table 4.19, and 0+2 in Table 4.20. This includes
numerous doublet C+2 lines, whose presence is not surprising given that dielectronic
recombination is dominant recombination mechanism for (3+3 (Osterbrock 1989, Kwok
2000). However, several quartet (3+2 quartet lines are also observed in our spectra,
as are N +2 quintet and 0+2 sextet lines, more tentatively ID’d. These lines must be
formed by dielectronic recombination, and their presence is a signature of its operation
at the location we observed in IC 418. Unfortunately, recombination coeflicients for
their multiplets are unavailable for direct abundance determination.

It should be noted that the effective recombination coefficients for abundances
calculations from the majority of C”, N”, and 0+2 lines are derived directly from
the photoionization cross-sections of the initial states, with special attention paid to
the resonances within them that give rise to dielectronic recombination. Separate
coefficients gauging the effects of low-temperature dielectronic recombination alone
on one-body recombination lines, from Nussbaumer & Storey (1984), have shown

that, with the exception of a few cases listed below, dielectronic recombination makes

180

Table 4.18 C II dielectronic lines.

 

 

Line(s) A A0 S/N FWHM I(A)/I(Hfl) Notes
(A) (A) (km/ S) I(H5)=100

Multiplet 12 (2324p 3P0 - 2s2pPP°)3p 2P)
5121.828 5121.850 103.7 20.8 0.0268
5125.208 5125.232 29.6 14.9 0.0058
5126.963 5126.960 12.7 16.9 0.0030
Multiplet 14 (2s2p(3P°)38 4P0 - 2s2p(3P°)3p 4D)
6779.940 6779.954 - - - 17.9 0.0109
6780.600 6780.626 - - - 17.7 0.0055
6783.910 6783.937 12.4 19.1 0.0022 - ~ -
6787.210 6787.361 45.5 46.1 0.0073 (1)
6791.470 6791.466 51.5 19.2 0.0066 - - -
6800.680 6800.678 33.1 17.7 0.0050
Multiplet 16 (2s2p(3P°)3s 4P0 - 2s2p(3P°)3p 4P)
5132.947,3.282 5133.114 14.9 39.5 0.0044 - - -
5143.494 5143.424 19.6 51.8 0.0095 (2)
5145.165 5145.165 12.3 14.8 0.0040
5151.085 5151.117 16.4 20.5 0.0046
Multiplet 17 (2p3 2P" - 2s2p(3P°)3p 2D)
5032.128 5031.963 69.0 19.3 0.0434 ~ - 1
5035.943 5035.808 75.7 21.7 0.0558 (3)
Multiplet 20 (2s2p(3P°)3p 4D - 232p(3P°)3d 4F")
7113.040 7112.965 34.6 35.4 0.0052
7115.630 7115.642 30.8 21.1 0.0043
7119..760,.910 7120.052 41.5 42.1 0.0070

Multiplet 30 2s2p(3P°)3d 4F” - 2s2p(3P°)4p 4D)

 

5259.055 5258.999 7.6 24.3 0.0031
5259.664,.758 5259.664 7.2 28.9 0.0032
(1) Large F WHM, could be blend.

(2) In blend with [Fe III] A5143.290?
(3) In blend with [Fe II] A5035.484.

181

Table 4.19 N II dielectronic lines.

 

 

 

Line(s) A A0 S/N FWHM I(A)/I(Hfi) Notes

(A) (A) (km/S) I(Hfi)=100
Multiplet 63 (38 5P - 3p 5D")
5526.234 5526.212 7.1 25.8 0.0015 (1)
5530.242 5530.215 10.8 19.2 0.0021 - - -
5535.347,.384 5535.359 16.9 26.4 0.0050 (2)
5543.471 5543.517 15.3 27.6 0.0045 - - -
5551.922 5551.930 7.5 12.0 0.0006
Multiplet 66 (3p 5D° - 3d 5F)
5172.973 5172.786 - - - 56.4 0.0049 (3)
5173.385 5173.564 - -- 30.7 0.0045 -- -
5175.889 5175.862 8.1 14.0 0.0018
5179.520 5179.521 18.4 18.6 0.0033

(1) Perhaps S II A5526.243?

(2) Probably dominated by C II 4s 2S - 5p 2P0 but could

include these two lines.
(3) Probably dominated by [Fe III] A5172.640, may also in-

clude a contribution from N II A5172.344 line from the
same multiplet, which according to LS coupling, should
be as strong as A5172.973 or stronger.

only a minimal contribution to each line’s total recombination coefficient. Given
the generally weaker strengths of lines which are powered exclusively by dielectronic
recombination (C+2 quartets, N+2 quintets, and 0+2 sextets), as compared to the
other lines assumed well described by one-body recombination alone, we believe it
would take a significant enhancement of dielectronic rates to seriously compromise
calculations made upon that assumption.

Garnett & Dinerstein (2001a) have reported an overabundance of 0+2 calculated
from multiplet 15, with respect to other multiplets, in numerous PNe. This mul-
tiplet’s upper level is primarily populated by dielectronic recombination, and the

overabundance persists even when taking into account the low temperature dielec-

182

Table 4.20 0 II dielectronic lines and abundances.

 

 

Line(s) A A0 S/N F WHM I(A)/I(HB) Value (0+2/H+) Notes

(A) (A) (km/s) I(H6)=100 x104

Multiplet 15 (33’ 2D - 3p’ 2F")

4590.974 4590.959 73.2 16.5 0.0143 7.856

4595.957,6.176 4596.171 37.8 15.5 0.0095 6.906

Multiplet 16 (38’ 2D - 3p’ 2D")

4347.217,.413 4347.990 9.3 26.0 0.0052 4.213 (I)

4351.260,.457 4351.266 16.5 19.2 0.0080 4.331 ~ - -

Multiplet 36 (3p’ 2F“ - 3d’ 2G)

4185.439 4185.433 22.9 16.2 0.0081 3.190

4189.581,.788 4189.783 34.0 21.2 0.0124 3.664

Multiplet 94? (3s"' 68° — 3pm 6P)

4465.408 4465.404 32.4 14.8 0.0059 ~ - ° (2)

4467.924 4467.919 22.6 14.7 0.0041 - - . (3)

4469.378 4469.375 12.1 13.5 0.0022 - - - (4)

Multiplet 106‘? (3p’” 6P” - 3d’” 6D0)

4143522,.733 4143.758 226.1 23.1 0.3140 (5)

41459066076 4146.047 17.3 19.9 0.0059 (6)

 

(1) Large wavelength difference between observed and tabu-
lated values but abundance fits well with other member
of multiplet.

(2) Most likely N II 3p 3D - 3d 3P0 A4465.529.

(3) Alternate ID is Fe II A4467.931.

(4) More likely 0 II 3d 2P - 4f.D 2[1]° A4469.462, but sextet
line is positioned well and is at about the right intensity.

(5) This is He I A4143.759, but the sextet line could be
blended with it.

(6) Alternate ID is Ne II 43 2P - 5p 2S" A4146.064. Given the
apparent lack of lower order Ne II lines, it seems unlikely
that a higher order line is present, so the sextet line could
be a good choice.

183

tronic recombination rates of Nussbaumer & Storey (1984). Dinerstein & Garnett
(2001b) proposed “enhanced” dielectronic recombination, perhaps on the interface of
a significantly hotter central “bubble” of the nebula and the nebular shell itself, to
be potentially responsible. The authors show that a correlation exists between nebu-
lar surface brightness (a proxy for age), and the amount of the discrepancy between
recombination and collisionally excited line O+2 abundances. Smaller, younger, and
higher surface brightness PNe exhibit less of a discrepancy than older, dimmer, and
larger PNe. This represents the bubble, expanding with time, carved out the center
of the PNe by a strong central star wind.

High temperature dielectronic recombination is an attractive alternative excitation
mechanism. At higher temperatures, higher energy autoionizing states are accessible
by recombining electrons. These add more contributions to the total recombination
rate to a particular ion than are included in the low temperature case. Furthermore,
Storey (1981) has shown that these higher energy states are more likely than low
lying autoionization state to decay via stabilizing transitions rather than autoionizing.
Other ions in the vicinity of the interface could also be affected. Ne”, with the
highest ionization potential of any recombination line for which abundances were
measured, would possibly be the most susceptible to this mechanism. The inclusion
of its possible effects would probably reduce its factor of six abundance discrepancy.

IC 418, with an estimated age of perhaps less than a thousand years (Phillips,
Riera, & Mampaso 1990), high surface brightness, (2.3 x 10'12 in units of absolute
H6 flux per square arcsec as determined by Acker et al. 1992), and low abundance

discrepancy in 0”, would seem to fit this paradigm well (i.e. have a smaller bub-

184

ble size). Yet, our calculations of 0+2/H+ from multiplet 15, using the coefficients of
N ussbaumer & Storey (1984) (see Table 4.20), reveals a significant departure from the
abundances determined from other multiplets under opacity case C. Our long duration
observations revealed two additional multiplets (16 and 36) that are also primarily
populated by dielectronic recombination (Nussbaumer & Storey 1984), yielding sim-
ilar but smaller overabundances. This would seem to conflict with the Garnet &
Dinerstein notion of younger PNe not having a significantly large “bubble” for this
enhancement to be seen over a large portion of the nebula, or specifically at the large
distance from the central star we observed at.

Prior to adjustment to case C, the other 0+2 multiplet abundances showed much
greater scatter and were higher overall. We note also that the calculations of N 033—
baumer & Storey (1984) assume Optically thin conditions for all lines. Could a similar
adjustment to case C reconcile the abundances from multiplets 15, 16, and 36? An
examination of the Grotrian diagrams of 0+2 from Bashkin & Stoner (1976) shows
that none of the suspect multiplets originates from a level that has an obvious reso-
nance transition to the doublet sequence’s 2p3 2D” “ground state”, although two of
the multiplets are one step removed down a cascade path from an upper level that
does. However, no members of the multiplet that would connect the 4d 2‘F level with
the upper level of multiplet 15 (3p’ 2F") are visible in our spectra. Unfortunately, for
the other multiplets, similar connecting transitions listed in Bashkin & Stoner (1976)
are not accessible in our bandpass. Given that multiplets 15 and 36 follow the same
cascade path, that the upper level of 36 is inaccessible to the “ground state” either

directly or via a direct cascade from another level, and that these levels are of high

185

orbital angular momentum, it is likely that these multiplets’ strengths are immune
to changes in Opacity case.

For enhanced dielectronic recombination to work, significantly higher tempera-
tures would be needed; on the order of 35,000—65,000K estimated to reconcile the
abundances discrepancy of NGC 6720 (Garnett & Dinerstein 2001b). At such tem-
peratures it might be expected that the thermal widths of lines from these multiplets
would be much broader. No distinct evidence of broadening is seen of this in our line
profiles, but this is not conclusive. The thermal width of an 0 II line is only 5 km
sec‘1 at 10000 K ; a five fold increase in temperature would only increase this width
by a factor of 2.2, just over our instrumental resolution. Furthermore, Dinerstein &
Garnett (2001b) are unable to adjust physical parameters to retain other observed
properties, such as the strengths of [0 III] lines, under these scenarios. Finally, the
strengths of the sextet lines, weaker by an order of magnitude than most other 0 II
recombination lines, suggest that dielectronic recombination is probably not going on
at enhanced rate, perhaps not enough to explain the over-large strengths of multiplets
15, 16, and 36.

We wonder instead if the dielectronic recombination coefficients for these multi-
plets are erroneous. Garnett & Dinerstein (2001a) data shows that multiplet 15 yields
a consistently higher 0 II abundance with respect ot other 0 II lines. Multiplet 36,
in the same cascade path of multiplet 15, also yields a higher abundance. It would
make sense that transitions along this same cascade path could all be miscalculated.

Finally, any enhanced processes should go on in a narrow zone (e.g. the interface

region between the bubble and the shell). Since ions are concentrated at different

186

locations, it seems unlikely that enhanced dielectronic recombination can explain all

their abundance discrepancies, as well as 0”.

4.3.3 Temperature Fluctuations

Temperatures as determined from collisionally excited lines may be overestimates,
because collisional excitation is the strongest at the highest temperature portions the
region occupied by a particular ion. Overestimates in temperature lead to underes-
timates in ionic abundances. Such fluctuations in temperature arise from naturally
occurring density variations within those regions, subtly aflecting temperature diag-
nostic line intensities differently (Kingdon & Ferland 1995b).

To gauge the level of deviation in temperature from the diagnostic line derived
value in the region occupied by a particular ion, Peimbert (1967) defines a temper-
ature fluctuation parameter, t2, the rms scatter about an average or “ion weighted”

temperature, To:

 

 

_ fT.N.N(X)dode
To(X)= fN.N(X)dode ’ (4'5)
and
fix) E f[Te—TO(X)]2N(X)Nede€ (4.6)

T02(X) f NeN(X)de€ ’
where Q is the solid angle observed and the integration is along the line of sight
through the nebula, and N (X) and Ne are the p0pulation of a particular ion “X” in
the source level of a particular emission line and the local electron density respectively.
Each ion observed will have its own t2(X) and TO(X) (Kingdon & Ferland 1995b).

In the low density limit, a collisional line’s emissivity can be expressed as a single

187

collisional term. If the fluctuations are small, the emissivities may be expanded about
the ion-weighed temperature T0(X). Two such expansions may be taken in ratio, to
yield a relation between the temperature Te(X) measured from the diagnostic line

ratios, T0(X), and t2(X) (Peimbert 1967):

Te(X) z T0(X) [1+ (T33) — 3) 3(5)] , (4.7)

 

 

where AB is the sum of energies of the upper levels from which the two lines arise.
This relation may be calculated for any pair of lines of the same ion, provided they
don’t arise from the same level (i.e. from the same fine structure state in a multiplet)
and that satisfy AE << K T... Unfortunately, this rules out an analysis of Ne+2
for which only AA3869,3969 (from the same level) are available. We used [0 II]
AA7319,7330 (AE = 116448 K“) from the 0+ 2p3 2P0 level, to remain as close
as possible to the low density limit, since ample evidence suggests that the critical
density is reached for the lower energy O+ 2p3 2D" level. At the critical density,
the emissivities for the lines (AA3726,3729 for 0+) no longer consist of only a single
collisional term; collisional de-excitation must also be taken into account, and the
emissivity can no longer be simply expanded. The AA7319,7330 lines originate from
levels with higher critical densities. Nevertheless, no correction is made for collisional
excitation from the 2p3 2D” level itself (i.e. the emissivities of the AA7319,7330 lines
may also not consist of a single collisional term), so the results here must be treated
with some caution. A more thorough numerical treatment of this problem (Rubin
et al. 2001), would be more appr0priate for dealing with 0+. For O+2 we used the

[0 III] AA4363,5007 lines (AE = 91303 K“), which are from levels of higher critical

188

density than any density calculated from forbidden line diagnostics in this study.

To observationally determine the parameters TO(X) and t2(X), a second inde-
pendent temperature indicator, expandable in terms of its own To and t2, must be
employed. We used the Balmer jump temperature, Te(H+), with temperature param-

eter inter-dependence (Liu et al. 2000):
Te(H+) = TO(H+)[1 — 1.67t2(H+)]. (4.8)

For IC 418 we assumed that T0(H+)z T0(X) and t2(H+)¢=s t2(X), which holds fairly
well for 0+2, according to the models of Garnett (1992) and Kingdon & Ferland
(1995b), at the IC 418 central star temperature, log Te” z 4.6, and hydrogen column
density, log N (H)z4.5 (HAF). Kingdon & Ferland (1995b) have also shown that the
departures of the observationally determined if2 and the value determined directly
from its definition (eq. 4.6) via direct integration of the radiation field of model
spectra, should be minimal for the physical conditions exhibited by IC 418. The
validity of the above assumptions for the case of 0+ is not discussed in the literature.
However, it seems reasonable since these assumptions are often made for N +, an ion
which should reside in a similar portion of the nebula as O+ does.

The resulting system of equations (eqs. 4.7 and 4.8) can be solved for TO(X) and
t2(X), which are in turn used to recalculate Te(X) and Te(H+) from Taylor expan-
sions around T0 of the individual diagnostic line and H6 line emissivities. Finally,
ionic abundances are recalculated employing the new electron temperatures. The
resultant parameters and abundances are listed in Table 4.21, where we have em-

ployed both the listed Balmer jump temperatures from Table 4.2 and the higher value

189

Table 4.21 Temperature fluctuation t2 and To values and corrected abundances,
N+‘/H+, using different Balmer jump temperatures Te(H+) and Model value of
t2 = 0.005.

 

Ion Lines A Te(H+) To t2 Value (N+‘/H+)
(A) (K) (K) (X104)
(1) (2)

 

0+ [011] AA7319,7330 5300 6106 0.079 8.995
6600 7294 0.057 4.140 3.491
Model 9781 0.005 1.770

0+2 [0 III] AA4363,5007 5300 6299 0.095 3.289
6600 7188 0.049 2.377 1.486
Model 8737 0.005 1.288

(1) Corrected abundance from collisionally excited lines.

(2) Recombination line abundance.

 

using a continuum fit more immediately redward of the discontinuity (5300K and
6600K respectively).

It is immediately apparent that the level of fluctuations are much too strong for
the level of abundance disagreement exhibited by the ions. Observationally deter-
mined values of t2 (from a variety of ions, but usually 0”) range from PNe 0.00
to 0.09 (Esteban et al. 1999), with typical value of t2=0.03—0.04 (Liu & Danziger
1993, Garnett & Dinerstein 2001b). It is difficult to reconcile any of these t2 values
with model predicted t2 values for the IC 418 physical parameters, such as t2=0.006
from Garnett (1992) or t2=0.005 from Kingdon & Ferland (1995b) for 0”. Model
predictions are generally much lower than observed values, due to the real difficulty
in inducing large scale fluctuations within the small region in which a particular ion
is confined, without invoking an external excitation mechanism, other than natural

occurring density variations.

190

Large values of temperature fluctuations might cause the temperature sensitive
auroral line [0 III] (0”) A4363 to yield a very difl'erent abundance from other in-
dividual [0 III] lines. Yet, the other [0 III] lines don’t show extremely different
abundance from [0 III] A4363. did not show an excessive amount of abundance scat-
ter. Marginally tighter abundance agreement is exhibited when t2=0.005 is adopted
for 0”, but the same is not true for 0+. The large 152 for 0+ may be due to ignoring
the collisional contribution from the critically dense 2p3 2DO level.

Since we see better agreement in abundances when using smaller t2 values than
the ones calculated observationally, the uncertainty in our Balmer jump temperature
and diagnostic line temperature determinations are the most likely reason for the
large t2 values. Kingdon & Ferland (1995b) provide an order of magnitude estimate

of the error in the t2 value:

0(t2) 2 102:0) .

 

(4.9)

[\D

In the system of eqs. 4.7 and 4.8, for 0+, the dominant source of error is the 40%
uncertainty in Te(O+) value (see Table 4.2). Using 40% for 0(To) and TO(O+2)=
Te(O+) results in 0(t2)(O+)z 0.20. The tabulated error for Te(O+) is most likely
overestimated, given the agreement with other temperature diagnostics of similar
ionization potential, and external agreement of this temperature with that calculated
from the same ion in other studies of IC 418. However, even a more likely figure of 5-
10% can still significantly affect the value of 0(t2)(O+). Similarly, for 0+2 the largest
uncertainty is in the Balmer jump temperature. The difference between the “high”

and “low” Balmer jump temperatures yields an error of about 25% and 0(t2)(0+2)z

191

0.125. Even the uncertainties in the fits to the continua (about 600 K ), used in Balmer
jump temperature derivations, significantly affect the recalculated temperatures and
abundances. Given the extraordinary accuracy needed to pin down t2, moderate real
temperature fluctuations arising from mundane sources, can easily go undetected.
Diagnostic line temperatures of 8600 K for 0+ and 8430 K for 0+2 are necessary to
bring the collisional abundance into agreement with the recombination values. Using
these values as their respective ion’s To we obtain t2(O+)=0.031 and t2(0+2)=0.014,
which are in line with commonly observed values of t2 (Liu & Danziger 1993, Garnett
& Dinerstein 2001b), and are larger but more comparable to the model values than the
values we determine observationally. Liu & Danziger (1993) suggested that all values
of t2 Z 0.04 require a non-conventional excitation source. One such mechanism is
shocks induced by a radiation driven, “fast” wind from the central star, impinging on
the slower wind generated during the PN pre-cursor’s asymptotic giant branch phase
(Peimbert, Sarmiento, & Fierro 1991). The wind deposits significant kinetic energy
into the gas. IC 418 has been shown to have a strong central star wind; a terminal

1 was determined from P Cygni profiles in central star emission

velocity 940 km sec-
lines (Cerruti-Sola & Perinotto 1989). The calculated amount of power carried by
the wind in IC 418 is low among PNe studied by Capriotti (1998), but the fraction
of momentum absorbed to the momentum carried by the wind is in the middle of
the range. So it is conceivable that shocks could play a role in creating temperature
fluctuations.

Signatures of shocks (Frank 1994) include line broadening, or a sharp temperature

discontinuity at the boundary between the central hot bubble carved out by the fast

192

wind, and the dense shell created during the “slower” wind phase. Such signatures
are not obvious in our line profiles or temperature diagnostics. Since we obtain more
realistic abundances as well as better agreement between collisionally excited line and
recombination line abundances when the model t2 values are adopted, we attribute
our larger calculated t2 values primarily to Balmer jump temperature determination

uncertainties, or uncertainties in our diagnostic line temperatures.

193

Chapter 5

Conclusions

We have presented here emission line spectra of the planetary nebula IC 418. The
spectra are the richest ever acquired for this PN, and among the most detailed of
any PNe spectra. Roughly 600 lines in the spectra with credible identifications are
revealed. Emission lines from a wide variety of ions are observed in these spec-
tra, produced through both recombination-cascade and collisional excitation. We
have compared the ionic abundances calculated from lines of both production mech-
anisms, in an effort to better understand the nature of discrepancies seen in such
comparisons in other PNe spectra (Liu et al. 1995a,2000). Finally, we tested leading
candidate explanations of these discrepancies, taking direct advantage of the assets
of our observations: numerous lines and well-defined line profiles.

The steps used in the reduction and analysis of the spectra have been discussed,
with particular attention paid to automated processes, which reduce the time invest-

ment and provide increased accuracy.

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Abundance Discrepancies

It has been shown repeatedly elsewhere that recombination line derived abundances
always exceed those determined from collisionally excited lines of the same ion. Our
results allows us to make several comments on this issue:

1) Our data shows enhanced recombination line abundances, but at a
different level and nature than is exhibited in other PN e.

For 0+, 0”, Ne+2 we measured collisionally excited and recombination lines.
For these ions the recombination line abundance excess depended upon the ion. The
magnitude of this discrepancy ranges from a factor 1.2 for O”, to 2.1 for 0+, and
5.8 for Ne”. The O+ excess has seldom been measured. The N+ recombination lines
were too seriously contaminated by continuum fluorescence to use.

Our 0+2 and Ne+2 overabundances differ from the trend seen by Liu et al. (1995a)
in NGC 7009 and Liu et al. (2000) in NGC 6153, where the recombination line ionic
abundances showed remarkably similar enhancements over their collisional counter-
parts. The NGC 7009 analysis indicates about a factor of five abundance discrepancy
for C”, N”, and 0+2, while for NGC 6153 including Ne+2 a constant factor of ten
enhancement was found. The C+2 collisional abundance from HAF or HKB in IC
418, derived from C III] AA1907,1909, yielded a recombination line overabundance
ranging from 2-5. The overabundance factors among all these ions has no distinct
trend in ionization potential. This argues for an ion-specific process acting to en-
hance recombination line strengths, rather than a universal process affecting all the

ions similarly argued for Liu et al. (2000). It should be noted that NGC 6153 and

195

N GC 7009 are higher ionization PNe, so the scatter in overabundance factors might
be typical of lower ionization, younger PNe.
2) Abundance discrepancies appear to be real.

For 0+ and O”, the collisional abundances do overlap the recombination abun-

dances, within their mutual uncertainties:

Collisional: o+/H+ = 1.663(+19.687, —1.308) x 1074,
0+2/H+ .—. 1.201(+0.188,-0.142)x10"",

Recombination: O+/H+ = 3.489(i0.103)x10’4,
0+2/H+ .—. 1.487(:l:0.338) x 10-4.

The errors in the recombination line abundances reflect 10 errors about the aver-
age of the summed multiplets used to calculate the final abundances. The errors
in the collisional abundances reflect the line intensity measurement and reddening
uncertainties.

However we believe that the collisional abundance uncertainty for 0+ is greatly
overestimated, despite our best efforts at providing as realistic an uncertainty estimate
as possible (see § 4.2.1). Apart from this we note the collisional abundances from
individual 0+ forbidden lines agree better than the formal uncertainty estimate (see
Table 4.3). The abundances from individual recombination lines within multiplets
also show good agreement.

For 0”, we note the large scatter in the recombination lines is mainly due to
the inclusion of three particular multiplets in the total ionic recombination value.

In seven of the ten multiplets included in the recombination average, the summed

196

abundance exceeds the collisionally excited value. If the contributions to the average
are weighted by the total observed multiplet intensity, the resultant abundance is
OJrz/H‘L=1.574x10‘4 which suggests that much of that lower abundances generally
come from weaker, less accurately measured lines.

In the case of Ne”:

CollisionalzNe+2/H+ .—_ 4.344(+0.761,—0.616)x10‘6,

Recombination: New/HJr = 2.536(i0.367) x 10"5 ,

the collisional and recombination abundances do not overlap, differing by more
than generous uncertainty estimates.

Independent measurements of the collisional line abundances in IC 418
(HAF,HKB) also show smaller ionic abundances for these ions than the recombi-
nation values calculated here. Therefore, while the uncertainty estimates we have
made would allow the abundances for 0+ and 0+2 to overlap, we conclude there is
ample corroborating evidence for the abundance discrepancies in these ions and Ne+2
to be real.

3) The choice of coupling scheme and opacity conditions is shown to be
important for individual emission line abundances, but its importance in
some ions is masked by non-recombination excitation processes.

Abundances from individual 0 II recombination lines showed less scatter than
their counterparts in C II and N II. This suggests the advantages of non-LS coupling,

as we used for 0 II.

197

Our evidence suggests that opacity case C (in which transitions terminating on
the O“L 2p3 2D° level are optically thick) best describes IC 418. This choice has a
physical basis. Densities from multiple diagnostic ratios indicate that IC 418 has an
aggregate density exceeding the critical densities of the O+ 2p3 2D” fine structure
states, leading to significant p0pulations in those states, and consequent strong self-
absorption of photons from transitions ending on those states. This is the definition
of case C. Finally, the idea that 0+ may be in case C in IC 418 has precedent in
Harrington et al. (1980).

The union of intermediate coupling and case C serves to bring O“2 abundances
derived from the doublets and quartets into much closer agreement with one another
than is achieved under either case A (all lines optically thin) or case B (same as case
C except with 0+ 2p3 4S0). This was especially true for certain doublets.

The pattern of recombination line abundance scatter among the multiplets of 0",
N0, C+, and N+ is generally in line with ground state enhancement mechanisms pre-
dicted by Grandi (1975a,1976) for those ions, particularly continuum fluorescence.
These abundances were calculated employing effective recombination coefficients cal-
culated under pure LS coupling. But the potential advantages of using a better
coupling scheme may have been cloaked by the ground state enhancement effects. It

is not clear what the overall agreement would be in their absence.

Sources for Abundance Discrepancies:

Numerous solutions have been pr0posed to solve the abundance discrepancy problem.

We have tested some of the most applicable to our data.

198

1) Continuum fluorescence from the ground state is evidenced in many
ions.

Grandi (1975a,1976) has demonstrated that several ions are susceptible to exci-
tation via continuum fluorescence from the ground state. Our observations confirm
that many of the recombination lines in C II, N I, N II, and O I, predicted to be
enhanced by continuum fluorescence, indeed evidence an enhancement. These lines
are generally super-luminous as compared to other recombination lines considered
“immune” to ground fluorescent contributions, because they arise from multiplets of
higher energy and angular momentum more different from the ground state. The
pattern of their enhancement also fits a picture of the strongest lines emanating from
multiplets fed directly by a resonance transition, with weaker, but still enhanced,
strengths for lines within multiplets further down the cascade chain.

Profiles for lines enhanced by continuum fluorescence generally fall into two cate-
gories. The first category includes lines in which continuum fluorescence is the dom-
inant excitation mechanism, such as O I A8446. This category also includes lines for
which the calculated abundances are extremely unrealistic, ten to a hundred times
greater than the general N‘Fi/H+ z 10‘4 exhibited by collisionally excited lines or
recombination lines from other ions, including many lines of N I. The profiles in this
category clearly resemble the profiles of the collisionally excited lines of the recombined
atom, as opposed to the ion of the next higher stage of ionization.

The second category includes lines which show less enhancement (a factor of 2-
10) above the strength of lines from fluorescent “immune” multiplets. This category

includes numerous C II and N II recombination lines we observed. Yet, their line

199

profiles are indistinguishable from other recombination lines of the same ion, or from
the collisionally excited line of the next higher ionization state, and do not conform
to collisionally excited lines of the recombined ion.

It is not intuitively obvious why lines with lower but still substantially enhanced
strengths do not more closely resemble the profiles of lines from the recombined
atom. This may indicate that for these C II and N II lines, the bulk of the continuum
fluorescence comes from gas closer to the region where the recombination is occurring,
whereas for lines of lower ionization parentage, the regions of recombination and
continuum fluorescence are more separated. There is no obvious progression in profile
size or morphology with enhancement, though subtle details might have been missed
even at our high resolution.

Another probable manifestation of continuum fluorescence is the probable en-
hancement of the [N I] AA5198,5200 density diagnostic lines. As mentioned in § 4.1.1,
the intensity ratio is near the high density limit. Bautista (1999) has shown that
continuum fluorescence is capable of pushing their diagnostic intensity ratio beyond
the high density limit. Because of the strong enhancement exhibited by N I recombi-
nation lines, we believe it likely that the diagnostic ratio is affected. None of the ions
showing discrepancies were calculated with this density, although the C", N", and O"
abundances may have been slightly affected.

2) Dielectronic recombination is occurring in IC 418. But there is no
evidence for “enhanced” dielectronic recombination affecting standard re-
combination line-derived abundances.

Garnett & Dinerstein (2001a) have suggested that smaller, younger PNe should

200

show less of an abundance discrepancy in 0+2 than older, larger PNe. They at-
tributed O+2 abundance discrepancies to an enhancement in dielectronic recombina-
tion brought on by shocks created at the boundary of a hot bubble and the denser
nebular gas shell. For younger PNe, this bubble has not yet had time to propa-
gate very far through the nebula, leading to less enhancement. As evidence of this
mechanism, these authors point to enhanced abundances from multiplet 15, which is
primarily populated by dielectronic recombination (N ussbaumer & Storey 1984).

IC 418 is a fairly young and small PNe, and does exhibit a low abundance dis-
crepancy in 0”. However, abundances determined from multiplets 15, 16, and 36,
all of which are populated primarily by dielectronic recombination, greatly exceed
the average O+2 abundance from the other recombination lines. This is unexpected,
since according to the Garnett & Dinerstein (2001a), younger PNe shouldn’t show
much of an enhancement in dielectronic recombination, because the “bubble” hasn’t
had sufficient time to propogate through the nebula. It seems unlikely that our ob-
servations, at a significant distance away from the central star, would intercept the
region of enhancement.

We lack compelling physical evidence for such a process within our data: there
is no obvious line broadening or temperature discontinuities among our diagnostics.
The observed strengths of lines which must exclusively be created by dielectronic
recombination (C II quartets, N II quintet, 0 II sextets), indicates that dielectronic
recombination is probably not going on at a rate which would substantially aflect
abundances from recombination lines, or explain the over-large strengths of multi-

plets 15, 16, and 36 of 0 II. Finally, enhanced dielectronic recombination should

201

occur in only a small area, so this mechanism cannot be used to explain abundance
discrepancies in other ions. A plausible explanation of the abundance discrepancies
in multiplets 15, 16, and 36 of 0 II, is that the published dielectronic recombination
coefficients are erroneous.

Without enhanced dielectronic recombination, the generally weak dielectronic re-
combination rates with respect to one body recombination rates, suggest that dielec-
tronic process are probably not responsible for the levels of discrepancy that do exist
in our data.

3) Temperature fluctuation determinations are inconclusive.

We calculated the t2 parameter of Peimbert (1967) to gauge the effects of temper-
ature fluctuations within the zones of the nebula occupied by 0+ and 0+2. We obtain
it2 which would yield significant overabundances from collisionally excited lines with
respect to recombination lines when they are used to recalculate abundances. The
i2 value for 0+2 in particular conflicts with the much lower model values of Garnett
(1992) and Kingdon & Ferland (1995b) for the IC 418 physical parameters. This low
model values reflect the real difficulty in establishing large t2 over the limited regions
in which any particular ion resides in the nebula, assuming that the cause of such
fluctuations are restricted to moderate natural variations in density that are present
throughout that region. However, the application of the model determined t2 values
is insufficient to reconcile abundances (see Table 4.21).

The calculated 1t2 value for 0+2 also greatly exceeds the observed average O+2
t2 value of 0.03—0.04 among PNe (Liu & Danziger 1993), and the O+ t2 value is

higher still. To reconcile abundances, values of t2(O+) and t2(0+2) smaller than

202

what we observed, larger than the model values, but closer to the composite PNe
observed “average”, are needed. However, these values necessitate the existence of
external excitation mechanisms (e.g. shocks), not included in models of smooth gas
with only small density variations (Kingdon & Ferland 1995b), and for which there
is no evidence in our data (line broadening, temperature discontinuities).

We note that the t2 values for both ions decline significantly when a higher Balmer
jump temperature is utilized, but insufficiently to remove the overabundances in 0+
and 0+2 (see Table 4.21). We believe that a poorly determined Balmer jump tem-
perature is mostly to blame for the high t2 value for both ions 0+ and 0+2. As seen
in eq. 4.9 a small error in Balmer jump temperature can lead to a large error in t2.
The jump temperature is used by both ions in their t2 calculations. The calculation
in the jump temperature was complicated by many factors (see § 4.1.2) which lead
us to believe it is extremely untrustworthy.

While our observed levels of t2 are not entirely dismissable (values as large have
been observed in other PNe), without a good determination of the jump temperature,
we cannot say whether fluctuations at the level we observe, or at level necessary to
reconcile recombination and collisional abundances, actually exist in IC 418. We can

only say that model t2 values are insuflicient for this purpose.

Automated Processes for Spectral Reduction/ Line Identification

We have demonstrated the utility of various automated software packages, designed
specifically for the reduction and analysis of emission-line region spectra. Among

these, are our new routines for fitting Gaussians to line profiles, and code designed to

203

aid in the identification of emission lines. Some work remains in perfecting the fitting
routine, specifically in the areas of error estimates and multiple Gaussian fitting.
EMILI, the code designed to aid in emission line identifications, was an essential
tool for this analysis. Manual identification of 805 lines would have been tortuous and
error prone. The use of EMILI allowed non-conventional lines, such as the sextets of
0 II, to be considered as possible IDs, on an equal footing with other lines. Numerous
improvements are envisioned for the code in subsequent versions, based partly on the
experience of using it on this data set. However, we believe that even as it stands
now, EMILI is a useful tool, and we have decided to make it available in the public

domain in its present form.

Future Work

Unanswered questions remain. For example, why does IC 418 have a distinct C IV
absorption line (Williams et al. 2003) yet barely detectable C III recombination lines?
And, why does the Ne+2 abundance show the greatest discrepancy among all the ions
selected. As always, follow-up work is essential.

Some of the future work would include additional observations in the UV, IR, and
optical. Many nebular ions have important transitions in the UV such as collisionally
excited lines C III] AA1907,1909 and N III] AA1747,1754. The latter has not yet been
observed in IC 418 and is an important comparison for the N II recombination lines.
In the IR, fine structure lines of [0 III] are temperature insensitive, and serve as a
check of the effects of temperature and density fluctuations. It does not appear that

an IR IC 418 spectrum has been obtained recently. Additional deep observations

204

in the optical, concentrating on an approximate range of z3300—7500A , would add
strong Ne II recombination lines as well as covering the rich C II, N II, O II spectra in
this bandwidth. A large departure in our O+2 abundance from HAF can be directly
attributed to our far stronger [O III] AA4959,5007 lines. We observed I A4959 = 72.7233
and 15007 2 214.9530, where I(H52100)), and they measured I A4959 2 29.52 and
15007 = 85.87. It would be interesting to see if our particular choice of position for this
study “hit the jackpot” with [O III] emission. Abundance gradients in IC 418 would be
sought through multiple spectra at different locations in all bandwidths. Finally, the
construction of a model nebula (determined with the CLOUDY ionization code) could
address questions regarding the extent of continuum fluorescence contributions on
many ions, and refine our list of trustworthy transitions for abundance determination.

In summary, we have created one of the most extensive lists of emission lines in
a PNe ever compiled. Using this information, our observations of IC 418 have shown
that an abundance discrepancy exists in this object, as in other PNe, with some
differences exist in its nature. The most prominent difference is that no common
factor for 0+, 0”, and Ne+2 describes each ion’s recombination line overabundance
with respect to collisionally excited line derived value. Recent surveys of NGC 7009
and NGC 6153 (Liu et al. 1995a,2000), both higher ionization objects, have observed
such a factor among the doubly ionized ions. After the examination of various possible
mechanisms for explaining the discrepancy, we find that no single mechanism appears
satisfactory as a sole explanation, at least within the limits of our data. Finally, we
have determined numerous lines which yield untrustworthy abundances, and which

should perhaps be avoided in abundance determinations of this and other PNe.

205

APPENDICES

206

Appendix A

Mechanics of Data Reduction Steps

The majority of the data reduction steps detailed here utilized various tasks of the

data reduction package IRAF.

A.1 Bias Correction and Image Trimming

The initial step in image processing is the removal of the pedestal voltage or bias that
is applied to the CCD before exposure, to guarantee a correct reading by the chip’s
analog to digital converter. A so-called “overscan” region adjacent to the portion of
the CCD used for imaging records this bias level for individual frames. This bias level
must be removed to insure a linear ratio between the counts in each pixel and the
number of photons recorded in that pixel. The columns in each line of the overscan
region are averaged, then the variation from line to line, if any, is fit with a low order
polynomial, in the case of these observations the with a constant slope. The need

for a non-linear fit would indicate a serious problem with the particular image. This

207

function is then subtracted column by column from the actual imaging portion of the
CCD. The overscan region is then removed or “trimmed” from the image section.

Any residual bias level remaining after subtraction is in turn subtracted out
through the use of a bias frame. This bias frame is constructed by taking several
0 second exposures of the CCD which record only the bias level across the chip. Each
of these frames is inspected for large scale defects, such as a slope across the chip or
a concentration of unusually high pixel values, which greatly exceed the average for
the entire image. The frames are then co—added using the median of each pixel value.
The combined bias frame is corrected for its own bias level in the same manner as
object frames. The overscan region is then trimmed from the image section, and the
remaining image subtracted from the object frames.

In the blue set-up, two amplifiers with different gains were used, in order to speed
up the read out times. Each amplifier had its own overscan regions, and the regions
of the CCD covered by each amplifier were calibrated separately employing tasks

customized for IRAF by CTIO staff in the ared package.

A.2 Flat Fielding

The response of individual pixels in a CCD to illumination is non-uniform. In ad-
dition, the echelle spectrograph has a response functin which varies systematically
over the whole CCD (due to vignetting in the optics) and along each echlle order
(the echelle blaze function). To account for these factors object frames must be “flat

fielded”. Two different methods were used to construct the flat field, depending upon

208

the instrumental set-up.

Within the blue and intermediate instrumental set-ups, a bright quartz lamp
uniformly illuminates the slit, and several brief exposures are taken with the decker
completely open. The images, after the bias removal steps, are inspected for defects
and co-added, with a common region within each image chosen from which to calculate
the relative scaling. We scaled by the mode of the pixel values in the common region
for each image, then coadded all the images using the median at each pixel, across
the entire image. This takes into account the time intensity variation of the quartz
lamp (i.e. the lamp “warms up”). The combined image is then fitted with a high
order polynomial in both directions. To prevent functional “ringing” in these fits as
the result of bad columns on the CCD, these columns are “patched” with a similarly
sized copy of the image from the immediately adjacent region. The order of the
fit was adjusted until functional ringing was minimized. The resulting fitted image
is then Operated on by a wide—windowed boxcar median smoother along each line
of the image to provide a smoothed version of the image which records only the
overall instrumental intensity signature. The smoothed version is then divided into
the fitted version, to create a final flat field, normalized to unity. This flat field records
individual pixel to pixel variation of intensity response that can be divided in turn
into each object frame after bias correction and trimming.

In the red instrumental set-up, the flat field frames were taken in a similar manner,
but with a decker, larger than the that used in obtaining the object spectra, but
not large enough to cause overlapping of the orders in the bluest portion of the

spectra. This resulted in an object-like 2-D spectrum of the bright quartz lamp used

209

to illuminate the slit. The flat field images were then co-added with median filtering,
employing the mode from a section of one of the central orders for scaling. The
portions of the CCD containing the individual orders were isolated from the inter-
order region. The total intensity was summed along the total length of the slit at
each column along the path or “trace” followed by the order across the CCD, to yield
a 1-D spectrum of the flat field. Data within the order at a particular column on the
2-D spectrum were divided by the value of the 1-D spectrum at that same column
in order to normalize them. Then a series of low order polynomial fits was made
to smooth the data in swaths parallel to the center Of the trace across the length
of the slit. Thus both the intensity profile within the slit and the individual pixel
variations can be accounted for, and the smoothed flat field could be divided into all
other spectra.

The departure in the flat field creation method from the method followed for the
blue and intermediate set-ups is required by the presence of fringing. Fringing re-
sults from internal reflections and consequent interference of light bouncing off the
interfaces of the air-substrate and substrate-silicon layer (CCDs are back illuminated
through the substrate). It is further complicated by variations of the thickness of
the substrate layer across the entire breadth of the chip on a size scale similar to
the wavelength of the light. This appears as narrow waving bands of higher or lower
sensitivity in the 2-D flat field spectra, which must be eliminated. The strong wave-
length dependence of the fringing necessitated the use of a finite decker to isolate the
wavelengths involved for the correction method described above. Fringing was not

evident in either the intermediate or blue set-ups.

210

A.3 Scattered Light and Sky Background Correc-

tions

For nebular object spectra, the next reduction step involves the removal of scattered
light. Scattered light manifests itself in a variety of localized phenomena, including
phantom orders between and within spectral orders, and fuzzy ghost images. In
addition, there is a general scattered light profile which contributes to the nebular
continuum where it falls inside orders. Localized scattered light artifacts must be
recognized by eye and excluded on a individually. However, it is possible to globally
fit and remove the overall scattered light profile, since this information is recorded
in the regions in between spectral orders. We began by isolating the regions in
between the orders, then fitting low ordered functions first across the dispersion to
the data within these orders. A second fit was made in the dispersion direction to
the first fit’s values at each point across the dispersion. The resultant scattered light
spectrum was then subtracted from the original 2-D Object spectrum. Care was taken
to exclude from the fits regions of the spectra contaminated by flaring in the vicinity
of strongly saturated lines (spill over of saturate pixels into adjacent columns and
rows). Afterwards, 1~D cuts were taken across the scattered light subtracted 2-D
spectra, to confirm that the inter—order regions were properly normalized to zero by
this process. These operations were carried out in the IRAF echelle package tasks
apall, which allows the isolation of the inter-order regions, followed by apscat, which
performs the fitting and scattered light subtraction.

For the flux standard star spectra and narrow decker quartz spectra used for flux

211

calibration, sky subtraction, as opposed to scattered light subtraction, establishes
the zero point of the flux calibration scale. This process occurs during the extraction
of the 1-D spectrum from the 2-D image, rather than beforehand, for the scattered
light subtraction. It was possible to use this procedure for these spectra because the
standard star and quartz lamp profiles did not fill the entire slit and a region existed
between each end of the slit and where the profile tapers off from its center to a
constant, which is the ambient background or “sky” illumination level. A linearly fit
established in these sky regions interpolates the sky contribution to the standard’s
profile. As each pixel was summed over the portion of the slit designated for the
standard star, the value of the background at that same pixel from the iterpolation
function was subtracted.

The 1-D PNe spectra were extracted from the 2D images using the routine optezt
(Rauch et al. 1990), in the mode where no sky subtraction is done, by summing along
the slit at each position in a particular order, across the CCD. The 1-D standard star
and quartz calibration frames were extracted with the IRAF echelle package task

apall, with sky subtraction carried out as described above.

212

Appendix B

RDGEN

RDGEN is a component of the publically available spectral line detection and mea-
surement software package known as VPFIT, written in FORTRAN by Carswell et al.
(2001). RDGEN is specifically tailored to detect and provide rapid measurements
of emission and absorption lines in extracted, wavelength calibrated Object spectra
with non-negligible continua, such as the planetary nebula spectrum examined in this
project. Only the emission line detection feature in RDGEN was used in the present
study. I was the first MSU user of this program, and this appendix is designed as a
“user’s guide” intended for those (e.g. my thesis advisor) who will want to use this

program in the future. Further information for this program may be found at:

http://www.ast.cam.ac.uk/"rfc/rdgen.html

B. 1 Inputs

RDGEN requires as its inputs an array of flux measurements, wavelength values, the

213

accumulated error in those fluxes, and estimates of the flux in continuum, at all points
in a particular extracted spectra. RDGEN accepts standard IRAF format extracted
long slit and echelle spectra, where the information is encoded at each image pixel
or “channel” along the spectra or spectral order. Other Options allow the use of
ASCII tables of these values. The IRAF format is the most convenient if standard
IRAF tasks were employed to reduce the object’s spectra. If the spectrum has been
wavelength calibrated to a linear scale (relating each channel number to a specific
wavelength as was done here), an estimate Of the instrumental resolution, in terms
of the number of channels spanned, must be provided for each pixel in the spectrum
or across each spectral order. The user must also specify the detection limits down
to which they wish the code to attempt to locate lines, in terms of the accumulated
probability of finding a line at random amid the continuum at the local level of noise.
This parameter is refered to in the code as “-log probability of chance occurence”. The
value of this parameter differs from the S/ N in a particular line, and setting its value

generally will depend upon the characteristics of the spectra and user preference.

B.2 Method

RDGEN considers a line, a local region of the object spectrum, spanning several chan-
nels, in which the flux value in the Object spectrum exceeds the value in the continuum.
Progressing from lower to higher numbered channels, the code begins a prospective
emission line at the first channel in which the flux value exceeds the continuum value,

and ends when the flux falls below the continuum value. If the number of pixels

214

spanned exceeds the instrumental resolution, and exceeds the lower detection limit
in terms of liklihood of non-random occurence, it is considered a ‘” detected emission
line”. The search continues until the end of the spectrum or spectral order, or a
user-defined wavelength limit.

Over each pixel which the line spans, the code keeps track of several parameters:

9 The sums of the signal, 3,- (Object spectrum flux value minus the continuum
value); continuum, 6,; and the ratio of the signal to continuum values, si/ci, i.e.

the equivalent width per unit channel, in each channel i.

e The sum of the product of the equivalent width per unit channel and the wave-

length A,- at that channel, (A,- x (s,/c,)).

o The channel number posessing the highest equivalent width per unit channel
within the line (the channel i where si/c, is the maximum), essentially the

“peak” of the line, and the wavelength value at that channel.

0 The code also keeps a seperate tally over those channels in which the error value
a, is positive. This includes the sum of the variances 0,2, the signal, and the
cumulative “-log probability” Of the line. The latter measures the probability
in each channel of the channel’s signal value appearing completely at random
in that channel, given the channel’s error value and Gaussian statistics. This
quantity is essentially one minus the area under the normalized Gaussian curve

out to the number of o by which the signal exceeds the error estimate. The

215

code defines the log probability as:

19,: — log [é—erfc (jig-ll , (8.1)

where erfc(s,/\/20,) is a modified version of the complimentary error function.

 

After summing all quantities over the line, the code checks that the user’s inclusion
criteria. The number of channels spanned by the line are compared against the
instrumental resolution. The line is checked for “real” detection, by comparing the

line’s overall minus log probability against chance occurence, defined by:

x 2 L8.— (B.2)

pa; = —log[%erfc (5%)], (13.3)

where pa: is the value of minus log probability parameter and all quantities sum over
n channels in the line. The code limits p56 to a maximum value of 40 for the strongest
line in the spectrum.

The code then also computes the flux, central wavelength, S/ N, and equivalent
width, employing the following ratios of tabulated sums acquired while scanning the

line. The flux, F, is calculated by averaging:
F = — 81', (13.4)

wavelength A:

 

A = (B.5)

S/N:

and equivalent width EW:

Ext/=93 51', (B?)
n . c.-

l

where AA is the wavelength difference between the first and final channel over which
the line spans. NO profile fitting is done to make any of the measurements above.

F inallyn the code calculates various other line attributes, such as FWHM and line
skew, linearily interpolating between the channel values for the wavelengths where
necessary.

The code may also be utilized to detect absorption lines, as numerous tools exist
within RDGEN to break up blended line profiles into components and to carry out other
absoprtion line specific tasks, as described in Carswell et al. (2001). RDGEN cannot
be set manually to look only for emission lines, but the absorption line detection
process does not intefere with the emission line detection process, and both go on
simultaneously. However, program output must be manually filtered to screen out
absorption line detections if the code’s primary use is emission line detection.

Output is stored by default in a file called “fort.9” in the working directory. Each
row in the file contains one detected spectral line and its statistics. Absorption lines
may be part of blends or complexes which RDGEN may break up, and thus several
subsequent rows may be related to an initial absorption line. A “em” entry in the
first column indicates the detection of an emission line, whereas “abs” indicates an
absorption line, with subsequent rows, until the next “em” prefaced row, containing
related measures for the absorption line complex. Each emission line will have only

one row.

217

B.3 Operation

Here we demonstrate the use of RDGEN to detect emission lines in the full, long
spectra “blue418x.ec”. The input files used in this example were all in IRAF echelle
format.

For each individual flux calibrated emission spectrum, the extraction process
yielded an error array. These error arrays were co-added together at the time their
companion object spectra from within the same instrumental set-up were co-added,
and the same scaling was applied to both the Object spectra and error arrays, during
the co—addition, to maintain the same S/ N. For the blue, full, long spectra the error
array took the form of a standard IRAF image file of exactly the same dimension as its

respective Object spectrum: “blue418x.sig”. RDGEN automatically accepts an IRAF

I 6

image sharing the same root as the Object spectrum with a ‘.sig” or ‘.err” suffix as
an array of 10 error values, and will assume an array of 10 variance values when the
image has a “.var” suffix. RDGEN will prompt if it finds no error file sharing the same
root name as the object spectrum, or doesn’t find an image file with one of three
suffixes listed.

RDGEN also requires an array of continuum flux values, or an Object spectrum nor-
malized through division by a fit to the continuum. The estimates of the continuum
were made by applying a running boxcar median filter of various window sizes (51, 81,
and 101 pixels) to the object spectra. This lends itself to a quick and fairly accurate

estimate of the continuum level in locations away from strong lines. However, the

presence of strong, wide, and closely spaced lines leads to a corresponding “bump” in

218

the continuum. The extent and magnitude of these bumps increases with decreasing
window size, but the ability to correctly follow small scale variations in the continuum
improves. For each individual order of the object spectra, a median filter spectrum
which best fit the continuum Sharpe across the order with a minimum of “bumpi-
ness”, was chosen to represent the continuum for that order. In some cases bumps
were manually interpolated under, while in other cases, with a foreknowledge of the
program’s mechanism, a bump was retained to force the detection of lines residing
on the wings of stronger lines. RDGEN will first look for an image with the same root
name as the Object spectrum but with a “.cont” suflix. For example, “blue418x.cont”
is the final fit to the continuum for the long, blue, spectrum “blue418x.ec”. If no file
with this suffix is present, RDGEN will ask manually for the name of the continuum fit
file. If none is specified, RDGEN will assume that the spectrum has been pre-divided
by the continuum (i.e. the continuum level will be assumed to be one everywhere in
the spectrum).

The Object, error, and continuum spectra were all wavelength calibrated by the
same dispersion solution, and shared the same linear wavelength relationship between
pixel and wavelength value. The image header for the dispersion solution information
contains the wavelength span per channel ratio for every echelle order. This ratio,
along with the instrumental resolution (in this example 10 km sec‘1 ), allows the
calculation of the instrumental resolution element in pixel space. For all orders, the
instrumental resoultion was a uniform 3 pixels/ channels.

RDGEN is invoked by executing the rdgen command in the directory containing

the VPFIT software package. Executing rdgen yields:

219

*****************************************

* ALL SIGMAS MULTIPLIED BY 1.00000 *

* SEE VP_SETUP.DAT FILE *
4*********444444444444444444*************

0.0500000007< b < 100.

Drop system if b < 0.0500009991 & logN < 14.
or if logN < 8.

or if b > 1001.

Maximum data array length: 125000

Failed to find help file
>>

The RDGEN command prompt is >>. As in IRAF, an external batch file is allowed

to be used. The mechanism is:

>><b1ue418x.scr

where “blue418x.scr” is a batch file made up of many commands to be read in order.

The first command from the batch file is:

>>rd
Filename for data?
>

where rd requests that RDGEN read in the data from an Object spectra or file. In this

example the reply is:

>>rd

Filename for data?

> b1ue418x.ec

> Order number? [ 14], max 27
> 6

220

> IRAF v2.10 wavelength coefficients
>>

RDGEN will recognize an echelle format spectrum with multiple orders from the
construction of the image file, and will prompt for an order number. Only one order
may be operated on at a time. Upon sucessfully reading the data and interpreting
the wavelength linearization information in the object spectra’s header, RDGEN will
confirm its sucess with the “wavelength coefficients line” comment as seen above.
RDGEN will also prompt for continuum and error array spectra information if suffix
formats are missing.

To get RDGEN to begin line detections, the command “ab” must be issued at the

command prompt:

>>ab
Restricted output(r), fluxes (f)? [neither]

Choosing I will print the S/ N statistic in the “flux” column, while choosing f, will
print the flux in the “flux” column. The default (choosing “neither”) is to print the

flux statistic. Selecting “neither” or any other Option returns:

Sig. lims.: line, components, opt peak [5.0,same,as cpts]

This line queries the user to enter what “significance limit” (Sig. lims.) the code
should attempt to detect lines down to. This is the “-log probability against chance
ocurrence” statistic that was mentioned previously. A value must be set that is

221

high enough to screen out completly spurious detections, yet be low enough to allow
extremely weak legitimate lines to be picked up. For emission line detection, only the
“line” parameter is relevant, with the other parameters used only for absorption lines,
and their default values of 5.0 can be retained. A value of 3-5 seems to work best for
“line”, as determined from previous uses of the program with similar spectra. These
values yield line detections of a S/ N at which the detection is considered “legitmate”
from manual inspection of the program’s output.

Next the code inquires about the size of the resolution element in the particular

spectrum or spectral order:

Resolution, min sepn (chan) [3,nres/2+1]

For each echelle order, it was determined that the default value of 3 was correct
for the present spectra. The “min sepn (chan)” statistic is used exclusively for the
absorption line detection portion of the code, and thus the default was selected.

Finally the code inquires about the range of wavelengths to search:

Wavelength range -1ow, high [ 3814.5, 3909.7]:

The prompt displays the wavelength limits, as determined from the image header,
for the particular order or spectrum under examination. The user may accept the
entire order by using a carriage return, or specify the wavelength limits manually.
Only one range in wavelength may be specified. To search over multiple ranges in
one particular order or spectrum, additional calls to ab and rd are needed.

222

After answering the query, RDGEN proceeds to find emission lines within the spec-
ified wavelength range, down to the probability parameter and other limits specified
by the user. The output is echoed to the screen and to the file “fort.9”. The output
consists of a FORTRAN formatted list of lines, each containing information about a
particular emission line, or a component of an absorption line. The user is then re-
turned to the standard RDGEN command prompt: >>, where the entire process may
be repeated. If a batch file has been used, the next instruction in is then immedi-
ately implemented, and sucessive output is concatenated to the “fort.9” file. For the
study here the final output file was interpreted by PERL scripts, to generate input
files suitable to various plotting programs, for use in screening spurious detections
and establishing S / N limits, and for use by the Gaussian fitting program detailed in

Appendix C.

B.4 Code Benefits and Limitations

RDGEN provides a quick, un-biased, approach to emission line detection, calculating
many line attributes that can immediately be used in additional programs. Its in-
formation is drawn directly from standard format IRAF images, necessitating little
prepatory work. The ability to use simple ASCII format input files means that the
program can be easily adapted to handle non-IRAF image formats. In general, the
code automates a manually difficult and demanding chore, the detection of emission
lines in an even handed and quantified manner, and does so with a minimum of

prepatory work to the actual object spectra.

223

TO use the code, however, both an error estimate and continuum fit for the spec-
trum must be present. Standard IRAF extraction techniques do not necessarily gen-
erate either of these companion spectra, although the modified Rauch et al. (1990)
routines do generate an error array. Since the line detection scheme employed by
the code utilizes the difference between a perceived level of the continuum and the
actual signal in the spectrum, in spectra with a noisy continuum where one searches
for extremely weak lines, an extremely accurate value of the continuum must be as-
sured to avoid missing legitimate lines or interpreting spurious noise as a line. An
incorrectly flat continuum also may undercut strong blended lines and cause the code
to interpret close lines (i.e. [O II] AA3727,3729A) as a single line; or undercut scat-
tered light features, and interpret them as lines as well. Where the continuum fit
falls into negative values (on the edges Of some orders in the blue and intermediate
spectra where the scattered light subtraction over compensated for the actual level),
the code will refuse to detect lines. In essence, the line detection is only as good as
the continuum fit. Constructing accurate continuum fits and error arrays can be a
time consuming process, especially when their creation is not an automatic part of
the extraction process, or when it is necessary to tailor them to the various artifacts,

line types, and general continuum shapes found within individual spectral orders.

224

Appendix C

Profile Fitter

C. 1 Introduction

It is desirable to systematically and impartially fit Gaussian profiles to more than
1500 lines originally detected by RDGEN and deemed legitamate after manual inspec-
tion. Measurements and fitting by hand suffers from a line to line bias in both the
extent of the line’s profile above the continuum, and the level of the continuum itself.
Instead we have coded a program in FORTRAN that attempts to fit single Gaussian
profiles at all positions at which legitamate lines were detected in each Spectrum’s full
slit extraction, using the data from their respective central cavity extraction spectra.
Either the long or short duration spectra was used, depending upon whether the line
was saturated according to Table 2.3. Simultatneously, it fits the local continuum
level immediately surrounding the line with a linear function. This removes much of
the observer bias regarding the line extent and continuum level, and puts all measure-

ments on a more equal-footing, measured in precisely the same way. This appendix

225

is intended to both describe the method used and to serve as a user’s manual for this

code.

C.2 Method

A typical line profile is spread over a number of individual pixels in an extracted
spectrum. The input spectrum contains the amount of flux at each pixel or location
(nebular signal plus continuum), and each pixel has a wavelength value assigned to
it. The functional form of a Gaussian line profile superimposed on a linear continuum

may be represented as:

y(a:) = A+B$+Cexp [—(—1-:—2—02i)2[ , (C.1)
where :1: is the wavelength, y(:c) is the flux at wavelength 2:, A is the zero point of
the line describing the local continuum fit, and B the slope of that fitted line, C
the amplitude of the Gaussian function at its peak, D the center of the Gaussian
line profile, and a the width of the distribution. The flux in a particular line is the

integral of the entire profile over the entire breadth of the line minus the contribution

from the continuum:

f=C[:exp [ix—113i] . (C2)

202
where I integrate over a wide pixel window, much larger than the profile, as an
approximation, so as to take advantage of the symmetry in the intergrand. Recasting

a into F, the full width at half maximum (FWHM) with the following form:

F = 20\/21n 2, (0.3)

226

we arrive at an expression for the flux, after integration, equal to

_¢Hc
r_%flfi, an)

and where the original equation eq. G] can now be described as...

27132; mil—28-0) ’
a; 769"" ‘ F ’

where again :1: represents the wavelength value minus some starting point, at each pixel

 

 

 

Mfl=A+Bn+ (on

in which the line profile resides, and y(:r) is the flux value, signal plus continuum) at
that pixel.
The code attempts to fit the best profile by altering the five adjustable parameters:

A, B, D, f, F and solving for the minimum x2 as defined by

2 2
n (y. — A — Bx.- - 7—2V’:2%exp ['72 mph-D] )
2 _ Z

02'2

 

i=1

where a,- is the error, provided by the complimentary error array to the Object spectra,
at each pixel i over which the line spans (i = 1...n)

To perform the X2 minimzation, the CERN code function minimization subrou-
tines MINUIT were employed. The MINUIT subroutines may be called as external
functions to any FORTRAN program, and the function a user wishes to minimize may
be constructed as a seperate FORTRAN function, whose name can be fed to the spe-
cific MINUIT routines of interest. The MINUIT routines used here are migrad which
does the function minimization, and minos which does the error matrix calculation
and provides the final errors on the fitted parameters. As mentioned, the adjustable
parameters are wavelength, line flux, FWHM, and the slope and zero point of the

local continuum.

227

The migrad routine Operates, in the case of this profile fitting code, by calculating
the function: X2 (eq. C6) and perturbing repeatedly the adjustable parameters by
user-supplied characteristic step sizes, following a path towards the minimization of
the function, until such time that the change in the function between the parameters
drops below a user-specified tolerance, or a user-supplied number of parameter ad-
justment iterations has. been exhausted. The minos routine then follows, attempting
to calculate an error matrix at the end of a run, and the specific numeric uncertainties
in the fitted parameters. The errors in each parameter may or may not be symmetric
about the final value.

As input migrad requires an initial estimate of each of the parameters, and an
initial step size by which to perturb those parameters when looking for the path
towards minimization. In addition migrad also requires the name of the external
FORTRAN function which holds the function to be minimized, the number of calls to
the minimization routine, and the aforementioned tolerance value at which further
calls to the minimization routine are curtailed. The user must include a also include
an associated error array, binned to the same wavelength scale as the object spectra
under scrutiny, in the format of a IRAF echelle spectra.

Operation of the profile fitter begins with the submission of a group of line de-
tections, one for each order or spectrum, in this case of the present data from the
RDGEN line detector program, and the associated parameters for those lines, specifi-
cally wavelength and FWHM. Also required is the name of the spectrum in which to
make the measurements, the format of which again must be an extracted wavlength

calibrated echelle spectrum, in standard IRAF echelle format, with the wavelength

228

solution for each pixel previously binned to a linear scale. The user than specifies
two parameters known as the window and halo, in units of km s”, to be used with
every line in the input list of detections. The window indicates the actual perceived
size of the line, i.e.the width that is clearly visible above the continuum. The halo
should cover a wider range, including a region immediately outside of the window,
from which information regarding the local continuum in the vicinity of each line
detection is drawn.

Selecting the first line detection from the input list, the code fits eq. C6 to the
set of pixels centered on the nominal wavelength supplied by RDGEN and extending
over the halo pixels to either side. The wavelength value at the bluemost pixel within
this group is treated as a “reference” wavelength from which all wavelength values
are measured at all other pixels within the line’s pixel group. The MINUIT function
minimization routine absolutely requires that all parameters be nearly the same order
of magnitude to avoid precision problems. Since the flux values at each pixel, which
are typically 10‘14 — 10‘16 erg cm‘2 A“ s"1 and the error array the square of that,
greatly differ from the wavelength and FWHM (the former in A from the “reference”
pixel and the latter converted to A in the code) are typically on the order of unity,
it was necessary to rescale all the flux and error values at each pixel in the line’s
group within the object before submitting the data to the fitting routines. This was
accomplished by taking the logarithm of the flux and its error at each pixel within the
line, summing these logarithms, Obtaining the average, taking the inverse logarithm of
that average, then dividing the flux and errors at each pixels by the resultant values.

If the flux was negative in a pixel or pixels, the logarithm was taken of the negative

229

of the flux in that pixel or pixels.

The code proceeds by calculating the initial values of the slope and zero point
of the local continuum fit. Only the rescaled flux values for those pixels in the
region between the halo and window on either side of the line are included. The
flux values for the pixels in this region are then fitted with a linear least squares
algorithim, weighted by the error amounts at those pixels, to establish a linear fit
approximating the continuum in the immediate vicinity of the line. The zero point
need not necessarily be the flux value at the “reference” wavelength pixel, although
all wavelength values remain measured against it. The step sizes by which to adjust
the slope and zero point are taken as three times the uncertainties in the parameters
as determined from the fit. Next, the code calculates an initial flux value in the line
by employing eq. C4 and the FWHM included with the line’s input information.
The peak flux within the line profile (signal including the continuum contribution) is
sought, and the interpolated continuum level from the fit is subtracted to yield the
parameter C in the equation. The initial wavelength and F WHM values are drawn
directly from the input list. The step sizes are arbitrarily taken to be 10%, 1%, and
10% of their initial values repsectively for the flux, wavelength, and FWHM. These
values seem to work best from repeated use of the code, and have been hard-wired into
it. Finally, upper and lower bounds to the line flux, FWHM, and wavelength are set,
with values equal to those reported in Table C.1. These are used as a sanity check for
the output parameters, and to prevent the migrad from running away from a phyically
sensible set of values. The error calculation routine minos will fail to calculate an

error matrix if any parameter has exceeded this value after the termination of the

230

migrad run. The slope and zero point of the local continuum are unbounded.

The code then commences to send the initial parameters and step sizes, the array
of data points (flux versus wavelength at each pixel within the line), and the tolerance
and number of desired iterations, to the embedded calls in migrad. Repeated use
of the code has demonstrated that a value of 0.001 for the tolerance and 5000 for
the number of iterations applied by MINUIT seem to work well, although the routines
appear to be fairly insensitive to the choice of these parameters. The MINUIT routines
attempts to minimze the function of eq. C.6, until either satisfactory results have been
reached (tolerance has been achieved between sucessive iterations) or the number of
function iterative calls has been exhausted. From this point the associated MINOS
routines attempt to generate an error matrix, from which the uncertainties in the
fitted parameters can be drawn. Upon completion, if the MINUIT has failed to converge
to a good minimization, or if the resultant output parameters violate the upper or
lower bounds set for them, the original estimates are retained.

After completion of minimization, the code returns all parameters to their original
scales. It then writes a new IRAF echelle spectrum in which the fitted profile, using
the returned parameter values, replaces the original data. This output spectrum can
then be plotted on top of the input spectrum as a way of visually assesing the quality
of the fit. The values of the parameters are also written to another output file. In the
event that migrad fails to converge to physically meaningful parameters and minos
fails to arrive at a good error matrix, the original estimates for the parameters are
utilized instead of the originals, and the occurence is noted in the output file. If the

parameters exceed the upper and lower bounds set for them, the occurence is noted

231

in the output file, but the parameters are retained for inspection. The code then

proceeds to the next line detection.

C.3 Operation

The code is invoked by writing on the unix command line gmod. Optionally a single
numeric arguement may follow the command, if the user wishes the code to only make
measurements in one particular echelle order i.e. gmod 6 would request that the code
only make measurements in order 6 of the spectrum to be specified later.

Upon execution the code will request the following information:

> gmod
Enter the root name of the Line List
1zblue418x
Enter the root name of the IRAF echelle image
blue418x.ec
Enter the name of resulting fitted IRAF image
testblue
Enter the distance bounds from line centeroid (km/s)
to sample continuum from (outer then inner):
75 30

The first questions ask for the root name of the input line detection list. The code
requests that each echelle order have a list of lines in the format diagramed in Fig-
ure C.1, with nomenclature: “root.?”, where the “'?” refers to individual apperture
(not absolute order number) in the echelle spectrum. A seperate list of line detections
must be included for every order in the spectrum, unless single order mode has been
invoked on the command line, in which case only the file for the specificed order need
be present. In the above example the root specified is “1zblue418x”. A segment of a

232

8 3756.88 0.008 3756.46 3757.29 0.444 27.13
33 3769.63 0.004 3769.28 3769.88 0.225 38.30
35 3771.49 0.000 3770.94 3772.14 0.393 1284.00
42 3778.01 0.018 3777.67 3778.32 0.166 9.39
45 3780.97 0.017 3780.67 3781.22 0.338 8.60
51 3785.70 0.002 3785.37 3785.97 0.257 71.58

1 3787.39 9.999 3787.16 3787.54 0.228 99990.00
69 3802.28 0.017 3801.93 3802.62 0.410 10.73
71 3803.54 0.016 3803.26 3803.96 0.329 11.87
75 3806.59 0.002 3806.26 3806.91 0.239 99.49
86 3812.69 0.009 3812.49 3812.85 0.144 9.93
91 3814.29 0.016 3814.01 3814.47 0.176 7.58
94 3817.97 0.014 3817.74 3818.16 0.256 7.73
99 3820.49 0.002 3820.00 3821.11 0.295 167.60

102 3822.64 0.009 3822.26 3822.91 0.388 18.33

1 3830.57 9.999 3830.04 3831.06 0.540 99990.00

1 3832.50 9.999 3832.15 3832.92 0.202 99990.00

1 3834.41 9.999 3834.06 3834.76 0.252 99990.00

(1) (2) (3) (4) (5) (6) (7)

Figure C.1 A sample line detection input file “1zblue418x.6”, with columns entries
explained in the text.

sample line detection file, “1zblue418x.6”, is detailed in Figure C.1. These files must
be ASCII files in free FORTRAN format, where each row includes information about
one particular line detection. The use of a “2” as the first character of any row in
such a file causes the code to skip the line in that row. Column (1) is the RDGEN
“ID” number for line detection and column (7) is the RDGEN S/ N for the detection,
which are simply echoed to the output and not used by the code. Columns (3)-(5)
are information from RDGEN no longer required in the code in its current incarnation.
Numeric place-holders may used in each Of these column’s stead, although some value
must be present. Column (2) is the wavelength of the line detection, and column (6)
is the FWHM, both in A, which are directly used by the code. The line detections

within an order must be listed in increasing wavelength order for the code to operate.

233

The second question requests the root name Of the IRAF echelle spectrum from
which you wish to measure the profiles. This name need not share the same nomen-
clature as the line list root, but it must end in a “.ec”, the standard suffix which
indicates an echelle spectrum generated by standard IRAF tasks. The code will also
look for a companion error spectrum with the same prefix (before the “.ec”) but with
a “.sig” suffix. The code will again warn if this file cannot be found. Both the object
and error spectrum must be wavelength calibrated in exactly the same manner.

The third question requests the name for an output spectrum that will be gener-
ated using the fitted values of the parameters. The output will be named precisely
what is stated here, without any extensions such as “.ec”. This output spectrum will
be the input spectrum, but with the fitted profiles written in place of the original
data. Across each order the bluest lines are written in the output spectrum first, so
where there are closely spaced lines, the output profile of one line may be overwritten
by that Of the sucessive line, if the lines halos overlap. The output spectrum can
than be used like any other IRAF format spectrum, and may be operated on by any
standard spectral tools included in the relavent IRAF packages.

The last question requests the range of the halo and window for each line re-

1. In the example above all pixels within 70 km s’1 to

spectively in units of km s—
either side of the Specified wavelength center, are included in the fit are included for
profile fitting purposes, while only those pixels between 35-70 km s‘1 are included
for determining the local continuum values. Only one set Of values may be used per

application of the program. Thus if the user requires multiple window and halo sizes,

the program must be run again. The use of the “2” comment character in the input

234

lists may facilitate repeated application using the same input list.

For this data analyzed here, the window size was adjusted so as to encompass the
entire line profile including the expansive wings of strong lines and to place the con-
tinuum sampling region as far away from the wings as possible. Meanwhile, for weak
lines, the window and halo were shortened so as to not include too much continuum
in the fit, and to minimize overlapping halos from closely spaced weak lines. A series
Of three different halo and window sizes were used (in km 8"): (55,35), (90,65), and
for the broadest lines (300,250).

Upon answering this question the code will echo the choosen parameters to the

screen:

Line List Root:

12b1ue418x

IRAF Image Root:

b1ue418x.ec

IRAF sig file:

b1ue418x.sig

Extent of continuum window from centeroid: 75. 30.
Output name:

testblue

then wait for a carriage return to commence the process.

A string of information from MINUIT will then flow onto the screen. Currently
the code does not echo the information to a seperate file, due the vast quantity Of
information provided, and the fact that where MINUIT fails to converge to a good
minimization, or when the parameters it provides violate the set upper or lower
bounds, this information is echoed into the profile fitter’s own output file. This
output file, named “res” is placed in the working directory, and the output spectrum

235

containing the fitted profiles is also placed in that directory. A seqment from a sample
output file, created by using a segment of the data analyzed here, using the above
response to the queries in this example are shown in Figures C.2-C.3

The output format consists of the following information inscribed in the columns
of Figure C.2. The first three rows name the input line detection list root name, the
spectra in which the fitting and measurments were accomplished, and the window
and halo sizes used for the particular run of the code, respectively. After the “column
descriptor” rows, column (1) is the echelle aperture number from which the line was
drawn, column (2) is the fitted wavelength (in A), and columns (3) and (4) are the
possibly non-symmetric errors (in A) arrising from the fit. Column (5) lists the change
from the RDGEN determined wavelength (in km sec"1 )2 the profile fitted value minus
the RDGEN value. Column (6)—(8) yield the fitted FWHM and its associated, possibly
non-symmetric errors (all measured in km sec‘1 ), and columns (9)—(11) are the same

2 sec‘1 for the flux, and the percentage of

for the line flux (as measured in erg cm"
the final line flux divided by a hundred). Column (12) echoes the S/ N determined by
RDGEN for the line or a numeric place-holder, and columns (13) and (14) state the
“ID” assigned by RDGEN (or again a numeric place-holder) and wavelength value (in
A) for the detection respectively. Finally, entries in the final column, column (15),
as detailed in Table C.1, indicate lines were the various MINUIT routine returned a
value significantly different from the initiailly determined value, failed to converge

to a good fit, or was unable to determine an uncertainty value for a parameter or

parameters.

236

8:

Av:

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Figure C.2 A segment from the output file “res” to the profile fitter. A legend for

IS

in the text. The entry for the line fitted in Figure C.3

1s given

the various columns

listed at the bottom.

237

NOAO/IRAF' V2.11EXPORT shar eeOhoward.pa.msu.edu Hon 21:53:44 02-Dec—20
[testblue[‘,15]]: ic418 4.3“ II 1800. apzl5 beam:50

 

 

 

 

 

6.00E—14 j l I l l I -~
5.00E-14
4.00E-14
3.00E-14
2.00E-14
l I l J l J
4438 4438.25 4438 .5 4438.75 4439 4439.25

I aveleng th (angstroms)

Figure C.3 The fitted profile of a line from the full slit, long exposure, blue spectrum.
The actual data are the dotted line, superimposed upon the solid line which is the
fit.

C.4 Benefits and Limitations of the Code

The benefits to utilizing such a code are three fold. First, for the measurement of line
wavelengths, F WHM, and fluxes, it is important to measure each line consistently,
that is by applying the same methods of determining the continuum level and fitting
the profiles. This is a difficult task to perform repeatedly for a large number of lines.
Secondly, the code operates directly from IRAF input spectra, with a minimum of
preparatory work. Finally, the code automatically calculates the errors in the fitted

parameters.

238

Table C.1 Legend for entries in final column of the profile fitter output.

 

Entry Meaning

3 Final line flux is >3 or < :1;
initial value

4 Final wavelength is outside of
specified window bounds

5 F WHM is < instrumental resolution
(here 9 km s") or exceeds twice
the window size

M migrad failed to converge to a
a set of phyiscially meaningful values
within the number of iterations
or down to the tolerance

E minos failed to calculate an
error matrix

 

 

However, the code currently suffers from a number of limitations in its current
incarnation. First, it is limited to single Gaussian fits. Several of the lines in the
present study are blended Gaussians that had to be manually de-convolved using the
“d-d” Operation in the IRAF task splat. Secondly, the code has no way of knowing a
priori of the location of lines it is currently attempting to fit, as it acts sequentially in
order of wavelength. Thus, line halos may overlap, and the local continuum estimates
may include pixels from the previous or next line to be fitted. This can skew the
fit, despite the use of weighted least squares to de-value those pixels in the fit. This
necessitated a manual inspection of fitted profiles against their Observed counterparts,
and in some case manual fitting with the Gaussian profile fitter “s-s” in splat.

Finally, an area of continuing work is the inability of the code to generate reliable
errors for the fitted parameters in every line detection. This was a main impetus in

using the MINUIT code in place of a simplex method such as “amoeba” which does

239

not have such a mechanism for formal error determination. Currently only about
a quarter of line detections return a set of error estimates. The code may fail to
return error estimates because minos is unable to provide a positive definite error
matrix after parameter fitting by migrad, or because it is prevented from doing so
because during minimzation migrad has perturbed a parameter or parameters beyond
the upper and lower “sanity” bounds. Both the numbers and quality of error values
returned, in the sense that they agree with eyeball estimates of the wavelength and
flux uncertainties from comparing the fitted profiles with the original spectra, have
improved with sucessive incarnations of the program. However, due to the nature of
the function being minimized here, or as yet undetermined error in the correct usage
of the MINUIT routines, it cannot be said with certainty that the error estimates are
completely accurate. Thus, it was decided to not employ the errors determined by
MINUIT for the IC 418 data analysis.

Nevertheless, as evidenced in Figure C.3, the code is highly successful in providing
good fits to almost all of the line profiles with single Gaussian morphologies, in a bare
fraction of the time that would be required to manually make such measurements.
The profiles that we had to measure by hand were either double-peaked, or blended
on wings of other lines. While the code is currently keyed to output from the RDGEN
line detection routine, the input list flexibility in the free FORTRAN format, and
the minimum of information required, makes it highly adaptable to the results of
other procedures that provide wavelengths and FWHM initial estimates for lines to
be fitted. The use of a seperate FORTRAN function for the actual function to be

minimized, means that new functions, such as one allowing the simultaneous fitting

240

of two Gaussian profiles as an example, can be easily swapped in without disturbing
the main body of the code. Because the input spectrum is drawn directly from an
IRAF format spectrum, a minimum of work was necessary to utilize the code, whereas
other automatic fitters might require additional preperatory steps to convert IRAF

echelle spectra to some other format.

C.5 Future Work

It is desired that the code return accurate estimates for all parameters and their errors
as often as possible. Therefore additional work will go into investigating procedures
that will allow minos to calculate accurate error estimates for a majority of line
detections, or determining if the nature of the particular function simply prohibits
this.

A number of values, such as the parameter adjustment step size for the flux,
FW HM, and wavelength, and the number of iterations and fitting tolerance are cur-
rently hard wired into the code. Although these parameters work fairly well in the
function minimization portion of the code, it might be advantageous to allow users
to be able to adjust these on an individual run basis, without recompiling the source
code.

Finally, multiple Gaussian fitting would be of great benefit in resolving line blends,

which are still numerous even at the spectral resolution used here.

241

Appendix D

EMILI User’s Manual

Presented here is the user’s manual for the current public release version of EMILI
(Version 4.0). It is intended as a stand-alone manual giving the EMILI user explicit
insturctions as to the structure of input files, the format of the output files, and how
to use the program. Greater detail relating to the EMILI logic and process can be

found in § 3.

D.1 Introduction and Purpose

The EMILI code is designed to aid in the identification of weak emission lines, partic-
ularly those weak recombination lines seen in high dispersion, signal to noise spectra.
The program utilizes a three facet approach to Obtain this goal. First, we derive
maximum utility from a large atomic transition database: Atomic Line List v2.04
(van Hoof 1999). Even for those transitions which lack values for atomic parameters,

we can make rough estimates of line strengths, so that every transition can be con-

242

sidered as a possible ID for some observed line. Thus, many more transitions can be
utilized here than could be considered manually, or that could be included in emission
spectra models which rely on precise knowledge of such atomic parameters. Secondly,
the code carries out time-consuming checks, which are usually done manually, such as
searches for other multiplet lines, in a rapid and automated fashion free from observer
bias. Finally, the program provides an easily understood ranking criteria to allow the
user to readily chose among potential IDs.

The code is not meant to model the emission spectra of its target Objects, but
rather to aid in the identification of weak lines by providing many alternative IDs
and by informing the user of the results of simple tests that can strengthen or weaken
each IDs’ case. It is an efficient, automated version of the sort of traditional line
identification methods used manually for decades.

The code is written entirely in FORTRAN 77, for ease of interpretation by other
users (maybe I speak too soon before you get a chance to actually LOOK at the
code!). This distribution (number 4) contains all of the subroutines, default data
files, and sample input and output, in a single zipped file. Please see Section D.3 for

the installation and operation of the code.

D.2 User Inputs

EMILI recognizes the following user inputs, some required and some Optional, de-

pending upon which facilities of the program the user wishes to utilize.

243

Required: Input Line List

Optional: Matched Line List,

Abundance Table

In addition a Command/Parameter List is required to set global parameters and

the names of input/ output files.

D.2.1 Input Line List

This is a list of unidentified lines that the user wants to identify. These lines must have
Observed wavelengths between 3000-11000A, the range of a typical optical echelle spec-
trum. The user specifies the Observed wavelength in A, the measurement/systemic
error on either side Of the Observed value, also in A, the flux of the line with respect
to H6, the FWHM in km/s, and the signal-to—noise of the line. Currently the final
two parameters, FWHM and signal to noise, are not employed directly by the EMILI
code, and are simply propagated into the output to give the user full knowledge of
each line the code identifies. Placeholder numeric values can be employed for these
parameters.

Users submit a line list in the form of an ASCII text table, with the information
for each unidentified line comprising one line in the table ended with a carriage
return. Information is read in FORTRAN free format, with blank space separating
each individual element on the line. Each element in the line is a FORTRAN “REAL”

variable. The code currently accepts up to 1500 unidentified lines. No blank lines

244

6363.89 -0.08 0.08 7.58e-03 56.70 485.20
6371.42 -0.08 0.08 4.33e-04 31.00 198.30
6379.65 -0.11 0.11 8.62e-06 25.50 10.70
6382.99 -0.11 0.11 1.95e-05 44.10 16.10
6392.50 -0.11 0.11 9.28e-06 17.60 6.20
6402.27 -0.08 0.08 1.07e-04 21.90 75.50
6454.39 -0.11 0.11 1.01e-05 22.40 5.40
6456.00 -0.11 0.11 1.25e-05 19.30 8.70
6461.85 -0.08 0.08 5.83e-04 18.60 93.50
6527.26 -0.08 0.08 2.84e-04 29.30 70.60
6548.10 -0.08 0.08 5.35e-01 39.80 10430.00
6562.80 -0.08 0.08 3.12e+00 31.30 14100.00
6578.05 -0.08 0.08 5.37e-03 18.30 870.50
6583.47 -0.08 0.08 1.63e+00 40.20 11370.00
6610.65 -0.11 0.11 2.79e-05 25.00 11.70

A BC D E F

Figure D.1 A subset of the Input Line List from ic418.in. Listed in columns from
left to right are: A. Observed wavelength (A) B.,C. errors in measurement (A), D.
flux with respect to H6 E. F WHM (km/sec) F. signal to noise.

should be left at the end of the table, and no special indicators are needed to signify
the end Of the file. The Input Line List is read in by a statement in the main routine:
em4.f. An example of a segment of an Input Line List is given in Figure D.1 (from

the file ic418.in included with the distribution).

D.2.2 Matched Line List

This list includes manual identifications made for some of the unidentified lines in the
Input Line List, usually for strong lines where the identifications are unambiguous.

The user specifies the observed wavelength (in A), the laboratory wavelength of the

245

Table D.1 The ionization energy bins used to determine ICF values and velocity
corrections to the observed line as a function of putative ID ion’s ionization energy.

Bin Ionization Energy (ev)

 

 

 

 

 

1 0-13.6
2 13.6-24.7
3 24.7-54.5
4 545-1000
5 > 100

 

 

 

 

Table D2 The lines specifically used to calculate the ICF values, and their defaults
in each bin.

 

Bin Energy Range (ev) Default Value Signature Lines

1 0-13.6 0.01 Mg 1] A4571, Na I AA5890, 5896,
[S I] A7775, [C I] A8727,
Ca II (H&K) AA3934, 3968

 

 

 

 

 

2 13.6-24.7 0.3 up

3 24.7545 0.3 He I A5876, 4471

4 54.5-1000 0.2 He 11 A4686

5 > 100 0.1 [Fe X] A6375, [Ne V] A3426,

 

 

 

 

 

[Fe v11] A6087, [Ar X] A5533

 

transition he or she believes is responsible for the line (also in A), the ion responsible
for the transition in spectroscopic notation, and the observed flux in the line with

respect to H5. EMILI can use this information in two ways:

1. Velocity Structure Correction: All the ions from elements Z S 30, are grouped
together into five “bins” determined by ionization energy. The energy bounds
of these bins are described in Table D.1. For each manual identification in the
Matched Line List the velocity difference between the observed and laboratory
transition is credited to the bin in which the source ion belongs. Recombination

lines here are assumed to originate from the ion of the next higher ionization

246

state than that given in the spectroscopic notation, while collisionally excited
and a few intercombination lines (those going to near-ground energy levels) are
assumed to originate from the ionization state indicated by the notation. The
average is then taken for each bin to establish a correction to be applied to the
wavelength of each observed line, appropriate for the ion responsible for a tran-
sition being tested as a possible match to that line. Thus, the systemic velocity
and any ionization energy dependence of the expansion velocity of the object
can be accounted for, if not already done beforehand in the data. Alternatively,
this feature may be turned off, or manual values for the correction in each bin
can be specified in the Command/Parameter List. The calculated or submitted

values will be listed in the Full Output List (see Sect. D.5.1).

. Ionic Abundances: To establish ionic abundances for all ions Z S 30 the pres-
ence of certain “signature” lines (see Table D2) is sought in the Matched Line
List. The relative strengths of these lines with respect to H6, if present in
the spectra and recorded in this list, are used to establish ionization correction
factor (ICF) values for each energy bin. These are roughly percentages that
particular ions of that element take up of the entire abundance for that ele-
ment. Ionic abundances are calculated from the bin for the ion, and the bin for
its next lower stage of ionization. If the ion and the next lower stage ion have
ionization potentials which reside in the same bin, the ICF value for that bin
is multiplied by the abundance for the overall element listed in the Abundance

Table. If they reside in different bins, then the average of the ICF values is

247

utilized to Obtain an ionic abundance through multiplication with the overall
elemental abundance. Exceptions to these rules include the ionic abundance
for ionized hydrogen, which is defined as the second bin ICF value times the
hydrogen abundance, and the ionic abundances for first and completely ionized
helium, which are defined as the are the overall helium abundance multiplied
by the third and fourth ICF bin values respectively. If some of the signature
lines are not present in the spectra or not recorded in the Matched Line List
because their manual identification is ambiguous, the code will attempt to make
reasonable guesses as to the ICF values from those lines that are present. Al-
ternatively, the program can use a default set of reasonable ICF values, or a
manually chosen set, as specified in the Command/Parameter List. The calcu-

lated or default values will be recorded in the Full Output List.

While the Matched Line List is optional, it must be present to utilize the ICF value
and velocity correction calculation routines present in EMILI. If a Matched Line List
is not used, one must specify the ICF and velocity correction values for each energy bin
manually in the Command/Parameter List, or indicate in the Command/Parameter
List the desire to use the default values.

If included, the Matched Line List must take the form of an ASCII table, with
the information about each specified line comprising one line of the table, and ended

by a carriage return. These values must appear in the following order:

0 observed wavelength: A FORTRAN “REAL” variable, read in free format.

0 laboratory wavelength: Also a FORTRAN “REAL” variable, read in free format.

248

e the element notation: This is a three place character variable: FORTRAN
“CHARACTER*3”. If the line is a forbidden line, the first character L11_11S_i1_ in-
clude the “ [“ symbol. Non-forbidden lines or intercombination lines must start
with the elemental notation. If the notation doesn’t reach three characters the

remaining space should be filled with blank spaces.

0 a single blank space between arguments.

e the ion notation: This is a six character variable: FORTRAN “CHARACTER*6”.
The particular ion must be specified in Roman numeral format, with the stan-
dard astronomical convention (i.e. Na I is neutral sodium, Na II is first ionized
sodium etc...). If the line is an intercombination or forbidden line, the next char-
acter immediately after the end of the Roman numeral specification must be
the “J” character. If the entire information comprises less than six characters,

blank spaces should be used to fill out the remaining places.

9 the flux with respect to H6: A FORTRAN “REAL” variable, read in free format.

Users are limited to 50 matched lines in total. A line with a “Z” in its first
character will be ignored by the code and does not count in the total number of
matched lines that can be specified. No blank lines should exist in the file, and no
special end of file indicators are necessary. The Matched Line List is read by the
subroutine: matchlist4.f. An example Of a Matched Line List is given in Figure D.2

(from the file ic418.match included with the distribution).

249

5006.
.467
.035
.915
.088

6583
3726
4958
6548

3728.
9530.
9068.
.087

7319

7320.
7329.
.754

7330

5875.
.744
.499
.893

7135
4471
6730

6678.
.745

3868

845

785
929
905

135
679

650

153

A

5006

6583.
3726.
4958.
6548.
3728.
9530.
9068.
7318.
7319.
7329.
7330.
5875.
7135.
4471.
6730.
6678.
3868.

.843

450
032
911
050
815
600
600
920
990
66

73

640
773
486
816
152
750

B

D.2.3 Abundance Table

[0
[N
[0
[O
[N
[O
[S
[S
[O
[O
[O
[0
He
[Ar
He
[S
He
[Ne

fl”

III]
II]
II]
III]
II]
II]
III]
III]
II]
II]
II]
II]
I
III]
I
II]
I
III]

C

Figure D.2 A Matched Line List (ic418.match). Listed in columns from left to
right are: A. observed wavelength (A) B. laboratory wavelength of transition (A),
C. spectroscopic notation for the transition’s source ion D. flux with respect to H6

2.15e+00
1.63e+00
1.24e+00
7.27e-01
5.36e-01
5.23e-01
4.23e-01
1.78e—01
3.69e-02
1.01e—01
5.86e-02
5.63e-02
1.37e-01
8.26e-02
4.49e-02
4.42e-02
3.87e—02
3.09e-02

D

EMILI comes with a default abundance table: abun.dat, which are solar abundance
values for each element Z S 30, with respect to hydrogen. One may specify an
alternative abundance table in the Command/Parameter List. Values need not be
with respect to hydrogen in a user supplied table, but in that case the numeric absolute
abundance of hydrogen m be specified. This is necessary in order to normalize the
other elemental abundances to the values used by the code to calculate the Template

flux: (see Sect. D.4). EMILI will query you if a possible line ID does not have a

matching abundance for its source ion.

If an abundance table is specified, it must be in the format of an ASCII table,
where information about individual elements must be placed on an individual line
in the that table, one element per line. As usual, blank spaces must separate the
information on each line, and each line must be ended by a carriage return. Each
line must follow this order: The element, listed in standard notation, is a FORTRAN
“CHARACTER*2” variable, followed by a blank space, followed by the value of the
numeric abundance (read in as a free format FORTRAN “REAL” variable). Again, no
end of file indicator is necessary, and the file must not include blank lines. The user
must use elements which are on_ly_ Z S 30. The code currently can’t accept additional
elements, and the transition database only has information for Z _<_ 30 elements.

The abundance table is read into the program from the subroutine: matchlist4.f.
For an example of a properly formatted Abundance Table, see abun.dat, included

with the distribution.

D.2.4 Command / Parameter List

Here is where EMILI receives additional information for its calculations. This in-
formation comes in two classes: input and output file names, and parameter speci-
fications. Some of these parameters are required and some are optional. A sample
command list: ic418.cmd is included with the distribution and is shown in Fig-
ure D.3.

The command list is a simple ASCII text table, with each line setting

251

a file name or parameter. Each line in the list consists of a command
(A , L , M , I , 0 , D , T, N ,deplete , vel , icf) followed by various arguments. Each line may
be no more than 60 characters in length, with individual arguments no longer than
15 characters, ended with a carriage return, one command per line. There may be
up to 5 arguments depending upon the command. Commands may be placed in any
order. A “Z” placed in the first column of any line will cause the code to skip that
line. EMILI will warn before run time, if commands are repeated or if they conflict.
The list is read in by the subroutine: openall4.f. A detailed description of each
line in the example list (Figure D3), and a description of em possible command
perturbation is given below.

Required:
0 “L ic418.in” This specifies the name of the file for the Input Line List.

0 “T 10000” This sets the electron temperature to 10000 K. This is utilized in

the calculation of Template Flux values.

0 “N 10000” This sets the electron density to 10000 electrons/cm3. This is also

utilized in Template Flux calculations.

0 “I 10” This sets the instrumental resolution or natural line width, whichever is
the largest, to 10 km/sec. This is utilized by the Multiplet Check, to determine
if certain multiplet lines are too close to be fully resolved, and thus not searched

for during that phase of the code’s calculations.
0 “vel+” Commands starting with “vel” indicate how the velocity structure

252

 

abun.dat

ic418.match
ic418.out
ic418.dat
10000

10000
10
ic418.in

FHZHDOEW

t:
I'D
l—I
...

icf+
Z deplete Fe 50 1 2

Figure D.3 A Command/Parameter List (ic418.cmd).

should be calculated. The calculation may be carried out in three different

ways, reflected in these three options:

— “ve1+” Calculate the velocity correction for each energy bin (see Table
1) from the data of the Matched Line List. In order to use this option
you must specify the file name for the Matched Line List with the “M”

command.

— ve1-: Assume that the observed lines already have been corrected to the

nebular rest frame, and that there is no ionization energy dependent ve-

253

locity flow. This essentially sets the velocity correction value to zero for

each energy bin.

— “vel 99 99 99 89 89” Use the values specified as arguments as the ve-
locity correction values (in km/ sec) to apply to an ion residing in each of

the five bins.

o “icf+” Commands beginning with “icf” specify how the ICF values for each
bin should be specified and consequently used to calculate ionic abundances.
These calculations may be performed in three different ways, specified here by

three different formats:

— “icf+” Calculate the ICF values for each bin from the data of the Matched
Line List. If this option is used a Matched Line List must be specified with

the “M” command.
— “icf-” Use the default ICF values for each bin (see Table D.2).

— “icf 0.1 0.2 0.3 0.3 0.1” Use the values specified as arguments as the
ICF values to be applied to ions in each of the five energy bins. These must

sum to one.

Optional:

0 “M ic418.match” This specifies the name of the Matched Line List. If this
command is not included, one must choose to use manual or default values for

the velocity correction and ICF values for each bin.

254

 

“0 ic418.out” This specifies the name of the file to include the Full Output
List. If the command is not included, an “.out” will be tacked onto the Input

Line List name and used as the file name.

“D ic418.dat” This specifies the name of the Summary List. If this command
is not included, a “.dat” will be tacked onto the Input Line List name and used

as the file name.

“A abun . dat” This specifies the name for the Abundance Table. If not present in

the Command/Parameter List the code will utilize the default table: abun.dat.

“deplete Fe 50 1 2”

Lines beginning with “deplete” tell EMILI to reduce the abundance of certain
ions, after the ionic abundances have been calculated using the ICF values. This

command may have up to four arguments specified in the following order:

1. The element to deplete.
2. The factor by which to deplete (negative values enhance).
3. The lower end of the range of ionization states to deplete.

4. The upper end of the range of ionization states to deplete.

The following examples illustrate the options that EMILI will assume if specific

arguments are missing:

— “deplete Fe 50 1 2” No arguments are missing. This example would
ask EMILI to deplete the abundances of Fe I and Fe II by a factor of fifty.

255

— “deplete Fe 50 1” Argument four is not present in the command. EMILI
will assume that only the ion indicated by argument three will be depleted.

Thus in this example only Fe I would be depleted by a factor of fifty.

— “deplete Fe 50” Both arguments three and four are missing. EMILI will
deplete all the ions of the indicated element. In this example all the ions

of iron are depleted by a factor of fifty.

Arguments one and two must be present for a valid command.

D.3 Installing and Running the Code

1. One should un-compress and un-archive the file: em4.tar.gz into an empty
directory. All of the subroutines and data files will be placed in that directory

after un-archiving. No additional sub-directories are created. Follow these

commands:

>cd (name of the directory in which to place EMILI)
>gunzip em4.tar.gz

>tar -xvf em4.tar

2. In that directory, compile the code by executing the make file: ./em4.mak.

This is included as part of the distribution.

256

>./em4.mak

The code should compile and run, although in differing Unix platforms the
various compilers may complain. On my Red Hat distribution with the generic
“f7?” compiler, I receive no complaints. The make file assumes that a “f77”

compiler exists on your machine.

3. Run the code from the command line:

>./em4 cmdlist

where cmdlist is the name of the file containing the Command/Parameter List.

One should now see various things, starting with a welcome message, followed
by a check of the Command/Parameter List for errors and proper format. If all is
well, the program will echo to the screen the parameters you have entered, wait for
a carriage return, then read in the transition and level information databases, before
executing. If there are any “fatal” errors in the Command/Parameter List, you will
need to correct them before the program will run. Don’t be alarmed if it takes a while
to read in the transition database, as it includes 280,000 transitions in the specified
optical range. EMILI will describe what it is doing every step of the way.

You will know the program is working on the data the user provided when long
“block” lists of information begin scrolling on your screen, one for each line in
your Input Line List. The screen output is echoed into the Full Output List (see

257

Sect. D.5.1) along with the ICF and velocity correction values, either specified in the
Command/Parameter List or calculated by the code, as well as the other parameters
specified in the Command/Parameter List.

When completed the program will drOp you back to the shell, where you can look
at the Outputs (see Sect. D5) in your favorite text editor.

Try it with the included command/ parameter and line lists: ic418.cmd,

ic418.match, and ic418.in:

>./em4 ic418.cmd

Yields:
Full Output List: ic418.out
Summary List: ic418.dat
On my 700 MHz notebook it takes about 5—6 minutes to process the 805 lines in

the list: ic418.in.

BA The EMILI Process

The process begins by reading in the information about each unidentified line the
user wishes to have EMILI identify from the Input Line List. If the user supplies
a Matched Line List, and if the appropriate commands have been issued in the
Command/Parameter List, the code will use the pre-identified lines to make Ionic
Abundance calculations, and to determine if any Velocity Structure may be present,

calculating any necessary correction values. If the Matched Line List is not sup-

258

plied, or if the ICF value and velocity structure commands have been set not to use
the Matched Line List, the same calculations will be carried out with the default or
manually specified values.

For each unidentified line, the code searches the transition database for all lines
within 200 km/sec, to account for the largest possible systemic velocity for nearby
emission-line regions. These comprise the first set of putative IDs for that line. The
Velocity Structure Correction (manually specified or computed by the code), appro-
priate to each putative ID’s source ion, is then applied to the observed wavelength of
the line being identified in order to bring the observed value into the nebular “rest
frame” for the region where that ion resides. Further consideration is given only
those putative IDs for which the residual wavelength difference after correction is
less than (currently) five sigma of the observed value’s measurement error (transition
wavelength uncertainties are currently not included in the error). For each surviving
putative transition a Template F lua: with respect to H5 is calculated, which is a pre-
dicted, order-of-magnitude estimate of the strength of that line, under the specified
nebular conditions (temperature and density supplied by the user). This estimate is

based on makes several simplifying assumptions about each transition:

1. Each transition has both a collisionally excited and recombination component

to its strength.

2. The collisionally excited portion of the flux uses order of magnitude estimates
of collision strengths and transition probabilities according to the type of tran-

sition (electric dipole, magnetic dipole, electric quadrupole) it represents. The

259

collisional component assumes a simple two level atom, and allows for collisional

de-excitation.

3. The recombination excited portion also uses a generic spontaneous transition
coefficient, and is considered insensitive to either temperature or density, influ-
enced mostly by the direct abundance of the source ion. It also assumes a two

level atom and does not employ any branching ratios.

Only transitions which are within a factor of 103 of the highest calculated template
flux among all putative IDs considered at this stage are retained. This assumes that
the transitions predicted to be the strongest are the most likely to actually manifest
themselves in the spectrum as an observed line.

Upon these remaining putative transitions a Multiplet Check is carried out. This
involves looking for companion multiplet lines in the Input Line List, of the same
or stronger transition type, which are approximately close both in wavelengths and
expected observed flux. It is expected that the ratio of the products of the statisti-
cal weights and Einstein coefficients between the putative ID transition and another
transition from the same multiplet, should be fairly close to the ratio of their associ-
ated lines’ observed flux ratio, within a factor of three. If the Einstein coefficients are
not available for these transitions, or when comparing different types of transitions
(such as magnetic dipole versus electric quadrupole) the code assumes that the ratio
of observed fluxes should at least be within a factor of ten (or 10’4 when a weaker-
type transition type is compared to a stronger type). Since multiplet lines arise from

the same element and creation mechanism, they should also show the same residual

260

velocity differences between corrected observed values and laboratory wavelengths.
This check is only carried out for lines originating from pure LS coupling levels.
Finally, the code uses the residual wavelength difference between the corrected
wavelength of observed line and the putative ID’s laboratory transition, the relative
strength of its Template Flux with respect to other putative IDS surviving to this
stage, and the results of the Multiplet Check to rank the potential IDs. This is done
by assigning a numeric Identification Index (IDI) value, derived from these criteria,
to each putative ID. See Table D3 for a detailed explanation of how this score is

calculated.

D.5 Outputs

EMILI generates two output files, whose names the user may specify in the Com-

mand/Parameter List:

Outputs: Full Output List,

Summary List

We describe the Full Output List, and Individual Line Identification Within that

list, and Summary List in the following sections.

D.5.1 Full Output List

The distribution comes with a sample Full Output List: ic418.out, which will be
regenerated if the code is run with an unaltered command list: ic418.cmd. The out-

put consists of five parts (the first four depicted in Figure D.4) listed in the following

261

Table D3 For each observed unidentified line, all putative IDs are ranked, by defining
a “score” or IDI value for each transition. The IDI is awarded on the basis of the
putative ID meeting the main criteria listed below. A lower score generally means a
better ID.

1. Flux Basis (F)
Putative ID template flux satisfies the following condition:
F Condition
0 Exceeds computed fluxes of all other putative IDs by factor 2 10.
1 Within a factor of 10 of the largest putative ID template flux.
2 Within a factor of 100 of the largest putative ID template flux.
3 Within a factor of 1000 of the largest putative ID template flux.

 

 

2. Wavelength Basis (W)

The residual wavelength difference (in km/s) between the corrected observed line’s
wavelength and that for the putative ID is within a number of measurements sigmas
(a) of the observed line’s corrected value:

W Conditions
0 g 0.50
1

2

3

 

 

S 1.00

_<_ 1.50

3 2.00m

(a) code currently set to include only transitions 0 S 5

 

3. Multiplet Basis (M)

For a putative ID, the number of detected multiplet members, D, out of a possibly
observable number, P:

 

 

M Conditions

0 P/D =1/1,D > 2
1 P/D = 0/0,2/1

2 P/D=1/0,(> 2/1)
3 P/D =(>1)/0

 

IDI = F + W + M, with equal weight to each factor.

262

EMILI Output File

Input Line List: emiliB.in

Input Matched List: emili8.match
Results List: emilis.out

Short Results List: emiliS.dat
Abundance Table: abun.dat
Electron Temp: 10000.

Electron Density: 10000.

Inst. Resolution: 10.

ICF Values: Bin/B

ix 1: 0.00999999978
ix 2: 0.498415828
ix 3: 0.489584208
ix 4: 0.00100000005
ix 5: 0.00100000005

Velocity Structure: Bin/Veltkm/s)

irvcor 1: 4.26208973
irvcor 2: 4.08970976
irvcor 3: 1.74469769
irvcor 4: -0.0550202653
irvcor 5: -0.0550202653

Figure D4 The header for the EMILI output file generated by its run on the included
data. Information regarding the input/output files, specified temperature, density,
and instrumental resolution, is contained here, as are the values for the ICFs (labeled
here as “is: 1” — “i2: 5”) and the velocity corrections (labeled here as “irucor 1” —
“irucor 5”) for the five ionization energy bins. No elements were depleted in this run.

order:

1. Parameter Summary: This will echo those parameters specified in the Com-
mand/Parameter List, including file names, electron temperature or density,

and the instrumental resolution/ natural line width.

2. I CF Values: The value for each ionization energy bin is listed here.

3. Elements Depleted: The ions that were depleted or enhanced in the Com-

mand/Parameter List, and the amount by which they were depleted or en-

263

hanced.

4. Velocity Structure: The velocity correction in km / sec applied for all ions residing

in each energy bin.

5. Individual Line Identifications: There then follow several “blocks” of informa-
tion. The output contains one such block of information for each unidentified
line in the Input Line List. This block includes an individual line’s potential
identifications (up to 100 per each line), derived from the results of the checks
carried out by the code. Following the first row, which reiterates the observed
parameters of the line, each succeeding row lists a “putative” ID, drawn from
the transition database, that the code has judged to be a possible ID. Each
transition is listed in order of velocity residual between the corrected observed
wavelength and the laboratory wavelength of the putative ID, starting with the
greatest value to one side of the corrected observed wavelength, proceeding to
the greatest value on the other side. An example of an identification of a line
observed at 6347.19A after correction to the nebular rest frame, from the in-
cluded Full Output List ic418.out is given in Figure D.5. We detail the format

of this figure in the following section.

D.5.2 Sample Line Identification

Format of a sample Individual Line Identification from the Full Output List (see

Figure D5):

264

Observed Line: 6347.19 5.13-04 S/N: 83.30 FWHM: 47.7

6347.15 | 6346.860 N II 470862882 262 3.56-04 13.8 5/0 8
6347.19 | 6346.970 Mg II 806382603 262 1.03-04 10.4 2/0 8
6347.15 | 6347.030 Mn III 1680117006 6 1.38-06 5.8 7/0 9
6347.15 I 6347.0303 Ni II 1880698124 6 5.93-06 5.8 0/0 70
6347.10 | 6347.014 Ca I 1342797915 7 9.58-07 4.0 1/0 70
+ 6347.15 I 6347.110 Si II 940585992 262 6.78-04 2.0 1/1 2A 6371.370 0.6
6347.15 I 6347.170* Si II 940655642 6 1.28-04 -0.8 0/0 2A
+ 6347.15 | 6347.230 C1 II 1142065248 6 1.06-06 -3.6 3/0 70
6347.10 | 6347.243 Ch I 1342715984 7 1.03-06 -6.8 1/0 8
6347.10 | 6347.250S Si I 940079130 6 2.83-05 -6.9 0/0 6C
6347.10 | 6347.3303 Si I 940078106 6 2.83-05 -10.7 0/0 70
6347.15 | 6347.380 Ni II 1880493233 6 6.03-06 -10.7 1/0 9
6347.10 | 6347.340 [V II] 1544610843 38 2.53-05 -11.2 5/0 9
6347.10 | 6347.346$ Fe I 1745668264 7 3.63-05 -11.5 0/0 70
6347.10 | 6347.3463 Ni I 1879307325 7 2.03-06 -11.5 0/0 8
6347.10 | 6347.422 Ca I 1342798940 7 9.53-07 -15.2 1/0 9
6347.15 | 6347.543 Fe II 1746262248 7 2.73-04 -18.4 6/0 8
6347.15 | > 6346.560 Si II 940680287 262 1.13-04 28.0 1/0 0<

A BC D EFGHIJ

Figure D.5 An example of EMILI output from the Full Output List (ic418.out). This
is an identification of a line observed at 6347.19A (after correction to the nebular rest
frame as established by the Balmer and Paschen series of H6. EMILI suggests that Si
11 A6347.100A is the most likely ID. This ID has a small residual wavelength difference
(indicated by small value in km/ sec in column G). It also has a Template Flux (column
F) nearly the same value as what was observed (top line, second numeric value). An
additional multiplet line, Si II 6371.370A (column J), was found to correspond with
another line in the Input Line List and indeed the code found the only other multiplet
line it expected to find (column H). Thus, this putative ID did well (column I) with
a low score and a primary (“A”) ranking.

The first row contains the observed parameters of the particular line, including
observed wavelength, flux with respect to H5, signal to noise, and FWHM in km/ sec,
drawn from the Input Line List. There then follows a table of information, whose
columns provide the following information:

Columns:

0 A. The observed line’s wavelength corrected appropriately for the ion responsi-

265

ble for the putative ID transition in that row. A plus before the value indicates
that the transition’s laboratory wavelength and the corrected observed wave-

length are less than one sigma of the observed value’s measurement error apart.

B. The putative ID’s laboratory wavelength. A “$” following the wavelength
value indicates that the transition involves a non LS coupling level as either or
both the origin and destination level. As mentioned, the Multiplet Check is not
currently carried out for such putative IDs. An “*” following the wavelength
value indicates that all of the multiplet lines involving the particular putative
ID, are unresolvable because they are all within the natural line width or in-
strumental resolution specified in the Command/Parameter List. These are
collapsed into a statistically weighted single line of the wavelength proceeding
the “*”. The Multiplet Check is not carried out for these lines. The code is
currently limited to collapsing lines down if all of the multiplet lines are within
the instrumental resolution/natural line width. Thus, if two of six lines of a
particular multiplet, could be blended, the code considers each of those two as
a separate ID. This will be a focus of continuing work in the next version of the

code.
C. The spectroscopic notation for the putative ID.

D. An internal reference number for this transition in the Atomic Line List
v2.04. This integer, along with the integer in column E, can be used with an
auxiliary reader included with the EMILI distribution (see Sect. D.5.4) to ob-
tain information about the electronic configuration, term notation, and angular

266

momentum j values belonging to the levels this transition traverses.

E. A second internal reference number for the transition.

F. The Template F luz calculated for the putative ID.

G. The residual wavelength difference, measured in km/sec, between the cor-
rected observed value of the line, and the laboratory wavelength of the putative

ID.

H. The Multiplet Check statistics, with the numbers of expected multiplet lines,
followed after the slash by the number of lines found to have potential matches

in the Input Line List, not including the putative line itself.

I. The EMILI assigned IDI value (see Table D.3) which serves as a measure
of the “goodness” of the match based upon the criteria mentioned above, with
lower numbers indicating better IDs. EMILI also assigns a letter “A,B,C, or
D” to indicate primary, secondary, tertiary, and fourth ranked identifications,

based upon the relative numeric scores.

J. Here is where supporting results from the Multiplet Check are noted. Ad-
ditional multiplet lines’ laboratory wavelengths that were found to correspond
with other lines in the Input Line List are listed here along with the residual
velocity difference with those observed lines, for comparison with the same value
in column E. Up to three lines, if they can be found, will be displayed here,

listed in order of decreasing observed strength.

267

In the final row of each individual line identification, beginning with a “>” and
ending with a “<”, in the location where a rank would go in the column I, is listed
the transition with the strongest calculated Template Flux in the anulus between
the initial EMILI acceptance radius and twice that radius away from the observed
wavelength. As mentioned, EMILI is currently set to accept only those transitions
within 50 of the observed wavelength for template flux calculations, where a is the
measurement uncertainty of the line being ID’d. Thus, this row includes the predicted
strongest template flux transition in the region 5 — 100 away from the wavelength for
that line in the Input Line List. The putative ID has no bearing on the rank of the
other putative IDs (no IDI score is assigned), but the multiplet check is carried out.
This was primarily put in to handle occurrences where the transition’s laboratory
wavelength in the database appears to be highly suspect (such as is the case for [Ne

III] A3868A), and to allow them to be considered as additional alternative IDs.

D.5.3 Summary List

This file contains a summary of the EMILI results (see Figure D6 and the included
file ic418.dat). For each unidentified line subjected to testing by the code, the corre-
sponding primary ID or IDs, indicated by an “A” in column G in the Full Output List
along with their laboratory wavelengths, are listed adjacent to that line’s measured

attributes (observed wavelength and flux with respect to H6).

268

4058.29 4.28-05 I N II 4058.16,
4065.23 5.53-05 I Fe III 4065.25,
4067.33 3.63-05 I [Fe III] 4067.30,
4068.67 1.88-02 I [S II] 4068.60,
4069.63 2.03-04 I 0 II 4069.62,
4069.89 2.03-04 | 0 II 4069.88,
4072.15 3.3E-04 | 0 II 4072.15,
4074.51 1.08-04 I C II 4074.48,
4075.89 4.48-04 I 0 II 4075.86,
4076.37 7.68-03 I [S II] 4076.35,
4078.81 5.63-05 I 0 II 4078.84,
4079.64 2.53-05 I [Fe III] 4079.70,
4082.32 5.38-05 I N II 4082.27,
4083.87 4.83-05 I [Fe II] 4083.78, 0 II 4083.90,
4084.67 4.73-05 | [CO IV] 4084.59,
4085.10 7.6E-05 | 0 II 4085.11,
4087.15 4.53-05 | 0 II 4087.15,
4089.29 1.13-04 I 0 II 4089.29,
4092.92 3.23-05 | 0 II 4092.93,
4093.92 4.93-05 I N III 4093.68, Na I 4093.88,
4095.65 4.23-05 I 0 II 4095.64,
4096.51 2.8E-05 | [Fe III] 4096.61,

A B C

Figure D.6 A segment from a Summary List (ic418.dat). From left to right the
columns are: A. a unidentified line’s observed wavelength B. that line’s measured
flux with respect to H6 C. the EMILI primary IDs (labeled “A” in the Full Output

List) associated with the line.

D.5.4 Reader

A separate program is included with the distribution which reads the EMILI out-
put and provides more detailed information regarding the transitions the user may
choose as IDs then collating the information in an additional output file. Specifically,
this reader will take a EMILI Full Output List, marked-up according to a simple
scheme, and extract the information for user-chosen putative IDs, using the previ-
ously mentioned internal reference numbers found in the output, then tabulate it in a
ASCII text file. These internal reference numbers provide information regarding the

transition’s atomic parameters and type. This allows for more rapid EMILI-derived

269

identifications, without generating gigantic lists of such information in the actual
EMILI output files during run-time.

To use the reader, the user simply marks on the EMILI Full Output List an “it”
in the first space of the any row containing a putative ID of interest. This may
be done for as many lines and for as many putative IDs for those lines as the user
wishes. Entries will be generated in a user-named file. The routine will reference the

transition database and provide information about these transitions in the same file.

For instance, suppose I were to mark an “*” in the first space of the row containing
the putative ID that begins with:
*+ 6347 . 15 I 6347. 110 Si II 940585992 262

The reader would generate a corresponding entry in the reader output file:
*+ 6347.19 47.7 5.1e-4 83.3 2A Si II 6347.11 28 332. (IS) .48 . . .

where from left to right are observed wavelength, FWHM, flux, and S/ N (as supplied
in the Input Line List), then the ion, accepted rest (laboratory) wavelength, the
upper and lower energy level terms and electron configurations, and finally the upper
and lower total angular momentum j values for the levels traversed by the particular
putative lD transition (entry is truncated here for space reasons). If additional IDS
are marked for the same emission lines, these will align in the output file with the
transition information for the first ID that the reader encounters in the individual
line output lists.

To invoke the reader simply compile at the command prompt:

>./emread.mak

270

then run at the command prompt:
>./emread arg1 arg2

where “arg1” is the name of the marked-up EMILI Full Output List and “arg2” is

name chosen by the user for the results file.

D.6 Future Improvements

In future editions of the code, we plan on making three major improvements.

1. Broader Line List: A still larger and more comprehensive transition database
is currently being constructed (Atomic Line List v2.05), which will expand the
transition list to include all elements Z s 36 (up to all fourth row elements),

and will include improved Coulomb calculations of transition probabilities.

2. Cross Correlation: Presently the code does not seek corroborating information
about a particular putative ID, from the putative IDs of other unidentified lines,
beyond those comparisons made during the Multiplet Check. Future editions of
the code will compare the expected line strength ratio between different lines of
differing multiplets with the observed value, and compare the velocity residuals

between putative IDs of the same ion and creation mechanism.

3. Multiple Iterations: We plan on making the code iterative, using the best IDs
from an initial run to re-calculate and improve the accuracy the ionic abun—

dances and velocity structure corrections, for use in successive runs.

271

We will also be attempting to optimize the weighting given to each component
(residual wavelength difference, relative template flux, and multiplet check results)
used to construct the final score and subsequent rank for each putative ID for a partic-
ular unidentified line. This in order to ascribe more importance to those components
which might be more or less appropriate for differing observing parameters (i.e. less

emphasis on the residual wavelength difference for lower dispersion spectra etc.).

D.7 Contact Information

This code is always evolving, and as such is still undergoing testing and revision as
I write this, so please pardon the dust (a.k.a. numerous test comments scattered
throughout its length). I cannot guarantee that the code is entirely “bug-free” yet
(caveat emptor). However I hope you are able to use the code with as little trouble
as possible, and that it provides you with interesting and accurate results. I am most
happy to answer any questions and would appreciate reports of any errors you believe

the code is making. Suggested improvements are always welcome.

sharpeera.msu.edu

For further details and updates please stop by the EMILI web page at:

http://www.pa.msu.edu/people/sharpee/emili.html

272

Appendix E

IC 418 Line List

Here is presented the IC 418 Line List. Columns are defined as follows:

(1) The observed wavelength of the line corrected to the nebular rest frame

for ionized hydrogen.
(2) The full width at half maximum intesity (FWHM) of the line in km 3*.

(3) The observed intensity of the Line, F (A), with respect to the observed
intensity of H6 (F(H6) = 1.31 x 10‘11 erg cm‘3 S”) in units of F()\) *

100/F(H6).

(4) The de-reddened intensity of the line, I (A), with respect to the de-
reddened intensity of H6 (I(H6) = 2.87 X 10‘11 erg cm‘3 8‘1) in units of

I(A) ... 100/I(H6).

(5) The signal-to-noise (S/ N) of the line. A value of 99999.0 indicates that

no S/ N was calculated for this line because it wasn’t detected by RDGEN

273

initially, or was a member of a line blend for which S / N of the components

were not calculated.

The EMILI IDI value and rank for the ID transition, where available.
An “*” in this column indicates an IDI value greater than 9. A “<” in
this column indicates that the ID was the strongest predicted transition
outside of, but in the vicinity of, the initial EMILI search radius. IDs not

chosen from the EMILI output have no data in this column.

The source ion of the ID transition.

The tabulated wavelength for the ID transition. All wavelengths are air
wavelengths, and are drawn primarily from the Atomic Line List v2.04.
Exceptions include non-EMILI ID’d He I lines, H I Balmer and Paschen
lines above an upper level of n = 40, and an additional few cases noted
by a “I”. A “*” following the wavelength indicates that the line is a
blend of all the closely spaced members of the same multiplet, and is
a statistically weighted average of their wavelengths. A “?” after the
wavelength indicates a questionable but possible ID based upon the EMILI

results and the literature.

The velocity difference between the tabulated wavelength of the ID tran-
sition and the observed wavelength of the line. This value is determined

from:

A—Ao

 

6V 2 c kms

274

(10) The spectroscopic term notation and electron configuration of the lower
level of the ID transition. Term notation is either in the LS or one of two

intermediate coupling schemes:

0 LS Coupling: (25+1L) where S is the spin of the valance electrons,

 

and L the total orbital angular momentum of those electrons.
For example: 2P0 = 2P0 in the table. An example of an ID transition

with a lower level based on this coupling is O II A4393.483.

o LK Coupling: (252+1[K]) where S2 is the spin of the external excited

 

electron(s), and K the coupled value of the total orbital angular mo-
menta of the core and external electron(s) (L), in turn coupled with
the total spin of the core electrons. This is distinguished from the
JIK coupling by the inclusion of the L value (in the usual LS spec-
troscopic notation a.k.a. P for L21, D for L=2 etc...) at the end of
the electron configuration.

For example: 2[5/2] = 2[5 / 2] in the table. An example of an ID tran-

sition with an upper level based upon this coupling is N II A4432.735

o J1K Coupling: (232+1 [K I) where S2 is the spin of the external excited

 

electron(s), and K here is the value of the total angular momentum
of the core term (J1) coupled with the orbital angular momentum of
the external electron(s).

For example: 2[5]° = 2[5]o in the table. An example of an ID tran-

sition with an upper level based on this scheme is Ne II A4391.991.

275

(11)

The electron configuration takes the form of, as an example, 232.2p4 in the
table which is equivalent to 2322p4. Core electrons and extrenal electrons
may be seperated in this scheme by a core term, in parenthesis and in LS
coupling, followed by an extrenal electron or term (also in LS coupling).
Values enclosed in “<” and “>” in the core term indicate its total angular

momentum J value.

Iron lines are all based on LS coupling and employ specific alphanumeric

level identifiers in place of LS scheme notation.

The spectroscopic term notation and electron configuration of the upper

level of the transition.

The total angular momentum j value for the lower state of the ID tran-
sition. A “****” here indicates that the level is a blend of several closely
spaced j values, or that the line was a blend of several transitions from the
same level, such as a blended multiplet line indicated by an “*” following

the wavelength in column (7).

The total angular momentum j value for the upper state of the transition.

The EMILI multiplet check results, in the sense that if “5/ 1” appears in
the table, 1 out of 5 lines expected to be present from the same multiplet
in the line list, were matched by the code. EMILI did not carry out the
check for transtions from Non-LS coupled levels, lines from blended levels,

or lines judged by EMILI to blends of all multiplet transitions from the

276

same upper level. The check was also not done for non-EMILI IDs.

277

 

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