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LIBRARY
Michigan State
University

 

 

 

This is to certify that the
dissertation entitled

He II Reverberation In N06 5548

presented by

Aaron Patrick LaCluyzé

has been accepted towards fulfillment
of the requirements for the

 

 

Ph.D. degree in Astrophysics and Astronomy

'(LLK Q “KXMV

Major Professor’s Signature

8/27/65

Date
Doctoral Dissertation

MSU is an affirmative-action, equal-opportunity employer

 

PLACE IN RETURN BOX to remove this checkout from your record.
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DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5108 KIProglAcc8PreleIRC/DateDue Indd

 

HE II REVERBERATION IN NGC 5548

By

Aaron Patrick LaCluyzé

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Astrophysics and Astronomy

2008

ABSTRACT

HE II REVERBERATION IN NGC 5548

By

Aaron Patrick LaCluyzé

Despite decades of study, the exact nature of the central engines of Active Galactic
Nuclei (AGN) is still a mystery to be solved. Although great strides have been made,
there are some outstanding questions that still need to be resolved, and new tools
are needed to answer them. The goal of this project was to craft a new method
to accurately measure highly blended weak emission lines in AGN. In particular,
the reverberation behavior of He II A4686 and He II A1640 were investigated to
reconcile a discrepancy between theoretical models, which predicted that the two
lines should have the same lagtime and previous observational studies, which found
that the optical line had a reverberation lag several times longer than the UV line.

The optical and UV He II emission lines were measured to have a reverberation lag
time of 5 - 6 days, with good overlap between the two lines. Furthermore, a previously
measured strong lines, C IV, which were also involved in the heavy blending, was
measured to have a lagtime consistent with previous measurements. This helps to
validate the technique that was used. This technique, which required a large software
development effort, included using an automated fitting routine to simultaneously fit
multiple emission line template profiles that were, themselves, created from observed
data.

One rather surprising result was the clear indication that He II and C IV are not
created by the same gas within the BELR. This is contrary to what was predicted by

the typical model of the BELR but consistent with previous measurements.

Copyright by
AARON PATRICK LACLUYZE
2008

For Lise, Dodger, Anna and Dclcnn

iv

ACKNOWLEDGMENTS

First and formost, I must thank my wife, Jennifer, and my parents Paul and Mary.
Without their help and support, I would not have made it this far. I also want to
thank my advisor, Dr. Jack Baldwin. His patience has been saint—like.

There have been a great many graduate students over the years who have helped
me though all of this. Thanks to Pete, Bob, Mike, Fred, Ryan, and Chuck, all of
whom helped me understand what graduate school is all about. Brian, Chris, Ken,
Nathan, and Katie helped me make it through the long years that followed. Thanks
also to the current pool of grad students who have kept me sane while I finished.
Special thanks goes to Charles, who was willing to answer my silly questions about
software.

A very special thanks goes to Dan Reichart, who took a chance on me and has
been very patient while I tied up loose ends.

I am grateful to the National Science Foundation for their support of this work
under grant AST-0305833, and to NASA for their support under ADP grant NAG5-
13075. I also thank Jack Baldwin, Mark Bottorff, Gary Ferland and Kirk Korista,
the co—investigators on the latter grant, for their help.

Thanks to Christopher Waters for the LATEX class used to format this thesis.

TABLE OF CONTENTS

List of Tables ........................................................ viii
List of Figures ....................................................... ix
1 Introduction ...................................................... 1
1.1 A Brief history of AGN ...................... 2

1.2 AGN Standard Model ....................... 3

1.3 Reverberation Mapping ...................... 6

1.4 The Importance of He II Emission ................ 9

2 Data Set Description ............................................. 16
2.1 Background on AGN Watch and data set for NGC 5548 . . . . 16
2.2 Ultra-Violet Data From IUE and HST .............. 17
2.2.1 Non-linearity of IUE at Low Flux Levels ........... 18

2.3 Optical Data ............................ 23
2.3.1 Corrections to the Optical Data ................ 25

2.3.2 Observed vs. Rest Frame ................... 28

3 Data Fitting and Measurement .................................. 29
3.1 Automated Fitting Routine .................... 29
3.2 Building the Blend ......................... 32
3.2.1 Fe II Template ......................... 33

3.2.2 Other Templates ........................ 35

3.2.3 Fitting Parameters ....................... 38

3.2.4 Fitting Windows ........................ 40

3.3 Minuit and the X2 Minimization ................. 42
3.4 Error Estimation .......................... 46
3.5 Cross-Correlation Lags ...................... 47

4 Results ........................................................... 55
4.1 Cross Correlation Centroid Distribution ............. 55
4.2 Light Curve Error Estimation ................... 59
4.3 Sensitivity to Profile Templates .................. 61

5 Discussion ........................................................ 67
6 Summary ........................................................ 72
A Code for contin.f ................................................. 75
B Code for cfunk.f .................................................. 87

vi

C Code for uvcontin.f ............................................... 91

D Code for uvfunk.f ................................................ 104
E Code for functions.f .............................................. 108
F Template Profiles ................................................. 115

References ....................................................... 137

vii

1.1

1.2

2.1
2.2

2.3

3.1
3.2

3.3

4.1

4.2

F.1
F2
F3
F4
F5
F6
F7

F8

LIST OF TABLES

Reverberation Lags From Previous Studies ................. 13
Other C IV A1549 / He II A1640 Lag Ratios ................ 14
IUE UV Data ................................. 22
Optical Data Site List ............................ 24
Optical Data ................................. 27
Fitting Windows ............................... 42
Optical Profile Summary ........................... 54
UV Profile Summary ............................. 54
CCCD Results ................................ 57
Profile Permutations ............................. 63
C IV BELR Template ............................ 115
He II BELR Template ............................ 116
He I BELR Template ............................. 121
H6 BELR Template ............................. 125
C IV NELR Template ............................ 134
O III ...................................... 134
He II NELR Template ............................ 135
0 III 1663 BELR Template ......................... 135

viii

LIST OF FIGURES

1.1 Simplified Cross-Sectional Representation of an AGN ...........
1.2 Simplified Illustration of Reverberation Mapping. .............
1.3 Simplified Grotrian Diagram of He II ....................
1.4 NGC 5548 Optical Detail ..........................

1.5 NGC 5548 HST UV Detail ..........................

2.1 Typical UV spectrum. ............................
2.2 Ratio of IUE to HST flux levels as a function of IUE detector counts

2.3 Typical optical spectrum. ..........................

3.1 Typical Optical Spectrum ..........................
3.2 Typical UV Spectrum ............................
3.3 Fe II Optical Template ............................
3.4 Fe II UV Template ..............................
3.5 Example Optical RMS Spectrum ......................
3.6 UV RMS Spectrum ..............................
3.7 Ha BLR Profile ................................
3.8 He II BLR Profile ...............................
3.9 He I BLR Profile ...............................
3.10 C IV BLR Profile ...............................
3.11 Optical Fit Overlay ..............................
3.12 UV Fit Overlay ................................

3.13 UV Continuum Light Curve .........................

ix

10

11

12

19

30

31

34

35

36

37

38

39

40

41

44

45

49

3.14

3.15

3.16

3.17

4.1

4.2

4.3

4.4

4.5

4.6

4.7

5.1

Optical He II Light Curve .......................... 50
UV He II Light Curve ............................ 51
C IV Light Curve ............................... 52
H,3 Light Curve ................................ 53
Composite Centroids for Optical and UV He II .............. 56
Cross Correlation Centroid Distribution for C IV ............. 58
Composite Centroids for Optical and UV He II and C IV ......... 59
Cross Correlation Centroid Distribution for H6 .............. 60
He II Error Estimation Test ......................... 61
He II Error Estimation Test ......................... 62
He II A4686 Profile W'idth .......................... 64
Standard LOC Model ............................. 70

 

CHAPTER 1:
INTRODUCTION

 

Since their discovery by radio telescopes in the late 1950’s, quasars have captivated
researchers. Despite decades Of intense study, only a general theoretical model exists
with many details still unclear. Under the current standard model quasars are just one
manifestation of a larger class of objects called active galactic nuclei (hereafter AGN).
Because even the most nearby of AGN are at very large distances from us, direct
imaging of their central cores is impossible. This makes verification of theoretical
models difficult at best. We must therefore resort to indirect methods to attempt to
gain insight into the actual physical workings within the core region. One technique
that can be used to study the inner regions of AGN is reverberation mapping, where
the lag time between a change in the driving continuum radiation and the response
of an emission line is used to indirectly measure the distribution Of gas around the
central engine.

In this work, I present a new analysis of He II reverberation in N GC 5548, a
relatively nearby and well studied low luminosity AGN, classified as a type 1 Seyfert
galaxy. The remainder of this chapter will give a brief introduction to AGN, an
overview of the reverberation mapping technique, and a discussion of why He II

emission is both interesting and important to our understanding of AGN.

1.1 A BRIEF HISTORY OF AGN

During the late 1950’s, radio astronomy was beginning to produce vast catalogs of
radio sources. Using these catalogs, astronomers attempted to match radio sources
with Optical counterparts. During this process, it became clear that several of the
radio sources had fairly blue star-like point source optical companions. These strange
objects were dubbed quasi-stellar radio sources (QSOS), or quasars for short. The
most famous of these objects are 3C 48, the first to be observed, and 3C 273, the
first to be identified with a bright (mu 2 12.8) stellar-appearing object; see Schmidt
(1963), Oke & Schmidt (1963) and Greenstein & Schmidt (1964).

The spectra of these objects caused both initial confusion and decades Of debate.
Since the objects were star-like in appearance, the emission lines that were detected
were not immediately identified. Schmidt and his collaborators made the first steps
toward understanding by showing that in 3C 273 these unidentified emission lines
were actually the well known Balmer lines of Hydrogen that had undergone a redshift
of z 2 0.158. This sort of redshift had been seen before in galaxies, but a combination
of being at a high redshift as well as being bright and stellar in appearance was both
new and interesting. This led to debate within the community as to the nature of
these Objects. They could be extremely bright, distant objects with a redshift due to
the Hubble flow (the expansion of the Universe itself.) This would explain the point-
like appearance, but would imply an extremely large luminosity. Or they could also
be much less luminous star-like objects with the redshift arising from a large peculiar
radial velocity relative to Earth. The latter hypothesis would imply a more ordinary
luminosity, but would give no reason for the high velocity. While Schmidt and his
colleagues assumed the former, there was no explanation at the time for how quasars
could generate enough energy to be luminous enough to appear so bright at these
vast extra—galactic distances. It is important to understand that like many Objects in

astronomy, the definition of a quasar was originally based mainly on appearance.

During the decades since, there have been a variety of Objects discovered that have
many properties in common with quasars. This much larger group of seemingly re-
lated objects are known collectively as active galactic nuclei. These AGN are galaxies
in which the central core can outshine the rest of the stars in the galaxy combined.
The defining characteristic is that the continuum radiation produced by these objects
is not only luminous, but spans a large range in energies, extending from x-ray out
to the far IR or radio regime. In most cases, there are also a variety of emission lines
that, while common to most AGN, are of differing strengths depending on the object
in question. The gas creating these emission lines is believed to be fed in from the
host galaxy, making them a good tracer of chemical evolution in the central part of
massive galaxies over a wide range Of lOOkback times. (Hamann & Ferland, 1999;

Hamann et al., 2002)

1.2 AGN STANDARD MODEL

\Nhile there has been a great. deal of debate on the exact structure of AGN, a “stan-
dard model” has been embraced by a large portion Of the astronomical community.
Under the standard model, all AGN, from radio galaxies to blazars, are the same type
Of object, with distance, viewing angle, and the total output energy being the major
factors that dictate which classification each object is given. The object of interest in
this study, NGC 5548, is a type 1 Seyfert galaxy. Seyfert galaxies are a type of AGN
that show clear emission lines, nuclear x-ray emission, and sometimes a small-scale
radio jet but are otherwise radio quiet. Seyfert galaxies are the most common type
of AGN.

In the standard model (Gaskell, 2008, and references therein), the method of
energy generation is accretion of matter onto a super-massive blackhole. This central
black hole has a mass of about 106 —— 108M@ and is surrounded by an accretion disk

that is on the order of a light day in diameter (see figure 1.1.) This size is inferred

from variations in the output intensity that are on the order Of a day for lower energy
objects like Seyfert galaxies, while more luminous QSOS show variability on time
scales closer to a year, implying a correspondingly larger central engine. As gas falls-
in toward the black hole, it collapses into an accretion disk due to angular momentum
conservation. Internal friction within this disk causes the gas to heat up and begin
to emit radiation like a blackbody. The closer the gas is to the center, the higher
its angular speed, and the higher the temperature. This creates a superposition of
blackbody radiation of varying temperatures generating a powerful and relatively flat
continuum. Secondary processes then convert some of this thermal radiation into
additional x—ray, IR, and radio light. While some of this radiation escapes the AGN,
some Of it is reprocessed into emission lines by cooler gas that lies outside of the
accretion disk.

The first region Of gas that is encountered by the continuum radiation on its jour-
ney out from the accretion disk is the so called broad emission line region (BELR,
sometimes written as BLR). This gas is in close to the accretion disk, at a distance
of several light days to tens Of light days from the central source in a typical Seyfert
galaxy. Because the gas is in close to the central mass, it has a large velocity on the
order of 10,000 km/s. This broadens any emission lines from the gas in the BELR,
hence the name broad-line region. This Doppler-broadened emission, however, isn’t
seen in all types of AGN . The standard model postulates that outside the BELR there
is a large dusty torus, a doughnut-shaped collection of gas and dust that blocks the
emission coming from the interior. The angle of the object to our line of sight will
dictate our ability to observe the broad emission lines. This is the primary classifica-
tion difference between type 1 and type 2 Seyfert galaxies, with type 1 showing broad
and narrow emission lines and type 2 showing only narrow lines (see figure 1.1.)

One consequence Of the location of the BELR is that it is quite sensitive to any

variability in the continuum emission. The emission lines are generated by gas that

Observer
A

NELR

. C
Black BELR . .
H016 . . .

O

0.0 . Q
- " o O

Accretion .0

Disk Dusty . -. Observer
(Continuum Toms O O B
. . Source) . .

  

Figure 1.1 Simplified Cross-Sectional Representation of an AGN - This figure shows
a typical AGN cross-section, seen edge-on. This figure is not to scale in any way and
is meant as a general guide to the relative location of regions of interest in an AGN.
When an observer is at position A, the emission from the interior BELR can be seen.
When an observer is at position B, the dusty torus will block the BELR emission
and only the lines from the N ELR will be seen. This leads to a distinction between
Seyfert 1 galaxies, which show BELR emission, and Seyfert 2 galaxies, which do not
show BELR emission.

has been been excited by being continually bathed in radiation from the central en-
gine. When the central engine’s emission changes in intensity, the broad line emission
also changes on a time scale directly related to the light travel time from the central
source to the emitting gas. This variability in the central continuum is Often seen in
AGN, although the exact cause is not well known. It is also important to understand
that the variability is not predictable or periodic as it would be in certain types of
variable stars. As such, obtaining meaningful observations of this variability can be
a long and difficult process spanning many months to years. Because this variability
is not regularly periodic, extensive Observations need to be made to ensure that the

Object is Observed in both a quiet baseline state as well as during a period of more

intense activity.

Outside of the dusty torus is another large region of gas that also reprocesses the
continuum radiation into emission lines. This gas is much further from the central
engine and as such does not exhibit the large Doppler broadening seen in the BELR.
This region is therefore called the narrow emission line region (NELR, sometimes
written as NLR). Unlike the BELR, the NELR is fairly insensitive to short term
variations in the continuum intensity. As such, we can treat the narrow emission

lines as being constant over the time scales during which the BELR is observed.

1.3 REVERBERATION MAPPING

Although AGN are very luminous, it was quickly deduced that for the core to coher-
ently vary in brightness on timescales of days or weeks as observed, it must be very
small, only light-days to light-weeks across (Terrell, 1967). This means that even the
most nearby AGN have cores, including the BELR, that are on the sub-arcsecond
scale and cannot be resolved by either ground or space based instrumentation. Direct
imaging of the cores of AGN is simply inconceivable for the foreseeable future.

We can exploit the response of the BELR to changes in the continuum to indirectly
measure the size of the BELR by making a few basic assumptions (Peterson & Horne,
2006). We assume that the continuum originates from a single central source. Because
the size of the BELR is expected to be about a factor of 100 larger than the size of
the accretion disk, this assumption is well justified.

We also assume that the most important time scale to be considered is the light
travel time required for photons to travel a distance r from the central source to the

BELR clouds:

7..

There are two other time scales that should be considered because they may at

first glance seem important. The first is the recombination time scale:
—1
Tree = (71603) (1.2)

Here a B is the Hydrogen case B recombination coefficient, and ne is the particle
density of the line producing gas. Case B describes the situation where low-density
ionized clouds form Hydrogen emission lines such that the higher Lyman lines scatter
Often enough tO be degraded into a Balmer line and either a Lya or the two-photon
continuum and the electron density must be low enough for collisions to be slow
compared with spontaneous emission (Ferland, 1999). This is thought to describe
line formation in most AGN (Osterbrock, 1989). A typical BELR density of 17.6 m
1010cm—3 gives a Tree 2: 0.lhr, much shorter than the light days of TLT.

A second possibly important time scale is the dynamical time scale for the motion
of the BELR gas itself.

7.

In the case of a typical Seyfert galaxy, the type of AGN of interest in this work,
Tdyn z 3 — 5years. This is much longer than the several months of the observing
campaign used here, but can become an important factor with longer campaigns.

A final assumption that needs to be made is that there is a simple relationship
between the observed continuum and the ionizing continuum. Because the ionizing
continuum is driving the line variations, we must assume that the ionizing continuum
and the observed continuum vary in phase with one another. There is some evi-
dence that there is a delay between the long wavelength continuum and the shorter
wavelength continuum variations (Gaskell, 2008), but the time scale Of this is still
significantly shorter than the timescale for the emission-line response.

To better understand the principle behind this technique, imagine a situation

where we have three test clouds at a common distance r from the central engine (the

l

 

1’

 

iii

Figure 1.2 Simplified Illustration Of Reverberation Mapping — The dark circle repre-
sents the accretion disk central engine of the AGN, producing the broad spectrum
continuum radiation. The three objects labeled “A”, “B”, and “C” are representa-
tive BELR clouds all at the same distance r from the central engine. Because of the
additional distance that lines emitted by clouds “B” and “C” must travel compared
to “A”, there is a delay in the response of the observed broad emission to a change
in continuum luminosity.
black hole and its accretion disk, see figure 1.2.) If the central engine is variable and
has a sudden increase in continuum luminosity, this pulse of increased intensity takes
a finite amount of time to reach the gas which re—processes this continuum radiation,
giving rise to the BELR lines. The pulse in the continuum luminosity continues
onward to our Observer at some distance which is large compared to r. The response
of cloud “A” to the increased continuum is seen by our observer almost immediately
after the increase in the continuum as cloud “A” is along the line of sight from the
observer to the central engine. The response of cloud “B” is seen after an additional
time T = r/c corresponding to the additional distance that the emission line radiation
must travel. The response of cloud “C” has an additional distance of 7‘ compared to
cloud “B”, or 27‘ compared to cloud “A”.

While it takes a finite amount of time for all Of the gas to respond, the calculation
of a cross correlation between the light curves of the continuum and the responding

emission line yields a mean response time for the emitting gas, which is reported as

the characteristic lag time. This is the principle behind reverberation mapping and

is the best tool currently available to study the inner structure of AGN. .

This generalized discussion of the nature of the BELR is for the most part spec-
ulative. Very little is actually known about the true structure of this region. While
the cartoon picture of discrete clouds is useful for illustrative purposes, it may not

reflect the true nature Of the region.

1.4 THE IMPORTANCE OF HE II EMISSION

In order for an emission line to be produced efficiently, there must exist a specific
combination of gas density and incident radiation strength. This is the crux Of the
“Locally Optimally-emitting Cloud” (LOC) model put forth by Baldwin et a1. (1995).
If the gas is too diffuse, there is not enough reprocessing to significantly affect the
radiation output. If the gas is too far from the central engine, there isn’t enough
incident flux to cause significant excitation or ionization/recombination. This is the
central premise behind several models of the inner regions of AGN. Each emission
line has an optimal location in space around the central engine where it can be
produced efficiently. This corresponds to a characteristic distance from the center,
assuming a roughly spherically symmetric distribution of gas. This distance is set by
the ionization parameter, the ratio of incident ionizing flux to the gas density.

In this work, the primary goal is to measure the reverberation lags of He II A4686
in the optical region and He II A1640 and C IV A1640 in the ultraviolet region in NGC
5548. The He II lines are produced by singly ionized helium which is hydrogenic in
nature. This means that, having only one electron, He II behaves in many ways Similar
to hydrogen and is therefore relatively easy to understand. Theoretical predictions
(Baldwin et al., 1995) Show that the optimal conditions for producing both the A4686
and the A1640 lines are virtually identical as both emission lines should be produced
by the same recombination and radiative cascading process (MacAlpine, 1981), as

illustrated in figure 1.3. This means that they should both have about the same

reverberation lag times. In addition, Bottorff et al. Showed that plasma simulations
assuming a simple model for the BELR gas distribution (see discussion of LOC model
in chapter 5) suggest that the He II lines (A1640 and A4686) Should have a Similar
reverberation lag as C IV (A1549).

 

 

 

 

 

 

 

 

4
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3 :1-
CW
Vv—d
:25:
2
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MOM
omv
CONN
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Figure 1.3 Simplified Grotrian Diagram of He II, showing only the first four energy
levels. The lines between energy levels are labelled by the approximate wavelength
of the photons emitted when an electron drops from the higher to the lower energy
level, or the wavelength of light absorbed to move an electron from the lower energy
level to the higher one. Of particular note are the paths that would lead from level 4
to level 3 and from level 3 to level 2 that would produce A4686 and A 1640.

From an Observational standpoint, there is only one Object, NGC 5548, where
the A1640 and A4686 lines have been measured in the same campaign. Because the
BELR is changing over time, it is important to measure both lines during the same
time period in order to accurately measure the lag ratio. Wamsteker et al. (1990)
studied the intensity ratio of the He II A1640 and A4686 in observations from both
IUE and ground based data sources from 1978 - 1986. While reverberation mapping
was not the goal of that study, the authors did find that the intensity ratio of the two
lines, f(A1640)/f(A4686), varied from 4 to 10 during the study. A changing flux ratio
would imply that the two lines are responding to the continuum changes on different

time scales, implying different reverberation lag times for the two He II lines. While

10

Wamsteker et al. did some fit synthetic profiles to some Of the blended emission
lines, they did so by using several generic line components rather than true template

profiles generated from the Observations.

 

    
    

 

4 I l l l l l T
HB
3.5 - Hy a
3 .— q
’6? Hel4471
U)
9 l
3,3 2
52 ............................................
‘3’ 1.5 - ---------------------------------- q
“- 1 He II 4686
0.5 - _
O l l 4 l l l 1

 

 

 

4200 4300 4400 4500 4600 4700 4800 4900
Wavelength (Angstroms)

Figure 1.4 NCG 5548 Optical Detail - Example of NGC 5548 optical Spectrum, as
used in Dietrich et al. (1993). The continuum was approximated as a straightline
under the region of interest (dashed line.) The He II A4686 emission was defined
to be in a simple bin above this pseudo-continuum from 4593 - 4770 A. This area
includes contamination from the wing of H6 as well as He I and a weak iron multiplet
that is contaminating the entire region.

NGC 5548 was later a target for study by the International AGN watch (see
chapter 2 for more information on this data set.) The UV He II A1640 and C IV A1549
(Clavel et al., 1991) and the optical He II A4686 (Dietrich et al., 1993) were among the
emission lines studied to determine their reverberation lag times. These two studies
found that the two He II lines may have different reverberation lags (between 4-10

days for the UV line and 7 days for the optical) and the He II A1640 did not agree well

11

with C IV (between 8-16 days). The authors did caution, however, that blending with
other nearby emission lines is an issue (see figure 1.4.) The emission lines were defined
to be in a simple wavelength bin, and all flux above a straight-line pseudo-continuum
was assumed to be from the line in question. This does not correctly account for
the wings of surrounding lines that could be contaminating the measurement. The
optical He II A4686 line is contaminated by H6, He 1, and a Fe II multiplet that is

under the entire region (see section 3.2 for more discussion on these contaminants.)

 

 

 

 

 

 

25 I I I I fi
20 - CIV -
70‘
g 15 - -
(D
2’
m
3
i, 10 - A
‘x’
3
E
5 '- -l
0 - Hell 1640+Olll]1663 ~
1 450 1 500 1 550 1600 1 650 1 700

Wavelength (Angstroms)

Figure 1.5 NCG 5548 HST UV Detail - Example of N GO 5548 UV spectrum, as used
in Korista et al. (1995). The continuum was approximated as a straightline under
the region of interest (dashed line.) The He II A1640 emission was defined to be in
a simple bin above this pseudo-continuum. This area includes contamination from
the wing of C IVA1549 as well as O III] A1663 and a weak iron multiplet that is
contaminating the entire region.

Korista et al. (1995) did a similar analysis for the UV data, but included measure—

ments from HST as well as IUE. Once again, a straight line continuum and wavelength

12

bins were used in a manner similar to the Dietrich et al. study (see figure 1.5.) In the
case of the UV Spectrum, the He II A1640 line is heavily blended with the O III] A1663
emission aS well as the wing of C IV and a weak Fe II multiplet that is contaminating
the entire region. In this case, no attempt has been made to deblend the 0 III] A1663

emission, and the effects on the reverberation lag were simply estimated.

Table 1.1: Reverberation Lags From Previous Studies - This table, taken from data in table
1 of Peterson & Wandel (1999), shows the best measured values for the reverberation lags

of several emission lines from NGC 5548 using the 1989 AGN Watch data set.

 

 

Line Lag (days)

 

He 11 A1640 3.013;?
He 11 A4686 asigj
C 1v A1549 9.5iff,

 

The AGN watch data was also further analyzed by Peterson & Wandel (1999) in
order to estimate the mass of the central black hole. During this study, more careful
attention was paid to the reverberation lag measurements. These values are shown
in table 1.1. While it is true that the two He 11 lines do agree within formal errors,
the UV He II and the C IV do not overlap, which is not predicted by simulations
(Bottorff et al., 2002). In fact, Bottorff et al. argue that if this discrepancy is
real, it is a significant failure in a general picture that otherwise fits together all of
the reverberation results. Under any situation where the A1640 and A4686 lines are
formed by cascades following recombination, as is thought to be the case, the two lines
must be formed in the same volume of gas and therefore should vary together with
the same reverberation time scales. Bottorff et al. further Show that the C IV A1549

should be produced under conditions similar enough to the region that favors He II

13

production and there should therefore be only a small difference in the reverberation
lag times of C IV and either He II.

While the He II A1640 and A4686 lines do formally overlap in the one object where
both line are measured in the same campaign, there are several other AGN where
only the He II A1640 and the C IV A1549 were measured. These measurements are
summarized in table 1.2. In each case, the lag ratio of C IV A1549 to He II A1640

differs from unity by a convincing margin.

Table 1.2: Other C IV A1549 / He II A1640 Lag Ratios - This table, taken from Bottorff
et al. (2002) summarizes the (C IV A1549) / (He II A1640) lag ratio for several Objects, which
Bottorff et al. considered to have reliable lag measurements of both lines. It is clearly Shown

that this ratio is greater than 1 in all of the Objects.

 

 

 

Object (1549) / (1640) Lag Ratio References

NGC 5548 3.3 Bottorff et al. (2002)

NGC 3783 5.0 Reichert et al. (1994)

Fairall 9 3.4 Rodriguez-Pascual et a1. (1997)
NGC 7469 2.4 Wanders et al. (1997)

3C 390.3 3.8 O’Brien et al. (1998)

Average 3.6

 

The conclusions of Bottorff et al. (2002) concerning the existing data were that,
“the best estimate of the lag times is that the A1640 feature varies 3 times more
rapidly than A4686” and that “the He II A1640 lag times are measured to be several
times Shorter than those of C IV A1549”. The first of these points would be extremely
surprising, while the difference between the He II and C IV lag times is not predicted

by the simplest models of the BELR.

14

One possibility, tested in this work, is that the He II lag measurements are simply
in error. The He II emission lines are quite weak compared to most of the well-
studied AGN emission lines. There is also considerable contamination by surrounding
emission lines. In the case of He II A4686, it is contaminated by the blue wing of H6
(and possibly to a some extent the red wing of H7), He I A4471 and a Fe II multiplet.
The UV He II A1640 line is Similarly contaminated by C IV A1549 and O III A1663
as well as a Fe II multiplet. Previous measurements of these lines, such as those
described above, have not fully accounted for these blending problems. Emission
lines were defined either by a simple bin or approximated using a blend of Gaussian
profiles. Neither of these methods fully account for contamination by other emission
lines that may be varying at slightly different rates.

In this work, we present a new re—analysis of archival data of N GC 5548, a nearby,
well Observed, type 1 Seyfert galaxy. Careful attention has been paid to separating
contamination from the He II emission so as to present the most careful measurement
of the reverberation lags to date. This has also been done in a more automated fashion
than in previous studies in order to remove some of the the human subjectivity that
is always present in data analysis. The software tools that were developed were
designed to be compatible with previously existing software that is used by several

collaborators.

15

 

CHAPTER 2:
DATA SET DESCRIPTION

This chapter will outline the basic details of the data used for this study. It is
important to understand that gathering the amount of data needed for a study like
this is a huge undertaking. For example, several years of observations are needed to
get a really good baseline covering multiple reverberation events, and these should
have a time sampling of at least one observation every few nights. In this case,
archival data from a previous effort were used. This archival data set, despite some
of its shortcomings, is the most complete set Of observations in terms of both spectral

and temporal coverage Of any AGN that has been taken.

2.1 BACKGROUND ON AGN WATCH AND DATA SET

FOR NGC 5548

The archival data set used here was taken as part of a project instigated by the
International AGN Watch, a consortium of scientists who were interested in studying
several AGN in detail, with careful consideration given to sufficient time resolution of
Observations. To this end, one of the objects chosen for study was NGC 5548, a nearby
Seyfert 1 galaxy. NGC 5548 is of interest because it is close (2 = 0.017175 2 71 Mpc)
and although it is a fairly typical type 1 Seyfert galaxy, it is also highly variable.
This allows for extensive study using reverberation mapping techniques. This work

spanned more than a decade and produced a series of papers entitled “Steps Toward

16

Determination Of the Size and Structure of the Broad-Line Region in Active Galactic
Nuclei I-XVI”. Clavel et al. (1991), Peterson et al. (1991), Peterson et a1. (1992), and
Dietrich et al. (1993) are of particular interest for the study described here.

Because of the need to compare lines in the optical as well as the ultraviolet,
data from both ground and space based Observations are necessary. The Earth’s
own atmosphere blocks far too much UV radiation to allow for Observations in this
wavelength regime to be taken from the ground. The UV data used here were taken
using the International Ultraviolet Explorer (IUE), with some additional Observations

taken with the Hubble Space Telescope (HST).

2.2 ULTRA-VIOLET DATA FROM IUE AND HST

The International Ultraviolet Explorer (IUE) satellite was launched in January of
1978. It carried an 18-inch telescope with a UV Spectrograph. Although it initially
had an expected service life of three years, it remained in operation until it was
decommissioned on September 30, 1996. During 1988-1989, the AGN Watch used it
for regular observations of NGC 5548 for roughly eight months (Clavel et al., 1991,
and references therein.) During this time, a coordinated effort was made to obtain
ground-based optical observations of NGC 5548 to complement the UV data from
IUE.

This IUE data set is the longest regularly sampled set of observations of NGC
5548 in the UV. Although the resolution is somewhat low at roughly 2 A per pixel, it
is difficult to ignore this large data set. The observations span Julian Dates 2447510
- 2447745 (14 December 1988 - 7 August 1989) and were taken quite regularly about
four days apart, with a total of 60 different days with Observations. On any given
day, one LWP (1900-3300 A) and at least one SWP (1170-1970 A) spectrum were
taken. Observations were taken in low resolution mode (1000 km 8’1 F WHM) with

the large aperture (10” x 20”.) In the analysis described here, the SWP and LVV P

17

Spectra from any given day were combined together to create a single Spectrum for
each date, with multiple SW P Spectra averaged together when more than one was
taken on the same day.

One drawback, in both the IUE and optical data sets, is the sampling rate. Ideally,
observations would be taken on a time scale shorter than the shortest reverberation lag
that is being studied in order to ensure sufficient temporal coverage of the emission
line’s reaction to the changes in the continuum. In the case of IUE, spectra were
taken quite regularly at about four day intervals. The primary lines of interest for
the original AGN Watch study have lag times on the order of tens Of days and would
be adequately sampled by measurements every four days. Due to the techniques used
for the reverberation analysis, this data can still be used for He II, and aliasing due to
the regular sampling also should not be an issue (see section 3.5 for further discussion

Of this point.)

2.2.1 NON—LINEARITY OF IUE AT Low FLUX LEVELS

The IUE data have a variety of known problems. Because of the age and nature Of
the instrument, several different corrections need to be made to the raw data before
they are useful for scientific measurements. These corrections can be as complex as
taking into account the angle of the instrument relative to the magnetic field of the
Earth. These corrections are well known and have been applied to the data Obtained
from the AGN Watch.

Koratkar et al. (1997) made a detailed comparison Of near simultaneous spectra
of several AGN taken with both IUE and the HST F OS. They found that there were
three objects that had observations taken with both instruments no more than 24
hours apart. These objects were Mrk 509, NGC 3783, and NGC 5548. While detailed
comparisons of the two instruments had previously been done, such as Bohlin et al.

(1990), they were typically done with bright spectrophotometric standard stars. It

18

 

 

 

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u. 10- _
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1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200
Wavelength (Angstroms)

Figure 2.1 Full Typical UV Spectrum - While the emission lines of interest all lie on
the left half of this Spectrum, the extended coverage allows a more accurate fit of the
ionizing continuum.
was thought that since the Spectral energy distribution of AGN is both significantly
different in shape and much fainter than that of standard stars, a direct comparison
of actual AGN might be more illustrative Of the differences between IUE and HST.
Koratkar et al. found that while the IUE and HST measurements of strong emission
lines agreed to within 15%, the results for weaker lines disagreed by a much greater
amount, reaching a factor of six for the faintest lines.

Koratkar et al. concluded that IUE did have a nonlinear response at low flux levels,
but they were unable to characterize it well enough to accurately evaluate its effect on
their data set. Koratkar et al. analyzed the reduced, flux-calibrated Spectra, in which

the total counts in each pixel had been divided by the exposure time and multiplied

19

by a detector response function. However the actual non-linearities in IUE’S SIT-
Vidicon detectors are expected to depend only on the charge on the photocathode,
which is proportional to the counts recorded after conversion in the ADC. We therefore
repeated their analysis in terms Of raw detector counts to see if a better non—linearity
correction function could be derived.

The data for this comparison came from near simultaneous observations of NGC
5548 using both IUE and HST on 5-6 July 1992, Observations that were also used by
Koratkar et al. in their 1997 paper. The IUE observation (LWP23450) was retrieved
from the archive in both the raw format and as a NEWSIPS (de La Pena et al., 1994)
extracted final spectrum. IRAF was used to extract a spectrum from the raw file
and parameters were adjusted until the extracted spectrum matched the NEWSIPS
spectrum as well as possible as a way Of finding the number Of raw counts that
went into each pixel in the fully-reduced N EWSIPS extracted spectrum. This was,
unfortunately, a very subjective process, but Should be sufficient to decide if further
investigation would be fruitful. In the end, we simply wish to determine if the ratio
of the flux from IUE to the flux from HST is a simple function of raw detector counts.

The HST data have 0.4 A per pixel resolution, much higher than those of IUE.
To better facilitate a comparison, a boxcar smoothing was applied to the HST data
until a resolution similar to that of the IUE data was achieved. A scale factor was
applied so that the HST and IUE data had similar flux levels for the Mg II emission
around 2850A before a ratio of the IUE flux to the HST/FOS flux was computed for
each separate pixel in the IUE spectrum. This ratio was then plotted as a function
Of the raw count numbers from the raw IUE spectra (see figure 2.2). This did show a
good deal of discrepancy at low counts (less than 100 raw counts). At very low count
levels, this ratio varied drastically. There was no apparent pattern to the fluctuations,
and as such there was no straightforward way to remove this effect. While the IUE

detector does have some problems at low count levels, no systematic non—linearities

20

 

 

 

 

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Figure 2.2 Ratio of IUE to HST flux levels as a function of IUE detector counts for
near simultaneous observations of NGC5548 - It is clear that there is an issue with
nonlinearity at low count levels, but it is unclear how to accurately characterize this
effect in order to correct for it.

were measurable above the noise level. Fortunately, Since even the relatively faint
emission lines such as He II 1640A are floating atop the continuum, these problems
with extremely low raw counts should not be significant in this present study.

The IUE data are too important to ignore, but they must be used with care due
to both the low resolution and the known linearity issues. The HST data have much
higher resolution and are of better quality. Unfortunately, while sampled daily, there
is only about one month of data. This is far too short a time period to do significant

reverberation mapping.

21

 

 

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22

2.3 OPTICAL DATA

The optical data taken for the AGN Watch to complement the UV data were obtained
at a variety of sites scattered around the globe. Telescopes used in the AGN Watch
study ranged in size from 1.8m to 6m and a variety of spectrographs were used. A
complete listing of all observatories used in the AGN Watch study can be found in
the notes for table 1 in Peterson et al. (1991). Because of the range of resolution
and quality, only a subset of these observations were chosen for analysis in this work.
This subset is listed in table 2.2, and the actual observations used are listed in table
2.3. Both the signal to noise and the spectral coverage varied substantially from site
to site. Even within one site’s data, spectral coverage could be different from one set
of observations to the next. Because He II was not the line of primary interest in the
original project, the optical observations are not entirely ideal for its measurement.
Even so, there are some observations with both sufficient signal strength and spectral
coverage to make an attempt at a He II measurement. After carefully comparing the
merits of the different data sets, we chose to use only the subset of observations that
were used in Dietrich et al. (1993), paper IV of the larger AGN Watch study.

The file names listed in table 2.3 include a letter designating the observatory site
code given in table 2.2. In some cases, more than one observation was taken on a
given night at a given site. In this case, not only will there be a letter suffix to denote
site, but an alphabetical letter is added to uniquely identify it. If more than one
observation was taken from a given site and they were all usable for this study, the
multiple observations were averaged together before fitting and a suffix of “x” was
added. In the cases where more than one observation was taken on a given night from
multiple sites, the spectra were fit individually and the resultant flux measurements

were averaged together before the cross correlation function was calculated.

23

 

 

 

 

 

 

 

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a
(D
9
3 4 - q
13
X
E 3t ‘
2 - U .
1 l L l l l
4000 4500 5000 5500 6000 6500

Wavelength (Angstroms)

Figure 2.3 Full Typical Optical Spectrum - This optical spectrum was taken from site
H, which has fairly good signal to noise and spectral coverage. Not all of the optical
observations are of this quality.

Table 2.2: Optical Data Site list - This lists the site code as well as the correction scale

factor for the optical observations found in table 2.3 as derived in Dietrich et a1. (1993)

 

 

 

Data Source Site Code P.A. Aperture Geometry Scale Factor

Ohio State CCD A 90° 5.0” x 7.6”, 1.0” x 7.6” 0.953 :l: 0.020

INT 2.5m C 0, 72.1, 75.4 1.5 x 6.0 0.930 i 0.000

Hale 5m D 61, 66.9 1.0 X 40,10 x 7.0 0.918 :l: 0.000
4.0 x 8.0

Ohio State IDS G . . . 0, 7.0 0.953 i 0.020

3m Shane H 59,... ,130 2.1 x 7.9 0.903 t 0.064

 

Steward I 60, 90, 130 4.5 x 27.2 0.924 :1: 0.053

24

Table 2.2: Optical Data Site List (continued)

 

 

 

Data Source Site Code P.A. Aperture Geometry Scale Factor

MDM K 0 1.7 x 3.0, 2.4 x 3.0, 0.949 :t 0.014
6.7 x 3.0

Calar Alto M 0,90 1 x 10.0 . . . 4 x 10.0 1.000 i 0.000

1m Nickel N 0 4.6 x 19.2 0.963 :1: 0.000

McDonald CCD J 0,90 8.0 x 9.0, 7.0 x 7.2 1.116 :1: 0.000

McDonald IDS Q 90 4.4 x 4.4 0.920 :t 0.000

 

2.3.1 CORRECTIONS To THE OPTICAL DATA

Unlike the IUE data which were taken from a very stable environment above the
Earth’s atmosphere, the optical spectra are affected by transmission changes and
smearing due to the atmosphere, and also by instrumental flexure as the telescope
tracks the object. Some differences in the instruments used for the optical observa-
tions, such as spectrograph slit width, also must be taken into account. The UV data
set does not need this sort of correction because the UV observations were all taken
with a single instrument.

In order to accurately compare the optical data, they first needed to be rescaled
and wavelength corrected. Since observing conditions may have changed from one
observation to the next, the strong [O III] line at A5007 was used both to scale the
flux and to fix any minor wavelength calibration issues that might exist. Because
[O III] is formed in the narrow line region, it should remain insensitive to the short
time scale variations that are powering the BELR variations and should therefore
have the same flux in all observations. This rescaling was accomplished by manually

measuring the flux and the central peak using IRAF. All observations were then sealed

25

such that their slit width corrected flux (see discussion below) for [O III] A5007 was
the canonical value of 5.53 X 10‘13 erg/s/cm2. This value is taken from Dietrich et a1.

(1993)

26

 

 

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27

There are a variety of challenges associated with using the ground based optical
data. Due to variations in observing conditions, the absolute flux level from one
observation to the next must be corrected. A strong narrow line such as [O III] A5007
can be used as a reference standard to scale the data. Since the narrow emission
line region is both large in size and at a large distance from the central source,
it is relatively insensitive to continuum variations on short time scales (Peterson,
1993). We can therefore assume that the flux in [O III] A5007 remains constant
over the time it was observed. Furthermore, we can use this line to correct for any
errors in the wavelength calibration since its peak wavelength should also not change.
Unfortunately, the NELR that generates [O III] narrow lines is of a large enough
angular size that the amount of flux recorded is influenced by the slit width of the
spectrograph used. This means that in order to make any meaningful comparison
between the various ground based sites, a correction for slit width must be made
to the narrow lines. Dietrich et al. (1993) went to great lengths to determine these
correction factors for slit width, and we use their corrections here (as listed in the
last column of table 2.2) before scaling the observed spectra to have the same flux in
[O III].

Another important limitation of the optical data is the same as that of the IUE
data, poor spectral resolution. Even the best of the ground based optical data only
have a resolution of about 2 A per pixel. Some of the lower resolution data from the

AGN watch archive were not suitable for accurately measuring the He II emission.

2.3.2 OBSERVED vs. REST FRAME

While N GC 5548 is relatively nearby, it is still far enough away that cosmological
redshift needs to be taken into account. It lies at a redshift of z = 0.017175 (de
Vaucouleurs et al., 1991) which needs to be corrected for in order to put the emission

into a rest frame. To accomplish this, the IRAF task “dopcor” was utilized.

28

 

CHAPTER 3:
DATA FITTING AND MEASUREMENT

 

Previous reverberation measurements (e.g. Clavel et al., 1991; Dietrich et al., 1993,
and many others) directly Show that the emission lines from different ions respond
to continuum variations on different timescales. This is interpreted to mean that
the BELR covers a wide range of distances from the continuum source, and lines
coming from different ionization states are formed at different radial distances. Since
the He II lines are spectroscopically observed in blended features that also include
emission lines from ions of very different ionization levels (e.g. Fe+, H+, C+3, and
0+2), it is crucial to be able to accurately measure the flux in each of the separate
components in the blend in order to accurately measure the He II reverberation time
scale. Some previous studies simply defined continuum-subtracted wavelength ranges,
or bins, for each emission line. While this method is a decent approximation, it does
not accurately measure contamination from adjacent emission lines. In order to more
accurately fit these highly blended varying emission lines, new software tools as well

as reasonable approximations of the individual emission line profiles were needed.

3.1 AUTOMATED FITTING ROUTINE

The central difficulty to be overcome is the de-blending of spectral lines in the data.
The emission spectrum of an AGN is a very complicated structure since there can
be multiple overlapping emission lines that vary with slightly different lagtimes. To

accurately de-blend these components, one must fit each component individually at

29

every time slice. This can be done by hand, but it would be both time consuming
and very subjective; a fit by hand does not give a true “best fit” to the observations
but instead is simply what the observer feels looks best. An automated fit using some
mathematical technique would be efficient, consistent, and give at least some measure
of the quality of the fit.

To create the automated fitting routine, it was important to build upon existing
software tools used by my advisor and his collaborators. This would both make the
automated fitting routine useful for purposes other than this study and allow easy
use of previous measurements of N GC 5548 as a starting point. This should help to
explain the sometimes cryptic nature of the input parameters as well as the choice to

use FORTRAN.

 

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2.5

 

 

 

2

  

 

 

 

 

Figure 3.1 Typical Optical Spectrum of NGC 5548 - This spectrum, from the file
n57621h, is a detail region of a typical N GO 5548 optical spectrum. Several of the
important emission lines are labeled.

30

Figure 3.1 shows a portion of a typical optical spectrum for N GC 5548. While the
primary feature of interest for this study is the A4686 He II line, it is surrounded by
contamination from other lines in the blend. The wing of the Balmer H5 line as well
as a Fe II multiplet and the He 11 line from the NELR all contribute to the measured
flux around A4686. There is also contamination from the He I A4471 as discussed by
Vestergaard & Peterson (2005). To properly measure the flux from the He II A4686
line, all of the other contaminating lines must be fitted as well. In addition, the

underlying continuum component, which is also variable, was included in the fit.

 

 

 

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g 1486 l
:5: 1O _ He“ _,
n- 1640
5 ’ a
0 l l l l l l l

 

1400 1 450 1 500 1550 1600 1 650 1 700 1750 1800
Wavelength (Angstroms)

Figure 3.2 Typical UV Spectrum of N GO 5548 - This spectrum, from the file r57530uv,
is a detail region of a typical NGC 5548 UV spectrum. Several of the important
emission lines are labeled.

At its core, the automated fitting routine (hereafter AFR) uses a X2 minimization

technique to fine tune an initial guess at the fit. The goodness-of-fit statistic X2 is

31

basically defined as:

x2 = Zn: (fig—liy (3.1)

2:1

where A and B are the data spectrum and the blend built from profiles, respectively.
The a is some measure of the noise in the data spectrum. In the UV, since all of
the spectra were taken with the same instrument, this value was simply estimated
by looking at a relatively flat, uncontaminated area, and a value of 0.5 X 10‘14 w

chosen. Because the optical data come from different instruments, this value was
estimated in the program by applying a boxcar smoothing to the data in the fitting
windows and seeing how far the observed values deviated from this smoothed version.
This value would stay the same for any individual spectrum that was fit, so the actual

value of a is not all that important.

3.2 BUILDING THE BLEND

The continuum radiation was modeled as a simple power law:

A ’7
t' = A —— .2
Con lnuum ( 5600) (3 )

with both A and ’y allowed to vary within reasonable ranges. While the exact form
of the continuum emission from the central engine is not known, it is thought to
be a superposition of blackbody spectra of nearly continuously varying temperatures
coming from an accretion disk undergoing viscous heating. A power law does not
precisely describe this situation mathematically, but it is a reasonable approximation
for the relatively small wavelength ranges at which we are looking and is a good deal
more accurate than a simple straight line approximation which is often used.

To make the fit as realistic as possible, template profiles of the emission lines
are used whenever practical. In some previous studies (such as Dietrich et al., 1993),

emission lines, including both those arising from the NELR and BELR, were measured

32

in a simpler way. If the emission line was deemed to be weak, a wavelength range
(or bin) was defined for that line, and all flux within that range that was above the
continuum level (which was itself defined as a straight—line under the bin) was assumed
to be from the emission line in question. Contamination from adjacent lines was either
ignored or simply estimated. If the line was deemed to be strong, it was sometimes
modeled using a superposition of several Gaussians. If the shape was complicated,
more Gaussians were added until a shape that more closely approximated the true
shape of the actual emission line was created. Neither of these techniques truly
described the physical situation, and a new approach was needed. To this end, it was
decided to use observed spectra from actual AGN to create template profiles that

more accurately reflected the shape of the real observed emission lines.

3.2.1 FE II TEMPLATE

First noted by Phillips (1977, 1978), the Fe II multiplet of Seyfert 1 galaxies are very
similar from object to object. The primary difference between any two given Seyfert
1 AGN is the amount of Doppler broadening. With this fact in mind, the Seyfert 1
galaxy I Zw 1 has long been of interest in order to generate a template profile for
the Fe II emission in AGN. I Zw 1 has quite narrow broad lines such as Fe II and
H13, some of the narrowest permitted lines observed in any Seyfert 1 galaxy. Phillips
demonstrated that if the Fe II profile was Doppler broadened to match the width of
H6, the I ZW 1 template fit other Seyfert 1 galaxies well. Véron-Cetty et al. (2004)
have created a revised and improved version of the I Zw 1 optical template (see figure
3.3.) Vestergaard & Wilkes (2001) created a similar template for the UV emission
from data of I Zw 1 taken with HST (see figure 3.4) Vestergaard & Peterson (2005)
used these templates successfully to study the Fe II emission in NGC 5548 using the
same AGN watch data set used in this study. Although their focus was not He II,

they did find that the use of these templates improved the measurement of other

33

 

 

3 I I I I I I I I
2.5 - '-
«2‘
‘i' 2
E
o
'1-
a:
a) 4 _
5 1.5
to
l
o
C
x 1 I
2
LL
0.5 .,
l l L l l l l

 

 

0
3500 4000 4500 5000 5500 5000 6500 7000 7500 8000
Wavelength (A)

Figure 3.3 Fe II Optical Template - based on a broadened version of the Véron-Cetty
et al. (2004) optical template.

emission lines in the regions contaminated by Fe II.

This present work is the obvious extension of that idea, using all of the template
profiles at our disposal to disentangle these multiple overlapping lines. M. Vestergaard
kindly provided us with a set of Fe II template profiles with a variety of different
Doppler broadenings. We used the same templates that were used by Vestergaard
& Peterson (2005) in their study of NGC 5548 using a Doppler broadening of 6250
km/ sec, similar to the broadening used in their paper and which seemed to give a
good fit to the N GO 5548 data. The templates shown in figures 3.3 and 3.4 show this

particular broadening.

34

 

Flux (10’15 erg s‘1 cm’2 A)
0)

 

 

 

2 - _
1 _ -1
O " 1
_1 1 1 1 l
1000 1500 2000 2500 3000 3500
Wavelength (A)

Figure 3.4 Fe II UV Template - based on a broadened version of the Vestergaard &
Wilkes (2001) UV template.

3.2.2 OTHER TEMPLATES

The creation of the remainder of the template profiles was a rather subjective proce-
dure. As a starting point, a RMS (root mean squared) spectrum was created from
scaled and shifted data spectra (see figures 3.5 and 3.6.) In this way, we are left with
primarily the highly variable BELR emission with the nearly constant NELR emission
removed. From there, some smoothing was typically applied, and any sharp upturns
remaining on the edges were clipped to try to leave a smoothly changing template
profile. As this was a fairly individualized process, tabular copies of the templates
used are included in appendix F of this work.

The strong Ha line, seen on the right side of figure 3.5, was used to create a

template for the Hydrogen Balmer lines (see figure 3.7.) The Balmer lines should all

35

 

5 - Hell . . .

Hel

Flux (1 e-15 ergs/cm/s)

 

 

1 l l l l l

4500 5000 5500 6000 6500 7000
Wavelength (Angstroms)

 

Figure 3.5 Optical RMS Spectrum - Most of the non-variable N ELR lines have been
eliminated, leaving only the highly variable BELR emission. This can be used to
construct template profiles for the BELR emission that give a better approximation
of the true shape of the emission lines. The regions used for the creation of the Ha,
He I, and He II BELR templates are marked.

have similar profile shapes because they are all emitted by the same gas. This profile
can therefore be rescaled to fit H5 or H7 as needed.

The He II A4686 emission from the RMS spectrum was used to generate a BELR
He II template (see figure 3.8) for fitting both the A4686 and the A1640 broad line
components. This is important to note, as we have used the exact same template
profile to fit both the UV and the optical He II emission lines. Because we expect
the emission to originate from the same region within the AGN, they should have the
same shape.

The relatively strong He I line at A5876 was used to create a He I template

(see figure 3.9) for fitting the He I line at A4471, a line which contaminates the

36

 

 

 

 

 

30 I I I I I I I

25— «
g 20- ~
Q
U)
9
315— -
:53
310- 4
LL

5&- -1

MM cw

 

0
1 1 00 1 200 1 300 1400 1 500 1 600 1 700 1 800 1 900
Wavelength (Angstroms)

Figure 3.6 UV RMS Spectrum - This is a detail of the region of interest of the UV
rms Spectrum. Most of the non-variable N ELR lines have been eliminated, leaving
only the highly variable BELR emission. Like the optical rms spectrum, this can be
used to construct template profiles for the BELR emission. The C IV BELR profile
was created from the strong emission labeled in this spectrum.
measurement of the He II A4686 emission line.

Templates for O III] A1663 and the narrow line component of the He 11 A1640
blend were created in a similar manner, but an average rather than an RMS spectrum
was used as the starting point. In an average spectrum, the NELR emission is not

removed as in a RMS spectrum. These lines could also have been described with a

simple Gaussian or blend of Gaussians of appropriate widths, if necessary.

37

 

 

 

 

 

5 l I ‘r l
4.5 - 4
4 — 4
.2
6'. 3.5 ~ ~
6
.— 3 - -
'(D
a: _ a
a.) 2.5
:2
'o 2 - 1
g 1.5 - -
u.
1 r- —
0.5 — _
o l 1 l l l 1 l
6200 6300 6400 6500 6600 6700 6800 6900 7000

Wavelength (A)

Figure 3.7 Ha BELR Profile

3.2.3 FITTING PARAMETERS

Each profile will be Shifted in wavelength (actually in velocity) and scaled by a mul-
tiplicative factor as part of the automated fitting procedure. So for each template
profile that is to be used, we have to specify an original wavelength (Aold), a Shifted
wavelength (Anew), and a multiplicative constant. These parameters are given in the
input file, called “blendsin”. While three parameters are input, only the last two
are allowed to vary. In the input files for the fitter, the multiplicative constant is
actually expressed as a fraction of the total flux in the data spectrum. For example,
if a particular emission line carries 10% of the total flux, the scaling factor would be
0.1. This method is used in order to mirror more accurately the input files used in
the program Blends. (Blends, and several of the subroutines called by the automated

fitter were developed by Dr. Jack Baldwin. They are used extensively by both him

38

 

 

 

 

4 I I I I *I I I I
3.5- _
A 3~ _
.<
“1' 25A -
E a
0
'0, 2— .
9
Q)
59 1.5- -
'52
2: 1~ -
3
i:
0.5- .
0,. -
_05 I 1 J I I I I I

.4450 4500 4550 4600 4650 4700 4750 4800 4850 4900
Wavelength (A)

Figure 3.8 He II BELR Profile

and his collaborators, the author of this work included.) The only significant change
of which to be aware is that Blends assumes that the continuum shape has been
removed and that there is only an additive constant still included. This constant
continuum level is one part of the input file for Blends but is ignored by the AFR
which instead fits a power-law continuum described by equation 3.2. It still must
be included in the input file to preserve formatting. The long term aim here was to
produce a general-purpose automated fitting program for which the starting values
could be determined by using the existing Blends program to fit by hand, and then

the Blends output file would be used as the input file for the automated fitter.

39

 

 

 

 

4.5 I I I I I I I
4 _ .,
115 - 4
.2
<1 3 “ ‘
E
v- 2.5 _ i
'0)
a - fl
5 2
:2
'9 1.5 — -
E 1 ~ ‘
E
0.5 r _
O ._ ..
_05 I I I I I I I

' 5700 5750 5800 5850 5900 5950 6000 6050 6100
Wavelength (A)

Figure 3.9 He I BELR Profile

3.2.4 FITTING WINDOWS

While the spectra we are using may cover several thousand angstroms, we are typically
only interested in a small region around an interesting emission feature. In addition,
we may need to fit in areas away from the line of interest in order to constrain the
Shape of the continuum. There also may be regions of the spectrum where we do
not have a profile for the emission that is present. To accommodate these facts
better, the AFR does not calculate contributions to X2 everywhere in the spectrum
but rather only in certain regions of interest specified by an input file to define fitting
windows. These windows are defined by a pair of wavelengths, a starting and an
ending wavelength, with one pair per line in an input file called “window.txt”.

In choosing what regions to fit, it is important to fit only in areas where we have

profiles or where there is little or no emission (just continuum.) During testing, it was

40

 

 

 

 

25 I I I I I
20- .
4?
‘1‘
E
P 15— -
IUD
9
a)
to
To 10~ -
3‘?
2
LL
5- -
O 1 I I I l
1480 1500 1520 1540 1560 1580 1600

Wavelength (A)

Figure 3.10 C IV BELR Profile

found that the NELR lines can cause difficulties with the automated fitter in some
circumstances. The width of the NELR lines is directly tied to the width of the Slit
used on the spectrographic detector. Because a number of different instruments with
different Slit widths were used for the optical observations, a single template narrow
line cannot be used for all of the optical spectra. Since these lines are formed far away
from the continuum source, they are essentially constant in flux over the timescales we
are investigating. Therefore, fitting them in each individual spectrum is unnecessary,
and when possible only the wings corresponding to the broad line emission are fit. In
this way we are fitting only the broad edges of the emission line, which is, after all,
the part in which we are interested. This is fairly easily accomplished with the optical
spectra, where the NELR lines create well defined spikes, typically near the center of

the BELR line. The UV spectra, taken with IUE, don’t suffer from the changes in

41

NELR line width that affect the optical data. In this case, the He II narrow line is
included in the fit, but kept constant. This is possible because the UV observations
were all taken with the same slit width on the same instrument.

The actual values used for the fitting windows are listed in table 3.1. In addition to
these values, the file “window.txt” requires a number at the end of each line specifying
the amount of smoothing to apply when estimating the amount of noise in the fitting
region for the purposes of calculating X2- This number must be odd, and a value of
7 was chosen for the optical data. This value is ignored in the actual fit of the UV
data (the amount of noise is hardcoded in) but a value must still be present in the

input file.

Table 3.1: Fitting Windows - This table summarizes the windows in which X2 is actually
calculated. It is important to fit only in regions where we have template profiles or where
very little emission is contaminating the continuum. In the case of the optical data, we

have left gaps where the N ELR emission occurs.

 

 

Optical (A) UV (A)

 

4225 - 4275 1425 - 1730
4420 - 4676 1798 - 1836
4703 - 4838 2400 - 2650
5100 - 5170
5650 - 5700

 

3.3 MINUIT AND THE X2 MINIMIZATION

Once all of the physical corrections have been made to the observations and template

profiles as well as fitting windows have been chosen, the automated fitter takes over.

42

At its heart is a function minimization package called Minuit. Minuit was developed
at CERN, the European Organization for Nuclear Research as a generalized multi-
parameter function minimizer for use with FORTRAN programs. It is important to
understand that Minuit is only a function minimizer; it does not know any of the
actual details of the function it is minimizing. It is up to the end user to come up
with a useful quantity to calculate as well as some way of bringing all of the pieces
together. To that end, a fitter for the optical data called “contin.f” (see appendix
A) and a fitter for the UV data called “uvcontin.f” (see appendix C) were developed.
These each call the Minuit package as a subroutine. As mentioned in the previous
section, we are able to fit the NELR emission in the UV Spectra. Because of this,
there are some additional constraints that we can put on some of the components of
the blend. It is for this reason that there are two different versions of the fitting code.
A more elegant generalized version of this fitter should be able to handle both the
optical and the UV, and will hopefully be the subject of a future project.

When the fitter is run, it takes a list of input spectra from the file “sorted2.in”.
The spectra listed in this file must be in IRAF “.imh” format because of some of
the subroutines that are used to read in the data. The fitter also takes the list of
input template spectra and the windows it should use for calculating X2 (“blends.in”
and “window.txt”, discussed in the two previous sections.) If no fitting windows are
Specified, the fitter assumes that it should attempt to fit the entire spectrum. The
initial guesses at the parameter values for each of the template profiles, as well as any
constraints on those parameters, are then put into arrays that are passed to Minuit.
Minuit in turn passes these values to a user-supplied subroutine where the function
to be minimized is calculated. In the case of the optical data this subroutine is called
“cfunk” (see appendix B) and in the case of the UV data this subroutine is called
“uvfunk” (see appendix D).

The subroutine then takes the parameters it is given and creates the blended

43

 

2.2 I l 17 l I I I I

 

 

 

 

2 ~ 4
0'1" 1.8 - —
E
0
'w 16 - -
9
m
,‘I
é L4 - I u
E d u
E 12 .— ,1 W -" —l
l“ H 3.... m .
_ " WV“
1 l | l | l
Continuum He l Fe II He II HB
0'8 1 I l I I I I I I

 

4300 4400 4500 4600 4700 4800 4900 5000 5100 5200
Wavelength (A)

Figure 3.11 Optical Fit Overlay - This figure shows the relative postions of the various
components in the optical blend.

spectrum. This is done by first shifting the emission line template spectrum in velocity
space using a subroutine adapted from Blends. This “align” routine (as well as several
other useful subroutines) can be found in the listing for “functionsf” (see appendix
E) The routine from Blends was used because it has been well debugged and properly
handles the complexities of flux correction when moving a spectrum in velocity space.
The template is then scaled by some factor. This is done for each of the templates
in the “blends.in” list. A power-law continuum as described by equation 3.2 is then
added together with each of the shifted and scaled templates to create the final
blended spectrum. (Examples can be seen in figures 3.11 and 3.12 for the optical
and UV spectra respectively. Compiled lists of templates used can be found in tables

3.2 and 3.3 at the end of this chapter.) The subroutine then compares the blended

44

Spectrum’s flux value in each wavelength bin with that of the input spectrum that is
being fit (from “sorted2.in”) to calculate X2. This X2 value is then handed back to
Minuit. Minuit makes adjustments to the parameters and then calls the subroutine
again. This process is repeated until the value being returned is no longer changing by
more than some threshold value or until a set number of iterations has been reached
(each of these parameters are set by the user in the main fitting program code.) The
values used to create the blend are then used to calculate the flux in the template
profiles as well as in the power-law continuum. These are then output into a file
called, for historical reasons, “slope.txt”. This entire process is then repeated with

the next input spectrum from “sorted2.in.”

 

 

 

 

 

 

 

7 I I I I

6.5 - -
A 6 - _
‘1'
E
,° 5.5 - _
I”) ‘ ‘
9 5 1
OJ ' _

II. l '

Sb llkl“ l J l
5 5. . , my -
x l 41.. m - I
ll:- Continuum ‘A "h! L.

4 - ClV NELR Fell ‘w-ll —

om]
Hell NELR
35 _ C IV BELR He H BELR NELR
Olll]BELR
3 I I I I
1450 1500 1550 1600 1650 1700

Wavelength (A)

Figure 3.12 UV Fit Overlay — This figure shows the relative positions of the various
components in the UV blend.

Unfortunately, due to the nuances of data output when using FORTRAN, the

45

output file “slope.txt” is in a less than optimal state. Some simple manipulation
with, for instance, a Perl script can put this into a more user friendly format that can
be used for further analysis. In the end, we need separate light curve files that contain
the Julian date and flux in each emission line, as well as one for the continuum. The
Julian dates for each observation was deduced using a combination of IRAF header
information, file naming convention, and records from previous papers, in particular
Dietrich et al. (1993). These dates are listed in tables 2.1 and 2.3.

Some constraints were put on Minuit to keep results within physically plausible
ranges. The wavelength Anew was only allowed to shift by :l:7A, and the initial guess
for the flux in a line was only allowed to vary within a range of 0.1x and fix of the
original value. This was done because it was found that weak lines in a noisy spectrum
could easily be driven to zero or pushed well away from their intended area of fitting.
In addition, the NELR lines in the UV fit were held to constant values. These values
were chosen by first allowing them to change flux during a fit and seeing what the
median value was. This value was tweaked as necessary to allow for a good fit and
then hardcoded into the “uvcontin.f” and “uvfunkf” files. Because of the higher
quality overall of the calibration of the UV data, certain lines were also tied together
in Anew to prevent Minuit from driving them outside of physical ranges. The lack of
resolution and quality of the calibration prevented this in the optical data, so only

the wavelength range was constrained.

3.4 ERROR ESTIMATION

Minuit determines statistical errors during its fitting such that a change in a parameter
that results in an increase of 1 in the reduced X2 is treated as a 10 change in the
parameter. We have made several design choices that make this value given by Minuit
a bit suspect. In order both to make the final emission lines physically reasonable

and to ensure that the fitter does not accidentally set a weak line to zero to generate

46

a fit that looks better, we had to constrain the range of values that most parameters
could have. This is something that is not recommended by the author of the Minuit
Reference Manual, as it can lead to strange results for the error bars. It was, however,
necessary to ensure that weak lines such as He II 4686 would not be lost when fitting
these low resolution, noisy spectra. The error in any given parameter is also influenced
by how well the fitter has done at fitting the adjacent blended lines. These factors
seem to help explain the perplexing error values that we found from Minuit. The
error bars on the parameters, when used to recalculate the integrated flux in any
given line can be orders of magnitude smaller or larger than the calculated flux. This
renders these error bars essentially useless for the purposes of further calculation.
Due to these issues, the error in the flux needs to be estimated. AS will be
shown in the discussion of the cross correlation function, the final reverberation lag
is insensitive to modest changes in the size of the error bars, so it is only important
that we arrive at a value that is reasonable physically when we take into account the
quality of the source data. Given these facts, we have chosen to take as an error 10%
of the median flux value for the line in question. This error is Similar to the value

estimated by Dietrich et al. (1993).

3.5 CROSS-CORRELATION LAGS

As was well illustrated by Kaspi (2007), Blandford & McKee (1982) first gave a
name to and laid down the mathematical foundation that governs the technique of
“reverberation mapping”. The response of an emission line to continuum variations

is described by

L(v,t) = /w(’v,t — T)C(T)d7' (3.3)

47

Here, C(T) is the continuum light curve and L(v, t) is the responding emission—line
light curve. The quantity 20(1), T) is defined as the transfer function; that is to say
the function that governs the response of the emission-line, where v is the velocity
field of the BELR that causes the shape and broadening of the BELR emission. This
definition assumes that the object is able to be studied in great detail, with very well
sampled light curves over a long period of time. In practice this is not typically the
case. When using low resolution spectra and poorly sampled light curves, the two-
dimensional transfer function, 211(0, 7') collapses to a one-dimensional transfer function,
1,0(7'). This is expressed as the Single parameter of the time lag between the continuum

light curve and the emission-line light curve.

FCCFU) = macaw-1: C(t)L(t + T) (3.4)
t

Here, N is the number of points in the sum, 7' is the lag, and ac and 0L are
the rms of the light curves of the continuum and the emission-line respectively. The
centroid of this CCF is the measure of the Size of the BELR, and is often denoted as
RBLR 01’ RBELR-

Using this formalism, we are able to calculate a characteristic radius at which an
emission-line is produced by creating a light curve for both the continuum and the
emission-line in question and calculating a cross-correlation function for them.

Dr. Brad Peterson and his collaborators have developed software to compute this
CCF in a standardized way. There are two basic techniques, discussed in detail in
Peterson (1993). In the first method, the light curves for the actual observations
are interpolated into a smoothly varying function. This function is then sampled
regularly to calculate the cross-correlation function. In the second method, called the
discrete correlation function (DCF) method, only real data points are used without
any interpolation. The DCF method has some further subtleties such as exclusion of

points that have a zero time difference, that is to say it will not attempt to correlate

48

 

ill 1 ll ill) i
:25 l i ll 1 ill
3 5jl ( (l lllHlll -

 

 

 

O L I I I I I I I I

7500 7530 7560 7590 7620 7650 7680 7710 7740 7770 7800
Julian Date (—2440000)

Figure 3.13 UV Continuum Light Curve — as measured at A1337, as per Dietrich et al.
(1993)

points taken from the same spectrum. This is done to eliminate artificial “lags” at
very short times due to correlated errors in the measurement or calibration of the
spectrum. Unfortunately, as noted by Peterson (1993), the DCF method does not
work well when used on poorly sampled data. Because the data used in this study
does not have a sampling rate that is much smaller than the expected reverberation
lag time, we used only the interpolated method.

The implementation of the interpolated method was kindly provided to us by B.
Peterson in the form of code called lager'rb'. This code allows for the comparison of two
light curves for the purposes of calculating a cross correlation centroid distribution
(CCCD) The interpolation method makes repeated attempts at the creation of a cross

correlation function. On each attempt lagerrb’ first performs a flux randomization of

49

 

Flux (1 e-13 ergs/cm/s)
(.0

 

 

__1 1 I 1 1 I I l I I

7500 7530 7560 7590 7620 7650 7680 7710 7740 7770 7800
Julian Date (-2440000)

 

Figure 3.14 Optical He II Light Curve

the input data curve. It allows each point to have a value within the error bars
provided with a Gaussian weighting before creating a smooth interpolation between
the points and taking a subsample for the purposes of calculating the cross correlation
function. If the CCF is above some target threshold, in this case a CCF factor of 0.4,
it is deemed a “good” CCF. For a CCF that is “good”, a centroid of the distribution
above some cutoff value is determined. In the case of this study, the threshold is set
at 0.8 of the maximum. An alternate method is to simply look at the peak value of
the CCF rather than the centroid of the CCF. The relative merits of the two methods
has long been debated, however, B. Peterson has a preference for the centroid method
(see the discussion in the appendix of Peterson et al., 2004). Therefore we constrain
our discussion here to the centroid method.

The process above is then repeated some large number of times, in this case

50

 

14 I I I I I I I I I

55- l

Flux (1 e—1 3 ergs/cm/s)
0')
l—+—1
t—-+—<l
I——-I—-l
l-—+—-l
r_+__{l~-—+-—'I
l——+—l
l——l——l

 

 

_2 I I I I J A I I I

7500 7530 7560 7590 7620 7650 7680 7710 7740 7770 7800
Julian Date (-2440000)

 

Figure 3.15 UV He II Light Curve

10,000 iterations. This leaves us with a distribution of cross correlation centroids.
During the above process, interpolation of just one of the light curves can be done
or both can be done simultaneously. In order to counteract any problems that may
occur by interpolating the light curves, the process is typically repeated twice; once
interpolating the driving light curve and once interpolating the responding emission
line light curve. The value of Tcent is defined to be the centroid of the CCCD. The
error in this value is a 1 0 value where 67% of the centroids fall within 1 a of the
value of Teent. The results of the two separate interpolation runs are then averaged
to give the final characteristic reverberation lag time.

When running lagerr6, it is important to ensure that the maximum shift that is
tested for is at least twice the expected reverberation lag, so as to avoid skewing the

centroid calculation if the CCF has broad wings. In the case of the He II lines, a

51

 

Flux (1 e—1 2 ergs/cm/s)
01
1—1—1
IP—I—H

 

 

2 I I L J L I I I I

7500 7530 7560 7590 7620 7650 7680 7710 7740 7770 7800
Julian Date (-2440000)

 

Figure 3.16 C IV Light Curve

maximum shift of twenty days was used. Thirty days was used for C IV and fifty
days was used for HB. In each case a resolution of one day was used because of the
relatively sparse sampling rate of the original data.

Peterson (2006) noted that as the continuum source in an AGN gets brighter, it
also gets harder. This is to say that the amplitude of variability is larger at Shorter
wavelengths. Therefore, the UV flux rather than the optical flux should be a better
measure of the ionizing flux from the central engine. With this detail in mind, all

reverberation analysis done in this work uses the UV continuum as the driving light

curve.

52

 

16 I I I I I I I I I

10-

Flux (1 e-13 ergs/cm/s)

 

 

 

 

4 I I I I I I I I I

7500 7530 7560 7590 7620 7650 7680 7710 7740 7770 7800
Julian Date (-2440000)

 

Figure 3.17 H6 Light Curve

53

Table 3.2: Optical Profile Summary - This table compiles a list of the various optical
template spectra as well as the spectra used to generate them. The Fe II multiplet is from

Véron-Cetty et al. (2004).

 

 

Profile Name Emission Line From Notes

 

smooth_4686.imh He 11 A4686 BELR Optical RMS

Fe2_Opt_22.imh Fe II Multiplet External Source
smooth_halpha.imh H6 BELR Optical RMS
smooth-5876.imh He I BELR Optical RMS

 

Table 3.3: UV Profile Summary - This table compiles a list of the various UV template
spectra as well as the spectra used to generate them. The Fe II multiplet is from Vestergaard
& Wilkes (2001). The 0 III] BELR and NELR were generated from an rms and an average

of several selected spectra that showed prominent O III] emission.

 

 

 

Profile Name Emission Line From Notes
smooth_4686.imh He II A1640 Optical RMS

Fe2_UV.new.imh Fe II Multiplet External Source

c4_blr_smooth.imh C IV A1549 BELR UV RMS A tied to He II BELR

c4-1549_obs2.imh C IV A1549 N ELR UV Average A tied to He II BELR, flux constant
03-1663.imh 0 III] A1663 NELR A tied to He II BELR, flux constant
narrow_he2.imh He II A1640 NELR UV Average A tied to He II BELR, flux constant
03_b1r.imh 0 III] A1663 BELR A tied to He II BELR

 

54

 

CHAPTER 4:
RESULTS

In the preceding chapter, we laid out a formalism for how to calculate a characteristic
reverberation lag time for each of the emission lines we are intersted in studying.
In this chapter, we present the results of the cross correlation centroid distribution
calculations. It is important, however, to note that this is Simply a characteristic
radius. For any given emission line, there will be a region of some size where the
conditions are favorable for emission by the ionized gas within the BELR. The Tcent
discussed in this chapter is simply a parameter used to characterize this region. It
can be thought of as the distance in light-days from the central engine to where the
line is emitted, but it is important to keep in mind that the emission comes from a

region around Tcent rather than coming only from a distance of Tcent-

4.1 CROSS CORRELATION CENTROID DISTRIBUTION

Figure 4.1 shows the cross correlation centroid distribution (CCCD) for the optical
He II emission line (A4686) and the UV He II emission line (A1640) In the case of
this and subsequent CCCD figures Shown in this chapter, the actual CCCD plotted
is one generated when both. the driving continuum light curve and the responding
emission light curve are interpolated. While the final value of Tcent was determined
by averaging the two separate CCCD plots, one interpolating the driving continuum
only and one interpolating the responding emission line only, the general Shape and

location of the peak are similar in the case where both of the light curves are inter-

55

 

0.25 1 1 .

 

 

 

 

 

 

' Optical He'll —
uv Hell ---------
(O
5
E 0.2 - 5
3
9
(U
o
13 0.15 - _
0
I"?
(D
(D
8
o 0.1 ~ _]
3
a)
”5
C
.9
E 0.05 L _ -
LL
0 —1 IL--- J
—10 -5 10 15 20

 

Reverberation lag (Days)

Figure 4.1 Composite CCCD for Optical and UV He II - It is important to note that
the optical and UV He II emission-lines fall nicely on top of each other, implying that
they are produced with the same lag time, and therefore the same distance from the
central engine. Once again, please note that the CCCDS that are shown are for the
case where both the driving and responding light curves are interpolated.
polated simultaneously. Therefore, the plots where both light curves are interpolated
are used as representative of the important concepts that need to be illustrated.
Both the optical He II CCCD and the UV He II CCCD seem to be quite well
behaved, with well defined Gaussian—like shapes. This is a good indication that
we have found a strong correlation. The actual values for Tcent for each of the

interpolation cases, as well as the final averaged value for each of the emission lines,

are shown in table 4.1.

56

Table 4.1: CCCD Results - The results of the cross correlation centroid distribution cal—
culated by the lagerrb’ code are shown for three cases; interpolating only the first (driving
continuum) array, only the second (responding emission line) and both. The final value for
each emission line’s Tcent was determined from an average of the 1st array and 2nd array
cases. The prior results in column 1 are taken from table 1 of Peterson 86 Wandel (1999),
summarizing the 1989 AGN Watch data set. We consider the values for H6 to be unreliable,

as discussed in the text.

 

 

 

Emission Line Prior Result lst Array 2nd Array Both Arrays Final Value
He 11 A4686 85153;: 6.2 i 2.7 3.9 i: 2.8 5.2 d: 2.5 5.0 :l: 1.9
He 11 A1640 3.03;? 6.5 :h1.8 5.7 :t 2.3 6.3 :l:1.8 6.1 551.5
C 1v 9.5ff;3 11.9 :t 3.0 11.8 i 4.6 11.9 :t 3.4 11.8 :1: 2.8
H6 19.7232 12.7 a: 7.5 10.5 :1: 8.0 11.5 :1: 7.0 11.6 i 5.5

 

 

 

We also see that they both overlap quite well, indicating that the gas emitting
each of these lines comes from the same region within the BELR. This fact is further
reflected when the actual final values for Tcent are calculated for each of the lines
(table 4.1). The values agree well within the range of error values. When compared
with prior results (column 2 of table 4.1), we see that the He II A4686 has decreased
Slightly and the He II A1640 has increased. This result is not unexpected, as we assert
that prior studies have failed to adequately remove all of the contamination from sur—
rounding lines. Any contamination from a line with a slightly different reverberation
lag time will cause a shift in the observed cross correlation function.

The CCCD for C IV is shown in figure 4.2. Like the He II CCCDS, it is also
fairly well behaved, although it has a slightly broader shape. The value of Tcent =
12.514 :1: 2.730 is slightly longer than previous measurements, however it still agrees

within errors. When the CCCD for C IV is overlayed on the plot of the two He II

57

 

 

 

 

 

 

0.14 5 5 l 1 1

2 0.12 -

.9

E

8 0, _

E .

0

5

o 0.08 ~

.72

U)

8

o 0.06 -

0

3

a)

”5

c 0.04 -

.9

*6

‘2

u. 0.02 ~

0 I l I I l
-10 -5 O 5 10 15 2O

Reverberation lag (Days)

Figure 4.2 Cross Correlation Centroid Distribution for C IV - This plot shows the
results for interpolation of both the driving and the responding light curves. The
final Tcent is 12.514 :1: 2.730

CCCDS, it becomes quite clear that the He II emission lines and the C IV line do not
arise from gas at the same Tcent (see figure 4.3).

The CCCD for H6 is shown in figure 4.4. This is a good example of a situation
where this straightforward approach can fail. The CCCD appears to be a combination
of two Gaussians. One is fairly weak and is centered around 4 days. The other is much
stronger and is centered near 15 days. The shorter, weaker peak, is most likely due
to inadequate deblending of the H6 emission line. Because we were only interested
in H6 as a contaminant for He II A4686, only the blue wing of H6 was fit. A simple
centroid of this CCCD would yield a characteristic lag time (Toent) that is too small.

We note that the peak of the H6 CCCD shown in figure 4.4 is at about 15 days,

58

which is closer to the previously observed 19.7 day lag.

 

 

 

 

 

 

 

0.25 I I I I _ I
Optlcal Hell ——
UV Hell ---------
a) C IV """""""
8 .'
E 0.2 l- l ---. -
3 : 1
2 : l
m : l
0 .
(”3 0.15 - _
0
32
m
m
8
o 0.1 - -
a
U)
”‘5
c
.9 -----
g 0.05 r -
IL
0 41 "'- J
—10 -5 15 20

 

Reverberation lag (Days)

Figure 4.3 Composite Centroid Distribution for Optical and UV He II and C IV -
While is seems clear that the UV and optical He II come from the same characteristic
radius, it also seems clear that these two emission lines arise from a different region
than the region producing C IV.

4.2 LIGHT CURVE ERROR ESTIMATION

It was noted in chapter 3 that the errors on the continuum and emission line light
curves were estimated. It was further suggested that the exact value of those error
bars was not particularly important, so long as they stayed within physically plausible
bounds. In order to demonstrate this, the errors on both the UV continuum, the He
II A1640 and the C IV emission lines were both doubled and halved. This gives us

a range of error estimates from 5% to 20%. The cross correlation analysis was then

59

 

0.08 I I I I I

 

 

 

a) 0.07 - ,
C
.9
“-3 0.06 - _
2
to
o
u. 0.05 - -
o .
o
«3 0.04 — .
(0
a)
8
0:) 0.03 - -
‘5
§ 0.02 — -
2'5
92
LL 001- ~
0 l l I 1 FL I
-60 -40 -20 0 20 40 60

Reverberation lag (Days)

Figure 4.4 Cross Correlation Centroid Distribution for Hfi - This plot shows the results
for interpolation of both the driving and the responding light curves. The final Teent
was calculated by first fitting a pair of Gaussians to the CCCD. The center and a
values for the larger peak were then averaged to yield a final value of Tcent = 15.3:t4.3.
The peak with the shorter lag time is most likely due to inadequate deblending with
another feature.
repeated using these values. The results can be seen in figure 4.5 for the He II and
figure 4.6 for the C IV. From these plots, we can see that the exact value of the error
bars on the light curves does not change the intrinsic result. The gas producing the
He II UV emission line is not the same gas that is producing the C IV emission line.
It is clear from the C IV figure that as the error bars on the input light curves get
larger, the error associated with the width of the CCCD also increases.

With this result in hand, we feel confident that the 10% error that we have esti-

mated for our fits is reasonable and that it gives a reasonable result for the value of

Teent. The exact size of the error bars on our light curves can be debated, but that

60

does not change the intrinsic result.

 

 

 

 

 

 

 

 

0.25 I l I I I
10% error
20% error ---------
a, 5% error ----------
8
:3 0.2 - -
3
0
E
0
LL
0 0.15 ~ _
O
5
‘23
(I) .
o 0.1 ~ -
3
m m
“5
C
.9 '
g 0.05 - -
u.
O 1 1 [L J

 

 

-10 —5 0 5 10 1 5 20
Reverberation lag (Days)

Figure 4.5 He II Error Estimation Test - Three different estimations of the error in the
initial UV He 11 light curve are shown. The qualitative result is the same regardless
of the estimated error value.

4.3 SENSITIVITY To PROFILE TEMPLATES

All of the template profiles used in this work are based on the observed emission line
shapes in the Object of study, NGC 5548. The two key profiles, the He II A4686 BELR
profile and the C IV A1549 BELR profile were created from the variable component
of the emission line seen in the RMS Spectra of the optical and UV data respectively.
The He 11 A1640 line is more heavily blended but the Simplest assumption is that it
has the same profile shape as the He II A4686 line. This would be true if both lines

are formed by recombination and there is no velocity dependent reddening affecting

61

 

 

 

 

 

 

 

 

0.14 I I I I I I
' ' 10% error
20% error ---------
O ..........
2 0.12 _ 5/0 error _
.2
E
8 01 _
E u -l
0
t3
0 0.08 - -
.72
(I)
8 006 — -
8 .
3
m
‘5 _
c 0.04 - . -
.9
‘6
S
u. 0.02 - _
0 ' " '
-10 -5 0 5 10 30

 

Reverberation lag (Days)

Figure 4.6 C IV Error Estimation Test - Three different estimations of the error in
the initial light curve are shown. The qualitative result is the same regardless of the
estimated error value.

the A1640/A4686 intensity ratio after the lines are emitted.
In order to further test the robustness of the assumed template profiles, several
different alterations to the template profiles as well as the continuum Shape were

tested. The results of these permutations can be found in table 4.2.

62

Table 4.2: Profile Permutations - This table is a summary of the results of several per-
mutations on the profile shapes and components included. Most of these permutations do
not make a significant difference in the final result. The details of these permutations are

discussed in the text.

 

 

Change He II A1640 He II A4686 C IV A1549

 

Baseline 6.1 :l: 1.5 5.0 :l: 2.0 11.8 i 2.7
4686 FWHM + 25% 6.2 :l: 1.4 3.3 :t 5.2 12.0 2%: 2.7
4686 FWHM - 25% 6.3 :t 1.44 1.0 :l: 5.2 11.9 :t 2.8

Fe II 9000 km/S 6.23 i1.5 4.6 :l:1.7 12.1 :t 2.8
Fe II 3000 km/S 6.4 :l:1.5 4.6 $1.8 12.5 i: 2.8
Straight Line 6.3 i: 1.9 5.6 :l: 2.4 12.9 i: 3.3
No H6 - 6.1 :l: 1.5 -

No C IV 4.4 i1.8 3.0 21:1.8 NA
No 0 III 6.0 i1.5 5.1:t 2.0 12.6 :1: 2.8

 

The full width at half maximum (F WHM) He II template profile, created from
the variable emission in the optical spectrum, was increased and decreased by 25%.
While this change had a small effect on the A1640 reverberation lag time, it created a
large change in the optical. The reverberation values are misleading however, as the
CCCD for the two altered profiles are mostly noise with no well defined peak. This
can be seen in figure 4.7. The values presented in table 4.2 are simply the centroid
of this relatively featureless CCCD. The UV CCCD did not suffer as severely as the
automated fitter was able to compensate by boosting or suppressing all of the blended
profiles in the region around A1640. The contamination in the optical A4686 is less
severe, and the automated fitter is forced to use mostly the new He II profile to

attempt a fit. It is not unexpected, therefore, that the optical fit suffers more when

63

an incorrect profile is used.

 

 

 

 

 

 

 

0.18 I 7 l I .I
A4686 basellne
FWHM +25% ---------

a, 0-16 ' FWHM —25% ---------- -
.6

33 0.14 - -
D

2

8 0.12 - _
LI.

0

9 0.1 - —
.2

:3

O 0.08 - a
8

3

3’3 0.06 ~ -
O

S

:3 0.04 _ __: -
‘3 """

u- 0.02 '~--5-_-_-_.‘."“.-__'”"_ gulf-3, -

0 —1 Inf-"1--
—10 —5 0 5 10 15 20

Reverberation lag (Days)

Figure 4.7 He II A4686 Profile Width - The effect of altering the He 11 A4686 profile
F WHM by i25% is shown. When these altered profiles are used to fit the BELR
emission at A4686, the resulting CCCD is mostly featureless with no clear well defined
peak. This result is not unexpected as the Shape of this variable emission was used to
create the original profile. Because the blending in the optical is less severe than in the
UV, the automated fitter is forced to “fix” the fit by Simply boosting or suppressing
the He II emission, leading to a poor fit and therefore a poor CCCD.

The actual value for the broadening of the Fe II multiplet in NCG 5548 is not well
constrained. In their detailed analysis of the Fe II emission in NGC 5548, Vester-
gaard & Peterson (2005) were only able to place the very loose boundaries on the
range of broadenings that give acceptable fits to the observed Fe II emission. These
values ranged from between 4500 km/s to about 10,000 km/ S. While Vestergaard
and Peterson found that 6250 km/s yielded the qualitatively best fit for the optical,

they preferred a value closer to the higher end of the range for the UV. In this study,

64

we chose to use a value of 6250 km/ S for both the optical and the UV for the sake
of simplicity and because the Fe II contamination is fairly small in the regions of
interest. Even in AGN that have quite strong Fe II emission, such as Akn 120 studied
in detail by Kuehn et al. (2008), the reverberation lag of Fe II is not well constrained.
Kuehn et al. found that although the Fe II emission did respond in some way to
continuum variations, they were unable to measure a clear reverberation time scale.
Because of these loose constraints on the Fe II emission, we decided to try using two
different broadenings other than the 6250 km/ S that was used as our baseline value.
Broadenings of 3000 km / s and 9000 km / S were both substituted into the fit with very
little change to the reverberation results for either the He II lines of the C IV line.

Another area where our analysis deviated from previous studies is in our use of
a power-law to fit the entire continuum under our regions of interest. In previous
studies, a straight line “pseudo-continuum” was drawn under a local region and the
emission lines were measured as the flux above this straight line. In order to attempt
to simulate this with our automated fitter, we replaced the power law with a straight-
line. Because a straight line will do a very poor job of fitting the entire continuum
over a large range of wavelengths, the fitting windows were also adjusted to only
cover an area near the region of interest (1425 - 1730 A in the UV, and 4225 - 4275
A, 4420 - 4676 A, 4703 - 4838 A, and 5100 - 5170 A in the optical.) Six of the optical
spectra were rejected due to obviously incorrect fits (57509hx, 57556hx, 57599kx,
57645ix, 57664ma, 57766ix), but the remainder of the optical and the UV fit fairly
well. The resultant reverberation lags were Similar to the baseline case, with slightly
larger errors.

We also consider the possibility that some of our other profiles could be in error.
The H6 profile, whose wing contaminates the He II A4686 emission line could have
a Shape that is not well characterized by the Ha line that was used to create the

profile. To test this, the H6 emission was removed from the fit, and the window that

65

included the red wing of He II A4686 was shortened to 4703 - 4760 A. This likely still
includes some contamination from the wing of H6, but still gave enough of the He II
region to obtain a good fit. The H6 wing of the emission contaminating the He II
is likely the cause of the Slightly longer lag time that is seen in the cross correlation
analysis. The He II A1640 and C IV lines lags remain unchanged.

While the C IV profile in the UV was created from the variable C IV emission,
we also attempted to remove the C IV from the fit, with a corresponding adjustment
to the fitting window. The ranges 1425 - 1456 A, 1618 - 1730 A, 1798 - 1836 A,
2400 - 2650 A were used. This loss of range did have an impact on the ability of the
fitter to accurately create a blend, and several of the UV Spectra were rejected due
to obviously incorrect fits (the Spectra from dates 57526, 57586, 57606, 57621, 57629,
57649, 57657, 57713, 57737 specifically.) This loss temporal resolution as well as less
accurate continuum measurement did have an effect on the He II line lags, although
they still agree within error. The C IV lag was obviously not calculated.

The last major profile to be considered was the 0 III] emission that contaminates
the He II A1640. It was removed in a manner similar to that of H6 in the optical.
The profile was removed from the fit, and the fitting windows were adjusted. The UV
was then fit from 1425 -1652 A, 1798 - 1836 A, and 2400 - 2650 A. Once again, this
had a small effect, but the values for the reverberation lags still agree within error
with our baseline values.

Given that the qualitative results are fairly insensitive to these moderate changes
in template profile conditions, we take this as an indication that the exact shape of
the template profiles. This is true provided that something nearly approximating
the correct shape is used. In the case of the changes made to the FWHM of the He
II profile, it is clear that when a profile that is obviously wrong is used the results
begin to break down. We take this as good evidence in favor of our approach of using

template profiles generated from the observed data.

66

 

CHAPTER 5:
DISCUSSION

 

In this study, we have carried out a careful reanalysis of an existing set of observations
of N CC 5548. In our analysis, we have attempted to fit all of the lines in the complex
blended features that include He II A1640 and A4686. While our results for He
II are somewhat different from previous studies, they do agree within their error
bars. Our technique for fitting these lines was much more refined than in previous
studies. Our starting point was to create a template profile from the observed variable
component of He II A4686. We then assumed that the He II A1640 emission line had
the same profile shape as the He II A4686. This is expected if the lines are formed
by recombination and if there are no velocity-dependent reddening effects. Profiles
were also created from observed variable and constant profiles in order to attempt to
account for the presence of other emission lines that are known to be blended with
the optical and UV He 11 lines. In the Special case of the Fe II multiplet feature,
a profile from another AGN was used. Each of these profiles was then fit in an
automated fashion to each observed Spectrum to create light curves for each emission
line of interest and finally, an interpolated cross-correlation analysis was performed
to formally calculate a characteristic reverberation lag time for each of the studied
emission lines. This de-blending of lines that are known to contaminate one another
is more sophisticated than has been done in previous studies (e.g. Dietrich et al.,
1993; Korista et al., 1995)

We found that the two He II emission lines do have very similar reverberation

67

lag times, with formal values of 5.0 :i: 1.9 days for the optical He II line (A4686) and
6.1 :l: 1.5 days UV He II line (A1640) This result was not unexpected and is in good
agreement with predictions from simulations. Unless the two lines are formed in some
very different way than the Simple recombination processes that are thought to be
the case, they Should have the same lag times. Our reverberation measurements of
the stronger emission line of C IV A1549, with a formal value of 11.8 :l: 2.8, agrees
with previous measurements. These results are summarized in table 4.1.

The suprising result here is that both lines are inconsistent with the reverberation
lag of C IV. This is surprising because under the Simple LOC model, the He II lines
should come from the same region that forms C IV (Bottorff et al., 2002). While
it is true that He II has a higher ionization potential than C IV, and Since previous
observations have Shown that higher ionization potentials correspond to Shorter lag
times, it may seem reasonable to find that He II responds more rapidly than C
IV. In fact, previous reverberation results also find that C IV has a slightly longer
reverberation lag time than the optical He II. However, the Simulations of Bottorff
et al. (2002) seem to indicate that C IV and He II are emitted most efficiently in
Similar physical conditions. The question that must be asked, therefore, is if any of
the underlying assumptions of the LOC model may be in error.

The LOC model is based on only a few mostly straightforward assumptions.

1. The BELR gas covers a wide range in radial distance.
2. The BELR gas covers a wide range in density.

3. The radial and density distributions can each be described by simple power

laws.
4. The emitting region can be approximated as a sea of optically thick gas clouds.

5. Each cloud sees the same ionizing continuum shape, i.e. they are not in the

68

shadow of clouds closer in that partially absorb the radiation in a wavelength

dependent way.

In the case of N GC 5548, the first assumption is verified by the Observed reverber-
ation results. The large range of lag times found for the different emission lines seem
to support this basic premise. While C IV has a well determined lagtime of 10—12
days, H6 has a 20 day lag and Mg 11 may be upwards of 70 days (Clavel et al., 1991)
in NGC 5548 alone. Similar differences have been found for many other objects.

The second point, that the BELR gas covers a wide density range, is also probably
true. The observed spectrum seen in NGC 5548 contains a mix of lines that only
radiate efficiently at very different values of the ionization parameter (the ratio of the
incident ionizing flux to the gas density.)

However, the assumption that the radial and density distributions can each be
described by simple power laws is almost certainly an oversimplification of the true
Situation. This would at best describe the composite spectrum of many AGN com-
bined together, not that of any one specific object. Many studies of individual objects
Show emission line profiles that break up into a few major components at different
velocities such as that of (20207-398 (Baldwin et al., 1996) or J1546+5253 (Dhanda
et al., 2007). This is almost certainly a demonstration that the radius-density pa-
rameter space is not smoothly filled. Looking in more detail at the plots of various
LOC plane calculations of Korista et al. (1997) (see figure 5.1), there may be some
way to populate the LOC plane with a carefully chosen collection of optically thick
clouds that would re—create the observed lag difference between He II and C IV. It is
not clear upon first inspection how exactly one could create He II A1640 without also
creating C IV A1549 as well. One could, however, Simulate this specific collection of
gas using a program such as Cloudy (Ferland, 2006) to see if the intensity ratio and
reverberation lag ratio might be recovered. This would be fruitful ground for future

work.

69

 

24 . . , .
_ c1v1549 Helll640

£21— """ --------- ‘

 

 

       

 

1

12 13 14

l l I I l I". ‘1

78910111213 891011

Log n(H) Log mm

Figure 5.1 Standard LOC Model — The contours in this figure Show the standard
LOC model (solar chemical abundances and a cloud column density of 1023cm_2) for
several emission lines as a function of Hydrogen density, n(H), and incident ionizing
continuum, <IJ(H). Based on this model, it is difficult to find a place where C IV is
produced that does not also produce He II A1640. This figure is from data from
Korista et al. (1997)

Regarding the final assumptions, that the gas clouds in the BELR are optically
thick and do not filter the continuum “seen” by clouds futher out, there is some
evidence that this is not the case with all AGN. Casebeer & Leighly (2003) argue
that as least some AGN contain matter-bounded clouds. These clouds would absorb
radiation at some wavelengths while passing other wavelengths through. This would
certainly violate assumption 5 of the LOC model. It could give rise to a situation
wherein a region of highly ionized He++ gas could efficiently emit He II through
recombination but have carbon ionized to a state higher than C+++ and therefore
having no C IV emission lines. Commonly observed higher-ionization lines such as
0 VI A1034 or the coronal lines such as [Fe X] A6374 might also come from such a
region.

It is not clear how easily such a system could be constructed with the current
model framework. A good starting point would be to run Cloudy with a variety of
stopping densities well below the standard value of N(H) = 1023cm_2. This would

be a good follow-up project and a logical next step for future work.

70

This result, that the He II and C IV are not produced by the same gas, should
not necessarily be seen as a large setback for the LOC model. The LOC model does
a good job of recreating the spectrum of the average AGN. This does not mean that
it can easily predict the behavior of every individual AGN without first carefully

crafting a Specific set of BELR clouds.

71

 

CHAPTER 6:
SUMMARY

 

The goals of this project were to create new techniques and tools to more accurately
measure reverberation lag times for heavily blended emission lines. Once that was in
place, these tools would be used to measure the reverberation lag of He II, a relatively
Simple emission line, in both optical and UV Spectra. This was done in an attempt
to clear up a discrepancy between theoretical models, which predict that the optical
and UV He II are produced by the same gas and should therefore have the same
reverberation lag time and that these two emission lines should have nearly the same
reverberation lag time as C IV, and previous studies, which found that the optical
and UV He II lines were in marginal agreement and that the UV He II did not agree
with the C IV reverberation lag.

With these goals in mind, this project was quite successful. The optical and UV
He II emission were both measured to have reverberation lag times of roughly 5 -
6 days, with far better agreement in the lag-time probability distribution curves for
the two lines. Furthermore, the strong C IV line, which is also involved in the heavy
blending, was measured to have a lagtime consistent with previous measurements,
but the C IV and He II lagtimes do not overlap. This agreement with previous
measurements of the strong C IV line helps to validate the technique that was used.
Our technique, which required a large software development effort, included using
an automated fitting routine to simultaneously fit multiple emission line template

profiles that were, themselves, created from observed data.

72

One rather surprising result was the clear indication that He II and C IV are not
created by the same gas within the BELR. This is contrary to what was predicted by
the typical model of the BELR but consistent with previous measurements. This is
not necessarily a failing of the model, but possibly an indication of oversimplification
within the assumptions on which the model was based. The LOC model compared
to in this work is a very good predictor for the behavior of the average AGN, but
does not necessarily describe any individual AGN without careful crafting of a Specific

grouping of clouds.

73

APPENDICES

74

 

APPENDIX A:
CODE FOR CONTIN.F

 

This is the FORTRAN code of the optical fitter. It can also be used as a general
fitter, as it does not have any hard—coded parameters like the UV fitter does. It calls
cfunk.f as a subroutine.

character*5 plabe1(20),junk
double precision ptau(20),pincr(20),puper(20),ploer(20),zero
double precision ftau,err,eplus,eminus,arglis(2)
double precision PI
integer i
integer ip,ierflg,ivarbl,npar,n,nn
double precision x,Y, m, b,yavefile,sdevfile
double precision gauss, chisq,average,stdev,n0ise
double precision fitout(20),small,chiout(20),errout(20)
real xgauss
integer chistat,card,j,idof
real ran2
external cfunk
character*10 chtest
character*12 glob
integer chlen, IM, IER,xcur,ycur,NAX,IAX(7),IPIX
integer totcount
character chcur
real dxva1(5000),dyval(5000),rtest
real cxval(5000),cyval(5000)
real prix(5000),priy(5000)
real txval(5000),tyval(5000)
real ylim(5000)
real scaley(5000)
real wstart(30),wstop(30),wsig(30),nsmooth(30),woff(30)
integer IMAXD,iof,county,1count,iof2,wc0unt,wtest
integer iof3, iof5,iof40
character*26 irafname
real pxmin,pxmax,pymin,pymax,armin,armax
real xbar,sigx,ybar,sigy,yhigh,xhigh

75

double precision scale

common /myscale/ scale

common /mydata/ dxval,dyval,nnx,wstart,wstop,wcount,
c ncomps,totalo,totcount,wsig,woff,yhigh,xhigh

common /pridata/ prix,priy,lcount,xbar,sigx,b1end

parameter (nmax=50000)

common diff(nmax),xinput(nmax,30),shift(nmax),
c oname(30),wold(30),wnew(30),area(30),nxc(30),
c xlamc(30),dlamc(30),totalc(30),nx,xlam0,dlam

character*50 oname,objfile

dimension 0bj(nmax),blend(nmax),ratio(nmax),id(100)

dimension waves(nmax)

real crap, wkeep<30),akeep(30)

character*5 crap2

real cstart,cstop,1eft

double precision c0nerr,ag(4),ehigh,elow

c ***********************************

diff(1) = 3.14159

PI = 3.14159

open(71,file=’slope.txt’)
0pen(72,file=’error.txt’)
open(81,file=’chi.txt’)
open(88,file=’offset.txt’)
open(89,file=’frac.txt’)
0pen(90,file=’fracerr.txt’)
0pen(91,file=’left.csv’)

32 format(a4,8x,a1,10x,a5,4x,a5,5x,a5)

open(77,file=’wind0w.txt’)
wcount = 1
read(77,*,IDSTAT=iof5) wstart(wcount),wst0p(wcount),nsmooth(wcount)
do while (iof5.eq.0)
wcount = wcount + 1
read(77,*,IOSTAT=iof5) wstart(wcount),wstop(wcount),nsmooth(wcount)
enddo
close(77)

c This puts wcount back to the correct value. Pointed out by
c Neelam.

wcount = wcount - 1

write (*,*) "wcount = ",wcount

C ***********************************

76

c Start setting up our plot. We will output to a
file called plot.ps and make a 4 x 4 grid of plots
per page.

call pgbegin(0,’plot.ps/PS’,1,1)
This opens blends in and reads in the list of spectra to go get.
Some of them are put into an array. It should be noted that if a line
is not properly formatted (i.e. you forget to leave any blank space
between two numbers) it may not be a fatal error. This routine will
intrepret the poorly formatted line as the end of the file and the
program will continue without throwing and error. This can lead to
it only using a subset of the parameters in your blends.in file.

00

0000000

0pen(22,file=’blends.in’,Status=’old’)

readf22,*,IOSTAT=iof3) Objfile

write (*,*) objfile

read(22,*,IOSTAT=iof3) const

i=1

read(22,*,IOSTAT=iof3) oname(i),wold(i),wnew(i),area(i)

do while (iof3.eq.0)
i=i+1
read(22,*,IOSTAT=iof3) oname(i),wold(i),wnew(i),area(i)
enddo

ncomps=i-1

c Store the initial values from blends.in in case we need them later

do n=1,nc0mps,1
wkeep(n) = wnew(n)
akeep(n) = area(n)
enddo

c ***********************************
const = 3.20540747E-14

open (21,file=’sorted2.in’,status=’old’)
read(21,*,IDSTAT=iof2) objfile

do while (iof2.eq.0)
write (*,*) objfile

77

C ***********************************

c These are the initial values for the minuit parameters.

c General format is as follows:

c plabel(n) = ’name-of-variable’

c ptau(n) = initial value

c pincr(n) = initial step size

c puper(n) = upper limit (0 for none)

c ploer(n) = lower limit (0 for none)halphaO4-a 6562.8 6562.8 0.048
c npar = n (count of how many variables we have for minuit

c to manage)

c The ptau value will be passed to the xval array in your subroutine.
c Minuit will then step around and pass new ptau values to the xval
c array.

c These are the wavelength and area values for each of the input lines
c from blends.in.

npar = 0

do n=1,ncomps,1

npar = npar + 1
plabel(npar) = oname(n)'
ptau(npar) = wnew(n)
pincr(npar)=0.01
ploer(npar)=wnew(n) - 7.
puper(npar)=wnew(n) + 7.

npar = npar + 1
plabel(npar) = oname(n)
ptau(npar) = area(n)
pincr(npar)=0.00001
ploer(npar)=area(n) * 0.1
puper(npar)=area(n) * 6.

enddo

C
C
C

NOTE: For the continuum, we are trying to fit a power law,
so I am passing it the initial values for a
continuum = A * (lambda‘gamma) fit.

npar = (2*nc0mps) + 1
plabel(npar) = ’A’
ptau(npar) = 1.0e-14
pincr(npar)=1.e-15
puper(npar)=1.e-10
ploer(npar)=1.e-15

npar = (2*ncomps) + 2
plabel(npar) = ’gamma’

78

ptau(npar) = -1.8826
pincr(npar)=1.e-4
puper(npar)=1.
ploer(npar)=-2.

This gives us a total of (2*ncomps) + 2 parameters to
give to the fitter. This total value is in npar.

II!**********************************

c
c
c
c Open the iraf file. This is the file we are fitting
c our profile to. Building the fit array should take
c place in the subroutine, since minuit will need to
c
c
c

tweak parameters.
It must be a .imh, not a .fits
read spectrum to be fitted

write(*,*) ’input object file is ’,objfile

irafname = objfile

call t61n(0bjfile,nx,xlam0,d1am,id,0bj,nmax)
’,nx,xlam0,xlam0+nx*d1am,dlam

write(*,*) ’nx, lambda range,dlambda

nnx = nx

totalo=0.

yminobj=1.e30

ymaxobj=-1.e30

do i=1,nx
totalo=t0talo+obj(i)
yminobj=min(yminobj,objCi))
ymaxobj=max(ymaxobj,0bj(i))
waves(i)=xlamO-dlam+i*d1am

end do
do i=1,nx
dxval(i) = waves(i)
dyval(i) = obj(i)
enddo

c ***********************************
c SMOOTHING, from Neelam and Baldwin.

do iwin=1,wcount
do i=1,nx
if(waves(i).lt wstart(iwin)) istart=i
if(waves(i).lt.wst0p(iwin)) ist0p=i
enddo

istart=min(istart,nx)
ist0p=min(istop,nx)

xsig=0.

79

Even numbers break this.
c them. It will make chisq artifically small.

Don’t use

do i=istart, istop
nsm=min(nsmooth(iwin),2*(nx-i)+1)
sum=0.
do j=i—nsm/2,i+nsm/2
sum=sum+obj(j)
enddo
wdiff=obj(i)-sum/nsm
xsig=xsig+<wdiff*wdiff)
enddo

if(istart.lt.istop) then
wsig(iwin)=sqrt(xsig/(istop-istart))
else
wsig(iwin)=sum/nsm
end if
enddo
c ***********************************
c read in the blend component spectra
c The continuum (a power law) will be built in the subroutine cfunk.
do i=1,nc0mps
call t61n(oname(i),nxc(i),x1amc(i),dlamc(i),id,xinput(1,i),nmax)
totalc(i)=0.
do k=1,nxc(i)
t0talc(i)=totalc(i)+xinput(k,i)
end do
end do

do i=1,nx
blend(i)=0.
end do
nb0=nmax
nbx=0
c ***********************************
c Set up minuit to do it’s thing.
* Set-up parameters for minuit (aka unit numbers for input,0utput)
call mninit(5,6,7)

* Set the initial values of the adjustable parameters (aka the "x")
* in function fcn. Let MINUIT know about those parameters attributes
do ip=1,npar

zero=0.
c call mnparm(ip,plabel(ip),ptau(ip),pincr(ip),puper(ip),
1 ploer(ip),ierf1g)
call mnparm(ip,plabel(ip),ptau(ip),pincr(ip),ploer(ip),
1 puper(ip),ierflg)

0

80

if (ierflg.ne.0) write(*,*) ’Par: ’,ip,’ not entered sucessfully’
end do
* These set the strategies by which Minuit work, higher is more
* "accurate" but more costly in time (see p.24 in MINUIT Ref man
* v94.1). I think this call is optional
arglis(1)=2.

call mnexcm(cfunk,’SET STR’,arglis,1,ierf1g,O)

* Stuff for accurate error analysis, see p.22, optional also I think
arglis(1)=1.
call mnexcm(cfunk,’SET ERR’,arglis,1,ierflg,O)
* Supress warnings.
arglis(1)=1.
call mnexcm(cfunk,’SET NOW’,arglis,1,ierflg,O)
c Sets level of printout detail. -1 is minimum, 3 is highest.
arglis(1)=-1.
call mnexcm(cfunk,’SET PRI’,arglis,1,ierf1g,0)
* Now use Minimize the minimize the value of the function
G set the max number of iterations with arglis(1) and
c the precision required in arglis(2).
arglis(1)=50000.
arglis(2)=1.e-20
call mnexcm(cfunk,’MIGRAD’,arglis,2,ierflg,0)

C ***********************************

* Assuming convergence after <50000 iterations print out
* the current value of the function. Store the values in the
c array fitout.
write(*,*) " ------------------------------ "
write(*,*) "Results for ",objfile
write(*,*) ""
do ip=1,npar

call mnpout(ip,junk,ftau,err,eplus,eminus,ivarbl)

write(*,*)ip,’ ’,plabe1(ip),’ Orig: ’,ptau(ip),’ Final:’,ftau,err

fitout(ip) = ftau

errout(ip) = err
end do
This gets the current status of minimization. Since we are
’done’, this should be the final value of our minimized
function. These parameters are, in order: (1) minimum value
(2) estimated vertical distance to the minimum (3) the value of
parameter uncertainities (4) # of currently variable parameters
(5) the highest external parameter number defined by the user
(6) that status of the covariance matrix. See page 16 0f
minuit manual.

call mnstat(chiout(1),chiout(2),chiout(3),chiout(4),chiout(5)

00000000

81

1 ,chistat)
idof = totcount-(ncomps+2)
crap = chiout(1)/idof
write(*,*) "REDUCED CHISQ = ",chiout(1)/idof

write(*,*) "FMIN = ",chiout(1)
write(*,*) "FEDM = ",chiout(2)
write(*,*) "ERRDEF = ",chiout(3)
write(*,*) "NPARI = ",chiout(4)
write(*,*) "NPARX = ",chiout(S)
write(*,*) "ISTAT = ",chiout(6)
write(*,*) "xhigh = ",xhigh

write(*,*) "yhigh = ",yhigh

write(*,*) " ------------------------------ "
c ***********************************
c Output the values to a file. In this case, the file is called
c ’slope.txt’ (for historical reasons) and contains:
glob = objfile
31 format(a8,1x,E12.6,1x,f8.5,1x,f8.5,1x,f9.5)
write (89,*) glob,chiout(1)/id0f,fitout
write (90,*) glob,chiout(1)/idof,errout
write (81,*) glob,chi0ut(1)/idof
write (88,*) glob,xhigh,yhigh
c ***********************************
20 format(i2,1x,a20,2(0pf9.3),f7.3, 1pe10.2,1x,0pf7.3)
30 format(a20,2(0pf9.3),f7 3, 1pe10.2,1x,0pf7.3)
c ***********************************
c Here, we convert the fractions to flux values for the even parameters
do ip = 1, ncomps

fitout(2*ip) = fitout(2*ip) * totalo * dlam
errout(2*ip) = errout(2*ip) * totalo * dlam
end do

This is where we calculate the flux for the continuum. There is a

a problem with using this method if your spectra are not all the same
wavelength range. Trim your spectra or use a different method. I think
I may put some code here to take the "continuum" between a specific
wavelength range. It will still use the powerlaw that we fit, but it
would only keep the flux within a certain range.

I feel that the correct approach might be to re-evaluate the continuum
flux from the fitted parameters, integrating over a user specified range
and then do the calculation again with the parameters slewed to their error
limits to calculate the error in the flux.

ip = (2*ncomps)+3

c This method assumes that you have no reason to shift the continuum

c using the align routine.

C NOTE: This ’conwin.in’ method is no longer used. The continuum

0000000000

82

is calculated at a Specific point.

Here we open up the input file where the user has specified
the window to use for the continuum. If the read fails in any
way (for instance there isn’t a file there or it only contains
one number) we will notice and default to using the whole
spectral range.

open (40,file=’c0nwin.in’,status=’unknown’)

read (40,*,IOSTAT=iof40) cstart,cstop

if (iof40.ne.0) then

000000

cstart = xlamc(ncomps+1)

cstop = xlamc(ncomps+1) + (dlam * nx)
endif
close (40)

c As a test, let’s make the starting and ending wavelengths the
c full range for the spectrum.

write (*,*) ”Range = ",cstart," - ",cstop

fitout(ip) = 0.

conerr = 0.

ag(l) = 0.
ag(2) = 0.
ag(3) = 0.
ag(4) = 0.

c Find the flux value at 5100.
fitout(ip) = fitout(2*nc0mps+1) * (5100./5600.)**(fitout(2*ncomps+2))
c Calculate the four corners
ag(l) = ag(l) + ((fitout(2*nc0mps+1)+err0ut(2*nc0mps+1)) *
c ((5100./5600.)**(fitout(2*ncomps+2)+errout(2*ncomps+2))))

ag(2) = ag(2) + ((fitout(2*ncomps+1)-errout(2*ncomps+1)) *
c ((5100./5600.)**(fitout(2*ncomps+2)+err0ut(2*ncomps+2))))

ag(3) = ag(3) + ((fitout(2*ncomps+1)-errout(2*ncomps+1)) *
c ((5100./5600.)**(fitout(2*ncomps+2)-errout(2*ncomps+2))))

ag(4) = ag(4) + ((fitout(2*ncomps+1)+errout(2*ncomps+1)) *
c ((5100./5600.)**(fit0ut(2*ncomps+2)-errout(2*ncomps+2))))

c Now find the high and low, and subtract them.

elow = 9999.
ehigh = -9999.
do ii=1,4

if (ag(ii) gt.ehigh) then
ehigh = ag(ii)

endif

if (ag(ii).lt.elow) then

83

elow = ag(ii)
endif
enddo
errout(ip) = dlam * (abs(ehigh - elow)/2.)
write (*,*) "New con = ",fitout(ip)

write(*,*)conerr,fitout(ncomps+1),fitout(nc0mps+2)

errout(2*nc0mps+4) = 0.
d0 ip = 1, ncomps

errout(2*ncomps+4) = (errout(2*ip))**2 + errout(2*ncomps+4)
enddo

errout(2*nc0mps+4) = (errout(2*ncomps+3))**2 + errout(2*ncomps+4)
errout(2*ncomps+4) sqrt(errout(2*ncomps+4))

c Write out the values using fluxes instead of fractions.
write (71,*) glob,chiout(1)/idof,fitout
write (72,*) glob,chiout(1)/idof,errout
C WRITE OUT THE BLENDED SPECTRUM.
call t6out(’blends.fit’,nx,x1am0,dlam,blend)
left = 0.
do i=1,nx
diff(i)=obj(i)-blend(i)
if ((dxval(i).ge.4505.).and.(dxval(i) 1e.4832.)) then
left = left + abS(diff(i))
endif
end do

left = left * dlam
write (91,*) glob, left
call t60ut(’blends.diff’,nx,x1am0,d1am,diff)
c ***********************************
c Let’s make a plot of the output.
pxmin = dxval(i)
pxmax dxval(nx)
pymin -5.e-14
pymax = 1 e-13
c This makes it not ask to continue when you end it.
call pgask(.false.)
c Change window size.
CALL PGENV(pxmin,pxmax,pymin,pymax,0,1)
c Labels for the graph. X, Y, Title. In this case
c I have left the title off and used the Baldwin Plot
c Label System (BPLS).

84

CALL PGLAB(’wavelength’, ’flux’,”)
c Change font size for BPLS, then label, then change it back.
call pgsch(3.)
call pgtext(pxmin+10.,pymin+0.9*(pymax-pymin),irafname)
call pgsch(1.)
call pgtext(pxmin+10.,pymin,"residual")
c Here we plot the actual graph. # pts, xarray,yarray,symbol
c The first call sets the line style.
call pgsls(1)
call pgline(nx,dxval,dyval)
call pgline(nx,dxval,blend)
call pgline(nx,dxval,diff)
c These make the empty rectangle and the crosshatching in the
c test ranges.
call PGSHS (0., 5., 0.)
CALL PGSFS(B)
wtest = 1
do while (wtest.1e.wc0unt)
call pgrect(wstart(wtest),wst0p(wtest),pymin,pymax)
wtest = wtest + 1

enddo
CALL PGSFS(2)
wtest = 1

do while (wtest.le.wc0unt)

call pgrect(wstart(wtest),wstop(wtest),pymin,pymax)

wtest = wtest + 1
enddo
c ***********************************
c This will reset out wnew and area back to our inputs from the blends in.
c If you want your fit to continue to evolve, that is if you want the new
c starting values to be the last ending values, comment this line out.

do n=1,ncomps,1
wnew(n) - wkeep(n)
area(n) akeep(n)
enddo

c Grab the next value from our input. The while loop
c will test to see if we are done.
read(21,*,IOSTAT=iof2) objfile
enddo
close(71)
close(72)
close(81)
close(88)
close(89)
close(90)

85

close(91)
call pgend
end

86

 

APPENDIX B:
CODE FOR CFUNK.F

 

This is the cfunk.f subroutine. It is called by the optical fitter, contin.f.

subroutine cfunk(npar,grad,fval,xval,iflag,futil)
double precision fval,xval(*)

double precision stuff, crap, m, b

double precision PI,BIGX,SIG,i,x,chi,AMP

double precision AMP2,BIGX2,SIG2

double precision grad,futil

double precision sdev,t0tal,keepme

real yave,average,stdev,chisq,xgauss

real armin,armax

integer count,n,npar,iflag,count1,count2,c0unt3
integer icomp,ibb

logical 1ratio,lprint,slide,wfix

double precision XX(5000),YY(5000)

real dxval(5000),dyval(5000)

real prix(5000),priy(5000),xbar,sigx

real wstart(30),wst0p(30),wsig(30),woff(30)

real ybar, sigy,ydev,yhigh,xhigh

real sdx(5000),spx(5000),sdy(5000),spy(5000)
integer NNX,lcount,wtest,wcount,ns

integer totcount

double precision scale

common /mysca1e/ scale

common /mydata/ dxval,dyval,nnx,wstart,wstop,wcount,
c ncomps,totalo,totcount,wsig,woff,yhigh,xhigh
common /pridata/ prix,priy,lcount,xbar,sigx,blend
parameter (nmax=50000)

common diff(nmax),xinput(nmax,30),shift(nmax),
c oname(30),w01d(30),wnew(30),area(30),nxc(30),
c xlamc(30),dlamc(30),totalc(30),nx,xlam0,dlam
character*50 oname,0bjfile

dimension obj(nmax),blend(nmax),ratio(nmax),id(100)

87

open (36,file=’gauss.test’,status=’unknown’)
write(36,*) xval(4),xval(5),xva1(6)

do i=1,nx
blend(i)=0.
end do

c Here we need to hand the values back from the xval array to the
c variables that are used in the blends routines.
c NOTE: This is a dangerous side effect of using the "align" subroutine.
c We are writing over the wnew and area arrays each time. This means that we
c can slowly move the acceptable ranges as we fit more spectra.
c I will take steps to keep this from happening in the main program.
ibb = 0
do n=1,ncomps,1
ibb = ibb + 1
wnew(n) = xval(ibb)
ibb = ibb + 1
area(n) = xval(ibb)
enddo
c Now for the continuum.
C The y values need to go into the array xinput(XXX,1), I think.

oname(ncomps+1) = "continuum"
This is the array size, it is equal to the number of points
c in the wavelength space.
nxc(ncomps+1) = nnx
This is the starting wavelength, this is the same as the
data starting wavelength, xlamO
xlamc(ncomps+1) = xlamO
c This is the wavelength step, should pass from main program.
dlamc(ncomps+1) = dlam
I have no clue what this is. Let’s make it 1.
id(nc0mps+1) = ncomps + 1
c These are the y values. Here is where I Should calcluate them.
totalc(ncomps+1) = 0.
do i=1,nnx
xinput(i,ncomps+1) = (xval((2*ncomps)+1) *
c ((dxval(i)/5600.)** xval((2*ncomps)+2)))

0

00

0

totalc(ncomps+1) = totalc(ncomps+1) + xinput(i,ncomps+1)
keepme = dxval(i)
enddo
c This is the starting wavelength again. You will just have

88

c to trust me.
wold(nc0mps+1) = xlam0
This is the new wavelength to shift to. I suspect we Should
also keep this the same always.
wnew(ncomps+1) = xlamO
c This is the area, it will be used as a scaling factor.
area(ncomps+1) = totalc(ncomps+1)/totalo

00

C Now for the align call.
c Slide should be set to false.
slide = .false.
do icomp=1,nc0mps
call align(icomp,nout0,noutx,slide)
scale=area(icomp)*totalo/totalc(icomp)
do i=1,nx
blend(i)=blend(i)+shift(i)*scale
end do
nb0=min(nb0,nout0)
nbx=max(nbx,noutx)
fluxc=area(icomp)*totalo*dlam
enddo
c Adding in the continuum.

do i=1,nx
b1end(i) = b1end(i) + xinput(i,ncomps+1)
enddo
c Now to calculate the values to minimize
chi = 0.
sdev = 0.1

totcount = 0

xhigh = 0.

yhigh = 0.

wtest = 1

do while (wtest.le.wc0unt)
n = 1

countl = 0
do while (n.1e.nnx)
if (dxval(n).ge wstart(wtest).and.
c dxval(n).le.wstop(wtest)) then
countl = countl + 1
sdx(count1) = dxval(n)
de(count1) = dyval(n)

89

dxval(n)
b1end(n)

spx(count1)
spy(count1)

if (dyval(n).gt.yhigh) then
xhigh = dxval(n)
yhigh = dyval(n)
endif
endif
n = n + 1
enddo
c Only do the rest if our spectrum contained this window.
if (count1.gt.0) then
ydev = wsig(wtest)
ns = 1
do while (ns.le.count1)
chi = chi + chisq(sdy(ns),spy(ns),ydev)
ns = ns + 1
totcount = totcount + 1
enddo

endif
c Move to the next test region.
wtest = wtest + 1
enddo

close(36)
fval = chi
return
end

90

 

APPENDIX C:
CODE FOR UVCONTIN.F

 

This is the FORTRAN code of the UV fitter. It calls uvfunk.f as a subroutine.

character*5 plabel(20),junk
double precision ptau(20),pincr(20),puper(20),ploer(20),zero
double precision ftau,err,eplus,eminus,arglis(2)
double precision PI .
integer i
integer ip,ierflg,ivarbl,npar,n,nn
double precision x,Y, m, b,yavefile,sdevfile
double precision gauss, chisq,average,stdev,noise
double precision fitout(20),small,chiout(20),errout(20)
real xgauss
integer chistat,card,j,idof
real ran2
external uvfunk
character*10 chtest
character*12 glob
integer chlen, IM, IER,xcur,ycur,NAX,IAX(7),IPIX
integer totcount
character chcur
real dxval(5000),dyval(5000),rtest
real cxval(5000),cyval(5000)
real prix(5000),priy(5000)
real txval(5000),tyval(5000)
real ylim(5000)
real scaley(5000)
real wstart(30),wstop(30),wsig(30),nsmooth(30),woff(30)
integer IMAXD,iof,county,lcount,iof2,wcount,wtest
integer iof3, iof5,iof40
character*26 irafname
real pxmin,pxmax,pymin,pymax,armin,armax
real xbar,sigx,ybar,sigy,yhigh,xhigh
double precision scale
common /myscale/ scale

91

common /mydata/ dxval,dyval,nnx,wstart,wstop,wcount,
c ncomps,totalo,totcount,wsig,woff,yhigh,xhigh

common /pridata/ prix,priy,1count,xbar,sigx,blend

parameter (nmax=50000)

common diff(nmax),xinput(nmax,30),shift(nmax),
c oname(30),wold(30),wnew(30),area(30),nxc(30),
c xlamc(30),dlamc(30),totalc(30),nx,xlam0,dlam

character*50 oname,objfile

dimension 0bj(nmax),blend(nmax),rati0(nmax),id(100)

dimension waves(nmax)

real crap, wkeep(30),akeep(30)

character*5 crap2

real cstart,cstop

double precision c0nerr,ag(4),ehigh,elow

C ***********************************

diff(l) = 3.14159

P1 = 3.14159

open(71,file=’slope.txt’)
open(72,file=’err0r.txt’)
open(81,file=’chi.txt’)
0pen(88,file=’offset.txt’)
open(89,file=’frac.txt’)
open(90,file=’fracerr.txt’)

32 format(a4,8x,a1,10x,a5,4x,a5,5x,a5)

open(77,file=’window.txt’)
wcount = 1
read(77,*,IOSTAT=iof5) wstart(wcount),wstop(wcount),nsmooth(wcount)
do while (iof5.eq.0)
wcount = wcount + 1
read(77,*,IOSTAT=i0f5) wstart(wcount),wst0p(wcount),nsmooth(wc0unt)
enddo
close(77)

c This puts wcount back to the correct value. Pointed out by
c Neelam.

wcount = wcount - 1

write (*,*) "wcount = ",wcount

c ***********************************
c Start setting up our plot. We will output to a
c file called plot ps.

call pgbegin(0,’plot ps/PS’,1,1)

92

This Opens blends.in and reads in the list of spectra to go get.
Some of them are put into an array. It should be noted that if a line
is not properly formatted (i.e. you forget to leave any blank space
between two numbers) it may not be a fatal error. This routine will
intrepret the poorly formatted line as the end of the file and the
program will continue without throwing and error. This can lead to
it only using a subset of the parameters in your blends.in file.
open(22,file=’blends.in’,status=’old’)
read(22,*,IOSTAT=iof3) objfile
write (*,*) objfile
read(22,*,IOSTAT=iof3) const
i=1
read(22,*,IOSTAT=iof3) oname(i),wold(i),wnew(i),area(i)
do while (iof3.eq.0)

i=i+1

read(22,*,IOSTAT=iof3) oname(i),wold(i),wnew(i),area(i)

enddo
ncomps=i-1
c Store the initial values from blends.in in case we need them later

do n=1,ncomps,1
wkeep(n) = wnew(n)
akeep(n) area(n)
enddo

C ***********************************
const = 3.20540747E-14
open (21,file=’sorted2.in’,status=’old’)
read(21,*,IOSTAT=iof2) objfile
do while (i0f2.eq.0)
write (*,*) objfile
c ***********************************

0000000

c These are the initial values for the minuit parameters.

c General format is as follows:

c plabel(n) = ’name-of-variable’

c ptau(n) = initial value

c pincr(n) = initial step size

c puper(n) = upper limit (0 for none)

c ploer(n) = lower limit (0 for none)halpha04-a 6562.8 6562.8 0.048
c npar = n (count of how many variables we have for minuit

c to manage)

c The ptau value will be passed to the xval array in your subroutine.
c Minuit will then step around and pass new ptau values to the xval
c array.

c These are the wavelength and area values for each of the input lines
c from blends.in.

npar = O

93

do n=1,ncomps,1
npar = npar + 1
plabel(npar) = oname(n)
ptau(npar) = wnew(n)
pincr(npar)=0.01
ploer(npar)=wnew(n) - 5.
puper(npar)=wnew(n) + 5.

npar = npar + 1
plabel(npar) = oname(n)
ptau(npar) = area(n)
pincr(npar)=0.0001
ploer(npar)=area(n) * 0.05
puper(npar)=area(n) * 5.
enddo
c NOTE: For the continuum, we are trying to fit a power law,
c so I am passing it the initial values for a
c continuum = A * (lambda‘gamma) fit.
npar = (2*ncomps) + 1
plabel(npar) = ’A’
ptau(npar) = 1.0e-14
pincr(npar)=1.e-15
puper(npar)=1.e-10
ploer(npar)=1.e-15

npar = (2*ncomps) + 2

plabel(npar) = ’gamma’

ptau(npar) = -1.8826

pincr(npar)=1.e-4

puper(npar)=-0.5

ploer(npar)=-2.

c This gives us a total of (2*nc0mps) + 2 parameters to
c give to the fitter. This total value is in npar.

c ***********************************

c Open the iraf file. This is the file we are fitting

c our profile to. Building the fit array should take

c place in the subroutine, Since minuit will need to

c tweak parameters.

c It must be a .imh, not a .fits

c read spectrum to be fitted

write(*,*) ’input object file is ’,0bjfile

irafname = objfile

call t6in(objfile,nx,xlam0,d1am,id,0bj,nmax)

write(*,*) ’nx, lambda range,dlambda = ’,nx,xlam0,xlam0+nx*dlam,dlam
nnx = nx

94

totalo=0.

yminobj=1.e30

ymaxobj=-1.e30

do i=1,nx
totalo=totalo+obj(i)
yminobj=min(yminobj,obj(i))
ymaxobj=max(ymaxobj,obj(i))
waves(i)=xlam0-dlam+i*dlam

end do
do i=1,nx
dxval(i) = waves(i)
dyval(i) = obj(i)
enddo
c 1!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

This section is used to hardwire in some parameters that are
related. There is a corresponding section in the subroutine
as well as in the code below where we pass the parameters to
minuit. If you edit one, you may need to edit the others.

0000

c I know the constant flux level of some of the narrow lines.
c Here I convert that flux into a fraction of the total flux
to be used by the fitter.

0

I happen to know that the flux for the narrow_he2.imh line should
be around 1.4055E-13. With this and the totalo from above, I can
calculate the actual value for the scale factor for it.

IUE
ptau(12) = 1.4055e-13 / (totalo*dlam)
ploer(12)= 0.
puper(12)= 0.
c Similarly, the median value for the c4_1549_ob52 should be around
c 5.134e-13.

0000

c IUE
ptau(8) = 5.134e-13 / (totalo*dlam)
ploer(8)= 0.
puper(8)= 0.

c And finally, the median for 03-1665
ptau(10) = 1.04e-13 / (totalo*dlam)
ploer(10)= ptau(10) *0.05

puper(10)= ptau(10) * 5.0

c Now to tie some wavelengths together. You will also need to change some

c things in the subroutine to make this 0k.
c C IV BLR

95

 

ptau(5) = ptau(1) - 90.27

ploer(5) = 0.

puper(5) = 0.

C C IV NLR

ptau(7) = ptau(1) - 89.85
ploer(7) = 0.

puper(7) = 0.

C 0 III 1663 NLR

ptau(9) = ptau(1) + 22.75
ploer(9) = 0.

puper(9) = 0.

C 0 III 1663 BLR
ptau(13) = ptau(1) + 22.75

ploer(13) = 0.
puper(13) = 0.
c He II NLR

ptau(11) = ptau(1)
ploer(11) = 0.
puper(11) = 0.

c !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

C **********************************II!

c SMOOTHING, from Neelam and Baldwin. Even numbers break this.

c them. It will make chisq artifically small.
do iwin=1,wcount

do i=1,nx
if(waves(i).lt wstart(iwin)) istart=i
if(waves(i).lt.wstop(iwin)) ist0p=i

enddo

istart=min(istart,nx)
istop=min(istop,nx)

xsig=0.
do i=istart, istop
nsm=min(nsmooth(iwin),2*(nx-i)+1)

sum=0.
do j=i-nsm/2,i+nsm/2

96

Don’t use

sum=sum+obj(j)
enddo
wdiff=obj(i)-sum/nsm
xsig=xsig+(wdiff*wdiff)
enddo

if(istart.lt.istop) then
wsig(iwin)=sqrt(xsig/(istop-istart))

else
wsig(iwin)=sum/nsm
end if
wsig(iwin) = 0.5e-14
enddo

C **31‘********************************

c read in the blend component spectra
c The continuum (a power law) will be built in the subroutine uvfunk.
do i=1,nc0mps
call t6in(oname(i),nxc(i),xlamc(i),dlamc(i),id,xinput(1,i),nmax)
totalc(i)=0.
do k=1,nxc(i)
totalc(i)=totalc(i)+xinput(k,i)
end do
end do

do i=1,nx
blend(i)=0.
end do
nb0=nmax
nbx=0
c ***********************************
c Set up minuit to do it’s thing.
* Set-up parameters for minuit (aka unit numbers for input,0utput)
call mninit(5,6,7)

* Set the initial values of the adjustable parameters (aka the "x")
* in function fcn. Let MINUIT know about those parameters attributes
do ip=1,npar

zero=0.

call mnparm(ip,plabe1(ip),ptau(ip),pincr(ip),ploer(ip),
1 puper(ip),ierf1g)
if (ierflg.ne.0) write(*,*) ’Par: ’,ip,’ not entered sucessfully’
end do

97

c Here is where I set some of the parameters to be constant, so that
c minuit does not adjust them.

arglis(1) = 12
call mnexcm(uvfunk,’FIX’,arglis,1,ierflg,0)

arglis(1) = 8
call mnexcm(uvfunk,’FIX’,arglis,1,ierflg,0)

arglis(1) = 10
call mnexcm(uvfunk,’FIX’,arglis,1,ierf1g,0)

arglis(1) = 5
call mnexcm(uvfunk,’FIX’,arglis,1,ierflg,0)

arglis(1) = 7
call mnexcm(uvfunk,’FIX’,arglis,1,ierflg,0)

arglis(1) = 9
call mnexcm(uvfunk,’FIX’,arglis,1,ierflg,0)

arglis(1) = 13
call mnexcm(uvfunk,’FIX’,arglis,1,ierflg,0)

arglis(1) = 11
call mnexcm(uvfunk,’FIX’,arglis,1,ierf1g,0)
c!!!!!!!!!!!!!!!!!!!!!l!

* These set the strategies by which Minuit work, higher is more
* "accurate" but more costly in time (see p.24 in MINUIT Ref man
* v94 1). I think this call is optional
arglis(1)=2.
call mnexcm(uvfunk,’SET STR’,arglis,1,ierf1g,0)
* Stuff for accurate error analysis, see p.22, optional also I think
arglis(1)=1.
call mnexcm(uvfunk,’SET ERR’,arglis,1,ierflg,0)
* Supress warnings.
arglis(1)=1.
call mnexcm(uvfunk,’SET NOW’,arglis,1,ierflg,0)

c Sets level of printout detail. -1 is minimum, 3 is highest.
arglis(1)=-1.

call mnexcm(uvfunk,’SET PRI’,arglis,1,ierflg,0)

* Now use Minimize the minimize the value of the function

c set the max number of iterations with arglis(1) and

c the precision required in arglis(2).

98

arglis(1)=50000.

arglis(2)=1.e-20

call mnexcm(uvfunk,’MIGRAD’,arglis,2,ierf1g,0)
C ***********************************

* Assuming convergence after <50000 iterations print out
* the current value of the function. Store the values in the
c array fitout.

write(*,*) " ------------------------------ "
write(*,*) "Results for ",0bjfile
write(*,*) ""
do ip=1,npar
call mnpout(ip,junk,ftau,err,eplus,eminus,ivarbl)
write(*,*)ip,’ ’,plabel(ip),’ Orig: ’,ptau(ip),’ Final:’,ftau,err
fitout(ip) = ftau
errout(ip) = err

end do
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

oooooooooooooooooooooooooooooooooooooooooo

fitout(5) = fitout(1) - 90.27
fitout(7) fitout(1)- 89.85
fitout(9) fitout(1)+ 22.76
fitout(13) = fitout(1) + 22.76

fitout(ll) = fitout(l)
IlllllllIllllllllllllllllllllllllllllll

This gets the current status of minimization. Since we are
’done’, this should be the final value of our minimized
function. These parameters are, in order: (1) minimum value
(2) estimated vertical distance to the minimum (3) the value of
parameter uncertainities (4) # of currently variable parameters
(5) the highest external parameter number defined by the user
(6) that status of the covariance matrix. See page 16 of
minuit manual.
call mnstat(chiout(1),chiout(2),chiout(3),chiout(4),chiout(5)

1 ,chistat)
idof = totcount - ((ncomps+2) - 4)
write(*,*) "REDUCED CHISQ = ",chiout(1)/idof

00000000

write(*,*) "FMIN = ",chiout(1)
write(*,*) "FEDM = ",chiout(2)
write(*,*) "ERRDEF = ",chiout(3)
write(*,*) "NPARI = ",chiout(4)
write(*,*) "NPARX = ",chiout(S)
write(*,*) "ISTAT = ",chiout(fi)
write(*,*) "xhigh = ",xhigh

write(*,*) "yhigh = ",yhigh

99

write(*,*) n ______________________________ n
C ***********************************

c Output the values to a file. In this case, the file is called
c ’slope.txt’ (for historical reasons) and contains:
glob = objfile

31 format(a8,1x,E12.6,1x,f8.5,1x,f8.5,1x,f9.5)
write (89,*) glob,chiout(1)/idof,fitout
write (90,*) glob,chiout(1)/idof,errout
write (81,*) glob,chiout(1)/idof
write (88,*) glob,xhigh,yhigh

C ***********************************

20 format(i2,1x,a20,2(0pf9.3),f7.3, 1pe10.2,1x,0pf7.3)
30 format(a20,2(0pf9.3),f7.3, 1pe10.2,1x,0pf7.3)

C ***********************************

c Here, we convert the fractions to flux values for the even parameters
do ip = 1, ncomps
fitout(2*ip)
errout(2*ip)
end do

fitout(2*ip) * totalo * dlam
errout(2*ip) * totalo * dlam

This is where we calculate the flux for the continuum. There is a

a problem with using this method if your spectra are not all the same
wavelength range. Trim your spectra or use a different method. I think
I may put some code here to take the "continuum" between a specific
wavelength range. It will still use the powerlaw that we fit, but it
would only keep the flux within a certain range.

I feel that the correct approach might be to re-evaluate the continuum
flux from the fitted parameters, integrating over a user specified range
and then do the calculation again with the parameters slewed to their error
limits to calculate the error in the flux.

= (2*ncomps)+3

: 0 0 (Itfi 0 0 (1(3 0 0

H
’U

Here we open up the input file where the user has specified
the window to use for the continuum. If the read fails in any
way (for instance there isn’t a file there or it only contains
one number) we will notice and default to using the whole
spectral range.

NOTE: This ’conwin.in’ part is no longer used. We calculate
the continuum at a specific point.

0 (3 0 (5 0 (3 0

100

open (40,file=’conwin.in’,status=’unknown’)
read (40,*,IOSTAT=iof40) cstart,cstop
if (iof40.ne.0) then
cstart = xlamc(ncomps+1)
cstop xlamc(ncomps+1) + (dlam * nx)
endif
close (40)
c As a test, let’s make the starting and ending wavelengths the
c full range for the spectrum.

write (*,*) "Range = ",cstart," - ",cstop
fitout(ip) = 0.

conerr = 0.
ag(1)
ag(2) -
ag(3)
ag(4)

I
0000

c Find the flux value at 1337.
fitout(ip) = fitout(2*ncomps+1) * (1337./5600.)**(fitout(2*ncomps+2))

c Calculate the four corners
ag(1) = ag(1) + ((fitout(2*ncomps+1)+errout(2*ncomps+1)) *
c ((1840./5600.)**(fitout(2*ncomps+2)+errout(2*ncomps+2))))

ag(2) = ag(2) + ((fitout(2*ncomps+1)-errout(2*ncomps+1)) *
c ((1840./5600.)**(fitout(2*ncomps+2)+errout(2*ncomps+2))))

ag(3) = ag(3) + ((fitout(2*ncomps+1)-errout(2*ncomps+1)) *
c ((1840./5600.)**(fitout(2*nc0mps+2)-errout(2*ncomps+2))))

ag(4) = ag(4) + ((fitout(2*ncomps+1)+errout(2*ncomps+1)) *
c ((1840./5600.)**(fitout(2*nc0mps+2)-errout(2*ncomps+2))))

c Now find the high and low, and subtract them.
elow = 9999.
ehigh = -9999.

do ii=1,4
if (ag(ii).gt.ehigh) then
ehigh = ag(ii)
endif
if (ag(ii).lt.elow) then

101

elow = ag(ii)
endif
enddo
errout(ip) = dlam * abs(ehigh - elow)
write (*,*) "New con = ",fitout(ip)

write(*,*)conerr,fitout(ncomps+1),fitout(ncomps+2)
c Write out the values using fluxes instead of fractions.

write (71,*) glob,chiout(1)/idof,fitout
write (72,*) glob,chiout(1)/idof,errout

C WRITE OUT THE BLENDED SPECTRUM.
call t60ut(’blends fit’,nx,xlam0,dlam,blend)
do i=1,nx
diff(i)=obj(i)-blend(i)
end do

call t60ut(’blends diff’,nx,xlam0,dlam,diff)

c ***********************************
c Let’s make a plot of the output.

pxmin = 1443.
pxmax = 1750.
pymin = -5.e-14
pymax = 1.e-13

c This makes it not ask to continue when you end it.
call pgask(.false.)

c Change window size.

CALL PGENV(pxmin,pxmax,pymin,pymax,0,1)

c Labels for the graph. X, Y, Title. In this case

c I have left the title off and used the Baldwin Plot

c Label System (BPLS).

CALL PGLAB(’wavelength’, ’flux’,”)

c Change font size for BPLS, then label, then change it back.

call pgsch(3.)

call pgtext(pxmin+10.,pymin+0.9*(pymax-pymin),irafname)

call pgsch(l.)

call pgtext(pxmin+10.,pymin,"residual")

c Here we plot the actual graph. # pts, xarray,yarray,symbol

c The first call sets the line style.

102

call pgsls(1)

call pgline(nx,dxval,dyval)

call pgline(nx,dxval,blend)

call pgline(nx,dxval,diff)

c These make the empty rectangle and the crosshatching in the

c test ranges.

call PGSHS (0., 5., 0.)

CALL PGSFS(3)

wtest = 1

do while (wtest le.wcount)
call pgrect(wstart(wtest),wstop(wtest),pymin,pymax)
wtest = wtest + 1

enddo
CALL PGSFS(2)
wtest = 1

do while (wtest.le.wc0unt)

call pgrect(wstart(wtest),wstop(wtest),pymin,pymax)

wtest = wtest + 1
enddo
c ***********************************
c This will reset out wnew and area back to our inputs from the blends.in.
c If you want your fit to continue to evolve, that is if you want the new
c starting values to be the last ending values, comment this line out.

do n=1,ncomps,1
wnew(n) = wkeep(n)
area(n) = akeep(n)
enddo

c Grab the next value from our input. The while loop
c will test to see if we are done.
read(21,*,IOSTAT=iof2) objfile
enddo
close(71)
close(72)
close(81)
close(88)
close(89)
close(90)

call pgend
end

103

 

 

APPENDIX D:
CODE FOR UVFUNK.F

 

This is the uvfunk.f subroutine. It is called by the UV fitter, uvcontin.f.

subroutine uvfunk(npar,grad,fval,xval,iflag,futil)
double precision fval,xval(*)
double precision stuff, crap, m, b
double precision PI,BIGX,SIG,i,x,chi,AMP
double precision AMP2,BIGX2,SIG2
double precision grad,futil
double precision sdev,total,keepme
real yave,average,stdev,chisq,xgauss
real armin,armax
integer count,n,npar,iflag,countl,count2,count3
integer icomp,ibb
logical 1ratio,lprint,slide,wfix
double precision XX(5000),YY(5000)
real dxval(5000),dyval(5000)
real prix(5000),priy(5000),xbar,sigx
real wstart(30),wstop(30),wsig(30),woff(30)
real ybar, sigy,ydev,yhigh,xhigh
real sdx(5000),spx(5000),sdy(5000),spy(5000)
integer NNX,lcount,wtest,wcount,ns
integer totcount
double precision scale
common /myscale/ scale
common /mydata/ dxval,dyval,nnx,wstart,wstop,wcount,
c ncomps,totalo,totcount,wsig,woff,yhigh,xhigh
common /pridata/ prix,priy,lcount,xbar,sigx,blend
parameter (nmax=50000)
common diff(nmax),xinput(nmax,30),shift(nmax),
c oname(30),wold(30),wnew(30),area(30),nxc(30),
c xlamc(30),dlamc(30),tota1c(30),nx,xlam0,dlam
character*50 oname,objfile
dimension obj(nmax),blend(nmax),ratio(nmax),id(100)

104

open (36,file=’gauss.test’,status=’unknown’)
write(36,*) xval(4),xval(5),xva1(6)

do i=1,nx
blend(i)=0.
end do

c Here we need to hand the values back from the xval array to the
c variables that are used in the blends routines.
c NOTE: This is a dangerous side effect of using the "align" subroutine.
c We are writing over the wnew and area arrays each time. This means that we
c can slowly move the acceptable ranges as we fit more spectra.
c I will take steps to keep this from happening in the main program.
ibb = 0
do n=1,ncomps,1
ibb = ibb + 1
wnew(n) = xval(ibb)
ibb = ibb + 1
area(n) = xval(ibb)
enddo

IIIIIIIIIIIIIIIIIIIIIIIIIIIIII

wnew(5) = wnew(1) - 90.27
wnew(7) = wnew(1) - 89.85
wnew(9) = wnew(1) + 22.76
wnew(13) = wnew(1) + 22.76

wnew(11) = wnew(1)
IIIIIIIIIIIIIIIIIIIIIIIIIIIII

ooooooooooooooooooooooooooooo

c Now for the continuum.
C The y values need to go into the array xinput(XXX,1), I think.
oname(ncomps+1) = "continuum"

c This is the array size, it is equal to the number of points
c in the wavelength space.

nxc(ncomps+1) = nnx
c This is the starting wavelength, this is the same as the

c data starting wavelength, xlamO
xlamc(ncomps+1) = xlamO

c This is the wavelength step, should pass from main program.
dlamc(ncomps+1) = dlam

c I have no clue what this is. Let’s make it 1.
id(ncomps+1) = ncomps + 1

c These are the y values. Here is where I should calcluate them.
totalc(ncomps+1) = 0.
do i=1,nnx

105

xinput(i,ncomps+1) = (xval((2*ncomps)+1) *
c ((dxval(i)/5600.)** xval((2*ncomps)+2)))

totalc(ncomps+1) = totalc(ncomps+1) + xinput(i,ncomps+1)
keepme = dxval(i)
enddo
c This is the starting wavelength again. You will just have
c to trust me.
wold(ncomps+1) = xlamO
c This is the new wavelength to shift to. I suspect we should
c also keep this the same always.
wnew(ncomps+1) = xlamO
c This is the area, it will be used as a scaling factor.
0 area(ncomps+1) = xval((2*ncomps)+3)
area(ncomps+1) = totalc(ncomps+1)/totalo

C Now for the align call.
c Slide should be set to false.
slide = .false.

do icomp=1,nc0mps
call align(icomp,nout0,noutx,slide)
scale=area(icomp)*totalo/totalc(icomp)
do i=1,nx
blend(i)=blend(i)+shift(i)*scale
end do
nb0=min(nb0,nout0)
nbx=max(nbx,noutx)
fluxc=area(icomp)*totalo*dlam
enddo

c Adding in the continuum.
do i=1,nx
b1end(i) = b1end(i) + xinput(i,ncomps+1)

enddo

c Now to calculate the values to minimize

chi = 0.
sdev = 0.1
totcount = 0
xhigh = 0.
yhigh = 0.
wtest = 1

106

 

do while (wtest.le.wc0unt)
n = 1
countl = 0
do while (n.1e.nnx)
if (dxval(n).ge wstart(wtest).and.
c dxval(n).le.wstop(wtest)) then
countl = countl + 1
sdx(countl) dxval(n)
de(count1) = dyval(n)
spx(count1) = dxval(n)
spy(count1) b1end(n)

if (dyval(n).gt.yhigh) then
xhigh = dxval(n)
yhigh = dyval(n)

endif

endif
n = n + 1
enddo
c Only do the rest if our spectrum contained this window.
if (count1.gt.0) then

ydev = wsig(wtest)

ns = 1

do while (ns.le.count1)
chi = chi + chisq(sdy(ns),spy(ns),ydev)
ns = ns + 1

totcount = totcount + 1

enddo

endif
c Move to the next test region.
wtest = wtest + 1
enddo

close(36)
fval = chi
return
end

107

 

 

APPENDIX E:
CODE FOR FUNCTIONS.F

 

The following are some useful function that are called by the fitting code.

c Function to calculate a value in a gaussian.

c I will make this more generic later.

double precision function xgauss(AMP,BIGX,SIG,x)
c real function xgauss(AMP,BIGX,SIG,x)

implicit none

double precision AMP,BIGX,SIG

real X

c real AMP,BIGX,SIG,X

c gauss = AMP * exp(-((x - BIGX)**2)/(2.*(SIG**2)))
c xval(4) * exp(-((dxval(i) - xval(5))**2)/(2.*(xval(6)**2)))
c xgauss = SIG
c xgauss = (2.*(SIG**2))
c xgauss (((x - BIGX)**2)/(2.*(SIG**2)))

xgauss = AMP * exp(-((x - BIGX)**2)/(2.*(SIG**2)))
c write (*,*) xgauss
return
end

c Function to calculate the current part of the chi‘2

c sum. This is NOT the entire chi“2, although I may make one
c that handles an array. In this case, B is the value

c you have more confidence it (you divide by B).

c double precision function chisq(A,B,sdev)

real function chisq(A,B,sdev)

implicit none

c double precision A,B,sdev

real A,B,sdev

c chisq = ((dabs(A - B))**2.) / (sdev**2.)

108

chisq = ((abs(A - B))**2.) / (sdev**2.)

return
end

c Function to calculate the average value in an
c array. Pass it the array and the length of the
c array.

c double precision function average(YY,n)
real function average(YY,n)

implicit none

c double precision YY(*),total

real YY(*),total

integer n, i

total = 0.0

do 10 i = 1,n
total = total + YY(i)
10 continue

average = total / (dble(float(n)))

return
end

Function to calculate the stdev value in an
array. Pass it the array,the length of the
array, and the average value of the array.
NOTE TO SELF: REWRITE SO THAT IT WILL CALL
FOR THE AVERAGE USING THE ABOVE FUNCTION?

00000

c double precision function stdev(YY,n,ave)
real function stdev(YY,n,ave)

implicit none

c double precision YY(*),total,ave

real YY(*),total,ave

integer n, i

total = 0.0

109

do 10 i = 1,n
total = total + ((YY(n) - ave)**2)
10 continue

stdev = dSqrt((1.0/(dble(float(n))-1.0)) * total)

return
end

c Function to find the minium of an array.
c Pass it the array and the length of the array.

real function armin(YY,n)
implicit none

real YY(*),min

integer n,i

min = YY(1)
do 10 i=2,n
if (YY(i).lt.min) then
min = YY(i)
endif
10 continue

armin = min
return
end

c Function to find the maximum of an array.
c Pass it the array and the length of the array.

real function armax(YY,n)
implicit none

real YY(*),max

integer n,i

max = YY(i)
do 10 i=2,n
if (YY(i).gt.max) then
max = YY(i)
endif

110

10 continue

armax = max
return
end

c Function to make a not-so-random number

c This routine is not really random. Use the next
c one instead.

real function random(seed,randx)

integer seed

real randx

seed = 2045 * seed + 1
seed seed - (seed/1048576)*1048576
randx = real(seed+1)/1048577.0

return
end

c _________________________________________
c This one actually makes a decent random number.
c You need to initialize it with a seed. Thereafer
c call it with the same value (1) to get a random
c number. This is taken from Numerical Recipies in
c FORTRAN, 2nd edition, page 272
FUNCTION ran2(idum)
INTEGER idum,IM1,IM2,IMM1,IA1,IA2,IQl,I02,IR1,IR2,NTAB,NDIV,idum3
REAL ran2,AM,EPS,RNMX
PARAMETER (IM1=2147483563,IM2=2147483399,AM=1./IM1,IMM1=IM1-1,
c IA1=40014,IA2=40692,I01=53668,IQ2=52774,IR1=12211,
c IR2=3791,NTAB=32,NDIV=1+IMM1/NTAB,EPS=1.2e-7,RNMX=1.-EPS)
INTEGER idum2,j,k,iv(NTAB),iy
SAVE iv,iy,idum2
DATA idum2/123456789/,iv/NTAB*0/,iy/O/
idum3=idum
if (idum3.le.0) then
idum3=max(-idum3,1)
idum2=idum3
do 11 j=NTAB+8,1,-1
k=idum3/IQl

111

11

c The
c Dr.

idum3=IA1*(idum3-k*IQl)-k*IR1
if(idum3.lt.0) idum3=idum3+IM1
if (j.le.NTAB) iv(j)=idum3
enddo
iy=iv(1)
endif
k=idum3/IQ1
idum3=IA1*(idum3-k*IQl)-k*IR1
if (idum3.lt.0) idum3=idum3+IMl
k=idum2/IQ2
idum2=IA2*(idum2-k*IQ2)-k*IR2
if (idum2.lt.0) idum2=idum2+IM2
j=1+iy/NDIV
iy=iv(j)-idum2
iv(j)=idum3
if (iy.lt.1) iy=iy+IMM1
ran2=min(AM*iy,RNMX)
return
END

following are functions that were developed by
Jack Baldwin. (And possibly Dr. Brian Sharpee.)

subroutine align(icomp,nout0,noutx)

c sets up call to XPAND subroutine.

parameter (nmax=50000)

common diff(nmax),xinput(nmax,30),shift(nmax),

oname(30),wold(30),wnew(30),area(30),nxc(30),
xlamc(30),dlamc(30),totalc(30),nx,xlam0,dlam

character*50 oname

do i=1,nx
shift(i)=0.

end do

ilenb=nmax
xlamj=xlam0
dlamj=dlam
xlami=xlamc(icomp)
dlami=dlamc(icomp)
i=icomp

112

IF (SLIDE) THEN

DX=DLAMJ/DLAMI
CXJ=(XLAMI-XLAMJ+WNEW(I)-WOLD(I)+.5*(dlamj-dlami))/DLAMJ
ELSE

write(*,*)" "

write(*,*)"WOLD(I), DLAMJ, WNEWCI), DLAMI"
write(*,*) WOLD(I),DLAMJ,WNEW(I),DLAMI

write(*,*) " "

DX=WOLD(I)*DLAMJ/(WNEW(I)*DLAMI)

c write (*,*) "dx = ",DX
CXJ=((XLAMI-.5*dlami)*WNEW(I)/WOLD(I)-XLAMJ)/DLAMJ+1.5
c write (*,*) "CXJ = ",CXJ

00000000

CXI=1.
NCI=nxc(i)
IF (CXJ.GE.1.) GOTO 7300
CXI=1.-(CXJ-1.)*DX
CXJ=1.
NCI=NCI-CXI+1

7300 IF (CXI+NCI.LT.ILENB-1.) GOTO 7800
NCI=ILENB-1.-CXI

7800 continue

c write (*,*) "CXJ = ",CXJ

c write (*,*) " "

c write (*,*) xinput(1,icomp),ilenb,CXJ,CXI,NCI,DX,noutx
CALL XPAND(xinput(1,icomp),shift,ilenb,CXJ,CXI,NCI,DX,noutx)

c write (*,*) "shift(1) = ",shift(1)

c write(*,*) ’cxj,cxi,nci,dx,noutx,xlami,xlamj’,
c * cxj,cxi,nci,dx,noutx,xlami,xlamj
nout0=cxj

return

end

SUBROUTINE XPAND(bufi,bufj,ilenb,CXJ,CXI,NCI,DX,jstop)
LINEAR SCRUNCH FROM bufi TO bufj.
also returns jstop=last pixel filled in output buffer
NOTE TO SELF: I THINK THAT THIS ROUTINE IS STILL RETURNING
ODD VALUES, NEED TO DIG DEEPER.

0000

113

 

dimension bufi(1),bufj(1)

c write(*,*) ’XPAND cxj,cxi,nci,dx’,cxj,cxi,nci,dx

3000

3600
3700

3800
c write

4000

NCIX=NCI

IF (CXI+NCI.GE.ILENB) NCIX=ILENB-.1-CXI
JCH=CXJ+1

IF (AINTCCXJ).EQ.CXJ) JCH=CXJ
JSTOP=CXJ+NCIX/DX-1.

IF (JSTOP.GT.ILENB-1) JSTOP=ILENB-1
CX2=CXI+(JCH-CXJ)*DX

IX2=CX2
REM=(1.-AMOD(CX2,1.))*bufi(IX2)
CX1=CX2

CX2=CX1+DX

ICX1=IFIX(CX1)+1

ICX2=CX2

SUM=REM

IF (ICX2-ICX1) 3800,3600,3600
I=ICX1

SUM=SUM+bufi(I)

I=I+1

IF (I-ICX2) 3700,3700,3800
REM=(FLOAT(ICX2+l)-CX2)*bufi(ICX2)
(*,*) ’Prepare to die.’
bufj(JCH)=(SUM-REM)

JCH=JCH+1

IF (JCH-JSTOP) 3000,3000,4000
RETURN

END

114

 

APPENDIX F:
TEMPLATE PROFILES

 

This chapter contains table formatted versions of the template profiles that were used

in this study

Table F.1: C IV BELR Template - c4_blr_smooth

 

 

Wavelength

Flux

 

1486.46997070313
1488.43620073796
1490.40243077279
1492.36866080761
1494.33489084244
1496.30112087727
1498.2673509121
1500.23358094693
1502.19981098176
1504.16604101658
1506.13227105141
1508.09850108624
1510.06473112107
1512.0309611559
1513.99719119072
1515.96342122555
1517.92965126038
1519.89588129521
1521.86211133004
1523.82834136487
1525.79457139969
1527.76080143452
1529.72703146935
1531.69326150418
1533.65949153901
1535.62572157383
1537.59195160866
1539.55818164349
1541 .52441 167832

9.555542E—16
7.878893E—16
1.085533E—15
1.811270E—15
2.411968E—15
2.109406E—15
1.793699E15
1.600550E—15
1.742496E—15
1.45596OE—15
1.7551 1913-15
2.651444E—15
3.796852E—15
4.689520E—15
5.576753E—15
5.796336E—15
5.428699E—15
4.965610E—15
5.013607E—15
6.108739E—15
8.075923E-15
9.815303E—15
1.116838E—14
1.146565E-14
1.277366E—14
1.491611E—14
1.740484E-14
1.939291E—14
2.040391E—14

 

115

Table F.1: C IV BELR Template (continued)

 

 

Wavelength

Flux

 

1543.49064171315
1545.45687174798
1547.4231017828
1549.38933181763
1551.35556185246
1553.32179188729
1555.28802192212
1557.25425195694
1559.22048199177
1561.1867120266
1563.15294206143
1565.11917209626
1567.08540213109
1569.05163216591
1571.01786220074
1572.98409223557
1574.9503222704
1576.91655230523
1578.88278234005
1580.84901237488
1582.81524240971
1584.78147244454
1586.74770247937
1588.7139325142
1590.68016254902
1592.64639258385
1594.61262261868

2.098864E— 14
2.120340E—14
2.249443E— 14
2.318910E—14
2.252947E-14
2.163747E—14
2.057907E—14
1.949838E— 14
1.773638E—14
1.557651E—14
1.452734E—14
1.234087E— 14
1.079152E—14
9.238349E—15
8.286056E-15
7.320719E15
6.000376E-15
4.954878E—15
3.547751E—15
2.745185E—15
2.272479E—15
2.485506E-15
2.795652E—15
2.071041E—15
1.329357E—15
7.451243E-16
1.399852E—15

 

Table F.2: He II BELR Template - smooth_4686

 

 

 

Wavelength Flux
4474.65771484375 -2.226108E—20
4476.62394487858 4.524233E—18
4478.59017491341 1.649479E—17
4480.55640494823 2.093099E—17
4482.52263498306 2.183218E—17
4484.48886501789 1.529701E—17
4486.45509505272 1.689205E-17
4488.42132508755 1.888768E—17
4490.38755512238 1.936672E—17

4492.3537851572 1.720526E—17
4494.32001519203 1.499648E—17

 

116

Table F .2: He II BELR Template (continued)

 

 

Wavelength

Flux

 

4496.28624522686
4498.25247526169
4500.21870529652
4502.18493533134
4504.15116536617
4506.117395401
4508.08362543583
4510.04985547066
4512.01608550549
4513.98231554031
4515.94854557514
4517.91477560997
4519.8810056448
4521 .84723567963
4523.81346571446
4525.77969574928
4527.74592578411
4529.71215581894
4531 .67838585377
4533.6446158886
4535.61084592342
4537.57707595825
4539.54330599308
4541 .50953602791
4543.47576606274
4545.44199609756
4547.40822613239
4549.37445616722
4551 .34068620205
4553.30691623688
4555.27314627171
4557.23937630653
4559.20560634136
4561.17183637619
4563.13806641102
4565.10429644585
4567.07052648068
4569.0367565155
4571 .00298655033
4572.96921658516
4574.93544661999
4576.90167665482
4578.86790668964
4580.83413672447
4582.8003667593

1.495106E—17
1.766637E—17
2.027571E—17
2.271065E—17
2.647071E—17
3.023264E—17
3.306995E—17
3.657374E—17
4.009806E—17
4.391710E—17
4.984802E—17
5.583877E—17
6.007345E—17
6.353339E—17
6.812777E— 17
7.329635E—17
7.865452E—17
8631378E-17
9.506347E—17
1.046404E—16
1.153526E—16
1.233549E-16
1.299636E- 16
1.371751E—16
1.438533E-16
1.487064E-16
1.518830E—16
1.548249E—16
1.561565E—16
1.561655E— 16
1.557713E—16
1.554378E— 16
1.561853E-16
1.574520E—16
1.597001E—16
1.625481E—16
1.676775E—16
1.755404E—16
1.840473E—16
1.918970E—16
1.988599E—16
2.063728E16
2.157849E— 16
2.239470E— 16
2.312843E—16

 

117

 

Table F.2: He II BELR Template (continued)

 

 

Wavelength

Flux

 

4584.76659679413
4586.73282682896
4588.69905686378
4590.66528689861
4592.63151693344
4594.59774696827
4596.5639770031
4598.53020703793
4600.49643707275
4602.46266710758
4604.42889714241
4606.39512717724
4608.36135721207
4610.32758724689
4612.29381728172
4614.26004731655
4616.22627735138
4618.19250738621
4620.15873742104
4622.12496745586
4624.09119749069
4626.05742752552
4628.02365756035
4629.98988759518
4631.95611763001
4633.92234766483
4635.88857769966
4637.85480773449
4639.82103776932
4641 .78726780415
4643.75349783897
4645.7197278738
4647.68595790863
4649.65218794346
4651 .61841797829
4653.58464801311
4655.55087804794
4657.51710808277
4659.483338] 176
4661 .44956815243
4663.41579818726
4665.38202822208
4667.34825825691
4669.31448829174
4671 .28071832657

2.384045E-16
2.459172E—16
2.521743E—16
2.573554E16
2.610859E— 16
2.646214E—16
2.690273E—16
2.717301E-16
2.728816E—16
278722413- 16
2.867272E— 16
2.935437E16
2.989477E-16
3.032740E—16
3.077107E-16
3.143824E—16
3.227494E—16
3.289767E— 16
3.334984E—16
3.372909E-16
3.379981E16
3.371117E—16
3.371088E-16
3.377916E16
3.391300E—16
3.405739E—16
3.409171E- 16
3.391662E16
3.396290E—16
3.419186E—16
3.428730E—16
3.439865E—16
3.459071E—16
3.469655E- 16
3.483239E—16
3.522086E—16
3.545163E—16
3.554608E—16
3.582956E— 16
3.596801E—16
3.600871E—16
3.604621E-16
3.590709E—16
3.560959E- 16
3.531387153- 16

 

118

Table F.2z He II BELR Template (continued)

 

 

Wavelength

Flux

 

4673.2469483614
4675.21317839623
4677.17940843105
4679.14563846588
4681 . 1 1 186850071
4683.07809853554
4685.04432857037
4687.01055860519
4688.97678864002
4690.94301867485
4692.90924870968
4694.87547874451
4696.84170877934
4698.80793881416
4700.77416884899
4702.74039888382
4704.70662891865
4706.67285895348

47086390889883
4710.60531902313
4712.57154905796
4714.53777909279
4716.50400912762
4718.47023916245
4720.43646919727

4722.4026992321
4724.36892926693
4726.33515930176
4728.30138933659
4730.26761937141
4732.23384940624
4734.20007944107

4736.1663094759
4738.13253951073
4740.09876954556
4742.06499958038
4744.03122961521
4745.99745965004
4747.96368968487

4749.9299197197
4751 .89614975452
4753.86237978935
4755.82860982418
4757.79483985901
4759.76106989384

3.479621E-16
3.395000E-l6
3.321598E—16
3.261837E—16
3.217771E—16
3.182733E— 16
3.149227E—16
3.122995E—16
3.091749E—16
3.057804E—16
3.031961E-16
3.018968E-16
2.990091E—16
2.948490E—16
2.903954E— 16
2.823232E—16
2.745228E—16
2.686461E—16
2.626774E—16
2.583398E— 16
2.558496E- 16
2.513373E—16
2.452573E—16
2.418306E—16
2.419612E-16
2.429396E— 16
2.432827E—16
2.414252E—16
2.359441E—16
2.305466E—16
2.258931E—16
2.217075E—16
2.184997E—16
2.162233E— 16
2.150377E-16
2.115558E—16
2.063860E—16
2.011232E—16
1.970393E—16
1.968767E— 16
1.978460E—16
1.979965E—16
1.982249E—16
1.994668E16
2.002487E—16

 

119

 

Table F.2: He II BELR Template (continued)

 

 

Wavelength

Flux

 

4761 .72729992867
4763.69352996349
4765.65975999832
4767.62599003315
4769.59222006798
4771 .55845010281
4773.52468013764
4775.49091017246
4777.45714020729
4779.42337024212
4781 .38960027695
4783.35583031178
4785.3220603466
4787.28829038143
4789.25452041626
4791 .22075045109
4793.18698048592
4795.15321052075
4797.11944055557
47990856705904
4801.05190062523
4803.01813066006
4804.98436069489
4806.95059072971
4808.91682076454
4810.88305079937
4812.8492808342
4814.81551086903
4816.78174090386
4818.74797093868
4820.71420097351
4822.68043100834
4824.64666104317
4826.612891078
4828.57912111282
4830.54535114765
4832.51158118248
4834.47781121731
4836.44404125214
4838.41027128696
4840.37650132179
4842.34273135662
4844.30896139145
4846.27519142628
4848.24142146111

1.989347E—16
1.986144E—16
1.986824E-16
2007840E—16
2038013E-16
2.055911E—16
2079819E- 16
2.109205E—16
2.125124E- 16
2.124999E—16
2129367E-16
2.137377E—16
2.133939E—16
2.120735E—16
2.087943E—16
2.045651E—16
2.007191E-16
1.936779E—16
1.851315E—16
1.760814E-16
1.662250E—16
1.559882E-16
1.443273E—16
1.314655E—16
1.200364E—16
1.107629E-16
1.035315E16
9.607090E—17
8.986784E—17
8.399395E—17
7.803100E—17
7.272366E— 17
6.623011E—17
6.150891E— 17
5.820838E—17
5.501518E—17
5.234666E—17
5.102761E—17
5.060465E—17
4.909309E—17
4.514991E—17
4.132433E—17
4.860989E—17
5.703022E—17
5.280361E—17

 

120

Table F .2: He II BELR Template (continued)

 

 

Wavelength

Flux

 

4850.20765149593
4852.17388153076
4854.14011156559

3.763022E—17
1.218048E—17

-1.475658E—17

 

Table F.3: He I BELR Template - smooth_5876

 

 

Wavelength

Flux

 

5711.41650390625
5713.38273394108
5715.34896397591
5717.31519401074
5719.28142404556
5721 .24765408039
5723.21388411522
5725.18011415005
5727.14634418488
57291125742197
5731 .07880425453
5733.04503428936
5735.01126432419
5736.97749435902
5738.94372439385
5740.90995442867
57428761844635
5744.84241449833
5746.80864453316
5748.77487456799
5750.74110460282
5752.70733463764
5754.67356467247
5756.6397947073
5758.60602474213
5760.57225477695
5762.53848481178
5764.50471484661
5766.47094488144
5768.43717491627
5770.4034049511
5772.36963498592
5774.33586502075
5776.30209505558
5778.26832509041

1.798370E—17
2.056418E17
2450033E-17
1.889557E—17
1.191293E-17
3.978324E—18
4.286419E—18
4.278359E—18
2.7301 18B— 18
1.735316E—18
2.635988E— 18
3.759410E—18
4.240993E—18
6.857291E—18
1.196061E—17
1.663132E17
1.859282E—17
1.743692E—17
1.718315E—17
2.017405E—17
2.308250E17
2.502209E-17
2959958E—17
3.541167E—17
3.843989E—17
3.954854E—17
4.035626E—17
4.345871E—17
5.037816E—17
5.675592E—17
6.044200E—17
6.356995E—17
6.524549E-17
7.057997E—17
8411846E—17

 

121

Table F.3: He I BELR Template (continued)

 

 

 

Wavelength Flux
5780.23455512524 9.817483E—17
5782.20078516006 1.122901E-16

5784.16701519489
5786.13324522972
5788.09947526455
5790.06570529938
5792.03193533421
5793.99816536903
5795.96439540386
5797.93062543869
5799.89685547352
5801.86308550835
5803.82931554317
5805.795545578
5807.76177561283
5809.72800564766
5811.69423568249
5813.66046571732
5815.62669575214
5817.59292578697
58195591558218
5821.52538585663
5823.49161589146
5825.45784592629
5827.4240759611]
5829.39030599594
5831.35653603077
5833.3227660656
5835.28899610043
5837.25522613525
5839.22145617008
584] . 1876862049 1
5843.15391623974
5845. 12014627457
5847.0863763094
5849.05260634422
5851.01883637905
5852.98506641388
5854.95129644871
5856.91752648354
5858.88375651837
5860.84998655319
5862.81621658802
5864.78244662285
5866.74867665768

1.328877E-16
1.492696E—16
1.549276E-16
1.610768E—16
1.662751E-16
1.705157E—16
1.813911E—16
1.895944E—16
1.874678E—16
1.852574E—16
1.837783E-16
1.775525E—16
1.768070E—16
1.868581E-16
1.987073E—16
2133718E-16
2293091E—16
2.395498E—16
248808013- 16
2.617535E—16
2.770660E—16
2.922752E— 16
3.062284E—16
3.]76406E—16
3.259849E—16
3.343572E16
3.428737E—16
3.498115E—16
3.584567E—16
3.678721E-16
3.746906E16
3.792348E-16
3.841199E—16
3.890883E—16
3.933548E—16
3.984716E-16
4.0]0937E—16
4.016112E-16
4.034503E—16
4.037147E—16
4.019326E—16
4.016117E-16
4.005899E-16

 

122

Table F.3: He I BELR Template (continued)

 

 

Wavelength

Flux

 

5868.71490669251
5870.68113672733
5872.64736676216
5874.61359679699
5876.57982683182
5878.54605686665
5880.51228690147
58824785169363
5884.44474697113
5886.4]097700596
5888.37720704079
5890.34343707562
5892.309667] 1044
5894.27589714527
58962421271801
5898.20835721493
5900. 17458724976
5902.14081728459
5904.10704731941
5906.07327735424
5908.03950738907
59100057374239
5911.97196745873
5913.93819749355
5915.90442752838
5917.8706575632]
5919.83688759804
5921.803] 1763287
5923.76934766769
5925.73557770252
5927.70180773735
5929.66803777218
5931.63426780701
5933.60049784184
5935.56672787666
5937.53295791149
5939.49918794632
5941.46541798115
5943.43164801598
5945.39787805081
5947.36410808563
5949.33033812046
5951.29656815529
5953.26279819012
5955.22902822495

3.962944E—16
3.907658E—16
3.861842E—16
3.794923E—16
3.717947E—16
3.644897E—16
3.579477E—16
3.524358E—16
3.486686E—16
3.450174E—16
3.437430E—16
3.472859E—16
3.522810E-16
3.554158E-16
3.594253E— 16
3.650251E—16
3.698083E—16
3.727435E— 16
3.754703E16
3.764105E-16
3.757477E—16
3.731654E—16
3.675422E— 16
3.607532E—16
3.548780E— 16
3.493588E—16
3.425913E—16
3.349542E—16
3.266659E—16
3.171068E—16
3.085326E—16
3.014570E— 16
2.941019E—16
2.861237E—16
2.773342E—16
2661563E— 16
2.536590E—16
2.416549E—16
2.303582E—16
2.201736E— 16
2092005E—16
1.959612E-16
1.824040E-16
1.702803E16
1.585227E—16

 

123

Table F.3: He I BELR Template (continued)

 

 

Wavelength

Flux

 

5957.19525825977
5959. 1614882946
5961 . 12771832943
5963.09394836426
5965.06017839909
5967.02640843392
5968.99263846874
5970.95886850357
59729250985384
5974.89132857323
5976.85755860806
5978.82378864288
5980.79001867771
5982.75624871254
5984.72247874737
5986.6887087822
5988.65493881703
5990.62116885185
5992.58739888668
5994.5536289215]
5996.51985895634
5998.48608899117
6000.45231902599
6002.41854906082
6004.38477909565
6006.35100913048
6008.31723916531
6010.28346920014
6012.24969923496
6014.21592926979
6016.18215930462
6018.14838933945
6020.11461937428
6022.0808494091]
6024.04707944393
6026.01330947876
6027.97953951359
6029.94576954842
6031.9]199958325
6033.87822961807
6035.8444596529
6037.81068968773
6039.77691972256
6041.74314975739
6043.70937979222

1.471449E- 16
1.381627E—16
1.314515E— 16
1.253538E—16
1.200129E-16
1.]52927E—16
1.107399E—16
1.066755E- 16
1.040117E—16
1.01435413- 16
9.888097E—17
9666658E—17
9.494531E— 17
9.200690E—17
8.800691E—17
8.428245E—17
7.998856E—17
7.538843E—17
7.284490E— 17
7.045000E—17
6.797649E— 17
6.547438E—17
6.343528E—17
6.232525E—17
6.358009E-17
6.536425E-17
6.596458E—17
6.644891E—17
6.712898E-17
6.645418E—17
6.365165E-17
6.001508E—17
5.845642E—17
5.806977E—17
5.404528E—17
4.717112E—17
4.317035E—17
4.084554E—17
3.927451E—17
3.848322E—17
3.831944E—17
3.959378E—17
4.082546E—17
3.978679E—17
3692428E—17

 

124

Table F .3: He I BELR Template (continued)

 

 

Wavelength

Flux

 

6045.67560982704
6047.64183986187
60496080698967
6051.57429993153
6053.54052996636
6055.50676000118
6057.4729900360]
6059.43922007084
6061.40545010567
6063.3716801405
6065.33791017532
6067.30414021015
6069.27037024498
6071.2366002798]
6073.20283031464
6075. 16906034947
6077.13529038429

3.552637E—17
3.460570E—17
3.144946E—17
2699929E—17
2147413E—17
1.502911E-17
1.036778E—17
6.606877E18
2.603421E-18
-1.727231E-18
~5.237146E— 18
-8.889238E—18
—9.563139E—18
-6.476895E-18
-8.658044E—18
-5.760093E—]8
5.545684E— 18

 

Table F.4z H6 BELR Template - smooth_halpha

 

 

Wavelength

Flux

 

6204.93994140625
6206.90617144108
6208.87240147591
6210.83863151074
6212.80486154556
6214.77109158039
6216.73732161522
6218.70355165005
6220.66978168488
6222.6360117197
6224.60224175453
6226.56847178936
6228.53470182419
6230.50093185902
6232.46716189384
6234.43339192867
6236.3996219635
6238.36585199833
6240.33208203316
6242.29831206799
6244.26454210281

2470912E-17
3.138737E—17
3.393811E—17
3.531292E17
3.479353E—17
3.344160E— 17
3.429950E—17
3.524041E—17
3.535926E—17
3.462812E—17
3.301380E-17
3.197182E—17
3.341499E—17
3.459055E—17
3.406275E—17
3.462393E—17
3.578811E—17
3.744813E—17
3.920526E—17
4.]14707E—17
4.410804E—17

 

125

Table F.4: H6 BELR Template (continued)

 

 

Wavelength

Flux

 

6246.23077213764
6248.19700217247
6250. 1632322073
6252. 12946224213
6254.09569227695
6256.06192231178
6258.02815234661
6259.99438238144
6261.96061241627
62639268424511
6265.89307248592
6267.85930252075
6269.82553255558
6271.79176259041
6273.75799262524
6275.72422266007
6277.69045269489
6279.65668272972
6281.62291276455
6283.58914279938
6285.55537283421
6287.52160286903
6289.48783290386
6291.45406293869
6293.42029297352
6295.38652300835
6297.35275304318
6299318983078
6301.28521311283
6303.25144314766
6305.21767318249
6307.18390321732
6309.15013325214
6311.11636328697
6313.0825933218
6315.04882335663
6317.01505339146
6318.98128342629
6320.94751346111
6322.91374349594
6324.87997353077
6326.8462035656
6328.81243360043
6330.77866363525
6332.74489367008

4.627474E—17
4685538E—17
4.688901E—17
4.781967E—17
4.979140E—17
5.]58497E—17
5.360073E-17
5.437622E—17
5.426348E—17
5.494872E—17
5.661864E—17
6.035104E-17
6.403553E— 17
6.592892E—17
6.802436E—17
7.]85032E—17
7.480487E—17
7.511221E-17
7.520856E—17
7.597098E—17
7.802443E—17
8.163739E-17
8.707652E—17
9.544873E—17
1.050273E—16
1.]13931E—16
1.146173E—16
1.169401E—16
1.194395E16
1.229063E—16
1.250254E—16
1.239049E—16
1.2]9971E—16
1.199884E—16
1.166322E-16
1.132347E-16
1.]35615E—16
1.153381E-16
1.173775E—16
1.208985E—16
1.237250E—16
1.274813E-16
1.335145E—16
1.394530E—16
1.437759E—16

 

126

Table F.4: H6 BELR Template (continued)

 

 

Wavelength

Flux

 

6334.711 12370491
6336.67735373974
6338.64358377457
63406098138094
6342.57604384422
6344.54227387905
6346.50850391388
6348.47473394871
6350.44096398354
6352.40719401836
6354.37342405319
6356.33965408802
6358.30588412285
6360.272] 1415768
6362.23834419251
6364.20457422733
6366.17080426216
6368.13703429699
6370.10326433182
6372.06949436665
6374.03572440148
6376.0019544363
6377.96818447113
6379.93441450596
6381.90064454079
6383.86687457561
6385.83310461044
6387.79933464527
6389.7655646801
6391.73179471493
6393.6980247 4976
6395.66425478458
6397.63048481941
6399.59671485424
6401.56294488907
64035291749239
6405.49540495873
6407.46163499355
6409.42786502838
6411.39409506321
6413.36032509804
6415.32655513287
6417.29278516769
6419.25901520252
6421.22524523735

1.470713E—16
1.516006E—16
1.556169E— 16
1.592275E—16
1.629258E—16
1.656886E—16
1.680657E16
1.700208E—16
1.717445E— 16
1.737646E—16
1.756099E16
1.768902E-16
1.764521E-16
1.752646E— 16
1.753727E— 16
1.774204E— 16
1.810469E-16
1.856733E16
1.905573E— 16
1.955774E— 16
1.985264E— 16
2.008650E—16
2.035754E— 16
2.053441E—16
2055454E—16
2.026673E-16
1.997591E—16
1.963774E—16
1.922151E—16
1.881551E— 16
1.830282E16
1.770930E—16
1.721010E— 16
1687625E— 16
1.669813E—16
1.658638E—16
1.661034E—16
1653334E—16
1640935E—16
1631261E—16
1625696E— 16
1.631119E-16
1.660541E-16
1.693939E—16
1.727282E—16

 

127

Table F.4: H6 BELR Template (continued)

 

 

Wavelength

Flux

 

6423.19147527218
6425. 1577053070]
6427.12393534184
6429.09016537666
6431.05639541 149
6433.02262544632
6434.98885548115
6436.95508551598
6438.9213155508]
6440.88754558563
6442.85377562046
6444.82000565529
6446.78623569012
6448. 75246572495
6450. 71869575977
6452 6849257946
6454.65115582943
6456.61738586426
6458.58361589909
6460.54984593391
6462.51607596874
6464.48230600357
6466.4485360384
6468.41476607323
6470.38099610806
6472.34722614288
6474.31345617771
6476.27968621254
6478.24591624737
64802121462822
6482.17837631703
6484.14460635185
6486.11083638668
6488.07706642151
6490.04329645634
6492.009526491 17
6493975756526
6495.94198656082
6497.90821659565
6499.87444663048
6501.84067666531
6503.80690670014
6505.77313673496
6507.73936676979
6509.70559680462

1.774323E—16
1.821949E—16
1.885894E—16
1.985706E—16
2.115752E—16
2.284933E- 16
2494287E—16
2.716319E—16
2.933112E-16
3.166915E-16
3.419889E—16
3.677062E—16
3.968587E— 16
4.288621E—16
4609749E—16
4.935644E16
5.264588E— 16
5606630E—16
5.994395E-16
6.408052E—16
6.827488E—16
7.268004E—16
7.755210E—16
8.310800E—16
8.951710E16
9685033E—16
1.052640E-15
1.148176E—15
1.251438E—15
1.361126E—15
1.482315E—l5
1.614353E—15
1.752979E—15
1.895414E—15
2.040084E15
2.187079E—15
2.334599E15
2480961E-15
2626958E—15
2773383E—15
2.918876E—15
3.061826E—15
3.]97480E—15
3.327646E—15
3.453143E-15

 

128

Table F.4: H6 BELR Template (continued)

 

 

Wavelength

Flux

 

6511.67182683945
6513.63805687428
6515.60428690911
6517.57051694393
6519.53674697876
6521.50297701359
6523.46920704842
6525.43543708325
6527.40166711807
65293678971529
6531.33412718773
6533.30035722256
6535.26658725739
6537.23281729221
6539.19904732704
6541.16527736187
6543.1315073967
6545.09773743153
6547.06396746635
6549.03019750118
6550.99642753601
6552.96265757084
6554.92888760567
6556.8951176405
6558.86134767532
6560.82757771015
6562.79380774498
6564.76003777981
6566.72626781464
6568.69249784947
6570.65872788429
6572.62495791912
6574.59118795395
6576.55741798878
6578.52364802361
6580.48987805844
6582.45610809326
6584.42233812809
6586.38856816292
6588.35479819775
6590.32102823258
65922872582674
6594.25348830223
6596.21971833706
6598. 18594837189

3.572533E—15
3680501E—15
3.780276E—15
3.873117E—15
3.955677E—15
4.027324E—15
4090613E-15
4.142525E—15
4186529E—15
4.225201E-15
4.256342E—15
4.278422E-15
4.291480E—15
4.293124E-15
4.282466E—15
4.260930E—15
4.228644E—15
4.189292E-15
4153377E—15
4.121228E—15
4.092857E-15
4.074641E—15
4.060103E—15
4.043423E—15
4.020488E— 15
3.989100E—15
3.958606E—15
3.942636E15
3.942782E—15
3.958823E—15
3.997225E—15
4.057596E15
4.133325E—15
4.220459E—15
4.3]0659E—15
4.401957E-15
4.499583E—15
4603118E-15
4700990E—15
4.785036E—15
4848201E—15
4.881145E-15
4.879714E—15
4.846394E—15
4.791387E—15

 

129

Table F.4: H6 BELR Template (continued)

 

 

Wavelength

Flux

 

6600. 152178406 72
6602.11840844155
6604.08463847637
6606.0508685112
6608.01709854603
6609.98332858086
6611.94955861569
6613.91578865051
6615.88201868534
6617.84824872017
6619814478755
6621.78070878983
662374693882465
6625.71316885948
6627.6793988943]
6629.64562892914
6631.61185896397
6633.57808899879
6635.54431903362
6637.51054906845
6639.47677910328
6641.44300913811
6643.40923917294
6645.37546920776
6647.34169924259
6649.30792927 742
6651.27415931225
6653.24038934708
6655.20661938191
6657.17284941673
6659.13907945156
6661 . 10530948639
6663.07153952122
6665.03776955605
6667.00399959088
66689702296257
6670.93645966053
6672.90268969536
6674.86891973019
6676.83514976502
6678.80137979985
6680.76760983467
66827338398695
6684.70006990433
6686.66629993916

4.727138E—15
4657593E—15
4.578283E—15
4.478202E—15
4.353729E—15
4.206287E—15
4.038476E—15
3.857809E—15
3667759E—15
3.472053E—15
3.274302E—15
3.077654E—15
2.886332E—15
2702906E—15
2.529920E—15
2.370161E—15
2.224352E—15
2.090458E—15
1.965545E15
1.848374E—15
1.736192E—15
1627123E—15
1.522360E—15
1.424175E~15
1.332424E—15
1.245603E15
1.164588E—15
1.089870E—15
1.021842E—15
9.6]0996E— 16
9.062608E—16
8.564242E—16
8. 133149E—16
7.761119E- 16
7.408232E—16
7063557E— 16
6.757995E—16
6.474701E—16
6.191346E-16
5.920317E— 16
5664707E—16
5.436521E16
5.243954E— 16
5.064624E—16
4.905786E—16

 

130

Table F.4: H6 BELR Template (continued)

 

 

Wavelength

Flux

 

6688.63252997399
6690.59876000881
6692.56499004364
6694.53122007847
6696.497450] 133
6698.46368014813
6700.42991018296
6702.39614021778
6704.36237025261
6706.32860028744
6708.29483032227
6710.2610603571
6712.22729039192
6714.]9352042675
6716.15975046158
6718.12598049641
6720.09221053124
6722.05844056606
6724.02467060089
6725.99090063572
6727.95713067055
6729.92336070538
6731.8895907402
6733.85582077503
6735.82205080986
6737.78828084469
6739.75451087952
6741.72074091435
6743.68697094917
6745653200984
6747.6]943101883
6749.58566105366
6751.55189108849
6753.51812112332
6755.48435115814
6757.45058119297
67594168112278
6761.38304126263
6763.34927129746
6765.31550133228
6767.28173136711
676924796140194
6771.21419143677
6773.1804214716
6775.14665150643

4.774609E—16
4657864E—16
4.544573E—16
4.447459E—16
4.377419E—16
4.319426E—16
4.267059E—16
4233484E—16
4.221168E-16
4.228176E—16
4.235020E16
4.212616E—16
4.139987E—16
4.023766E—16
3.904572E—16
3.839514E—16
3.829168E—16
3.834688E-16
3.819233E16
3.740112E—16
3.585939E16
3.391528E—16
3.2]6520E—16
3.109380E—16
3.055293E16
3.008265E-16
2899299E—16
2712330E—16
2.502973E—16
2.305991E-16
2.]66122E—16
2.106724E—16
2.086952E—16
2.077926E—16
2072439E—16
2.051172E—16
2.029035E—16
2.019390E—16
2021970E—16
2.013463E—16
2.005507E—16
1.974665E—16
1.928130E—16
1.890513E—16
1.847589E—16

 

131

Table F.4: H6 BELR Template (continued)

 

 

Wavelength

Flux

 

6777.11288154125
6779.079] 1157608
6781.04534161091
6783.01 157164574
6784.97780168057
6786.9440317154
6788.91026175022
6790.87649178505
6792.84272181988
6794.8089518547]
6796.77518188954
6798.74141192436
6800.70764195919
6802.67387199402
680464010202885
6806.60633206368
6808.57256209851
6810.53879213333
6812.50502216816
6814.47125220299
6816.43748223782
6818.40371227265
6820.36994230747
68223361723423
6824.30240237713
6826.26863241196
6828.23486244679
6830.20109248161
6832.16732251644
6834. 13355255127
6836.0997825861
6838.06601262093
6840.03224265576
6841.99847269058
6843.96470272541
6845.93093276024
6847.89716279507
68498633928299
6851.82962286473
6853.79585289955
6855.76208293438
6857.72831296921
6859.69454300404
6861.66077303887
6863.62700307369

1.805759E- 16
1.783198E—16
1.757076E—16
1.737771E—16
1.732217E—16
1.733951E—16
1.727604E—16
1.721449E—16
1.719640E— 16
1.723211E—16
1.724544E—16
1.708294E— 16
1664712E-16
1621107E—16
1.583783E—16
1.544931E—16
1.512843E— 16
1.469733E-16
1.428561E-16
1.397207E—16
1.359377E-16
1.321583E—16
1.292932E16
1.285335E—16
1.267035E— 16
1.243141E-16
1.226796E—16
1.213784E—16
1.209083E—16
1.208359E—16
1.188904E—16
1.167562E-16
1.165240E—16
1.]62654E- 16
1.]53029E16
1.156900E—16
1.146683E-16
1.129787E—16
1.]25464E— 16
1.118631E—16
1.097402E—16
1.076880E—16
1.065333E— 16
1.036240E— 16
1.008830E— 16

 

132

Table F.4: H6 BELR Template (continued)

 

 

Wavelength

Flux

 

6865.59323310852
6867.55946314335
6869.52569317818
6871.49192321301
6873.45815324784
6875.42438328266
6877.39061331749
6879.35684335232
6881.32307338715
6883.28930342198
68852555334568
6887.22176349163
6889.18799352646
6891 . 15422356129
6893.12045359612
6895.08668363095
6897.05291366577
68990191437006
6900.98537373543
6902.95160377026
6904.9]783380509
6906.88406383991
6908.85029387474
6910.81652390957
69127827539444
6914.74898397923
6916.71521401405
6918.68144404888
6920.64767408371
6922.613904] 1854
6924.58013415337
6926.5463641882
6928.51259422302
6930.47882425785
6932.44505429268
6934.41128432751
6936.37751436234
6938.34374439716
6940.30997443199
6942.27620446682
6944.24243450165
6946.20866453648
6948.17489457131
6950.14112460613
6952.10735464096

9.941723E—17
9.836731E—17
9899505E—17
9.989987E—17
9.872328E—17
9.805009E—17
9.991049E—17
1.025136E—16
1.042061E—16
1.059879E—16
1.067030E—16
1.069361E—16
1.071202E-16
1.059941E—16
1.039432E—16
1.018756E—16
1.000824E—16
9.843286E—17
9.745626E—17
9.550489E—17
9.395984E—17
9.255356E—17
8.976951E—17
8.790642E—17
8.705714E—17
8640128E—17
8620677E—17
8.564016E—17
8.375203E—17
8.051756E17
8.026651E—17
8.030790E—17
8.059127E—17
8.205407E—17
8.242054E—17
8.276763E—17
8.359578E—17
8.405809E—17
8.503781E—17
8.780586E—17
9.]21252E-17
9.120476E—17
8.936094E—17
8.877355E—17
9.040408E-17

 

133

Table F.4: H6 BELR Template (continued)

 

 

Wavelength

Flux

 

6954073584675 79
6956.03981471062
6958.00604474545
6959.97227478028
6961.9385048151
6963.90473484993
6965.87096488476
6967.83719491959

9.342787E—17
9619375E—17
9.685842E—17
9.223746E-17
9675278E—17
1.106353E—16
9.989899E—17
6.706839E—17

 

Table F.5: C IV NELR Template - c4-1549-obs2

 

 

Wavelength

Flux

 

1545.45678710937
15474230171442
1549.38924717903
1551.35547721385
1553.32170724868
1555.28793728351
1557.25416731834
1559.22039735317

7.499969E—17
1.941433E-14
5.025726E—14
6.703341E— 14
4.388938E—14
2.777132E—14
1.335886E—14
4.519212E—15

 

Table F IBLIN Template]O III] 1663 NELR Template - 03-1663

 

 

 

Wavelength Flux
1653.59942114353 0.
1655.56565117836 3.818165E—15
1657.53188121319 1.653593E—14
1659.49811124802 7.897442E—14
1661.46434128284 1.]20051E—13
1663.43057131767 8.360156E—14

16653968013525 1.998717E-13
166736303138733 1659833E—13
1669.32926142216 2908810E—14
1671.29549145698 3.295298E—15
1673.26172149181 0.

 

134

Table F .7: He II N ELR Template - narrow_he2

 

 

Wavelength

Flux

 

1624.10595703125
1626.07218706608
1628.03841710091
1630.00464713573
1631.97087717056
1633.93710720539
1635.90333724022
1637.869567 27505
1639.83579730988
1641.8020273447
1643.76825737953
1645.73448741436
1647.70071744919
1649.66694748402

-5.407848E—16
3.087130E16
2.028263E—15
3.025209E—15
6.918567E—15
9.955625E—15
1.507005E— 14
1.842422E-14
1.869978E—14
1.393788E—14
1.094051E- 14
3.784189E—15
2.362817E—15

-1.916310E—16

 

Table F.8: O III 1663 BELR Template - 03-blr7

 

 

 

Wavelength Flux
1645. 3.998061E—14
1647. 4.024494E—14
1649. 4.194744E—14
1651. 4.336624E—14
1653. 4.381397E—14
1655. 4.454867E— 14
1657. 4.517564E—14
1659. 4.559542E—14
1661. 4.551842E—14
1663. 4.531951E—14
1665. 4.480633E—14
1667. 4.485704E—14
1669. 4.383002E—14
1671. 4.299172E-14
1673. 4.151335E—14
1675. 3.996005E—14
1677. 3.996005E—14

 

135

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