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This is to certify that the

dissertation entitled

GRAVITATICNAL LENSII‘C DEPLE'I‘ICN IN THE INDAO DEEP
WIDE FIELD

presented by
MICHAEL WAYNE DAVIS

has been accepted towards fulfillment
of the requirements for

Ph .D. degree in Astrophysics

3‘13) 4

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6/01 c:/CIRC/DaIeDue.p65-p. 15

GRAVITATIONAL LENSING DEPLETION IN THE NOAO DEEP WIDE FIELD
By
MICHAEL WAYNE DAVIS

A DISSERTATION

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

DOCTOR OF PHILOSOPHY
Department of Physics and Astronomy

2002

ABSTRACT
GRAVITATIONAL LENSING DEPLETION IN THE NOAO DEEP WIDE FIELD
By
MICHAEL WAYNE DAVIS

A new method to measure mass of a sample of field galaxies is proposed. The
mass of foreground galaxies may be estimated by measuring the reduction in the
density of surrounding background galaxies. The reduction in number density is due
to gravitational lensing depletion.

A foreground mass acts as a gravitational lens and will magnify the background
area surrounding the mass. This magnification lowers the number density of back-
ground galaxies found behind the mass. One can use the reduction in number density
to calculate the rotation velocity of the foreground galaxies.

To demonstrate this method, photometry is performed on four O.5° x 0.5° fields
from the NOAO Deep Wide Field survey. Photometric redshifts are derived from the
photometry. The results are placed in a catalogue for public access.

Red foreground galaxies (B — V Z 0.61) have a mean rotation velocity of 308 :l: 30
km/s, while blue foreground galaxies (B — V < 0.61) have a mean rotation velocity
of 210 i 35 km/s. The rotation velocities of red galaxies with B > 22 and B < 22
and the Tully-Fisher relation suggest a magnitude difference of 1.7 :l: 0.4. The real
magnitude difference is 1.9, consistent with the difference estimated from the Tully-
Fisher relation. The rotation velocity difference between red galaxies at redshift
z = 0.2 and z = 0.5 is 22 i 44 km/s, consistent with zero. The rotation velocity
difference between blue galaxies at the same redshifts is 172E 49 km/s, also consistent
with zero. This measurement is the first direct measurement of the rotation velocity

of distant blue galaxies.

Acknowledgements

This work made use of images and/ or data products provided by the NOAO Deep
Wide-Field Survey, which is supported by the National Optical Astronomy Obser-
vatory (N OAO). NOAO is Operated by AURA, Inc., under a cooperative agreement
with the National Science Foundation.

First, I would like to thank my advisor Prof. Edwin D. Loh. I have learned more
about astronomy and instrumentation under his guidance than I can imagine learning
from any other two advisors combined.

Second, I would like to thank Aaron “Cluze” LaCluyzé for the assistance provided
during this research. I am especially grateful for the use of fornax to run SExtractor.

I thank Karen Kinemuchi, Brian Marsteller, Brian Sharpee, and Chris Waters for
listening to my explanations and checking my reasoning while preparing this disser-
tation. Thanks also goes to Jason Biel, Karen, and Cluze for help with IA'IEX.

A special thank you goes to Dr. Robert Slater for assistance with meeting MSU
dissertation formatting requirements.

More thanks go to Ryan Kruse, Cluze, Dr. Charles Moreau, Dr. Peter Peterson,
Dr. Frédéric Pierre, Dr. Slater, and the rest of the gaming-and-trivia crowd for large
doses of stress relief.

A huge thank you goes to my wife Jennifer and son Jonathan for putting up with
my absences and living in Spartan Village while completing this work.

Finally, and most importantly, I would like to thank YHWH for creating this

universe and giving me a chance to study it.

iii

Table of Contents

iv

LIST OF TABLES vi
LIST OF FIGURES viii
1 Introduction 1
1.1 Motivation ................................. 1
1.2 Gravitational Lensing ........................... 1
1.2.1 Overview ............................. 1
1.2.2 Mathematics of Gravitational Lensing Depletion ........ 3
1.3 This Work ................................. 6
Photometry and Photometric Redshifts of the NOAO Deep Wide
Field 8
2.1 Background ................................ 8
2.2 Photometry Results ............................ 9
2.3 Redshifts .................................. 12
2.3.1 First Redshift Attempt ...................... 12
2.3.2 Second Redshift Attempt ..................... 14
2.4 Catalogues ................................. 21
2.5 Conclusion ................................. 24
Galaxy-Galaxy Lensing in the Deep Wide Field 25
3.1 Method .................................. 25
3.2 Lensing Data ............................... 26
3.2.1 Considerations .......................... 26
3.2.2 Results ............................... 28
3.2.3 Comparison ............................ 30
3.3 Alternate Depletion Sources ....................... 33
3.3.1 Blocking by Foreground Galaxies ................ 34
3.3.2 Blocking by Saturated Stars ................... 34
3.3.3 Cross-contamination ....................... 35
3.4 The Effect of Varying a ......................... 37
3.5 Galaxy Mass ................................ 39
3.5.1 Red vs. Blue ........................... 39
3.5.2 Near vs. Far ............................ 40

3.5.3

Bright vs. Faint ..........................

3.6 Summary .................................

4 Conclusions and Future Work

A Photometry and Photometric Redshift Techniques
A.1 Photometric Redshift Method ......................

A.1.1
A.1.2
A.1.3
A.1.4
A.1.5

Background ............................
Technique .............................
The Hubble Deep Field ......................
Results ...............................
Conclusion .............................

A.2 Photometry Method ...........................

A21
A22
A23
A24
A.2.5
A.2.6

Bibliography

Background ............................
Description of Photometry ....................
Isophotal Photometry ......................
Aperture Photometry .......................
Photometry Comparison .....................
Conclusion .............................

40
42

43

45
45
45
46
49
5O
54
54
54
54
56
58
61
63

66

List of Tables

2.1 Object List ................................ 22
2.2 Redshifts .................................. 23
3.1 Lensing Results .............................. 32

vi

List of Figures

1.1 Lensing diagram .............................

2.1 Magnitude difference between DWF frame 1 and frame 2 .......
2.2 Comparison of median of photometry in DWF frame 1 and 2 .....
2.3 Hubble diagram of DWF first release with templates to z = 1.5 . . . .
2.4 Correlation between highest and high redshift galaxies ........
2.5 Correlation between highest and medium redshift galaxies ......
2.6 Hubble diagram of DWF first release with templates to z = 1.0 . . . .
2.7 1(1sz of DWF first release .........................
2.8 Galaxy size vs. magnitude ........................
2.9 Star size vs. magnitude ..........................
2.10 Hubble diagram of large stars ......................
2.11 Hubble diagram of small bright galaxies ................
2.12 Hubble diagram of stars .........................

3.1 Depletion by near red galaxies. .....................
3.2 Depletion by near blue galaxies. .....................
3.3 Depletion by far red galaxies. ......................
3.4 Depletion by far blue galaxies .......................
3.5 Comparison between Wilson and this work’s foreground galaxies . . .
3.6 Autocorrelation of background galaxies .................
3.7 Best-fit r vs. redshift of foreground sample ...............
3.8 0 vs. magnitude ..............................
3.9 Luminosity function ...........................
3.10 Bright and faint galaxy correlation ...................

A.1 Spectral Energy Distributions ......................
A.2 Template spectra colors .........................
A.3 Photometric redshifts produced by this method ............
A.4 Photometric redshifts produced by FLY .................
AS Error and dispersion of photometric redshifts ..............
A.6 Redshift difference vs. magnitude ....................
A.7 Redshift difference vs. spectroscopic redshift ..............
A.8 Histogram of redshift errors .......................
A.9 Difference between FLY and this work .................
A.10 Median difference between FLY and this work .............

vii

2

9
10
12
13
14
15
16
17
18
19
20
21

28
29
30
31
33
35
36
37
38

46

50
51
52
53
55

A.11 Difference between isophotal and aperture magnitudes ........ 57

A12 Aperture photometric redshifts ..................... 59
A.13 Isophotal photometric redshifts ..................... 60
AM Aperture and Isophotal redshift difference ............... 61
A.15 Median redshift difference ........................ 63

viii

Chapter 1

Introduction

1 . 1 Motivation

An important area of astrophysics is the study of the evolution of galaxies. While
basic properties of nearby galaxies are known, it is more difficult to determine those
properties for distant (and older) galaxies. More importantly, it is uncertain whether
such properties as mass and luminosity change as galaxies age.

The goal of this research is to determine if the masses of red and blue galaxies
change with age. Gravitational lensing depletion is the tool used to make this mea—
surement. A brief summary of the history and application of gravitational lensing

follows.

1.2 Gravitational Lensing

1.2. 1 Overview

Gravitational lensing occurs when light rays are bent by a massive object [8].
Figure 1.1 shows a basic diagram of gravitational lensing. The apparent position of

the background object is moved away from the lensing object because of gravitational

Source plane Lens plane

 

 

 

 

 

 

(s

 

 

 

 

II
,5:
1i

Figure 1.1: Diagram of gravitational lensing. The effective position of the background
object is moved away from the lens.
bending. If a lensing object is placed in front of a field of objects, the number
of background objects surrounding the lens will diminish. This effect is known as
gravitational lensing depletion, or magnification bias. The shape of the background
objects will also distort so that they appear slightly elongated in the radial direction.
This effect is referred to as shape distortion or weak gravitational lensing.
Gravitational lensing depletion may only be measured if the baseline number
density of background galaxies is known. Foreground galaxies mixed with background
galaxies will contaminate the lensing signal. Also, minor fluctuations in background
density can affect the measured signal if the area covered by the background sample
is not large. Therefore, to measure gravitational lensing depletion, one must observe
a large area of the sky and somehow obtain good separation between foreground and
background galaxies. The difficulty in meeting both conditions has kept the number

of gravitational lensing depletion measurements small.

Tyson [28] first measured gravitational light deflection by foreground galaxies in
1984. They measured the shape distortion of 46,954 galaxies near 11,789 foreground
galaxies. Their images came from photographic plates with a minimum resolvable
angular separation of 20 arcseconds. Lacking redshift data, they also separated fore-
ground galaxies from background galaxies by flux.

Brainerd, Blandford, & Smail measured the shape distortion in 1996 [3]. Using
CCD technology they were able to measure the shape distortion of 3202 pairs of
galaxies with angular separations between 5 and 34 arcseconds. They measured an
average galactic rotation velocity of 220 :l: 80 km/s. Again, foreground galaxies were
separated from background galaxies by flux.

Fort et al. first measured a magnification bias around C10024+1654 [12]. They
used the measured bias to constrain the redshift distribution of the background galax-
ies. Taylor et al. used Fort’s technique to measure the mass of cluster Abell 1689 [26].

Wilson et al. first used galaxy-galaxy lensing to measure the rotation velocity of
bright elliptical galaxies [30]. This rotation velocity measurement was derived from
the shape distortion of background galaxies surrounding bright elliptical foreground
galaxies. They used two-color photometry to separate bright elliptical foreground
galaxies from background galaxies and determine the redshifts of the foreground
galaxies. The background galaxy redshifts were inferred from their flux. They mea-
sured a rotation velocity of 269g: km/s for bright elliptical galaxies assuming an

Einstein-deSitter cosmology.

1.2.2 Mathematics of Gravitational Lensing Depletion

The galaxy depletion due to gravitational lensing magnification follows the func-

tion [4]:

N

The left hand side is the angular correlation between the lens and the background
galaxies. The background density of galaxies surrounding the lens is N, while the
background density of galaxies for the image is NO. The % factor is the reduction of
the density of background galaxies due to gravitational lensing. The parameter a is

the change in number of background galaxies with magnitude, or:

dlogN
a— dm

 

(1.2)

This parameter represents the magnification of background galaxies due to gravita-

tional lensing. In most cases, 2.5a < 1, so gravitational lensing causes a net depletion
in the number density of background galaxies.

The parameter p is the gravitational lensing magnification factor. Galaxies have

2

flat rotation curves beyond a few kpc, so the mass distribution has the form pm or r“ .

This mass distribution leads to [22]:

 

1
:— 1.3
11 1-513 ( )

,.
The projected separation between the lens and the background object is r, while

2'50‘1 reduces to

the Einstein radius of the lens is RE. Assuming £1.13 is small, It
1 -- (2.5a — DETE. The right hand side of Equation 1.1 then reduces to (2.5a — DIE—1E.
There is a degeneracy in a and RE, so both quantities can not be derived solely from

the measured depletion.

The Einstein radius has the form [23]:

MD D
RE = \/47r02 LS 0L (1.4)
0 DOS

 

 

2 . .
The rotation velocity is constant, so £31 = 9; for any value of r. Substitutlng for

GM and r = RE yields:
'02 DLSDOL

=4 ——-—————- 1.

DLS is the luminosity distance from the lens to the background source, DOL is
the luminosity distance from the observer to the lens, and DOS is the luminosity
distance from the observer to the background source. The rotation velocity of the
lensing object is v.

The depletion is measured as a function of angular distance from the lens. Equa-
tion 1.1 is fit to the depletion, and the best fit value of RE is found. Once RE, the
distance to the lens, and the distance to the background are known, the rotation
velocity of the lensing object may be calculated.

Young et al. show that for a spherically symmetric mass distribution, the de—
flection of light is only dependent on the mass enclosed within the measurement
radius [31]. Therefore, the mass of the lensing object within a given radius may
be calculated from the rotation velocity. However, the rotation velocity can only be
measured out to the angular distance for which a depletion signal is measured. There-
fore, if the object extends beyond the radius for which a measurable signal exists, the

rotation velocity only limits the mass within the radius of the signal.

1 .3 This Work

This research uses galaxy-galaxy lensing depletion to calculate galactic rotation
velocity and, indirectly, mass. The data set is three color photometry in the NOAO
Deep Wide Field.

Once photometry is performed photometric redshifts are calculated for the objects
in the Deep Wide Field. The calculation of photometric redshifts allows a separation
of foreground and background galaxies. Three color photometry also allows the fitting
of galaxy type templates to the observations. These procedures are described in

Chapter 2.

Once photometric redshifts are determined, the galaxies are split into foreground
and background bins. The foreground bins are further separated by color. Then, the
depletion in the number of background galaxies surrounding the foreground galaxies
may be measured. This depletion is used to calculate the rotation velocity of the

foreground galaxies. These procedures are described in Chapter 3.

Chapter 2

Photometry and Photometric
Redshifts of the NOAO Deep Wide
Field

2. 1 Background

The NOAO Deep Wide Field (hereafter referred to as DWF) survey provides the
data set upon which this work is based. The DWF images were taken with the
8192 x 8192 pixel MOSAIC camera on the 4-meter telescope at Kitt Peak National
Observatory [15]. The images were taken in a wide blue filter (340 to 490 nm, dubbed
Bw), a red filter (550 to 800 nm, dubbed R), and a very near-IR filter (700 to 950
nm, dubbed I). The first data release of the DWF consists of four 36 by 36 arcminute
fields near the constellation Boétes. The pixels are 0.258 arcseconds wide. The data
were released to the public in January 2001.

The original image processing was performed by Januzzi and Dey [15]. The im-
ages were flat-fielded, bias subtracted, and combined into final composite images.

They placed the pixel scale, image seeing, gain, position solutions, and photometric

 

2.0

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Figure 2.1: The Bw-magnitude difference between DWF frame 1 (b1) and DWF
frame 2 (b2) plotted against magnitude of frame 1 (b1). There are over 900 objects
in common between the two frames.

zeropoints in the image header. The photometric zeropoint of each image is good to
0.01 magnitudes while the comparison between colors is good to about 0.03 magni-

tudes [16].

2.2 Photometry Results

The methods used to perform photometry and photometric redshifts are described
in Appendix A. These techniques are applied to the four frames of the DWF. The
Bw-band images are used as the fiducial source maps due to their low sky background.
The only other modification to the technique of Appendix A is the use of 32 x 32

pixel squares to measure background instead of 72 x 72. This reduced background

 

 

 

l
r I I I I I

 

 

 

Figure 2.2: A comparison of photometry in DWF frame 1 and 2. The median of the
magnitude difference between objects measured in DWF frame 1 and DWF frame 2
versus magnitude in frame 1. The crosses represent the median difference between
the two frames, the boxes represent the median photometric uncertainty at that
magnitude, and the line represents the dispersion of the median magnitude difference.
The data are grouped in bins 0.5 magnitudes wide.
square size is used because the magnitude difference between two adjacent frames is
smallest for a 32 x 32 background. The photometric errors of the objects are based
on the local background found in each background square.

There is overlap between the frames of the DWF. Frame 1 is centered about
right ascension 14h26m and declination 34°56’, while frame 2 is centered about right
ascension 14h26m and declination 35°56’. There is roughly 1 arcminute of overlap

between the two frames. This overlap region allows comparison of the photometry of

the two frames.

10

The results of photometry performed on frame 1 are consistent with the results
of photometry performed on frame 2. Figure 2.1 is a plot of the magnitude difference
between objects in frame 1 and frame 2 of the DWF versus Bw magnitude of the
first frame. The difference is centered around zero, so there is no consistent offset in
magnitude between the two frames.

There is no bias between magnitudes measured for frame 1 and magnitudes mea-
sured for frame 2. Figure 2.2 is a plot of the median of the magnitude difference
between frame 1 and frame 2, the median photometric uncertainty, and the disper-
sion of the median of the magnitude difference versus magnitude of frame 1. The
median of the magnitude difference between frames is expected to remain near zero
and stay smaller than the magnitude uncertainty. The median difference between
magnitudes meets this expectation for magnitudes from 19 < B < 25 where the bulk
of the galaxies lie. The large median differences at B < 18.5 and B > 25 are due to
small numbers of very bright or very faint galaxies present in both frames. Therefore,
there is no bias present. Furthermore, the dispersion of the median of the magnitude
difference is expected to be roughly \f2— greater than the median uncertainty. The dis-
persion of the median of the magnitude difference meets this expectation. Therefore,
there is no magnitude bias between these two frames of the DWF.

Pixels at the edge of the raw DWF frames were removed before performing pho-
tometry on all colors. This pruning was necessary to ensure that all frames were the
same size. The Source Extractor (SExtractor) software package used here required
that all images were the same size to perform detection in one image and photometry
in another. The frames were pruned to 8192 x 8192 pixels to match the size of the
detector. This size ensures that all objects present in one color will be present in the

other two colors.

11

18 16

B magnitude
20

 

24

 

Figure 2.3: The Hubble diagram (magnitude vs. redshift) of all four pruned frames
of the DWF. These redshifts were calculated with templates up to z = 1.5.

2.3 Redshifts

2.3.1 First Redshift Attempt

The photometric redshift technique of the Appendix was applied to the data set
after the completion of photometry. The only difference in creating fiducial galaxies
between the technique of the Appendix and this implementation is the use of the three
DWF filters instead of the four HDF filters. Otherwise, the fiducials are created in
the same manner as in the Appendix.

Stars and galaxies are separated based on their spectral energy distributions
(SEDs). Objects that best matched a fiducial galaxy are classified as galaxies. Ob-

jects that best matched a fiducial star are classified as stars.

12

 

 

 

 

 

 

 

 

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U 80 40 60 80 100 120 I40 160 180 300

arcseconds

Figure 2.4: The angular correlation between galaxies at z > 1 and galaxies at 0.8 <
z < 1. The correlation is positive, indicating autocorrelation.

The first pass at calculating photometric redshifts used templates ranging from
2 = 0.005 to z = 1.5. The resulting redshifts were combined into one Hubble diagram
(magnitude vs. redshift), shown in Figure 2.3. There is obviously an error for galaxies
at zph > 1, as the flux of objects should not increase with increasing distance.

The angular correlation of galaxies at high redshift (th > 1) and lower redshift
galaxies (zpl1 < 1) was measured to determine if the galaxies that were assigned
high photometric redshifts were really misclassified galaxies with lower redshifts. The
autocorrelation of galaxies as a function of angular separation 0 follows the functional
form 6'08 due to clustering. Therefore, if the angular correlation between galaxies
with high photometric redshift and lower photometric redshift is positive, then the

high redshift galaxies are really misclassified lower redshift galaxies.

13

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0.4

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angular correlation
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0 80 40 60 80 100 120 140 160 180 200
arcseconds

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Figure 2.5: The angular correlation between galaxies at z > 1 and galaxies at 0.6 <
z < 0.8. The correlation is again positive, indicating autocorrelation.

The galaxies assigned a high photometric redshift are misclassified lower redshift
galaxies. Figure 2.4 is a plot of angular correlation between galaxies with zph >
1 and galaxies with 0.8 < zph < 1. Figure 2.5 is a plot of angular correlation
between galaxies with zph > 1 and galaxies with 0.6 < zph < 0.8. Both show clear
positive correlation between the high and low redshift galaxies, indicating that most
of the galaxies assigned a redshift greater than 1 are probably lower redshift galaxies.

Therefore, templates with redshifts above 1 should be removed from the template set.

2.3.2 Second Redshift Attempt

The solution to misclassified high redshift galaxies is to recalculate photometric

redshifts with fiducials limited to a maximum of z = 1. This limit was chosen because

14

16

 

17

18

20

B magnitude
21

22

23

24

 

Figure 2.6: The Hubble diagram (magnitude vs. redshift) of all four pruned frames
of the DWF. The lines represent constant luminosity so that Bw = 25 and Bw = 22
at 22:].
it is the maximum redshift at which the 4000 A break may be detected in the I-band.
Figure 2.6 is the Hubble diagram for 57,685 galaxies brighter than B = 25 between
2 = 0.05 and z = 1.0. The brightest objects near 2 = 0.5 are probably misclassified
stars because galaxies at that distance are not that bright. The number of galaxies
at each redshift appears to increase with redshift and, aside from a few outliers, the
maximum magnitude of the galaxies decreases with redshift.

The rate of change of the number of galaxies as a function of redshift in the DWF
increases with redshift. The galaxies were separated into redshift bins. The galaxies
in each bin were counted down to a magnitude limit determined by the redshift of the

bin. The greater the redshift, the fainter the magnitude limit by the distance modulus

 

100
i
L
i

"r'I'Y‘T

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dN/dZ x 100
:1“:
+

+

 

 

 

Figure 2.7: The rate of change of number of galaxies versus redshift in the DWF. The

line represents % or 22.

(—5 log distance). One expects the number of galaxies in each bin to increase as the
square of redshift since redshift is approximately equal to distance. Figure 2.7 is a

2. There appear to be too

plot of $1,]; versus redshift. The line represents 431:1 or z
few galaxies at z > 0.7. The low count is probably due to the lack of k-correction
or luminosity evolution in the determination of the magnitude limits. The apparent
deficit at z = 0.35 could be due to the 4000 A break redshifted between the Bw and
R filters at redshifts between 2 = 0.23 and z = 0.38. There is a gap of 60 nm between
the Bw- and R-band filters. While the data do not fit the model, the rate of change

of galaxies with respect to redshift does increase at a rate close to that predicted by

the model.

16

 

 

 

 

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B mag

Figure 2.8: Isophotal area of galaxies versus redshift in the DWF.

The angular size of the galaxies increases as flux increases. This result is expected
because brighter galaxies will tend to be closer than far galaxies, so the brighter
galaxies should appear bigger than fainter galaxies. Figure 2.8 is a plot of the isophotal
size of galaxies versus magnitude. The isophotal size is the number of pixels within
a given isophote. In this case, the isophotal size is everything 1.90 above the local
background. There is a smaller range in the size of dim things because the galaxies
approximate point sources at large magnitudes.

The angular size of the stars also increases as flux increases. The size is expected
to increase with flux because the point spread function of stars is approximately
gaussian. For a typical DWF value of 1.3 arcsecond seeing, the point spread function

is exp(—0.41 x r2), where r is radius in arcseconds. As brightness increases, a larger

17

 

 

 

 

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26

 

B mag

Figure 2.9: Isophotal area of stars versus redshift in the DWF.

area of the point spread function is brighter than the background level. Therefore, the
brighter stars appear bigger than smaller stars. Figure 2.9 is a plot of the isophotal
size of stars versus magnitude. There is a small range in the size of both bright and
faint objects because the stars are point sources, not extended objects. The fact that
the sub-images that contributed to this sample had different seeing also contributes
to the size range of the bright stars. The bright objects (Bw < 20) that are smaller
than the main grouping (< 20 arcseconds) have been confirmed to be false detections
by visually inspecting the images. These objects have been removed from the catalog.

The size-magnitude plots show a distinction between stars and galaxies at mag-
nitudes brighter than 22. The slope of the size-magnitude relation for stars is much

flatter than the slope of the size-magnitude relation for galaxies. The slope is flatter

18

 

 

 

 

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0"; + "' + L
‘ma + ++ .
m - + ..
u: + + 1-
g- + _.
m; ‘—
ru‘ ..
I C
a [-
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0.]. 1

Figure 2.10: The Hubble diagram of the large bright objects identified as stars in the
DWF.

because stars are point sources, while galaxies are extended objects. A few objects
classified as stars follow the size-magnitude relation for galaxies and vice-versa. These
objects are potentially misclassified.

A Hubble diagram of the large stars shows some confusion between bright stars
and low-redshift galaxies. Figure 2.10 is the Hubble diagram of the bright stars
that are larger than most stars of similar magnitude. The redshifts are assigned to
the stars as if the stars were really galaxies. A number of the bright stars assigned
low redshifts are indistinguishable from bright, low—redshift galaxies. Therefore, the
objects classified as stars that are larger than most stars are probably misclassified

galaxies.

19

 

 

 

 

\D . 11L .+ I In-
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m " _
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01-. + .—
m: :
cu: __
1r; -
m] f
-( 1-
in1 _
(u ' I I
0.1 1

Figure 2.11: The Hubble diagram of the small bright objects identified as galaxies in
the DWF.

A Hubble diagram of the small galaxies shows some confusion between bright
stars and galaxies. Figure 2.11 is the Hubble diagram of the bright galaxies that are
smaller than most galaxies of similar magnitude. The brightest objects in this diagram
are probably stars, because galaxies cannot be as bright as those objects at high
magnitude. The fainter objects are not as distinguishable, but are not inconsistent
with classification as galaxies. Therefore, while the brightest objects are surely stars,
the fainter ones could be stars or galaxies.

A Hubble diagram of the remaining objects classified as stars shows a distinction
between stars and galaxies. Figure 2.12 is the Hubble diagram of both small bright
objects and faint objects classified as stars. The stars are again assigned redshifts as

if they were galaxies There is a large population of faint objects assigned a redshift

20

 

 

 

 

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«1+ .-

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m + :_

m I

+ I F

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m I

0—‘

 

Figure 2.12: The Hubble diagram of faint and small bright objects identifed as stars.
One out of every 10 objects fainter than 22nd magnitude are plotted.
less than 0.3. These objects are stars because there is not a large population of faint

nearby galaxies. Therefore, most of the objects classified as stars are truly stars.

2.4 Catalogues

Catalogues of stars and galaxies found in the DWF have been assembled and
posted for public use. Table 2.1 gives the position, fluxes, size, and ellipticity, for a
small sample of the objects in the DWF. Right ascensions are given as arcseconds
with an offset of 14 hours, 24 minutes. Declinations are given as arcseconds with an
offset of 34 degrees. The positions come from the SExtractor output, which derives

the positions from the position solution put in the FITS header by Jannuzi and Dey.

21

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22

 

z 62 TType x7 NB Type NBz | NB x2]
1.00 0.15 C10 4 022 0.00 15
0.00 0.10 F4V 0.2 010 0.00 0.4
0.31 0.14 G6V 1 036 0.30 1
0.68 0.10 027 0.2 056 0.10 1
0.02 0.81 054 0.3 056 0.01 0.3
0.00 0.11 022 4 BD17 0.00 22
0.63 0.64 010 0.3 057 0.02 0.4
0.01 0.21 038 0.2 035 0.03 0.2
0.00 0.07 AW 2 010 0.00 12
0.12 0.20 C15 0.2 019 0.10 0.3
1.00 0.01 088 32 087 0.96 77
0.19 0.44 G8V 0.2 037 0.19 0.2
0.00 0.06 A5v 0.7 010 0.00 8
0.64 0.20 045 0.2 067 0.13 0.8
0.68 0.70 020 0.2 060 0.04 0.4

N

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I—‘I—‘I—‘I—‘HH

 

 

 

 

 

 

 

 

 

 

Table 2.2: A partial table of redshift, object type, x2 of the fit, next best object,
next best redshift, and X2 of the fit of the next best object. The number refers to
the object number in the photometry table. The complete data may be found at
http://www.pa.msu.edu/“davism/DWFz.txt.

The position solution is accurate to 0.5 arcseconds, so it is reasonable to assume the
positions of the catalog have a similar accuracy [18]. Table 2.2 gives the redshift,
object type, x2, and second best fit object type, redshift, and X2 for a small sample
of the galaxies found in the DWF. The galaxy types are indicated by rest frame B-V
color. A ”C95” has a B-V color of 0.95, a ”C90” is 0.90, and so forth. The star types
are not intended to be accurate stellar classifications, but to label that the object (or
second best type) is a star. Likewise, the redshift listed for the stars is the redshift
as if they were galaxies. The complete tables may be found online as noted in the
captions of the sample tables. After pruning the original frames to 8192 x 8192 pixels,

there are 37 objects that are present in two frames and are double counted. These

objects have not been removed from the catalog.

23

2.5 Conclusion

The data from the Deep Wide Field are ready for further study and public release.
The Hubble diagram shows that the galaxies get fainter with redshift. The rate of
change of galaxy counts increases with redshift. Bright stars are smaller than bright

galaxies. Galaxies and stars are separated fairly well for Bw < 22.

24

 

Chapter 3

Galaxy-Galaxy Lensing in the
Deep Wide Field

3.1 Method

Galaxy—galaxy lensing depletion is the gravitational deflection of the position of
background galaxies in an area surrounding foreground galaxies. The mathematics
of lensing depletion are discussed in Chapter 1. This chapter takes the photometric
redshift data from Chapter 2, finds the lensing depletion signals from four galaxy sets
at two different redshifts, and then calculates the rotation velocity of these galaxies.

The choice of cosmology affects the calculated rotation velocity. While recent
observations conclude that the “proper” cosmology is dark energy dominated with
Rm 2 0.3 and DA 2 0.7, Wilson et al. show either a dark energy cosmology or
Einstein-deSitter has little effect on lensing results at low redshift [30]. However, for
the sake of completeness, both cosmologies are used to calculate rotation velocities.

The luminosity distance d is given by:

1

— z 3:2 a: —:1: :13 ’0'52: .
[JO/001+ >0+0m> (2+ >00 d (31)

25

This distance reduces to #00 — J1i+—2) for an Einstein-deSitter cosmology, but must

 

be evaluated numerically for a dark energy dominated cosmology. Then, depletion
curves as given in Eq. 1.1 are fit to the data to determine r, the angular size of the
Einstein radius. The corresponding linear size is given by RE :- r x DOL x (1 +

2319,13)—2 x (206265)“1. Substituting into Equation 1.5 gives:

 

 

D
I) = ——C——— 7' OS (3.2)
1+ 21...... 206265 x 441315

The appropriate values of DOS and DLS are substituted depending on the cosmology,
the median redshift of the foreground galaxies, and the median redshift of the back—
ground galaxies. The Hubble constant cancels out of the rotation velocity calculation,
so the value of H0 has no effect on the rotation velocity. However, the value of H0

will determine the projected size of the lens. A value of (100 km/s/Mpc) is assumed.

3.2 Lensing Data

3.2.1 Considerations

Two sets of foreground and background galaxies are selected so that galaxy ro-
tation velocity could be measured at two different redshifts. The first foreground
set runs from 2 :- 0.1 to z = 0.3 with a median of z = 0.2. The magnitude cut-
off is B < 23, 2 magnitudes below m* = 21 for galaxies from 2 = 0.1 to z = 0.3.
The second foreground set runs from 2 = 0.4 to z = 0.6 with a median of z = 0.5.
The magnitude cutoff for the second foreground set is B < 25, 2 magnitudes below
m* = 23 for galaxies from z = 0.4 to z = 0.6. This cutoff is different because 2 = 0.5
is roughly 2.5 times as distant as 2 = 0.2. That distance translates to a flux reduc-
tion of 2 magnitudes. The first background set consists of all galaxies with z > 0.6

with a median of z = 0.8. The second background set consists of all galaxies with

26

z > 0.9 with a median of z = 0.96. The first foreground set is paired with the first
background set and the second foreground set is paired with the second background
set.

The width and redshift of the galaxy bins are selected so the median redshift errors
for each bin do not cause overlap. The median redshift error at z = 0.3 (the high
edge of the first foreground bin) is 0.16, while the median redshift error at z = 0.6
(the low edge of the first background bin) is 0.13. Therefore, there should be no
overlap between the first set of foreground and background galaxies. The median
redshift error at z = 0.9 (the low edge of the second background bin) is 0.16. Given
the redshift error of 0.13 at z = 0.6 (the high edge of the second foreground bin) and
the redshift error at z = 0.9, there should be no overlap between the second set of
foreground and background galaxies.

Each set of foreground galaxies is further separated into red and blue galaxies.
Everything with a rest-frame B —V greater than or equal to 0.61 is considered red, and
everything with a rest-frame B — V less than 0.61 is considered blue. For reference,
red S0 galaxies have a B — V color around 0.95, while blue Im galaxies have a B — V
color around 0.3.

The number of galaxies in the background sample determines the background
magnification constant a (Eq. 1.2). The log of the number of background galaxies
with Bw < 24.9 is subtracted from the log of the number of galaxies with Bw < 25.1.
The difl'erence is divided by 0.2 to calculate %)—%E. For the background sample
0.6 g 2 g 1.0 there were 26375 galaxies down to Bw = 25.1 and 23283 galaxies down
to Bw = 24.9. These numbers give a = 0.27 :l: 0.02 assuming errors go as W. For
the background sample 0.9 3 2 S 1.0 there were 9083 galaxies down to Bw = 25.1
and 7654 galaxies down to Bw = 24.9. These numbers give a = 0.37 :l: 0.03.

27

 

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I) D 20 40 60 80 100 120 140 160 180 200
arcseconds

Figure 3.1: The angular correlation of red foreground galaxies with background galax-
ies. The background sample is z > 0.6. The foreground sample is 0.1 < z < 0.3.

3.2.2 Results

The first angular correlation measurement is between red galaxies between 2 = 0.1
and z = 0.3 and background galaxies between 2 = 0.6 and z = 1.0. Figure 3.1 is a
plot of the angular correlation between these two samples. There is clearly a depletion
in the number of background galaxies at radii less than 60 arcseconds, or 100 kpc at
z = 0.2. The Einstein radius of the best fit curve is r = 2.6 :l: 0.6 arcseconds. The
reduced X2 of the fit is 1.8.

The second angular correlation measurement is between blue galaxies between
2: = 0.1 and z = 0.3 and background galaxies between 2 = 0.6 and z = 1.0. Figure 3.2

is a plot of angular correlation between these two samples. There is again a depletion

28

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blue at 2:0.2

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' I I I I I I I I I r I I I I I I I I I I I I I I I I I I I I I I I I I I I Ifi
(P D 20 40 60 80 100 180 140 160 180 BED
arcseconds

Figure 3.2: The angular correlation of blue foreground galaxies with background
galaxies. The background sample is z > 0.6. The foreground sample is 0.1 < z < 0.3.
in the number of background galaxies at radii less than 60 arcseconds, or 100 kpc at
z = 0.2. The Einstein radius of the best fit curve is 7‘ = 1.4 :l: 0.2 arcseconds. The
reduced x2 of the fit is 0.89.

The third angular correlation measurement is between red galaxies between 2 =
0.4 and z = 0.6 and background galaxies between z = 0.9 and z = 1.0. Figure 3.3 is a
plot of the angular correlation between these two samples. There is clearly a depletion
in the number of background galaxies at radii less than 80 arcseconds, or 190 kpc at
z = 0.5. The Einstein radius of the best fit curve is r = 2.7 :l: 0.5 arcseconds. The
reduced X2 of the fit is 1.9.

The final angular correlation measurement is between blue galaxies between 2 =

0.4 and z = 0.6 and background galaxies between 2 = 0.9 and z = 1.0. Figure 3.4

29

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I I I I I I I I I I I I I T I 1 Ifi I r If I I I r I I I I I I I r I I I I I
D 20 40 60 80 100 120 140 160 180 200
arcseconds

Figure 3.3: The angular correlation of red foreground galaxies with background galax-
ies. The background sample is z > 0.9. The foreground sample is 0.4 < z < 0.6.

is a plot of the angular correlation between these two samples. There is a depletion
in the number of background galaxies at radii less than 60 arcseconds, or 140 kpc at
z = 0.5. However, this depletion is the noisiest of the four. The Einstein radius of

the best fit curve is r = 1.1 :l: 0.6 arcseconds. The reduced x2 of the fit is 2.0.

3.2.3 Comparison

The sample of foreground galaxies selected by this work is larger than the sample
of foreground galaxies selected by Wilson et al. [30]. Figure 3.5 is a color-magnitude
plot of the range of foreground galaxies selected by Wilson et al. and this work. The

rest-frame color of Wilson’s foreground galaxies is estimated from their measured

30

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blue at 2:0.5

IIIIIIIIIIIIIIIIIII

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angular correlation
~0.20-0.1'5-U.10 -0.0S 0.00 0.05 0.10 0.15 0.20

 

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I I I fiTTI IIiI—I I7 I I I IfiI I I I IrII I I I I I I I II I I
D 20 40 60 80 100 130 140 160 180 800
arcseconds

Figure 3.4: The angular correlation of blue foreground galaxies with background
galaxies. The background sample is z > 0.9. The foreground sample is 0.4 < z < 0.6.
color and estimated redshift. The magnitude of Wilson’s foreground galaxies is taken
as if they were at z = 0.2. The rest—frame color of the foreground galaxies of this
work is taken from Figure A.2. The large rectangular area represents the colors and
magnitudes of the foreground galaxies selected between 2 = 0.1 and z = 0.3.

The rotation velocity calculated for the red galaxies at z = 0.2 is 308:3; km/s
for an Einstein-deSitter cosmology and 297:3}; km/s for a dark energy cosmology.
Wilson et al. measured a rotation velocity of 2751313 km/s for an Einstein-deSitter
cosmology and 2551?; km/s for a dark energy cosmology for bright elliptical galaxies
at z = 0.2 [30].

As shown in Figure 3.5, Wilson’s foreground galaxy sample covers a smaller range

of magnitudes and galaxy types than the foreground galaxy sample in Figure 3.1

31

 

 

 

 

 

 

color I Zf l Zb 1 RE (arcsec) reduced x2] ”(9m = 1) _(km/s) v(QA = 0.7) (km/s) |
red 0.20 0.76 2.6 :t 0.6 1.8 308% 297"_‘_j'~;},—__1
blue 0.21 0.76 1.4 :l: 0.2 0.89 226iIg 21833
red 0.51 0.98 2.7 :l: 0.5 1.9 342:32 319:3:1
blue 0.51 0.98 1.1 :1: 0.6 2.0 216:3: 201133

 

 

 

 

 

 

 

 

 

Table 3.1: A table of foreground redshift, background redshift, Einstein radius, re-
duced x2, and rotation velocity for four foreground samples from the Deep Wide
Field. The reduced X2 is calculated with 11 degrees of freedom.

because they were selected with two color photometry. Wilson also did not have
photometric redshifts to determine the redshift of the background sample, unlike
this background sample [30]. Instead, the redshifts of the background galaxies were
estimated by comparing their flux with the luminosity function. Therefore, despite
two different methods of measurement, the two results agree.

The rotation velocity calculated for the blue galaxies at z = 0.2 is 22633 km/s for
an Einstein-deSitter cosmology and 21833 km/s for a dark energy cosmology. These
values are clearly distinct from the rotation velocities for the red galaxies at the same
redshift. Wilson et al. could not calculate the rotation velocity of blue galaxies due
to their selection method [30].

The rotation velocity calculated for the red galaxies at z = 0.5 is 3421’33 km/s for
an Einstein-deSitter cosmology and 319:3; for a dark energy cosmology. While the
two values agree, the choice of cosmology has a larger effect on the result at z = 0.5
than at z = 0.2.

Wilson et al. measured a rotation velocity of 285:2: for an Einstein-deSitter
cosmology and 253:3(5’ for a dark energy cosmology for bright elliptical galaxies at z =
0.5 [30]. Again, Wilson’s foreground galaxies were selected with two color photometry
while the background galaxies were selected by luminosity [30]. Therefore, the two
results agree despite two different measurement methods.

The rotation velocity calculated for the blue galaxies at z = 0.5 is 216:3 km/s

for an Einstein-deSitter cosmology and 201:;3 km/s for a dark energy cosmology.

32

 

 

 

 

 

 

 

 

 

 

 

 

 

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0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

V-I

Figure 3.5: A color-magnitude diagram of the foreground galaxies selected by Wilson
et al. [30] and the foreground galaxies selected by this work. The small box repre-
sents the galaxies selected by Wilson et al.. The vertical dashed line represents the
separation between red and blue galaxies. The horizontal dashed line represents the
separation between bright and faint galaxies.

These values are distinct from the rotation velocities for the red galaxies at z = 0.5.

Again, Wilson et al. have no results for blue galaxies [30].

3.3 Alternate Depletion Sources

There are processes other than gravitational lensing depletion that could either
reduce or increase the number density of background galaxies near foreground galax-
ies. These alternate sources of depletion are described and discussed in the following

sections.

33

3.3.1 Blocking by Foreground Galaxies

A depletion in the number of background galaxies could be caused by large fore-
ground galaxies biasing detection of background galaxies. The resulting depletion
curve would show no depletion outside the radius of the foreground galaxy and a
fairly sharp depletion inside the radius of the galaxy.

The measured depletion is not caused by foreground galaxies blocking background
galaxies. Figure 2.8 shows the area of the galaxies. The brightest galaxies between
2: = 0.1 and z = 0.3 are at 18th magnitude. The maximum area of an 18th magnitude
galaxy is 400 arcseconds. This area translates into a radius of %% arseconds, or 20
kpc at z = 0.2. The data show measurable depletion out to 60 arcseconds, or 100
kpc at z = 0.2. This depletion range is much beyond the reach of even the largest
foreground galaxies. Therefore, the measured depletion is not caused by foreground

galaxies blocking background galaxies.

3.3.2 Blocking by Saturated Stars

Saturated stars could contaminate the baseline number density of background
galaxies. Saturated stars completely wash out their immediate surrounding area so
that no galaxies are found at all. This masking has the effect of reducing the number of
background galaxies counted in the image and reducing the baseline number density.
As a result, the angular correlation measured around foreground galaxies would be
too high.

Saturated stars in this sample do not block enough background galaxies to con-
taminate their number density. First, as shown by Figure 2.9, saturated stars block
a small area of the sky. Given the size and number of saturated stars, they cover
66,000 pixels out of 270 million, or 0.02 percent of the sky. Second, if there was a
problem with saturated stars blocking background galaxies, then the baseline num-

ber of background galaxies measured in the sample would be artificially low. If the

34

 

 

 

 

 

 

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D 20 40 60 80 100 120 140 160 180 200
arcsecond:

Figure 3.6: Autocorrelation of galaxies with z > 0.6. The fit is 6-03, the expected
autocorrelation function of galaxies.

baseline number of background galaxies is low, then the angular correlation far from
foreground galaxies would be positive because too many background galaxies would
be counted. The data show that the angular correlation approaches zero at large
distances as expected. Therefore, saturated stars are not adversely affecting the de-

pletion measurements.

3.3.3 Cross-contamination

Contamination of the foreground or background samples can reduce the measured
depletion. Figure 3.6 shows the autocorrelation of the galaxies at z > 0.6. Galaxies
cluster together, so the autocorrelation of galaxies follows the form 0‘0'8. The angular

correlation between galaxy samples will rise if contamination between samples is large.

35

v I LLLLI I I I I I I I I I I I I I I I I_I_I_I_l I I I I I I II

 

 

 

 

 

 

I I I I I I I I I I I I I I I I I I I I I I I I I I T j I I 1 I I I

Figure 3.7: The best-fit r versus redshift. The 7‘ can be converted to Einstein radius
if it is positive. Otherwise, it stands as a measure of correlation between the two
samples. The width of each bin is 0.2.

There is no contamination between our background and foreground samples.
Seven different groups of red foreground galaxies from 2 = 0.15 to z = 0.7 were
correlated with a background sample at z > 0.6. The best-fit r is plotted against
the median redshift of the foreground sample in Figure 3.7. For low redshifts, r is
unchanging. As redshift increases past 2 = 0.4, the autocorrelation increases due
to galaxies in one sample being related to galaxies in the other sample. Beyond a
redshift of 0.5, some galaxies are placed in both foreground and background bins.
The increase in autocorrelation results in smaller r, until the last few are unphysical
negative numbers. Therefore, these depletion measurements are not contaminated by

misplaced galaxies.

36

 

0.5 0.6 0.7

IIIJIIIJLIJIIIIIII IIIIIIIILJI

alpha
0.4

0.3

0.2

IIIIIIIIIIIIIIIITIIIIIIIIIIII

 

 

 

0.1

I I I I I I I I I I I I I r I I I I I I I I I I I T 1 I r I j

24.6 24.4 24.2 24.0 23.8
magnltude

N
01
.L
m
UI
N
N
01
O
m
A
a)

Figure 3.8: A plot of a vs. magnitude. The difference in magnitude used to calculate
oz is 0.2. The triangles represent all galaxies with z > 0.6, the boxes represent the
red galaxies, while the circles represent blue galaxies.

3.4 The Effect of Varying oz

This section checks the effect the value of the constant a has on the calculated
Einstein radius. As a check on previous calculations, a was calculated for a number
of magnitudes for galaxies with z > 0.6. Then, the background galaxies were split
into blue and red bins and a was calculated for each color.

The rate of change of the number of background galaxies with magnitude is not
constant. Figure 3.8 is a plot of 0: vs. magnitude. The calculated value of a shows
a clear magnitude dependence. This magnitude dependence also shows up in the
luminosity function. Figure 3.9 is the luminosity function for the galaxies with z >

0.6. There is not an area where the rate of change in the number of galaxies levels

37

 

 

 

 

III 1 1 1 J I 1 1 1 1 l J 1 1 1 l 1 1 1 1 l 1 A 1 1
'4 + + + + r-
+-
.l +
.u + l
+ 'f'
O
8:. + -
u—o. >-
23 +
“1
'4 +
~d
8_ .—
v-1:: ..
'51 + F
‘1
III-1 I-
e- + l-
n‘ L
.. ,L l .
35 I -
Bd
04
a I r I I I I I I I T I I I I I I I I I I I I 17f
El 38 23 E4 85 26
Hagnltude

Figure 3.9: The luminosity function for galaxies with z > 0.6.

off, so this plot shows that there is some kind of slope in a. Furthermore the values
of a are independent of color.

The magnitude dependence of a and the color independence disagrees with pre-
vious observations. The value of a is —0.4 x cm, where (IL is from the Schecter fit to
the luminosity function [24]. Schecter gave a constant value of (IL = —1.25 [25], while
observations from the 2dF survey suggest aL ranges from —0.7 to —1.7, depending
on galaxy type [11]. These values suggest that alpha can range from 0.28 to 0.68.

The value of a has a large effect on the best-fit Einstein radius. The Einstein
radii for the near red and blue foreground galaxies is recalculated with a value of 0.17
for (1 instead of 0.27. The net result is to drop RE by 20 percent with no change in

the reduced X2 of the fit. The best fit Einstein radius for the near red sample drops

38

to 1.7 :l: 0.4, while the best fit for the near blue sample drops to 0.9 :l: 0.2. These
Einstein radii drop the rotation velocities to 240:3? for the red sample and 176flg
for the blue sample with a lambda-dominated cosmology. However, there is no clear
reason to adopt this value of (1 instead of the value measured at the background

cutoff, so the value measured at Bw = 25 will still be used.

3.5 Galaxy Mass

3.5.1 Red vs. Blue

The measured mass of red galaxies is greater than the measured mass of blue

galaxies. The red galaxies have an average rotation velocity of 308 i 30 km/s with a
flat dark energy cosmology, while the blue galaxies have an average rotation velocity
of 210 :l: 35 km/s assuming the same cosmology. Both values are higher than the
22515;?) km/s for red elliptical galaxies and 144:?3 km/s for blue galaxies predicted
by Fukugita and Turner [13]. However, if a reduced value of a is assumed as in the
previous section, the two results for the rotation velocities are much closer. Fukugita
and Turner predicted the rotation velocity of their galaxies by utilizing the luminosity
function of Efstathiou, Ellis, & Peterson [7] and the Tully—Fisher relation [27].
The rotation velocity of the red galaxies is comparable with 255:2g km/s reported
by Wilson et al. [30] assuming a dark energy cosmology. However, the uncertainties on
both sets of measurements are so large that the rotation velocity reported by Wilson
et al. is consistent with the rotation velocity of the blue galaxies. Again, Wilson’s
sample consisted of bright elliptical galaxies selected by V-I color.

The ratio of red/ blue rotation velocity is 1.5 :l: 0.4, comparable to the ratio of the
red and blue galaxies reported by Fukugita and Turner of 1.6 [13]. Therefore, while

the measured rotation velocities of galaxies appears a little high, the ratio of red and

blue rotation velocity agrees with the ratio of the red and blue rotation velocities

39

reported by Fukugita and Turner. Furthermore, if a smaller value of a is assumed,
the two results agree.

Finally, the measured rotation velocities are not inconsistent with the rotation
velocities from the Sloan Digital Sky Survey. Fischer et al. measured the shape
distortion of background galaxies several hundred arcseconds away from foreground
galaxies. They measured a rotation velocity of 240:1: 28 km / s for foreground galaxies.
They did not separate foreground galaxies by color, so this velocity is an average of
red and blue galaxies [10]. The average of the red and blue rotation velocities in this
measurement is 273 i 35 km/s for an Einstein—deSitter cosmology, and 259 :l: 33 km/s

for a flat dark energy cosmology. Both results are consistent with the SDSS result.

3.5.2 Near vs. Far

No matter what cosmology is assumed, the measured mass of red galaxies at
z = 0.2 agrees with the measured mass of red galaxies at z = 0.5. This result
coincides with the lack of mass evolution reported by Wilson et al. [30]. Lilly et
al. reported no luminosity evolution in galaxies redder than Sbc out to a redshift of
z = 1 [20]. Therefore, these results indicate that the mass-luminosity relation for red
galaxies does not change out to z = 0.5.

The measured mass of blue galaxies at z = 0.2 is the same as the measured mass
of blue galaxies at z = 0.5 for both assumed cosmologies. Lilly et al. report that
galaxies bluer than Sbc get brighter at z > 0.5. At z < 0.5, there is no change
in luminosity of blue galaxies [20]. These results indicate that the mass-luminosity

relation for blue galaxies also does not change out to z = 0.5.

3.5.3 Bright vs. Faint

The sample of near red galaxies was separated into bright and faint samples. The

bright sample consists of galaxies with Bw < 22 between 2 = 0.1 and z = 0.3. The

40

III II II I IIILLI III II LLII I I I I IIJ4J LJI I II I

 

ILIIIIIIIIIILILIIII

8::
IIIITfiIIIIIIIIIIII

——a—

 

 

 

 

angular correlation

-O.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20

‘\‘1
V

 

 

IIIIIIIIIIIIIILIIII
\:
l
TITIIITIITIIIIIIII

 

 

 

 

IIIIT‘IIIIII‘ITIIIIIIWFFTIIIIIIIIIIIIITT

20 40 60 80 100 120 140 160 180 200
arcseconds

0

Figure 3.10: Bright (+) and faint ([1) red galaxies at z = 0.2 are correlated with
background galaxes beyond 2 = 0.6. The curves are the best fits to each population.
cutoff for the bright sample is 1 magnitude fainter than m* = 21 for galaxies between
2 = 0.1 and z = 0.3. The faint sample consists of galaxies with 22 < Bw < 24
between the same redshift limits. The cutoff for the faint galaxies is 3 magnitudes
fainter than m*.

The mass difference between the bright and faint samples follows the Tully-Fisher
relation [27]. The Tully-Fisher relation states that M = —1010gv + C, where C is

0'5 according to Eq. 4.2. Therefore,

a constant [13]. Velocity is proportional to 'r
M = —510gr + D, where D is a constant different from C. It follows from this
equation that Mbright-Mfaint = —5(108(7‘bright) —10g(7‘faint)). The median magnitude
is 21.2 for the bright group and 23.1 for the faint group. The best-fit Einstein radius is

4.1 i0.5 for the bright group and 1.8i0.6 for the faint group. The median magnitude

41

difference between the two groups is 1.9. The magnitude difference estimated from
the Einstein radius difference is 1.7 :l: 0.4. Therefore, the galaxy mass increases with

luminosity and follows the Tully-Fisher relation.

3.6 Summary

The measurement of galaxy-galaxy lensing depletion yields many results. Red
galaxies, with an average rotation velocity of 308 :l: 30 km/s, are more massive than
blue galaxies, with an average rotation velocity of 210 i 35 km/s. Neither red nor
blue galaxies exhibit mass evolution out to z = 0.5. Furthermore, the mass-luminosity
relation appears to be constant out to z =: 0.5. The rotation velocities of red galaxies
at z = 0.2 follow the Tully-Fisher relation. The 258 d: 35 km/s average rotation
velocity is consistent with the 240 i 28 km/s average rotation velocity found by
Fischer et al. [10]. The depletion measurements are not affected by saturated stars,
contamination between foreground and background samples, or foreground galaxy
size.

These rotation velocities may not be used to calculate the mass of the entire
foreground galaxy. Instead, they may be used to constrain the mass within the area
for which a depletion signal is present. The resolution of this measurement is too
poor to differentiate between the small depletion signal present at 100+ arcseconds
and no depletion signal. A larger sample of foreground and background galaxies will

be needed to reduce the statistical errors.

42

Chapter 4

Conclusions and Future Work

A catalog of objects has been obtained from the N OAO Deep Wide Field. Three
color photometry (Bw, R, and I) is available for the objects. Galaxies and stars
have been successfully separated with few misclassifications for objects with a Bw
magnitude brighter than 23.5. There are 29,163 objects classified as stars in the DWF.
There are 57,685 objects classified as galaxies in the DWF. Photometric redshifts to
z = 1 have been estimated for the galaxies.

Gravitational lensing depletion has been used to measure the rotation velocity
of foreground galaxies in the Deep Wide Field. Red foreground galaxies have a
mean rotation velocity of 313 :l: 30 km/s, while blue foreground galaxies have a mean
rotation velocity of 227 :l: 40 km/s. The ratio of the rotation velocities of the red
and blue galaxies is consistent with the ratio of the predicted rotation velocities
of Fukugita and Turner [13], although the actual measured values of the rotation
velocity are in both cases higher than the predicted values. There appears to be no
change in rotation velocity for either set of galaxies out to a redshift of z = 0.5. The
unchanging rotation velocity is consistent with the unchanging rotation velocities of
bright elliptical galaxies found by Wilson et al. [30]. Finally, the rotation velocity of

red galaxies with Bw < 22 is greater than the rotation velocity of the red galaxies

43

with Bw > 22. The ratio of the rotation velocities of the bright and faint red galaxies
matches the expected value from the Tully-Fisher relation.

There are a number of vital conclusions that can be drawn from this work. First,
there is now a direct measurement of the rotation velocities of distant red and blue
galaxies. The results of this measurement indicate that galaxies have not accrued
mass since 2 = 0.5. The results also indicate that the relative masses of red and blue
galaxies have remained unchanged over the same time period. Second, the rotation
velocities of faint galaxies may be measured. Previous lensing measurements were
limited to bright foreground galaxies. Third, because the mass of neither red nor
blue galaxies appears to change to z = 0.5, and because Lillyet al. measured no
luminosity evolution in either red or blue galaxies out to z = 0.5 [20], it appears that
the mass-luminosity relation for galaxies holds out to z = 0.5.

Further work on the Deep Wide Field should reduce the uncertainties present in
these results. J annuzi and Dey are currently collecting spectroscopic redshifts in the
DWF [16]. Spectroscopic redshifts may be used to directly check the accuracy of the
photometric redshifts. J annuzi and Dey are also working on infrared photometry of
the DWF in the J (1-1.4 mm), H (1.4-1.6 mm), and K (2.0-2.4 um) bands [15]. Infrared
photometry will increase the number of available colors, improving the redshift fit.
IR photometry will also allow the 4000 A break to be measured for galaxies with a
redshift greater than 2 = 1. The two effects may allow for lensing measurements for
foreground galaxies at z > 0.5. This improved distance will check if blue galaxies
evolve at z > 0.5 as expected.

Finally, Jannuzi and Dey will eventually release data for 54 fields [15]. Twenty-
seven of those fields will be in the southern part of the sky instead of the northern
sky. The increased number of fields and the varying location will reduce the statistical
errors in the gravitational lensing measurements. The varying location will also reduce

errors due to clustering that may have cropped up in this measurement.

44

Appendix A

Photometry and Photometric

Redshift Techniques

A.1 Photometric Redshift Method

A. 1 . 1 Background

The photometric redshift technique is an alternative to measuring redshifts spec-
troscopically. There are two main advantages to obtaining photometric redshifts.
First, redshifts for large numbers of galaxies may be obtained from a few observa-
tions. Loh and Spillar noted in 1986 that redshifts for 200 galaxies could be obtained
on the Wyoming 2.3m telescope in three hours [21]. The rate at which redshifts
may be obtained is even greater with modern instrumentation and larger telescopes.
Second, photometry has a fainter flux limit than spectroscopy. Therefore, redshifts
may be obtained for fainter galaxies with the photometric method than with the
spectroscopic method.

The most distinctive feature of a galaxy spectral energy distribution (SED) is
the 4000 A break. This break is due to metal lines and Balmer absorption in the

galaxy, and appears as a sharp increase in galaxy luminosity as wavelength increases

45

 

 

 

 

m " . -
I ‘ [—
d I-
4 5 L
v-fl __] H —
I c1 I‘I: '3' x I-
2 '1’. W I
1 .
c) _ 8‘ _ ' _
u: 99.. -
0 III x‘f'. -
g u 'lif. r-
4) ‘ $3 -
dd —1 . ." _
w 4.
C xxx X x x x +-
CD Xx ..'
g 1 xxxx 'Yv F
x x x .
l a” _
(U a W —
: ++| any! :
.1 + ++ i-
m_ ++ >999? [—
d + D [-
-l + ++ D D >-
+ +
j b + D vb” :
. ,, v v .
v I v I V I V I v I I I v I V T
1000 10000
Hngstrams

Figure A.1: Spectral energy distribution of an SD galaxy (A), an Sbc galaxy (+), and
an Im galaxy (X).
past 4000 A [5]. Around 4500 A the increase in luminosity levels off a little. The
break appears to be present in all galaxies, so the position of the break in a galaxy’s
observed SED may be used as an indicator of redshift.

The goal of this Appendix is to check the photometric redshift and photometry
techniques using a published data set. The photometric redshift technique is discussed
first, followed by a discussion of photometry. Both techniques use the Hubble Deep

Field as a practice data set.

A.1.2 Technique

This implemenation of the photometric redshift technique uses observed galactic

spectra to create template SEDs. The effects of evolution are still uncertain, so

46

 

 

 

     

 

D_ I l I l [LI LJ I I J I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I r‘
’1 q + v- D
+ ..
-+ + -
ull ++ — D
. + + T in
In. _ + + r
O .7 +++ I—
(P +4++ .. D
-: ++
H++ I-
o - MW“, 3 '
o 1 — .0
. 3 U‘
-4 : I
H
I I I I l I I I I l I I I T I I I T I I I I I I I I I I I I I I I I l I I I I l I I I I .
D
B-V
Q I I I I I I I I I I I l I I I I L14] I 1 L1 I I I I I I l I I I I I I I I I J I I I P
D I!)
q .
D C! x I-
film X D 0?
I O X x X X r—c
(I) xxxxxxx _ A
- _‘ ...”linumunummmlnllmnunmprwnun-LI-IIIIII‘IIDUDDDU ODD _ +
(I: v- d " 0%
O P I
> D b
x - P 0‘
.4
M [- D
C). IIrrlIIIIIrIIIIIWfIIIIITIfiIIIIIIIIIIIIfilIrTT I!)

 

 

0.8 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1

Figure A.2: A color-color plot of the template spectra. U-B (+, upper-left scale), V-
R (x, lower left scale), and R-I (Cl, lower right scale) are plotted against B-V (both
horizontal axes).

theoretical model spectra are not used in this implementation. The template spectra
were observed by Kennicutt in 1992 [17]. The three template spectra are SO, Sbc,
and Irregular (Im), and are plotted in Figure A.1.

The template SEDs are blended to recreate the fine graduations between real
galaxy types. The flux of each galaxy template is normalized so that unit flux is at
4000 A. Then, a composite galaxy is created with varying percentages of neighboring
types. There are ninety total templates spanning the gaps between S0, Sbc, and Im.
Figure A.2 plots the colors of the template spectra. The SD has B — V = 0.95, the
Sbc has B — V = 0.71, and the Im has B — V = 0.30.

47

I I I i I I I I I I I I I I I I I I I I J I I I I I

 

 

 

 

T
w‘ r
N.‘ i I.
“'14 + ++ #-
el + + _
—d
500‘ "
“20': + * _
E. . + ~
“~91 + ++ Jr L
O. + + l'
- +޴ + I-
t: ” '
0‘ ..
_ + .
m'i ‘I' + I "
o
i + ’
O l'
d I I I I fiI r I I I I I I I I I T I I I I I I I I I I I I
0.0 0.8 0.4 0.6 0.8 1.0 1.2 1.4
Zspectroscop1c

Figure A.3: Photometric redshifts produced by this method plotted against spectro-
scopic redshift.

Next, the template SEDs are redshifted by discrete amounts to recreate the ex-
pected observed redshifts. The fiducials ranged in redshift from 0 to 1.5 because the
4000 A break is redshifted out of the visible filters around a redshift of 1 and there
is a large gap in the available spectroscopic redshifts for the Hubble Deep Field after
1.5. A redshift spacing of 0.005 within these limits is the smallest spacing for which
the X2 continues to decrease.

Finally, the fluxes of the redshifted SEDs are calculated for the filters used in the
observation. The transmission percentage of a filter at a given wavelength is multi-
plied by the flux. This multiplication ensures the model flux matches the observed

flux.

48

 

 

 

 

I I I I44 I I I I J I I I I I I I I I I I I I I I I I I
-] + F-
‘ + + + ‘
ru' .
._ + P.
"1_ v-
_ + + + r
+ + +
o“ + + + + P
o— + + —
-‘.. ++
_ + + II- + E
__ + +
*m-] + 'H- '-
_J .—d + —
LLO1 + + .
"' + + +
'5 ++ '
Moi] + + ++ _
0.. +++ + + -
q 4» ++ + _
+
1f" 4‘ +++ "
._ + I—
0. ++ .
1 h
+
m4 + -
.—4 —
D- + -
o‘ .
d IfI I I I I I I I I I T I T I I I I I I I I I I I I I T
0.0 0.8 0.4 0.6 0.8 1.0 1.8 1.4
Zspectroscoplc

Figure A.4: Photometric redshifts produced by FLY plotted against spectroscopic
redshift. A number of these spectrosc0pic redshifts were undetermined when the
most recent FLY data were published.

A.1.3 The Hubble Deep Field

The Hubble Deep Field (hereafter referred to as HDF) images were taken in De-
cember 1995, and version 2 of the reduction was released to the public in Febru-
ary 1996 [29]. These images were taken with the Wide Field Planetary Camera 2
(WFPC2) on the Hubble Space Telesc0pe through filters centered about 300, 450,
606, and 814 nm. These filters are referred to as F300W, F450W, F606W, and
F814W, respectively. F300W is 72 nm wide, F450W is 93 nm wide, F606W is 158
nm wide, and F814 is 176 nm wide [2].

Shortly after the release of the version 2 data products, F ernandez-Soto, Lanzetta,

and Yahil (hereafter referred to as FLY) released their first set of photometric redshifts

49

 

0.2
IIIILJLJ

1

0.

I 1 I I I I I I I I I I

J I I I I

 

0.0

 

delta Z

-U.1
IIIIIIIIIIJI

-0.2

I I I I I I I I I I I I

 

 

 

O
O
O
N
O
A

0.6 0.8 1.0 1.8 1.4

Figure A.5: Median error and dispersion of the photometric redshifts plotted against
spectrosc0pic redshift. The median error is represented by (+), while the dispersion
is represented by the line.

for the HDF [19]. In 1998, after obtaining J, H, and K band photometry of the HDF,
FLY released improved photometric redshifts and photometry [9]. This latest release

will form the basis of the redshift comparison.

A. 1.4 Results

This section describes the results of applying this photometric redshift technique
to the HDF. The analysis concerns galaxies for which spectroscopic redshifts are
available. The redshifts are calculated with the STARGAZE software package.

The photometric redshifts computed with this technique agree with spectrosc0pic

redshifts. Figure A8 is a plot of photometric redshifts computed by this technique

50

JIIIIIIIIIIIIIIIIJIJLIIIIIIIILIIIII

 

0.4

0.2 0.3
ITrIIIIIIIIIIIIIIII

IIIIIIIJJIIIIJIIIII
4.

 

 

0.0 0.1

 

delta Z

-0.4 -0.3 -U.E -0.l

IJI_LIIIIIIIIIIII_IIJIIIII
4-
—4—' :F
IIjIIIIIITIIIIIITIIIIIIIII

 

 

 

I I I I I I I I I I I I I I Fl I I III I IT I I I‘II Ifi I I IV—‘r

25 24 23 BE 81 80 19 18
mogn1tude

-0.5

Figure A6: The difference between spectroscopic and photometric redshifts plotted
against magnitude.

versus spectroscopic redshift. Figure AA is a plot of photometric redshifts computed
by FLY versus spectroscopic redshift. The median difference between photometric
and spectroscopic redshift is 0.00 :l: 0.08 for both groups of photometric redshifts.
Therefore, on average, there is no bias between photometric and spectroscopic red-
shifts. Phrthermore, the photometric redshifts are consistent with those calculated
by FLY.

While there is no average bias between photometric and spectroscopic redshifts,
there are some redshift regions that show a bias. Figure A5 is a plot of the median
of the difference between photometric and spectroscopic redshifts and the dispersion
of the median redshift difference. At z = 1, the redshift is overestimated by a median

value of 0.1. At 2 = 1.2, the redshift is underestimated by a median value of 0.08.

51

 

 

 

 

 

 

".
o- +-
- f-
m: I
O: I, '-
mi [3 :
—1 + F-
o- .
. + ], -
—rI" + l-
D‘ h
3 + 1 i“ t]+ :
qu .1 ¥ .1. L+++' i-
oo-I 'l'+ if}; ++IT "l »
.0 j I
and +3 ++ _
“1.1 [[3
01 __
l - .
m: I z
:51 :-
|‘ P
x3 :
9’3 F
"11 Jr
? I'I T W trr r II
0.1 1

Z spectroscopIc

Figure A.7: The difference between spectroscopic and photometric redshifts plotted
against spectroscopic redshift.

There is no bias at z = 0.2 because there is only one data point for that redshift. The
median dispersion is greatest at a redshift of z = 1, indicating that the redshift fit is
poorest for that redshift.

The spread in differences between the photometric redshifts and spectrosc0pic
redshifts increases with magnitude. Figure A6 is a plot of the difference between
photometric and spectroscopic redshift versus magnitude. This spread is expected
because photometric uncertainties are proportionial to 731.3" Therefore, the spread
in differences should increase as galaxies become fainter.

The spread in differences between the photometric redshifts and spectroscopic
redshift increases with redshift. There are two causes for this spread. First, the

higher redshift galaxies will be fainter due to increased distance. Second, the 4000 A

52

IIIIIIIIILIIIIIIJII IIIIIIIIIIIIILIIIIII

 

35

30

 

25

20

 

Number

10 15

S

ILIIIIIIIIIIIIIIIIIIJIIIIIIIIIIIII
TfiIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

 

 

,ii+++] ]] [411+

IljjI I

 

_
d
_

I I I I I I I I I I I I I I fiI I I I I I I I I I I

-30 -ED -10 0 10 20 30 40
deltaZ/Zerror

I
.b
O

zspectroscopic" photometric
Uzphotometric '

 

Figure A8: A histogram of

break is redshifted out of the F 814 filter near 2 = 1. Therefore, the distinguishing
feature used to determine photometric redshifts disappears from the photometry for
galaxies farther than 2 = 1. Figure A.7 shows that the spread in differences becomes
much larger at z = 1, confirming this hypothesis.

The calculated uncertainty in photometric redshifts is not representative of the dif-
ference between photometric and spectroscopic redshift. The calculated uncertainty
is derived from the photometric errors. Figure A8 is a histogram of the difference
between spectroscopic and photometric redshift divided by the photometric redshift
uncertainty. The histogram is centered about 0 :t 5. The FWHM of the histogram
is 8. The expected F WHM is 2% a: a, or 2.4. Therefore, the average differences

between spectroscopic and photometric redshift are 3.4 times larger than expected.

53

A.1 .5 Conclusion

The photometric redshifts calculated for the Hubble Deep Field agree with spectro-
scopic redshifts as well as previously published photometric redshifts. The calculated

uncertainties are smaller than expected by a factor of 3.4.

A.2 Photometry Method

A.2.1 Background

The goal of this section is to check my photometry method using a data set that
has already been published and analyzed. The Hubble Deep Field (HDF) serves as
this data set. A description of the HDF is given in the previous section. Shortly
after the release of the version 2 data products, Fernandez-Soto, Lanzetta, and Yahil
(FLY) released their first set of photometric redshifts for the HDF [19]. In 1998,
after obtaining J, H, and K band photometry of the HDF, FLY released improved
photometric redshifts and photometry [9]. This latest release will form the basis of
the photometric comparison.

FLY used the Source Extractor (SExtractor) software package to perform photom-
etry on the HDF. SExtractor is a program designed to “detect, deblend, measure,
and classify sources” in astronomical images [1]. SExtractor was chosen to perform
photometry on the HDF for its speed in handling large amounts of data and for

consistency with the methods of FLY.

A.2.2 Description of Photometry

The two available photometry methods are isophotal photometry and aperture
photometry. Isophotal photometry finds a source and divides it up by contours of

equal brightness, or isophotes. All the light within a certain isophote is counted as

54

 

 

 

 

.l.
E”. ++Jr + _
“(D + + .
a j I t] + + ++ .,. + -
E: - _ ++++ ,++ + —
ac: + [L
It: +I +T +
_ d I" ++ ++ : ++ I .
8 ~ J‘H .
.-I t +
s'w‘ 1L + -
LLD“ + + "
~§I

 

 

 

I I I I I l fi I I I TI —I I I I I T I IiI I I 1
3D 28 26 84 82 20 18
mIFLY_isoJ

Figure A9: The difference between FLY isophotal magnitudes and the isophotal
magnitudes of this work plotted versus FLY isophotal magnitudes for 976 galaxies in
the HDF.

the flux of the object. Aperture photometry finds a source and surrounds it with an
aperture. All the light within that aperture is counted as the flux of the object.
SExtractor employs the following procedure to determine the background flux.
First, it computes the local background histogram for a grid of size determined by
the user. Then, the outliers are thrown out until the limits of the histogram are
$30 around the median. If a of the new distribution is within 20 percent of the
original 0, the field is considered uncrowded and the mean of the new histogram is

the background. Otherwise, the background is estimated with:

background 2 2.5 - median — 1.5 - mean (A.1)

55

.80

 

0

15

10

0.

IILIIIIIIJIIJIIIIIII

magnitude
0 05

 

 

 

jIIIIIIfIIIITI‘rIITIITITrITIIIII

-0.05
lIIIIJIIJl

 

 

 

-0.10

30 88 86 84 88 80
mIFLY_1soJ

OJ

Figure A10: The median difference between the two isophotal magnitudes (+), the
dispersion of the difference (—), and the magnitude uncertainty ([3) plotted versus
FLY iSOphotal magnitudes for 976 galaxies in the HDF. The data are grouped into
bins 0.5 magnitudes wide.

This background is subtracted from the measured flux [1].

A.2.3 Isophotal Photometry

FLY calculated their photometric redshifts using isophotal photometry. Therefore,
isophotal photometry was performed on the HDF in an attempt to reproduce the FLY
photometry.

The following steps were taken to reproduce the results of the FLY photometry.
First, the parameters given in their first report were adopted. Namely, the images

were smoothed by a gaussian filter of full-width half maximum (FWHM) 3 pixels. The

56

 

 

 

 

 

0. L J L I I I I I I I I I I I I I I I I I I I I
m
”‘ ‘ + ++ ’
"' +
- 1 ' 4: + + ’
g d "‘31 + + "
_. 1 “I + b
50 ‘ .lEn 1' -
Q; T 1r": + _
~— * viii iii‘i‘i- H + -
S - ”m'.133|'| + '
I :3] : I!!-;: I" , +
‘ Hahn‘s; -
3 ~ 5 fini'ii. + -
(0m ._4 l5 Jail?“ .I F. + —
"'0 :-I'-I-:?'u.- '-'. — H-
I . . . f>:.~~-~."=..{.§ .' ' + 15. "
>' I] I “3: I‘II" “NW-1 , +
_I ' 'I If? V «‘53 7 ++ P
LL ‘ II! I. - gI :‘I-f-‘lkl {‘5 7§-_‘+ _ + .* + 4'
~ - “I A”; ,‘v'.-"*w.e-:~‘ a; + + +1 -
5 ' . . ‘-.:.-.'--"'.'.‘. .
- " “f 2' 'gy . .P". '.'- + "
O + t ’" ‘ in: 3‘13" - + + +
Q ] + I; + 'I' + + +E
d + -
ID " -
O I I I I I I I I I I I I I I I I I I I I IiI I
I
30 88 86 84 ea 80 18
mIFLY_1soJ

Figure A.11: The difference between FLY isophotal magnitudes and my aperture
magnitudes plotted versus FLY isophotal magnitudes for 976 galaxies in the HDF.
detection threshold was set to at least ten pixels with a signal—to—noise ratio greater
than 1.9 a each. Furthermore, where two or more sources overlapped, the light from
the overlapping pixels was excluded from both objects’ photometry. Finally, the
F814W image was used as a fiducial source map [19]. The area photometered in the
other three colors was based on the source area found in F814W. FLY did not clearly
specify a size for the background subsquares, so the background was measured in
72 x 72 pixel squares throughout the image. This size is large enough to surround
the largest sources, but small enough to pick up some of the local variation in the
background.

The next task was to match the resulting sources with the sources FLY found.

This extraction found 2925 possible sources. FLY published results for 1067 sources.

57

They limited their sources to those above 26th magnitude in the F 814W band if they
lie in a strip near the edge of the field, or above 28th magnitude in the remainder of
the field. The sources that had a center position within two pixels of sources found
by FLY were flagged. This pruning left 976 sources common to both catalogs. These
sources form the basis for the remaining analysis.

The isophotal magnitudes agree with those computed by FLY. Figure A.9 shows
the difference between FLY isophotal magnitudes and the isophotal magnitudes of this
work plotted against FLY isophotal magnitudes. There is little difference between
the two results for bright galaxies. As the galaxies become fainter, the spread of
differences increases. However, there does not appear to be a systematic shift toward
brighter or fainter magnitudes between the two results.

There is no bias between the isophotal magnitudes and FLY isophotal magnitudes.
Figure A.10 is a plot of the median of the difference between isophotal magnitudes
and FLY magnitudes, the dispersion of the median of the difference, and the me-
dian magnitude uncertainty versus FLY magnitude. The median difference between
magnitudes remains close to zero for all magnitudes and is never greater than the

uncertainty in magnitude. Therefore, there is no bias present.

A.2.4 Aperture Photometry

Does aperture photometry result in different photometric redshifts? In theory,
faint objects should appear brighter using aperture photometry. By definition, isopho-
tal photometry omits light from a source that falls outside the isophote. Aperture
photometry can count this light by utilizing a larger aperture, but the larger aperture
will increase background noise. There will be a noticeable difference between mea-
sured magnitudes if the 1.90 isophotal limit omits a sizable fraction of the flux of a

SOUI‘CC.

58

 

 

 

 

I I I I I I I I I I I I I IA I I L I I I I I LI 1 I I I
‘t‘ ’
.H "

- + -
m: + . + _
v—1

.1 + r-

. +
O. t

o- + -
10" . + -
o - .
s - ,, -

on
C1._ + _
4.
DC)q -+ + + I r
I + + L
, .
u-I + p
CO
QC5_ + 1 + + -
hJ . + + P

-1 + + l-
1r“ + +"' ++ .
c1q _

-< r-

.J + .
m... + + _
C)

'4 + '-
CJJ + + -
d I’LFT FT I I I I Ifl I I I I IJI I I I I I I I I I I I

0.0 0.8 0.4 0.6 0.8 1.0 1.8 1.4

Zspectroscopic IgoodJ

Figure A.12: Photometric redshifts calculated with aperture photometry plotted ver-
sus spectroscopic redshifts for 86 galaxies in the HDF.

The aperture surrounding each source is calculated in the following manner. First,
an ellipse with ellipticity c and position angle 0 is defined to surround each source
at its 10 isophotal limit. Then, the radius of this ellipse is doubled. Within this

aperture is calculated the “first moment:”

TI
r1 2 L (T) (A.2)
Z: I(1")
The aperture radius is krl. Most galaxies appear as ellipses in the sky, so elliptical
apertures will maximize coverage and minimize background. Therefore, the axes are
ckrl and krl/e for an elliptical aperture. The scaling factor k determines the relative

size of the aperture. The default k = 2.5 is used to maximize source coverage while

59

 

.4

l

1.2

1.0

th - isophot
0.4 0.6 0.8

++

0.2
IIIIIIIILIIIIIIIIILJIIIIJLIIL
+
4+-

IIj—IfiIIIIIIIIFIIfIfIIIIIIIIII

 

 

 

0.0

0.0 0.8 0.4 0.6 0.8 1.0 1.8 1.4
Zspectroscoplc IgoodJ

Figure A.13: Photometric redshifts calculated with isophotal photometry plotted
versus spectroscopic redshift for 86 galaxies in the HDF.

minimizing the number of background counts included in the measurement of the
source.

The results of FLY isophotal photometry and the aperture photometry of this
work diverge for faint objects. Figure A.11 is a plot of the difference between FLY
isophotal magnitudes and aperture magnitudes versus FLY magnitude. The median
difference between FLY isophotal magnitudes and aperture magnitudes clearly in-
creases for fainter sources. The aperture magnitudes are consistently brighter than
the iSOphotal magnitudes for sources fainter than 25th magnitude. Aperture magni-
tudes are expected to be brighter than isophotal magnitudes for faint sources, so this

difference matches expectations.

60

 

1

1

+

—+—
_+_

   
   

  

 

   
   

 

+

0.5

 

 

      
     

  

 

 

 

I.
ll

 

  
   

 

 

 

 

 

 

 

o '- I
2 5“““U II + -
ND EIIIIIHI: . "II-'.":':: I . it. I.
I O .. .i..;l.r.;'.’.‘f,lu.‘ .1 + '-
Q ,
0 ++ + ’
h: + -
In P
O F
I 4 I
o - I I + + I
T .. f
. + t ’
. + + '
‘9 #k i . L+ IL 1 I I | r l I 1 ' ' ' l ' I l
I 28 26 24 BB 20 18
mognltude

Figure A.14: zaperture — Zisophotal versus aperture magnitude for 976 galaxies in the
HDF.

A.2.5 Photometry Comparison

The next step was to calculate photometric redshifts for these galaxies using the
procedure described in Section 2.2. Photometric redshifts were calculated using both
aperture and isophotal photometry. There were 86 galaxies that had “good” spectro-
scopic redshifts as defined by Cohen [6]. Figure A.12 is a plot of photometric redshifts
calculated with aperture photometry against spectroscopic redshift. Figure A.13 is a
plot of photometric redshifts calculated with isophotal photometry against spectro-
scopic redshift.

There is no difference between photometric redshifts computed from aperture pho-
tometry and photometric redshifts computed from isophotal photometry for galaxies

for which we have spectroscopic redshifts. The median difference between photometric

61

and spectroscopic redshifts for aperture photometry is Zspectroscopic — thotometric =
6 x 10‘3. The median difference between photometric and spectroscopic redshifts
for isophotal photometry is Zspectroscopic — zphotometric = —8 x 10-4. In both cases,
the median difference is essentially zero. The dispersion of the difference for aperture
photometry is 9 x 10-2, while for isophotal photometry the dispersion is 9 x 10—2.
Therefore, both photometry methods produce identical photometric redshifts for the
galaxies for which spectroscopic redshifts are available. This result is expected be-
cause both photometric methods should produce identical results for bright objects.
The galaxies with spectroscopic redshifts are bright because more photons are needed
to resolve spectra than to resolve an image.

Because the galaxies for which we have spectroscopic redshifts were unrevealing,
the next step was to compare the difference between photometric redshifts for the
entire catalog. Figure A.14 is a plot of Zaperture—Zisophotal versus isophotal magnitude.
The spread in zaperture — zisophotal increases as the galaxies get fainter. This result
is not surprising because Figure A.11 shows that the magnitudes measured by each
method differ more as the flux of the sources decreases. However, Figure A.14 does
not indicate the presence or absence of a systematic redshift divergence between the
two methods.

There is no systematic divergence between isophotal photometric redshifts and
aperture photometric redshifts. Figure A.15 is a plot of the median of the differ-
ence between Zaperture and Zisophotala the dispersion of that difference, and the me-
dian redshift uncertainty versus isophotal magnitude. The median difference between
photometric redshifts remains nearly zero for all magnitudes and never rises above
the uncertainty in redshift. There is no systematic difference between isophotal and

aperture photometric redshifts.

62

JQ I I

 

020
h
L-
I-
i—
f-
n-
—
.-
y-
b—
I—
p-
p-

.15

0.10

05

U.

0
IlllIIlIIIIIIILLIII

 

 

0.00

I—ijl I I Ifi I 1 T I I I I I—I I I I I I [j I I I I

LJJJI LL #1

 

 

 

-0.10

"J
(D
N
O"!
N
4:
N
N
N
O
00

mag

Figure A.15: The median difference between photometric redshifts calculated with
aperture and isophotal photometry (+), the dispersion of the median difference (—),
and the median uncertainty of the differences (A) in each bin plotted versus aperture
magnitude for 97 6 galaxies in the HDF. The data are grouped into bins 0.5 magnitudes
wide.

A.2.6 Conclusion

There is no bias between redshifts created with isophotal photometry and aperture
photometry. There is a consistent magnitude difference between isophotal photometry
and aperture photometry for faint objects. Therefore, the luminosity function will
determine the choice of photometry method.

The luminosity function of a survey of galaxies is a measure of galaxy density with
respect to magnitude in a given volume of space. Figure A.11 shows that the magni-
tudes of bright galaxies are acceptable with isophotal photometry, but the magnitudes

of less luminous galaxies are consistently too faint. This error creates a luminosity

63

function that is artificially low for faint galaxies. Aperture photometry will be used in
further work to calculate photometric redshifts to prevent this deficit in the luminosity
function.

In conclusion, aperture photometry is the desired photometry method because
it does not systematically exclude light from faint galaxies. The correct luminosity

function of a galaxy sample may be determined from aperture photometry.

64

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