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THEE“

20:0

This is to certify that the
dissertation entitled

QUASARS, CLUSTERS AND COSMOLOGY

presented by

NEELAM DHANDA

has been accepted towards fulﬁllment
of the requirements for the

PhD. degree in Physics and Astronomy

 

 

14;);le

Major Professor's Signature

Date

MSU is an Affirmative Action/Equal Opportunity Employer

 

LIBRARY
Michigan State
University

 

 

 

QUASARS, CLUSTERS AND COSMOLOGY

By

Neelam Dhanda

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Physics and Astronomy

2010

ABSTRACT

QUASARS, CLUSTERS AND COSMOLOGY

By

Neelam Dhanda

PART A: Acceleration of the Universe and Modiﬁed Gravity:

We study the power of next-generation galaxy cluster surveys (such as eROSITA
and WFXT) in constraining the cosmological parameters and especially the growth
history of the Universe, using the information from galaxy cluster redshift and mass-
function evolution and from cluster power spectrum. We use the Fisher Matrix for-
malism to evaluate the potential for the galaxy cluster surveys to make predictions
about cosmological parameters like the gravitational growth index '7. The primary
purpose of this study has been to check whether we can rule out one or the other of
the underlying gravity theories in light of the present uncertainty of mass-observable

relations and their scatter evolution.

We found that these surveys will provide better constraints on various cosmolog-
ical parameters even after we admit a lack of complete knowledge about the galaxy
cluster structure, and when we combine the information from the cluster number
count redshift and mass evolution with that from the cluster power spectrum. Based
on this, we studied the ability of different surveys to constrain the growth history of
the Universe. It was found that whereas eROSITA surveys will need strong priors on
cluster structure evolution to conclusively rule out one or the other of the two gravity
models, General Relativity and DGP Braneworld Gravity; WFXT surveys do hold
the special promise of differentiating growth and telling us whether it is GR or not,

with its wide-ﬁeld survey having the ability to say so even with 99% conﬁdence.

PART B: Chemical Evolution in Quasars:

We studied chemical evolution in the broad emission line region (BELR) of nitro-
gen rich quasars drawn from the SDSS Quasar Catalogue IV. Using tools of emission-
line spectroscopy, we made detailed abundance measurements of ~ 40 quasars and
estimated their metallicities using the line-intensity ratio method. It was found that
quasars with strong nitrogen lines are indicators of high metallicities. Some of these
quasars have reached metallicities as high as Z ~ 2026). Our detailed analysis showed
that except in three QSOs, most of the different line-intensity ratios implied the sim-
ilar metallicities. This veriﬁes that this abundance analysis technique does produce
meaningful results. The exceptions are the line-intensity ratio NIV] /CIV, which gives
systematically low metallicities and the line-intensity ratio NV / He II, which gives sys-
tematically high metallicities.

We compared our ﬁndings with the predictions of the galactic chemical evolution
models. From this study it was concluded that such high metallicities are reached
either by requiring a top-heavy Initial Mass Function (IMF) for the quasar host
galaxy as suggested by theoretical models, or by physically catastrophic events such
as mergers that trigger star formation in already evolved systems which then leads

to extreme metallicities in such quasars.

Copyright by
NEELAM DHANDA
2010

To The Universe

ACKNOWLEDGMENTS

As this moment my thanks are due to many people.

I would like to thank my advisor Prof. Mark Voit and also Prof. Jack Baldwin for
letting me do this thesis on two separate projects, guiding me all along. And thanks
to all my other committee members, Prof. R. Sekhar Chivukula, Prof. S. D. Mahanti

and Prof. Steve Zepf for supporting me in this endeavour.

My sincere thanks to many. wonderful teachers I have had all my life. At this
moment my heartfelt thanks go out to Sir Jose Cherian, my Physics teacher in high
school who, I would say, is the person behind my passion for physics. Not forgetting
my science teacher, Mrs. Gurmeet Kaur for teaching us in a loving way, all the
wonderful things about science, I will always be indebted to you, Ma’am. And many
thanks to Prof. Ajoy Ghatak for making learning quantum mechanics and ﬁber optics
such a wonderful experience during my M.Sc days. Prof. Voit, you as a teacher were

amazing too! It was an honour to learn radiation astrophysics from you.

I would also like to thank my colleagues, Eric Pellegrini, David Ventigmilia and
Young Sun Lee for introducing me to the tricks of the trade, and answering my
numerous questions related to IRAF, IDL and LAM. Thank you for your immense

help all along these years.

Thanks to all those persons whom I met as strangers but kept as lifelong friends,
including Shweta, Sonal, Sheenu, Trupti and Saurabh. Finally, I would like to thank
my family for having faith in me all along, and for showing immense patience while
waiting for me and bearing me all this time as I near the completion of my Ph.D.

Thanks to Christopher Waters for the IA’IEX class used to format this thesis.

I, hereby, express my gratitude towards the Department of Physics and Astronomy,

Michigan State University for providing me with this opportunity to do research in

vi

this wonderful subject.
Finally, as Carl Sagan says, “What else can the exploration of Universe be, other

than a journey in self-discovery!” Indeed it has been!

vii

PREFACE

Astrophysics, or the study of heavens is a very vast area of research. We want to
understand how the Universe behaves overall and what do its various constituents
tell us. With a subject as intriguing as astrophysics, where each subﬁeld is equally
engrossing, one wants to understand it all. However it is not quite possible to cover
very many topics in the few years of graduate research. Nevertheless, I pursued
two widely different topics of research for my dissertation. As a result, this thesis
consists of not one single complete work but is based on two different projects I have
worked on in the last few years of my initiation into research in Astrophysics, and
it represents my small effort towards understanding this amazing Universe via the
two different studies I undertook: one, to comprehend the overall dynamics of the
Universe as reﬂected by the lst project; and two, to understand the nature of one of

it most exotic beings as reﬂected by the 2nd project. These are as follows:

Project 1: Acceleration of the Universe and Modiﬁed Gravity: Covered in Chapters
1-5, this project aims to understand the reason behind the recent acceleration of the

Universe using the tools of Galaxy Cluster Cosmology.

Project 2: Chemical Evolution in Quasars: Covered in Chapters 6-10, this project

studies the metallicity in Quasars with strong Nitrogen lines and compares the ﬁnd-

ings from this study to the results of Chemical Evolution Models of Quasars.

viii

TABLE OF CONTENTS

ix

List of Tables ........................................................ xiii
List of Figures ....................................................... xiv
1 Cosmology: Understanding The Universe ......................... 1
1.1 The Accelerating Universe ..................... 1
1.1.1 Problem With The Standard Model Of The Universe . . . . 2
1.1.2 The Repulsive Gravity Term ................. 3
1.1.3 This Project .......................... 6
1.2 A Short History Of The Universe ................. 7
1.2.1 Expansion History Of The Universe ............. 7
1.2.2 Growth History Of The Universe And Structure Formation 9
1.3 Cluster Cosmology ......................... 13
1.3.1 Cluster Of Galaxies ...................... 13
1.3.2 Clusters As Cosmological Probes ............... 14
1.3.3 Problems With The Cluster Counting Method ........ 15
1.3.4 Cluster Surveys ........................ 15
1.4 Conclusion ............................. 19
The Basics ....................................................... 21
2.1 Growth Function Parameterisation ................ 21
2.2 Growth History From Galaxy Clusters .............. 22
2.2.1 Cluster Mass Function ..................... 23
2.3 Mass Of A Galaxy Cluster .................... 24
2.3.1 Deﬁning The Cluster Mass .................. 24
2.3.2 Observing The Cluster Mass: Mass-Observable Relations . . 24
2.3.3 Evolution Of The Mass-Observable Relation ......... 26
2.3.4 Scatter In Mass-Observable Relations ............ 26
2.4 Counting The Clusters: Redshift Evolution Of The Cluster Num-
ber Density ............................. 28
2.5 Cluster Power Spectrum ...................... 30
2.5.1 Cluster Bias ........................... 30
2.5.2 Measuring The Cluster Power Spectrum ........... 31
2.6 Fisher Matrix Technique Of Finding Constraints ........ 33
2.6.1 Fisher Information From Redshift Evolution Of Galaxy Clus-
ters ............................... 33
2.6.2 Fisher Information From Galaxy Cluster Power Spectrum 34
2.7 Problems And Their Possible Solutions ............. 34
2.7.1 Degeneracy Between Different Parameters .......... 35
2.7.2 Lack of Knowledge About The Mass-Observable Relations . 35

X

2.7.3 Handling The Uncertainty In M — L Relation: self-calibrate
vs. Only Cosmology ...................... 36
2.8 Being Realistic ........................... 36
The Survey Experiment .......................................... 38
3.1 Survey Deﬁnition: Galaxy Cluster Surveys Studied ....... 39
3.1.1 eROSITA ............................ 40
3.1.2 Wide Field X-Ray Telescope ................. 40
3.2 Modeling The Universe ...................... 41
3.2.1 The Cosmological Parameters ................. 41
3.2.2 Cluster Structure Parameters ................. 42
3.2.3 Parameters Studied In This Experiment ........... 43

3.3 Progression Of The Experiment: From Only Cosmology To Self-
Calibration ............................. 44
3.3.1 Only Cosmology: ........................ 44
3.3.2 Self-Calibration: ........................ 44
3.4 Information Gathering From Galaxy Cluster Surveys ...... 45
3.4.1 Information Source 1: Cluster Number Counts ....... 45
3.4.2 Information Source 2: Shape Of The Cluster Mass function 51
3.4.3 Information Source 3: Cluster Power spectrum ....... 52
3.5 Processing Information: Constructing Fisher Matrices ..... 55

3.5.1 Information From The Redshift-Only Evolution Of Cluster
Number Count ......................... 56
3.5.2 Adding The Cluster Mass Evolution To The Redshift Evolution 56
3.5.3 Cluster Power Spectrum Calculations ............. 57
3.5.4 Using Priors From Other Experiments ............ 57
Constraints From Cluster Cosmology ............................. 59
4.1 Information Processing: Constraining Parameters ........ 59

4.1.1 Constraints From Redshift- Only Evolution Of Cluster Num-
ber Counts ........................... 60

4.1.2 Constraints From Redshift And Mass Evolution Of Cluster
Number Counts ......................... 62
4.1.3 Constraints From Cluster Power Spectrum .......... 64
4.1.4 Improved Constraints By Combining Information Sources 64
4.1.5 Conclusion ........................... 65
4.2 The Gravitational Growth Index: How Well Is It Constrained? 67
4.2.1 Constraints On GR Growth .................. 67

4.3 Is It GR Or Is It Not GR? Will The Next Generation Surveys
Be Able To Tell? .......................... 69
4.3.1 eROSITA Performance ..................... 70
4.3.2 WFXT Does The Job! ..................... 73
5 Summary And Conclusions ....................................... 76

6 Introduction To Quasars .......................................... 78

6.1 Salient Features .......................... 79
6.2 The Quasar Spectrum ....................... 80
6.2.1 The Continuum ......................... 80
6.2.2 The Emission Lines ...................... 80
6.2.3 Line Formation Process .................... 81
6.2.4 Absorption Lines ........................ 82
6.2.5 Quasar Abundance Analysis Using Broad Emission Lines . . 82
6.3 The Elemental Abundances In Quasars ............. 84
6.3.1 Sites Of Chemical Enrichment In A Galaxy ......... 85
6.4 Quasar Abundances And The Evolution Of Galaxies ...... 85
6.4.1 Mergers Vs. In—Situ Star Formation ............. 86
6.4.2 What Does Quasar Metallicity Tell Us About Any Of This? 87
6.4.3 Previous Results And New Questions ............. 87
Sample Selection And Data Reduction ............................ 89
7.1 The Project ............................. 89
7.2 Sloan Digital Sky Survey ..................... 91
7.3 The SDSS Quasar Catalogue IV ................. 93
7.3.1 Selection Effects In SDSS Quasar Sample .......... 93
7.4 Sample Selection And Data Reduction .............. 94
7.4.1 Main Sample .......................... 94
7.4.2 Initial Data Reduction Steps ................. 94
7.4.3 Data Reduction II ....................... 95
7.4.4 Automated Measurements Of Intermediate Sample ..... 97
7.4.5 Final Sample With Measurable NIII] And NIV] Lines . . . . 97
7.5 Final Data Reduction ....................... 97
7.5.1 Fe Subtraction ......................... 97
7.5.2 Proﬁle Fitting And Flux Estimation ............. 98
7.6 Abundance Analysis ........................ 99
7.6.1 Line-Intensity Ratio Measurement .............. 99
7.6.2 From Line-Intensity Ratio To Metallicity ........... 99
7.7 Mass Measurements ........................ 100
The Results ...................................................... 101
8.1 Metallicity Of Quasars With Strong Nitrogen Lines ....... 101
8.1.1 Best Metallicity Estimate: Mean Vs. Maximum Likelihood . 101
8.1.2 Metallicity From Individual Line-Intensity Ratios ...... 102
8.1.3 Best Metallicity Estimate (Zbest) ............... 103
8.1.4 Distribution Of Other Physical Properties .......... 104
8.1.5 Relations Involving The Supermassive Black Hole Mass . . . 105

9 Discussion ........................................................ 108
9.1 Metallicity And The BELR LOC Model ............. 108
9.2 Chemical Evolution Models And Extreme Metal Rich Quasars . 109
10 Summary And Conclusions ....................................... 115

xi

Appendices

A Figures for the Quasar Project ........................................................ 1 18
B Tables for the Quasar Project .......................................................... 157
References ...................................................................................... l 93

xii

3.1

3.2

3.3

31
B2
B3

B4

B5

B6

B7

B8

LIST OF TABLES

Survey parameter values for various surveys to be undertaken by 612051 TA
and WFX T .................................

Model Parameter values used for the Survey Experiment. .........

Total number of galaxy clusters detected by different survey deﬁnitions of
eROSI TA and WFX T for the two gravity models. ...........

Fe strengths for the N—Loud Quasars. ....................
Template proﬁles used in deblending various emission lines .........
Emission line-flux strengths ..........................

Best measurements of line-intensity ratios alongwith their corresponding
minimum and maximum values. .....................

Metallicity Estimates from individual line-intensity ratios. ........

Best Metallicity Estimates for the N-Loud Quasar Sample and their cor-
responding error estimates .........................

Quantitative comparison of how well the metallicity from different line-
intensity ratios relates to mean metallicity Zmean. ..........

Statistics and Student “t” test results for AISMBH for the two Quasar
sample sets. ................................

xiii

40

43

45

158

160

166

172

180

188

190

191

LIST OF FIGURES

1.1 This ﬁgure shows the comparison of survey parameters, the effective flux-
limits and sky coverage for past, current and upcoming X—ray galaxy
clusters (taken from Murray et. al., 2010). ...............

2.1 Growth Function plotted as a function of z, for the GR gravity model
(dotted line ) and the DGP gravity model (dashed line ) ........

2.2 ( from Popesso et. al., 2005) This ﬁgure shows the presence of scatter in
M — L relation in galaxy clusters .....................

3.1 Redshift evolution of cluster number counts based on the GR gravity model,
for (a) the eROSI TA wide-ﬁeld (dot-dashed line), all-sky (dottal line)
and deep ( dotted line) surveys and for ( b ) the WFX T wide-ﬁeld survey
(dot-dashed), medium (dashed) and deep (dotted) ﬁeld surveys. For a
given survey DGP has more clusters at a given 2. Among the two sur-
veys, WFX T surveys detects more clusters at all redshifts and at higher
redshifts where none are detected by eROSITA surveys. 0f WFX T,
wide-ﬁeld survey detects most number of clusters in all whereas deep-
ﬁeld and medium surveys detect more clusters at higher 2 ’3 due to their
higher ﬂux-limits. .............................

3.2 (a) Distribution of cluster number counts per unit redshift, for the two
gravity models, GR (dotted lines) and DGP { dashed lines). The higher
curves are for the WFX T wide-ﬁeld survey and the lower curves are for
eROSI T A wide-ﬁeld survey. (b) Growth Function plotted as a function
of z, for the GR gravity model ( dotted line) and the DGP gravity model
( dashed line ) ...............................

3.3 The sensitivity of redshift distribution of cluster number counts for dif-
ferent cosmological parameters. The curves show the distribution of
cluster number counts for a 10% increase (dashed lines) or decrease
(dotted lines) in the parameter value. The solid curves are for the
ﬁducial value of the respective parameter .................

xiv

19

22

27

46

47

49

3.4

3.5

3.6

3.7

3.8

4.1

4.2

The sensitivity of redshift distribution of cluster number counts for differ-
ent cluster structure parameters. The curves show the distribution of
cluster number counts for a 10% increase (dashed lines) or decrease
(dotted lines) in the parameter value. The solid curves are for the
ﬁducial value of the respective parameter .................

(a) Cluster mass function evolution in mass (luminosity) for GR (dotted
lines) and DGP ( dashed lines) at diﬁ'erent 25’s. The highest to lowest
curves are from 2 ~ 0.0, 0.2, 0.5 and 1.0 respectively. The shape of
the mass function changes with 2, as well as for the different gravity
models ....................................

The sensitivity of the shape of the cluster mass function for cosmologi-
cal and cluster structure parameters. The curves show the change in
cluster mass function evolution for a 10% increase (dashed lines) or
decrease (dotted lines ) in the parameter value. The solid curves are for
the ﬁducial value of the respective parameter ...............

(a) Redshift averaged cluster power spectrum for WFX T wide-ﬁeld sur-
vey. ( b ) Fractional uncertainties op(k)/ch(k), in estimating the given
cluster power spectrum ...........................

The sensitivity of the cluster power spectrum to Qm and a. The curves show
the distribution of cluster number counts for a 10% increase ( dashed
lines) or decrease ( dotted lines) in the parameter value. The solid curve
is for the ﬁducial value of the respective parameter. The cluster power
spectrum is relatively insensitive to the rest of the cosmological and
cluster structure parameters .......................

Constraints on the Qm-og plane from eROSI TA Wide-ﬁeld Survey. The
ﬁgure shows a step-by-step degradation of constraints from CC (dash-
dot line) to SC I (short-dashed line) to SC I] ( dotted line ) and ﬁnally
to the full self-calibrate case, SC III (long-dashed line ) for redshift-only
evolution of cluster number counts when 7 is held constant (left-panel)
and when it is unfrozen (right-panel). ..................

This ﬁgure shows the relative comparison of how constraints on Qm-ag
plane degrade after making 7 a free parameter for the two cases of 0C
(inner set of ellipses) and SC III ( outer set of ellipses). The dotted
lines are when 7 is held constant and dashed lines are for when 7 is
unfrozen ...................................

XV

50

51

53

54

55

60

61

4.3

4.4

4.5

4.6

4.7

4.8

4.9

Comparing constraints that can be obtained from different surveys to be un-
dertaken by eROSI TA and WFX T for the full self-calibrate case when
7 is held constant. ( eROSI TA: All-sky survey - long-dashed line, Wide-
ﬁeld survey - short-dashed line; WFX T: Medium survey - dotted line,
Wide-ﬁeld survey - dot-dashed line. ...................

Constraints for the 0m — 08 plane using redshift and mass evolution of
cluster number counts when 7 is held constant (left panel) and when
it is unfrozen (right panel).This shows a step-by-step degradation of
constraints from CC (long-dashed line) to SC I {dotted line) to SC
II (short-dashed line) and ﬁnally to the full self-calibrate case, SC III
(dash-dotted line) ..............................

Comparing the constraints from redshift-only { outer ellipses) and redshift
and mass evolution {inner ellipses) of cluster number counts for CC
(dashed lines) and SC 111 cases (dotted lines) when 7 is constant (a),
and when it is freed (b). .........................

Constraints from the cluster power spectrum only, for 0G case when 7 is
constant ( dotted line) and when it is freed ( dashed line) .........

Improvement in constraints, for 0G (top—left), SC I (top-right), SC II
(bottom-left) and SC III (bottom-right) cases, when the information
from the redshift and mass evolution (dashed-lines) is combined with
that from the cluster power spectrum (dash-dotted lines), 7 is held con-
stant here ..................................

Constraints on 7 - 9m plane in the GR Model for cluster mass function
evolution (dotted lines) and cluster mass function evolution + cluster
power spectrum (dashed lines) as we go from CC (innermost ellipses)
to SC III ( outermost ellipses) .......................

Combined constraints from cluster mass function evolution and cluster
power spectrum on 7 — Om plane for the full SC case from different
surveys, WFX T: wide-ﬁeld (dash-dotted line) and medium survey (dot-
ted line); eROSITA: wide-ﬁeld (short-dashed line) and all-sky survey
(long-dashed line). ............................

4.10 Degradation in the ability to distinguish the two gravity models from the 0C

case (top-left) to the SC I (top-right) to the SC II (bottom-left) and to
the full self-calibrate case SC III (bottom-right) for eROSI TA wide-ﬁeld
survey. The contours shown are for redshift-only evolution ( solid lines),
redshift and mass evolution ( dotted lines) of cluster number counts and

62

63

64

65

66

68

69

for the combined constraints with cluster power spectrum ( dashed lines). 70

xvi

4.11 Indistinguishability of the growth models and the improvement in con-
straints on growth as a result of adding priors on 0, ~ 10% (top-right),
~ 5% (bottom-left) and ~ 3% (bottom-right). The top-left panel shows
no prior case. The 20 contours shown are for the combined constraints
from the cluster mass function with the cluster power spectrum for SC
III case. The survey deﬁnition used is that of eROSI TA Wide-ﬁeld
Survey. The dash-dotted lines show the improved constraints when pri-
ors are added. The stars show the location for the respective ﬁducial
models. As we see from ﬁgure, the two models are completely distin-
guishable on 20 level after adding strong priors on 5. ......... 72

4.12 Indistinguishability of the growth models and the improvement in con-
straints on growth as a result of adding strong (~ 3%) priors on 0
(right panel) The left panel shows no prior case. The contours shown
are for redshift and mass evolution ( dotted lines) of cluster number
counts, for the combined constraints from cluster mass function with
the cluster power spectrum for the SC III case. The survey deﬁnition
used is eROSI TA All-sky survey. The dash-dotted lines show the im-
proved constraints when priors are added. The stars show the location
for the respective ﬁducial models. As we see from ﬁgure, the two models
are not completely distinguishable on 20 level even after adding strong
priors on 0. ............................... 73

4.13 20 constraints on 7 — 52m plane for the two gravity models from cluster
mass function evolution (dotted lines) and the combined constraints
with cluster power spectrum (dashed line) when full self-calibration
is allowed. WFX T medium survey {left panel) and wide-ﬁeld survey
{right-panel) deﬁnitions are used. Both surveys are able to distinguish
between the two models on a 20 level. The stars show the location for
the respective ﬁducial models. ...................... 74

4.14 20 and 3a constraints on growth from the WFX T medium {left-panel) and
wide-ﬁeld survey (right-panel) for full self-calibrate case, from combined
information from cluster mass function evolution and cluster power

spectrum. WFX T wide-ﬁeld survey will be able to distinguish between
GR and DGP model with 99% conﬁdence. The stars show the location

for the respective ﬁducial models. .................... 74
A.1 Characteristic Quasar Spectrum. ...................... 119
A2 Quasar Spectrum: An Example ....................... 120
A3 Abundance Analysis Results .......................... 125

xvii

A.4 Comparison of Maximum Likelihood Metallicity (ZML) and Mean Metal-
licity (Zmean) ................................

A.5 Metallicity from individual line-intensity ratios as a function of mean
metallicity. ................................

A.6 Comparing Best Metallicity Estimate before (Zmean) and after (Zbest) re-

moving the two deviant line-intensity ratios (NI V// CI V and N V/ CI V).

A.7 Distribution of Best Metallicity Estimate (Zbest) in the N—Loud Quasar
sample ....................................

A.8 Redshift (2) Distribution of the Intermediate Quasar Sample (top) and in
the N-Loud Quasar Sample (bottom). ..................

A.9 Distribution of F WH M (CI V) in the Intermediate Quasar Sample (top)
and N-Loud Quasar Sample (bottom) ...................

A.10 Distribution of Continuum Luminosity in the Intermediate Quasar Sample
(top) and in the N-Loud Quasar Sample (bottom) ............

A.11 Distribution of the Equivalent Width (EW) of the CI V Emission Line in
the N-Loud Quasar Sample. .......................

A.12 Distribution of Supermassive Black Hole Mass (M SM BH) for the Inter-
mediate Quasar Sample (top) and N-Loud Quasar Sample (bottom). .

A.13 Supermassive Black Hole Mass (M 5 M B H) as a function of redshift. . . .
A.14 Box Plot for the comparison of the M SM B H for the two data sets. . . . .

A.15 Metallicity from individual line-intensity ratios as a function of Supermas-
sive Black Hole Mass (MSMBH)- ....................

A.16 Best Metallicity Estimate (Zbest) as a function of Supermassive Black Hole
Mass (MSMBH). .............................

A.17 Supermassive Black Hole Mass (M SM BH) as a function of Continuum
Luminosity (L ,\(1450A). .........................

136

139

140

142

143

144

145

146

147

148

149

151

152

A.18 Supermassive Black Hole Mass (MSMBH) as a function of FWHM(CIV).153

A.19 Supermassive Black Hole Mass (AI S M B H) as a function of CI V Equivalent
width. ...................................

A.20 Continuum Luminosity (L A(1450A) plotted as a function of CI V Equiva-
lent width ..................................

xviii

155

A.21 Models of Chemical Evolution in Quasars (HF 93) and the metallicity dis-
tribution in the N-Loud Quasar sample .................. 156

Images in this dissertation are presented in color.

 

xix

 

CHAPTER 1:
COSMOLOGY: UNDERSTANDING THE
UNIVERSE

 

Cosmology, the scientiﬁc study of origin and evolution of the Universe, has been
around since times immemorial. However the last 25 years have marked the start
of a new epoch in the history of this ancient science. During these years, cosmology
essentially got reinvented from a pure theory based discipline to a largely observational
and data driven science. With the bombardment in precision data taken from ground
and space based telescopes, and many large-scale surveys taking place now and coming
up in the near future, we are increasingly living in an era which offers the possibility

of testing the foundational theories of cosmology with unprecedented accuracy.

1.1 THE ACCELERATING UNIVERSE

About a decade ago when two research teams, High Z Supernovae [Reiss et. al., 1998]
and Supernovae Cosmology Project [Perlmutter et. al., 1999], published the analysis
of their observations and measurements of Type IA Supernovae, their result came as
a shock not only to these scientists but it resonated almost as a supernova explosion
with the entire scientiﬁc community. The data from these surveys provided strong
evidence that the Universe has recently entered a phase of accelerated expansion and
this has been conﬁrmed further by numerous supernovae (SNe) observations since

then. Of late, the Cosmic Microwave Background (CMB) observations have also

provided a strong support to this [Larson et. al., 2010], indirectly, by verifying the
ﬂatness of the Universe which'when combined with the measurements of the mean
matter density (Om) of the Universe, imply the existence of Dark Energy which is
theorised to result in the acceleration of the Universe. No doubt the accelerated
expansion of the Universe, as is indicated by numerous observations, has been among
the most important breakthoughs of the last century which has forced us to reanalyse

the way we think about the composition and dynamics of the Universe.

1.1.1 PROBLEM WITH THE STANDARD MODEL OF THE UNIVERSE

The standard cosmological model is based on Einstein’s General Relativity (GR) ap-
plied to an expanding Universe which is homogeneous and isotropic on large scales.
These two (Einstein’s GR and the assumption of homogeneity and isotropy) are the
foundational ideas of this widely accepted model of Nature. The standard cosmologi-
cal model very well explains much of the observed behaviour of the Universe and has
seen many successes, e.g., the Big Bang Nucleosynthesis.

The Einstein’s Field Equations (EFEs) are given as,
Gut! = 87TTIJI/ (1.1)

(in the units of c = 1) and where, (Gm, = RW — gWR/ 2), is deﬁned as the Einstein
Tensor.

Here, the expression on the left represents the curvature of spacetime as determined
by the metric and the one on the right represents the matter energy content of the
Universe.

It has gradually become clear in recent years that either one or both of these
foundational ideas of standard cosmological model, with ordinary particles, is not

suffcient to describe what we observe. For example, this model does not explain

the observed rotation curves of galaxies, as well as the recently discovered late time
cosmic acceleration. In order to explain these observations, it is necessary to assume
either a new gravitational dynamics or new components of the cosmic energy budget
or, perhaps, both. In the next few paragraphs we touch upon both these explanations

brieﬂy.

1.1.2 THE REPULSIVE GRAVITY TERM

Ever since Sir Isaac Newton was hit by an apple in the 16008 till the end of last
century, the deﬁning feature of Gravity has been its “attractive” nature. However,
when Einstein formulated GR he allowed for gravity to push as well as to pull, by
including a “repulsive” term proportional to the metric tensor, gW, in order to make

the Universe static, neither expanding nor contracting as was believed at that time,

GI“! = SILT)“; — ngA (1.2)

It does not matter where we put this additional term, either to the RHS (as above)

or LHS like the following,

However, the “static” Universe so formed was practically unstable and robbed the
EFEs of their “formal beauty”. More importantly, the observations of the expanding
Universe proved that the cosmological constant was not necessary. This led Einstein
to discard the “repulsive” part altogether and so did most scientists until the SNe Ia
results were published in the late 19908.

Today the EFES sans the cosmological constant term do not explain the accelerat-
ing expansion of the Universe, and an additional term is needed for the observations

and theory to match. The term featuring repulsive gravity or Einstein’s cosmological

constant A, when put back into the EFES, does explain the accelerated expansion

phenomenon. But what is the physical explanation of A?

EXPLANATION 1: A As DARK ENERGY

Gravity is still an attractive force for all the known forms of matter and energy. In
simplest terms, an additional term involving A on the RHS of EFES represents the
presence of hitherto undetected energy which will account for ~ 75% of the mass-
energy content of the Universe. This mysterious form of energy with strange proper-
ties that give rise to repulsive gravity has been broadly termed as “Dark Energy”.

It can be represented by writing the EFES as,

Gm, = 87m“, + surggrk (1.4)

where, now the EFES are modiﬁed by adding the second term on the RHS which

represents Dark Energy.

EXPLANATION 2: No MYSTERIOUS DARK ENERGY BUT GR NEEDS A “SPACE-

TIME” MODIFICATION ON LARGE SCALES

In a. sense, the argument presented above also represents a “modiﬁcation” of the EFES
wherein the “energy content” of the Universe is modiﬁed to make way for repulsive
dark energy. Instead modiﬁcation of the LHS side of EFES by adding an additional
term can also explain the accelerating Universe and this leads us to the broad topic of
“modiﬁed gravity” (MC). The motivation behind this approach is that the geometry
of the Universe has not yet been tested on cosmological scales even though it is known
to work to a high degree of accuracy on the solar system [Shapiro, 1964; Will, 2001]
and the stellar [Hulse and Taylor, 1975] scales in its present form. EFES with modiﬁed

gravity can, in general, be represented as,

Gm, + Gﬁﬁ’k = 87rTW (1.5)

where the modiﬁed part is represented by the second term on the LHS, lumping
together all kinds of modiﬁed gravity theories in this term.

There exist countless ﬂavours of MG. Examples of the MG theories include Braneworld
Gravity theories e.g., DGP theory [Dvali, Gabadadze and Porrati, 2000] which seek
the solution to cosmic acceleration by introducing extra space-time dimensions; and
Scalar-Tensor gravity theories [Caldwell and Linder, 2005] which introduce new scalar
degrees of freedom to induce acceleration.This new topic has seen some frenzied ac-
tivity in recent years however we will not delve into the details of these MG models
here, except for a very brief introduction of the DGP gravity model which will be

used for structure growth comparison with the GR model in later Chapters.

DGP Gravity Model

DGP gravity model [Dvali, Gabadadze and Porrati, 2000] is the modiﬁed version
of the GR gravity model with 5 dimensional (5D) Minkowski Space. The usual 4D
space-time, which we are used to, is embedded in these ﬁve dimensions. The 4D
Newtonian gravity emerges on a 3—brane in this 5D space-time model of the Universe.
The extra dimension is inﬁnite in size. As a result the Einstein-Hilbert action term in
this model has two parts: a 4D GR term and a 5D extra dimensional term. The usual
4D term is dominant at short distances whereas the 5D term becomes important as
we go to large scales of the order of current size of the Universe.

The main motivation behind introducing this model (and many such MG models)
was to explain the acceleration of the Universe without the need for dark energy.
The acceleration of the Universe implies weakening of gravity. Since the accelera-
tion has started only recently, it might imply that the gravity weakens only at large

scales in the Universe. According to the Gauss’ Law of Gravity, the force of gravity

for normal 3+1 D Universe 0: 1/r2. However as we increase the number of spatial
dimensions, each extra dimension would increase the exponent in Newton’s gravita-
tional law weakening the gravity. For a 4+1 D Universe, the force of gravity thus
becomes 0: 1/r3.

. In a Universe where DGP is the underlying gravity model, this alteration in the
gravitational force results in different (slower) growth rate of structure formation.
This alteration in the history of structure formation by virtue of its slower growth
rate as compared to GR gravity model can be tested by counting the galaxy clusters

as we will be see in later Chapters.

EXPLANATION 3: BACKREACTION

Yet another direction of work on this problem taken by some physicsts involves relax-
ing the second foundational idea of cosmology: the assumption of homogeneity and
isotropy of the Universe [e.g., Futamase, 1996; Brandenberger, 2002]. It is argued
that since homogeneity is an approximate assumption, a note must be taken of how
the inhomogeneities on smaller scales affect the evolution of the metric variables as
per Newton’s third law. This has been termed as gravitational backreaction of small
scale inhomogeneities, whereby gravitational waves propagating in background space-
time affects its dynamics and hence its evolution. We will not go any further into the

details of this approach for the purpose of this project.

1.1.3 THIS PROJECT

This ﬁrst part of the thesis is a study that attempts to see whether we can determine,
using galaxy cluster survey data, which of the two main competing theories (Dark
Energy or Modiﬁed Gravity) is responsible for the acceleration of the Universe. Our
tool of choice for this work would be the upcoming galaxy cluster surveys that will

search for galaxy clusters over more than 10% of the sky. If we are to detect the

difference between the two, it would provide us with a better understanding of how
the Universe works. The path appears rather simple but as we will see, many road-
blocks are encountered on the way, mainly because the astrophysics of clusters is not
sufficiently well known. Much of this thesis deals with how to take into account those
astrophysical caveats while on our journey to discover whether Nature still swears by
GR with missing “Dark Energy” or needs “space—time” modiﬁcation or whether the
picture will still be hazy a few years from now and new methods need to be devised
to solve this problem. Before proceeding further in this direction, let us step back

and recapitulate our knowledge of the building blocks of Modern Cosmology.

1.2 A SHORT HISTORY OF THE UNIVERSE

According to the most accepted hypothesis, the Universe began with “Big Bang”, a
violent explosion that occured about 15 billion years ago. Ever since it has been ex-
panding with its dynamics governed by its matter and energy contents. The Universe
consists of matter and radiation as its “known” building blocks. The standard cos-
mological model with its “known” constituents cannot explain all the mass needed to
explain observations of galaxy rotation curves. This matter which does not emit light
is yet to be detected directly and is aptly termed as “Dark Matter” and accounts for
~ 22% of the mass-energy budget under the new cosmological standard model [e.g.,
Ostriker and Steinhardt, 2003]. In addition, the rest and most of the energy balance

to explain acceleration of the Universe is lumped under “Dark Energy”.

1.2.1 EXPANSION HISTORY OF THE UNIVERSE

Prior to the 19208 it was generally believed that our Universe is static, centered on the
Milky Way galaxy. This view received a major Shakedown when systematic motions
of recession were measured for spiral nebulae and the fantasy of a static Universe

was ﬁnally toppled in 1929 when Edwin Hubble announced his velocity-distance law

7

[Hubble, 1929], also known as the Hubble ’3 Law (v = H0 * r), which tells us that
Universe is expanding with galaxies moving away from one another. EFES provide
the theoretical basis for describing the dynamics of the Universe. For a uniformly
expanding Universe, which is also homogeneous and isotropic, these reduce to the

Friedmann Equation:

 

a(t) 2 87rGe(t) k
(at) ”2“): 3.2 w (“5)

where, a(t) represents the energy density and It represents the curvature of the Uni-
verse. a(t) is the scale factor and is related to redshift by, a = (1 + z)—1

Rewriting the expansion in terms of separate energy densities,
H2(a) = H3[nma—3 + Ora—4 + aka—2 + GA] (1.7)

where 52’s are the different energy density components for the matter, radiation, cur-
vature and constant dark energy, respectively, in terms of the critical energy density
pm) = 3H8/87rG, which is the current energy density for a ﬂat Universe.

Once again, the Ftiedmann equation can be written as a sum of all the different

energy density components,

 

 

8rrG
H20) = —3— p.- (1.8)
i
Separating the matter density term from the sum we can write this as,
H2 a _ 1 daI
Hg) = Qma 3 + 2: 9,4 exp (3/ [1+ vii/(TH?) (1.9)
0 if a
or,
H2 a _ 6H2
11%):an 3+.H—g- (1.10)

where the set i’ does not include matter part and w(a) refers to the equation of
state of each component [Linder, 2005]. We can think of the 6 H 2 part of the equation
above as being either due to an energy density component or as a modiﬁcation of the
Friedmann equation and interpret it to be related to some “acceleration physics”

responsible for accelerated expansion of the Universe. If we deﬁne,

ldln6H2

The effective acceleration physics equation of state can then be written as,

_1dln[f2m(a)—1 — 1]
3 dlna

 

w(a) = (1.12)

where,

Irma) = Qma—3/(H(a)/H0)2 (1.13)

Different cosmological models can have the same expansion history if their Qm(a)
and w(a) are the same. Even high precision measurements of the expansion history
of the Universe are therefore not suﬂicient to distinguish the different physical origins
for the same expansion behaviour, and hence the true nature of the acceleration of

the Universe cannot be studied by expansion history alone.

1.2.2 GROWTH HISTORY OF THE UNIVERSE AND STRUCTURE

FORMATION

The Universe is homogeneous and isotropic only on scales larger than ~ 100 Mpc.
Any window below that size will reveal inhomogeneties that exist in the form of
galaxies and stars, planets, animals and so on. This structure we see in the form of

galaxies and clusters has resulted from initially tiny ﬂuctuations in the matter density,

which were present in the early Universe.

THE MATTER POWER SPECTRUM

At some early time in the history of the Universe, these ﬂuctuations in matter density
can be represented by an overdensity ﬁeld. The overdensity at any given location is

given by [e.g., Voit, 2005],

6(x) = W (1.14)

where p is the average matter density.

The Fourier components of the overdensity ﬁeld can be written as,

6k(k) = /6(x)eik$d3x (1.15)

For the isotropic case, the power spectrum of the matter density ﬁeld is deﬁned as,

PE) 2 (i5ki2l (1.16)

The power spectrum essentially describes the amount of ﬂuctuation power contained
in at different length scales, k‘1 and hence gives a complete statistical description of
the initial ﬂuctuations from which the later structures emerged.

A related and equally important concept is the “variance in mass”. Variance in

mass within identical volume elements corresponding to the length scale k‘1 is given

by,

6M(r) _
M ‘

 

/ Mistral;~ — r])d3x (1.17)

where, W(r) is a Spherical window function which goes to zero outside comoving

radius r and whose integral over all space is unity. The variance in mass on this scale

10

is then given by,

2_ 6M2 _ 1 ,23

where, Wk is the Fourier transform of W(r).

An important cosmological parameter in the Cold Dark Matter models of structure
formation is the mass variance at the length scale of 8h-1 Mpc, also known as 08-
Observations suggest that the variance in mass is of the order unity at that length
scale, (SM/M ~ 1. This has been the motivation for expressing the normalisation of
power spectrum in terms of U8-

1

2 _ __ 2 3
08 _ (2703 /P(k)|Wk| d k (1.19)

where Wk is the Fourier transform of W(r) with r is the comoving radius having a

value of 8h‘1 Mpc.

GROWTH OF INITIAL FLUCTUATIONS

As the Universe expands, gravity acts, and as a result overdense regions become
more overdense and underdense regions become more underdense. After a certain
limit when the amplitude of a perturbation becomes non-linear, it will separate from
the Universe and collapse to form separate structures like the galaxies and galaxy
clusters we see in the Universe today.

The growth of perturbations with time in the linear theory is given by,

5m + 235m = 4rerm(a)5m (1.20)

The second term in the above equation features the Hubble expansion and acts as
a frictional term. The term on right hand side features gravity and acts as a forced

driving term. The perturbations grow as long as the gravitationally driven force term

11

is greater than damping introduced by Hubble expansion, and matter dominates.

IMPORTANCE OF GROWTH HISTORY

It can be seen from the above equation that, in GR the gravitational constant G is
a constant of nature and therefore the growth history of the Universe is completely
determined by the expansion history, a / a. Any discrepancy between the growth
observed and growth predicted by the observed expansion history will be able to test

the theoretical framework and reveal the possible modiﬁcations needed.

GROWTH FUNCTION

The function used to describe the growth of linear perturbations is called the growth
function, D(a). For a simple case of a density ﬂuctuation in the form of a uniform
density sphere which is slightly denser than its surroundings, its growth function can

be approximated by,

D(a) ~ —p ~ 1 * -.— (1.21)

where, the growth function D(a) is normalised at present times, D(l) = 1. The
rate of growth of ﬂuctuations is scale independent, meaning all ﬂuctuations grow at
the same rate. In the general case with dark energy, the growth function cannot
be solved analytically and at best can be approximated for different epochs in the
evolution of the Universe. Several different and useful approximate expressions exist
for the growth function. For a Universe with negligible radiation density, Wang and

Steinhardt (1998) derive a useful approximation,

a

D(a) ~ a * exp (falﬂ — [Qm(z)]aw)d—a) (1.22)

with aw deﬁned such that,

12

 

a = [an(zllaw (1'23)

where, Qm(z) is the matter density at z in terms of critical density [)ch = 3Hg/87TG.

This will be revisited in the next Chapter where we will see how the growth history
of the Universe can be described by one single parameter.

In order to differentiate between various gravity theories and to understand the
physical mechanism behind the dynamics of the Universe, it is essential to measure the
growth of structure as well. In GR the growth history of the Universe is completely
determined by its expansion history. Therefore, comparing the expansion history and
growth history would be an ideal test of the underlying physics. Any discrepancy

between the two would point towards modiﬁcations of GR on cosmological scales.

1.3 CLUSTER COSMOLOGY

1.3.1 CLUSTER OF GALAXIES

Galaxies are gregarious in nature, mostly. They are preferentially found in associa-
tions, either in groups, which generally have about 3 50 galaxies or in still larger ag-
glomerations called the galaxy clusters. A cluster of galaxies typically has anywhere
from ~ 50 galaxies (a poor cluster) to some thousands of galaxies (a rich cluster)
within a space of about 6h’1Mpc across. Clusters are the largest and most massive
gravitationally-bound objects in the Universe as of now. They are semi-independent,
self-gravitating units that have detached from the Hubble Expansion recently.

The mass of a typical galaxy cluster is ~ 1014 — 1015h-1MQ, (h E H(z)/H0)
The Mass-to—Light ratio of clusters reveals that most of the cluster’s mass emits
no light and exists as “Dark Matter”. Much of the “normal” mass in a cluster
exists in the form of hot gas (~ 107 — 108K). Some of this gas accumulated over

the ages when mass was unlocked from stars in galaxies and then probably was

13

pushed outside of a galaxy’s potential well by catastrophic events triggered by violent
mechanisms such as SNe explosions and mergers of galaxies. Most of the intracluster
gas never collected into stars and now occupies most of the cluster’s volume. The gas
loses energy through thermal bremsstrahlung and its characteristic X—ray spectrum is
usually used to determine the cluster mass. The spectrum of a cluster is used to ﬁnd
its temperature. Assuming that the galaxy cluster is in hydrostatic equilibrium, and
approximating the cluster to be a singular isothermal sphere, the gas temperature

then can be related to its mass through a simple equation,

kBT = (8.2 keV) (J—fﬂ (ma) >2/3 (1.24)

 

101511—1MQ H0
The third term in above equation shows that the M — T (or any mass-observable)
relation evolves with time. Departures from the hydrostatic equilibrium assumption
are usually not large. However, for any cosmological study, adequate care must be

taken to account for the dispersion that exists in any such relation.

1.3.2 CLUSTERS As COSMOLOGICAL PROBES

Clusters are the largest collapsed structures in the Universe. They are also huge and
luminous which makes them very detectable even from very large distances. Hence
they are excellent candidates for studying the structure growth over cosmological
scales and times. The number density of clusters in a comoving volume element traces
the large—scale structure growth. The large scale structure growth is exponentially
sensitive to cosmological parameters like 08 and a statistical analysis of this growth in
the form of cluster counting can put powerful constraints on the underlying cosmology
governing the Universe, including the forces responsible for its newfound acceleration.
A study of the evolution of cluster number counts over a redshift interval can therefore

provide powerful constraints on cosmological parameters.

14

1.3.3 PROBLEMS WITH THE CLUSTER COUNTING METHOD

A galaxy cluster survey with a large yield and having a well understood cluster
redshift distribution is an invaluable probe of cosmology. However, unbiased and
precise constraints require an understanding of the nature of cluster mass-observable
relations.

The only astrophysical parameter on which cluster number density depends is its
mass. Cluster mass is not a directly observable quantity and we need to infer it from
some directly observable quantity such as its temperature or luminosity. However
mass-observable scaling relations are not very well established mainly because the
astrophysics of clusters is not well known. As a result there exists considerable scatter
in such relations.

Evolution of these mass-observables in redshift domain as well as in mass domain
and the scatter present therein is another problematic aspect of cluster scaling re-
lations that is not well known. These uncertainties not only lead to degradation of
constraints but can also lead to biased and possibly faulty estimation of cosmological
parameters, and for our case it might just masquerade as a possible wrong signal
for a different gravity theory which will make this whole exercise of growth function
detection pointless if enough care is not taken into consideration. These topics are

further explored in Chapter 2.

1.3.4 CLUSTER SURVEYS

Many galaxy cluster surveys, ongoing and in the past, have progressively improved
our knowledge of the dynamics of the Universe. Coupled with new advances in tele-
scope technology as well as improved theoretical understanding derived from advances
in other areas of research like the CMB; precision cosmology using large scale clus-
ter surveys is giving us exciting new results. Some of the surveys completed or in

operation now are as follows:

15

SLOAN DIGITAL SKY SURVEY (SDSS)

The SDSS is the biggest sky survey to date and is described in detail in Chapter 7
later on when we talk about the second project that forms Part B of this thesis. SDSS,
however, it is not exclusively a galaxy cluster survey in a strict sense. Nevertheless,
the cluster data from SDSS have been used to put some very interesting constraints

on various cosmological parameters like 08 [Rozo et. al., 2009].

RED SEQUENCE CLUSTER SURVEY (RCS)

The RCS Survey was designed exclusively to identify a large sample of galaxy clusters
over a wide range of redshifts. Two optical telescopes, The Canada-France-Hawaii
3.6 m for the northern hemisphere and Cerro—Tololo Inter-American Observatory 4 m
telescope for the southern hemisphere were used for this survey, with a sky coverage
of 90 degz. The study resulted in improved constraints on cosmological parameters

including 0m and 08 [Gladders et. al., 2009].

MASSIVE CLUSTER SURVEY (MACS)

MACS was derived from the ROSAT (Rontgensatellit) All-sky survey done using the
German X—Ray Satellite Telescope, which ended its mission in the late 19908.

Together with other X—ray Surveys like the Bright Cluster Survey (BCS) and RE-
FLEX (the ROSAT-ESO ﬂux-limited X—ray sample), the data from MACS has been
used to obtain statistically signiﬁcant constraints on the cosmological parameters
[e.g., Mantz et. al., 2008].

Grand as they may be, the present galaxy cluster surveys however have not been
able to reach the point of precision where they are capable of distinguishing between
the Dark Energy and Modiﬁed Gravity models of acceleration of the Universe, among
other unanswered questions of cosmology. In the coming decade, ever bigger and

better galaxy cluster surveys will see the light of day. These surveys will arm us with

16

even more statistical power with catalogues containing tens to hundreds of thousands
of galaxy clusters based on various selection criteria having a quality and quantity

unmatched before. Let’s now take a look at some of the upcoming surveys:

SOUTH POLE TELESCOPE SURVEY (SPT)

The ﬁrst of the large cluster surveys using the Sunyaev—Zeldovich (S-Z) effect [Sun-
yaev and Zeldovich, 1970], SPT is presently conducting a survey over 4000 deg2 of
southern Sky using a 10 metre diameter telescope based in AntarcticaThe S—Z effect
is the Compton up—scattering of CMB photons by gravitationally bound hot gas in
clusters and this creates a local distortion in the CMB blackbody spectrum. The
SPT is expected to yield many thousands of clusters out to high z. One of the main
attractions of an S-Z based detection is that it is essentially redshift independent and
hence a survey like SPT can detect clusters out to very high redshifts as opposed to

optical or X-ray surveys which are limited in this area [Staniszewski et. al., 2009].

PLANCK

ESO’S PLANCK is a major space based mission which has been mapping the whole
sky bit by bit for the past one year, looking for CMB anisotropies, with unprecedented
sensitivity (AT/ T N 2 :1: 10—6) and angular resolution better than 10 arcmin. As a
side job, it will also yield a catalogue of hundreds of thousands of S—Z detected galaxy
clusters [Tauber, 2004].

LARGE SYNOPTIC SURVEY TELESCOPE (LSST)

This is the biggest optical ground based wide-ﬁeld survey coming up in the next
decade. It will use a 8.4 m telescope to scan 20,000 deg2 of the southern sky with

each patch of sky repeatedly scanned 1000 times in a Span of 10 years [u’wu"133t'°"9].

17

 

DARK ENERGY SURVEY

Dark Energy Survey (DES)[www'darkenergysum’ey'm'gl is a deep optical-near infrared
survey which aims to map a 5000 deg2 patch of the southern sky with a 500 Mega
Pixels CCD Camera mounted on a 4-metre telescope. It will make extensive observa-
tions in in g, r, i, 2 bands within a redshift up to, 2 ~ 1.3. They will detect clusters

and supernovae as well as make measurements of weak lensing.

EROSITA

Extended ROentgen Survey with an Imaging Telescopic Array or eROSITA is a
German X-Ray instrument that will ﬂy on board the Russian satellite Spectrum—
X-Gamma, which is scheduled to be launched from Baikonur in 2012 [ref., eROSITA
Mission Document, 2005]. eROSITA is expected to perform an All-sky survey as well
as a wide ﬁeld survey of nearly half the sky in the medium X—ray range up to 10 keV
with an unprecedented spectral and angular resolution. One of the main motivations
behind the design of this instrument is to unravel the nature of the force responsi-
ble for the acceleration of the Universe. It is expected to detect around a hundred

thousand galaxy clusters within its ﬂux-limit of ~ 1.0 * 10‘l5 ergs/sec.

WIDE-FIELD X-RAY TELESCOPE SURVEY

Wide-Field X—ray Telescope (WFXT) is a proposed NASA mission which will be
performing three extragalactic sky surveys in the soft X-ray band (0.4 keV - 6 keV)
with a sky coverage of 20,000 degz. With a sensitivity and angular resolution far

0—14erg/s/cm2, it intends

better than achieved ever before and a ﬂux—limit, f3; 2 3 =1: 1
to generate a dataset of Z 500, 000 galaxy clusters up to a 2 ~ 2.
The comparison of survey parameters for some of the past, ongoing and the next

generation X—Ray galaxy cluster surveys is Shown in Figure 1.1 [Murray et. al., 2010].

18

 

 

I I I IIIII] I TIIITTII I I IIIIIII I ITIIIII' I I IIIIII' I I

.1
an
.1
.1

III

10-11

(”) = angular resolution

10'”2 in Half-Energy Width

 

l lllllIII I [III

     
 
 

l 1 111m]

10"“

l I turn]

 

10-15

A ~v.1- A‘-

O
J.
(II
I IIIIIIII l Ilnﬂ'l'l I Tmtﬂl l Illnﬂl I In":

 

Flux limit [0.5-2.0 kev] erg em'2 3“

to" 10° 10’ 102 10‘ 10‘ 105
Area (degz)
Figure 1.1 This ﬁgure shows the comparison of survey parameters, the effective flux-

limits and sky coverage for past, current and upcoming X-ray galaxy clusters (taken
from Murray et. al., 2010).

1.4 CONCLUSION

From this Chapter, we learned that:

The Universe is expanding and this expansion is accelerating. In order to explain
this acceleration, The Stande Model of the Universe needs a Dark Energy compo-
nent or GR needs a modiﬁcation on large scales. We intend to see which of these
theories is correct. The expansion history of the Universe is not suﬂicient to distin-
guish between them since both of these can result in the same expansion, thereby
resulting in no conclusion. Therefore it is important to study growth history of the

structure formation in the Universe as competing gravity theories will result in dif-

19

 

ferent growth history.

In this project we plan to study the growth history using the galaxy clusters, using
the statistical power of upcoming surveys. However the inherent problems in this
method exists due to the insufﬁcient knowledge of the implications of astrophysical
processes going on in galaxy clusters. Taking into account the uncertainty due to this,
our goal in this project is to see if the next generation surveys will be able to rule
out one or the other of these theories while trying to ascertain the nature of cosmic

acceleration.

20

 

 

CHAPTER 2:
THE BASICS

 

In order to inch towards an understanding of the underlying cause of acceleration of
the Universe, one needs to know whether GR is valid on large scales or not. One way
to test GR on large scales is to study the growth history of density perturbations
in the Universe independently of the expansion history, since GR makes very speciﬁc

predictions about how perturbation growth is linked to expansion history.

2.1 GROWTH FUNCTION PARAMETERISATION

Growth of linear density ﬂuctuations in the Universe over a period of time is charac-
terised by the Growth function D(a), the slope of which determines the growth rate
of structure. One such model independent parameterisation of the growth function
is given by the following equation [Peebles, 1980; Wang and Steinhardt, 1998; Linder
2005; Linder and Cahn, 2007],

D(a) = a >1: g(a) = a >1: exp (foammm)? —1]%) (2.1)

where, g(a) gives the growth rate at a given time. Here a single parameter 7 (the
gravitational growth index) can signal a deviation of the growth function from the
predictions of GR. Figure 2.1 shows the difference between the growth functions of
GR gravity model and DGP gravity model. The difference between the two models

increases at higher z’s.

21

 

 

 

 

 

Figure 2.1 Growth Function plotted as a function of z, for the GR gravity model
(dotted line) and the DGP gravity model (dashed line).

Another advantage of such parameterisation is that for the GR directed growth,
7 is conﬁned to a narrow range of values near 0.55, independent of the nature of
the dark energy models, so we can focus on the one question we are interested in
answering for the purpose of this thesis: How well 7 can be constrained by a large

galaxy cluster survey to measure the growth function, D(a)?

2.2 GROWTH HISTORY FROM GALAXY CLUSTERS

Observing the evolution of galaxy clusters over a period of time can give us powerful
insights about the growth history of the Universe and can therefore reveal the nature
of the dynamical forces governing the Universe on cosmological scales. Because of this
tremendous cosmological implication, counting of galaxy clusters at different redshifts
in a given comoving volume of space has become a very important area of research

in cosmology.

22

 

2.2.1 CLUSTER MASS FUNCTION

The most important physical property of a galaxy cluster for cosmological purposes
is its mass. The Cluster Mass Function is deﬁned as the number density of clusters
greater than mass M at a redshift z in a comoving mass element. The following is a

good approximation of the cluster mass function [Voit, 2005],

_ QmPcrO 5c
””1011, Z) —— Terfc (m) (2.2)

Here, (Sc represents the critical threshold density contrast 6, with a value of 1.686
above which a density perturbation collapses and virializes. The differential mass

function on mass scale M and redshift z is then given by,

 

dn M 2 Qmpcro dc 5C2
= _ __ __ 2.
dln 0‘1 7r M exp 202(M, z) ( 3)
where,
0(M, z) E D(z) >1: 0(M) (2.4)

where, a(M) is given by Eqn. (1.18) and is normalised to 08- And, D(z) is a strong
function of 9m and 7 as seen in Eqn. (2.1).

We see from Eqn. (2.2) above that the number density has an exponential de-
pendence on various cosmological parameters via a(M, z). The large-scale structure
growth is therefore exponentially sensitive to these cosmological parameters and a
statistical analysis of this growth in the form of cluster counting can put powerful
constraints on the underlying cosmology governing the Universe, including the forces
responsible for its newfound acceleration.

The growth rate of galaxy clusters can be assessed by measuring the cluster mass
function, meaning that we need to weigh the clusters in a survey. Now, since a

cluster “mass” cannot be “observed”, we need a h Sical ro ertv of clusters which
P y P P .

23

 

can be directly observed, a mass-observable, and a well calibrated relation linking the

observable property to cluster mass. But ﬁrst of all how is a cluster’s mass deﬁned?

2.3 MASS OF A GALAXY CLUSTER

2.3.1 DEFINING THE CLUSTER MASS

Observational studies have indicated that the velocity dispersion of galaxies in a
cluster remains relatively constant, which implies that the underlying matter density
in the cluster diverges with its radius, p M(r) ~ r‘2. A consistent deﬁnition of cluster
mass is, therefore, needed in order to measure the cluster mass function because a
cluster’s mass and all the relations linking that mass to its observable quantities
depend on how one deﬁnes the outer boundary of a galaxy cluster.

Mass of a galaxy cluster is deﬁned as M A which is the amount of matter contained
in a spherical region of radius r A with a mean density of ~ A =1: pcr- While observing
clusters, the factor A is usually taken to be 200 or 500. It has been shown that using
A taken to be 200 leads to a mass-velocity dispersion relation which is independent
of cosmology [Evrard, 2004] and is the preferred deﬁnition in cluster simulations as
well. We will use this deﬁnition of a cluster’s mass, M200, the mass contained within

a radius r200, for the purpose of this work.

2.3.2 OBSERVING THE CLUSTER MASS: MASS-OBSERVABLE RE-

LATIONS

Of the many observables of galaxy clusters used as proxy for mass, gas temperature

and X-ray luminosity have been the most popular choices.

24

 

MASS-TEMPERATURE RELATION

The deep potential wells of galaxy clusters compress the intergalactic baryonic gas and
heat it to X-ray emitting temperatures. This gas temperature, therefore, reveals the
depth of a cluster’s potential well and is inferred from the cluster’s X-ray spectrum.
In most clusters, the intergalactic gas seems to be close to hydrostatic equilibrium.

Using this assumption a relation between gas temperature and the cluster’s mass can

be derived.

M GMT

where T0, M0 and a MT are the normalisation and exponent parameters, respectively,
which deﬁne the Mass-Temperature relation. However, the relation is only an approx-
imate one because several systematic as well as astrophysical processes going on in

clusters affect the ideal behaviour outlined above.

MASS-LUMINOSITY RELATION

A galaxy cluster’s mass can also be inferred from the correlation between mass and

its X-ray luminosity and is of the general form,

M )a’” (2.6)

“HOG;

which is deﬁned by the normalisation parameters, L0 and M0 and the exponent of the
relation, a M L- This correlation is not as tight as that between mass and temperature.
However, one advantage of using luminosity as a mass tracer is that it is easier to

measure than the gas temperature.

25

 

2.3.3 EVOLUTION OF THE MASS-OBSERVABLE RELATION

All mass-observable relations evolve with redshift. One of the reasons is that the
deﬁnition of mass used in these relations is linked to the critical density of the Uni-
verse pcr (the energy density required for ﬂat Universe), M A(z) ~ A at p0,.(z). Since
the Universe is expanding, for a given mass M, clusters would be hotter earlier in
time than now because the density was greater. This leads to an inclusion of 2 de-
pendent term in the mass-observable relations. In addition to the evolution of the
mass-observable relation due to the expansion of the Universe, the physics of galaxy
formation and evolution may also result in additional evolution of these relations. In

light of the above discussion, we rewrite the M - L relation as,

(=L—a"<i:>>’

The parameter ,0 is an index giving the strength of this evolution. For the self—

 

similar models where the expansion of the Universe is the only source of evolution of

the M - L relation, this parameter takes a value of 7/ 3.

2.3.4 SCATTER IN MASS-OBSERVABLE RELATIONS

The mass-observable relations described above are not exact and there exists consid-
erable scatter in such relations as has been shown by various observational studies of
clusters [Pratt et. al., 2009]. Figure 2.2 Shows the amount of scatter present in the
M - L relation from one such study, [POpesso et. al., 2005].

The presence of scatter in such relations is a large source of uncertainty in studies
involving estimation of cluster mass using a mass-observable. For the cosmological
studies, it is very important to take this into account due to the exponential depen-

dence of cluster mass function on cluster mass.

26

 

 

 

 

 

 

 

 

 

100 . I I I I I III] I r *1 I I III I I I I I—IIIr I 'I
E / A
// , ’ i
A F I S
V! I.
\ .
Ho 10 r a 2"; ; [fr-H '5
'- ec’ _ - a
Q) -' 7. " "f" I
i 13 .. .—: ‘. '...' + ‘
ﬁ—G— . .I
::., (v; 1.. J
H li-‘I' s,o
\>< 1 r _.,‘.:‘: I 11
_' ..
v .....
B ’ 3’: .
e- t—F ,
8 0.1 :- ’. .:’ .5
E FF .1. 3
E —e—— ,7 .
E .x' <
3 b ‘
_ 0.01 g ,
0 I :
t; :
2 ,
U
x : -- i
2 [V'
8 . .
0.m1 A A J J ALLL I l L A I 1111 L L L L LLJLI L L 1 L1 1 ll
0.01 0.1 1 10 100

Galaxy Cluster Mass (Msoo/1014Mol

Figure 2.2 (from Popesso et. al., 2005) This ﬁgure shows the presence of scatter in
M - L relation in galaxy clusters.

EVOLUTION IN SCATTER

It is also possible that the scatter present will be different at different 2. This evolution
in the presence of scatter in the mass-observable relations can be due to many factors.
One reason could be that at earlier times when the clusters were in the primitive stage
of formation, the proportion of relaxed clusters might be smaller than at late times
[e.g., Pratt et. al., 2009], resulting in higher amount of scatter. This evolution in
scatter also needs to be taken into account for a complete study in addition to the

scatter itself. The scatter in the M —L relation is parameterised by following equation,

Ural = Uml0(1 + 2)" (28)

where, 00 gives the scatter present in the M-L relation currently and its evolution

in time is given by the term (1 + z)", with n as the index describing the evolution

27

strength of scatter in 2. In addition to its evolution with z, scatter may also depend

on mass M, leading to a mass dependent term in its deﬁnition,

am, = 00(1 + z)" * M‘f’ (2.9)

with w giving the strength of evolution of scatter with M.

2.4 COUNTING THE CLUSTERS: REDSHIFT EVOLUTION

OF THE CLUSTER NUMBER DENSITY

The evolution of cluster number counts in redshift Space is a powerful function of the
underlying cosmology and therefore can give tight constraints on various cosmological
parameters. Since we can only observe some mass-proxy, we are actually observing
the redshift evolution of that observable.

For a cluster sample in a given survey, we can ﬁnd the number of clusters dN
within a given solid angle d!) in a redshift bin dz, lying between [2, z + dz], that fall
into the range [X , X + dX] of the mass-observable X, deﬁned by relation X (M, 2:).

The redshift evolution of the cluster mass function is then given by [Voit, 2005],

We.

d3N _ an ( )
(1de Z

m(X(M,Z),Z) -- dX (X(A/11Z)1Z) *

 

(2.10)

where, dn M / dM is the mass function evolution factor and szco / (1de is the comov-
ing volume element. How accurately we can tell about the background cosmology is
heavily dependent on how well we understand mass-observable relation as well as its

evolution with the redshift. The cluster number count at a given 2 is then given by,

(UV _ dV an
dz _ dz(z) [M dM(M,z)dM (2.11)

where, the ﬁrst term gives the volume of the region in the redshift interval dz at z,

28

and the second term gives the number density of clusters of all masses that are there.
This is what we would see ideally if we had a perfect telescope with no ﬂux-limit
and could scan the full sky. In the real world that does not happen and therefore in
addition to the usual cosmological parameters, galaxy cluster detection is sensitive to
the survey parameters such as the ﬂux-limit and solid angle coverage. At far away
distances low luminosity clusters will not be seen if the ﬂux-limit of a survey is high.
This ﬂux-limit is implemented by having a selection function, f (M, 2), for the survey

to describe the cluster number counts.

d__nM
21—3szng )/MdM ——(,)M 2 (M, z)dM (2.12)

Instead of mass we observe luminosity thus what we measure is,

d_N _ dV [Lmax an

dz — dz-(z) dL (l,z)f(L,z)dL (2.13)

Lmin
Also because of the fact that M — L relation is not perfect and there exits considerable
scatter in this relation, the above expression for cluster number count gets modiﬁed

as,

Lmax
= d—V(z)/Lm nd/M “”1” P (LIM) (M ,z)deL (2.14)
dz Md

where, P(L|M) is the probability density for a cluster of mass M to have a luminosity
L. For our luminosity range we use Lmin = 1040 erg S_1 and Lmax = 1047 erg S—l.
All the clusters lie roughly in this luminosity range. However the ﬂux-limit of the
survey generally imposes a more stringent constraint on Lmz-n which goes on increasing

as we go higher in 2, since L is a function of z. The minimum observable luminosity

at a given 2 is given by,

me<z> = f. * die) = f. * (re) * (1+ z»2 (2.15)

29

 

where, d) is the luminosity distance, r is the coordinate distance to redshift z and fx
is the ﬂux-limit of the survey.

In addition to 7., their redshift evolution, the cluster number counts also evolve
with mass. The cluster number density at a given 2 is a strong function of mass, as

can be seen from Eqn. (2.2).

2.5 CLUSTER POWER SPECTRUM

2.5. 1 CLUSTER BIAS

Observations have long shown that galaxy clusters Show a Spatial bias towards other
clusters, that is, they tend to cluster with one another [Bahcall and Soneira, 1983;
Bahcall et. al., 2003]. The ﬂuctuation in the number density of galaxy clusters
on large scales is much more pronounced than ﬂuctuations of the underlying matter
density. This is quantitatively characterised by a bias parameter b(M), which gives the
ratio of the ﬂuctuation in the number density of clusters of mass M to the perturbation

amplitude of the matter density.

— = b M >1: — 2-16
NM ( ) pm ( )

The bias parameter is taken to be independent of the length scale as long as that

length scale is large compared to that of a galaxy cluster. An analytic expression for

b(M) is given by [Sheth and Tormen, 1999; Mo and White, 1996]

 

a63/o2—1+ 2p

b(M,Z) = 1+ 6c 6c(1+ (063/02)p

(2.17)

with, a = 0.75, p = 0.3.

30

 

 

 

2.5.2 MEASURING THE CLUSTER POWER SPECTRUM

The power spectrum of the Spatial distribution of galaxy clusters is given by,

P6106, Z) = beff * P(k, Z) (2.18)

where, beff is the cluster mass function averaged linear cluster bias b(M, z) and is

given by [Majumdar and Mohr, 2004],

b _ fdM(dn/dM)b(M,z)
eff ’ fdM(dn/dM

 

(2.19)

For the primordial power spectrum of density perturbations, P(k) ~ knp, the matter

power spectrum at later stages of Universe is given by,

P09, 2) = 132(2) * r2(k) a: W (2.20)

The symbol [9 refers to the comoving modes with wave number (1 + z)k in physical
space corresponding to the comoving length scale k—l. The parameter 71,, is the
spectral index of the primordial density perturbations.

The Transfer Function, T (k) is a function which encapsulates in it the overall effect
of the modiﬁcation of the primordial power by different scale-imprinting processes
like the effects of pressure, and dissipation of density perturbations due to streaming
particles, except for those involving mode growth in the non-linear regime. T ( It) gives
the ratio of the late—time amplitude of a density perturbation mode to its initial value

[Peacock, 1998],

T(k) E —'——— (2.21)

the normalisation redshift 2 here, is taken to be arbitrary, so long as it refers to

a time before any scale of interest has entered the horizon and riﬂe) reﬂects the

31

 

original power spectrum imprinted by inﬂation or some other process. Several ﬁtting
forms exist for the matter transfer function [e.g., Bardeen et. al., 1986; Peacock and
Dobbs, 1994]. A well known ﬁtting form for the matter transfer function for cold
dark matter (CDM) cosmologies that account for all baryon effects in the large—scale
structure regime is given by Eisenstein and Hu (1999).

The average cluster power spectrum over a wide comoving space between Zmin and

2mm. is then given by [Majumdar and Mohr 2004],

_ ~12:in dz(dV/dz)n2(z)ch(k, z)
[361(k) = fzm‘: dz(dV/dz)n2(z)

zmz

 

(2.22)

Since the integration is weighted over comoving number density of clusters, the Pd
depends not only on cosmology, but also on the speciﬁc survey used for counting
the clusters since their detection as well as their redshift dependence depends on the
survey deﬁnition used.

The uncertainty in measuring the cluster power spectrum iS given by, opk, ([Feld-

man et. al., 2004; Tegmark, 1997]),

2 _ 4n2Pc2,(k)

O'Pd — W (2.23)

where Veff is the eﬂective volume utilized for measuring the power at mode It and is

deﬁned as [Tegmark, 1997],

_ 71(7) 90:) 2
V8ff(k)=/]:1+ﬁ(r)f3(k):] d3r (2.24)

 

Here, r'i(r) gives the expected number density of galaxy clusters in the given survey at
2. Only those regions where the cosmic signal [361(k) is greater than the Poisson shot
noise 1/r’1(r), will be contributing towards the effective volume, with little contribution

from the other regions.

32

2.6 FISHER MATRIX TECHNIQUE OF FINDING CON-

STRAINTS

After we get the information in different forms from different aspects of cluster detec-
tion, we need to process that information quantitatively as well as qualitatively. One
widely used method of forecasting survey constraints is by using the Fisher formalism
to form a Fisher Information Matrix and extract quantitative information from it.
The Fisher Information Matrix translates errors on observed variables measured in a
given survey into constraints on parameters of interest in the underlying model. It
is an elegant way of doing propagation of errors in the case of multiple correlated
measurements and observations based on some underlying multiple parameter model.

The Fisher Information of a likelihood function L(0) is a measure of the amount
of information a data set m carries about a parameter 0. If we have a cosmological
model which is fully speciﬁed by such a set of parameters 01-, the Fisher Information
Matrix is then deﬁned formally as the expectation value of the derivatives of the log

of the likelihood with respect to the parameters,

_ 62lnL

where, L is the likelihood function of the given model.

2.6.1 FISHER INFORMATION FROM REDSHIFT EVOLUTION OF GALAXY
CLUSTERS

The redshift evolution from cluster survey is constructed by binning the cluster num-

ber counts in redshift. The likelihood function for an observable will be then pro-

portional to dN / dz. The Fisher Matrix for the redshift evolution of cluster number

counts is then constructed as [Holder et. al., 2001],

33

F3 _2 armoryn 1

23 — "—06, Te, 7v; (2.26)

where, the matrix is summed over n redshift bins over the survey detection range

2min to zmax. Nn is the cluster number counts in a given bin n.

2.6.2 FISHER INFORMATION FROM GALAXY CLUSTER POWER SPEC-
TRUM
The sensitivity of the redshift-weighted cluster power spectrum BC) to different param-

eters is studied using the Fisher Information Matrix which is constructed as follows

[Majumdar and Mohr, 2004],

 

6P (119)513 (k) Akm
P _ Cl cl
Fa - 2’" a9,- 09, 02% (2'27)

where, we sum over n bins in k—space between kmz-n and kmax.

0pc, is the variance in calculation of F6109), and is given by Eqn. (2.19).

2.7 PROBLEMS AND THEIR POSSIBLE SOLUTIONS

After collecting the information in form of cluster number counts and cluster power
spectrum, we construct the respective Fisher Matrices to constrain different parame-
ters of interest as described above. This, however, does not promise to be a straight-
forward formalism in getting tight constraints on various parameters. Several prob-
lems are encountered when the method described above is implemented both because
of the nature of cosmological model as well as the non-direct detection of a galaxy

cluster’s mass.

34

2.7.1 DEGENERACY BETWEEN DIFFERENT PARAMETERS

There exist complex correlations not only between different cosmological parameters
but also between mass-observable scaling relations, which end up making the con-
straints on those parameters highly degenerate. For example, any straightforward
method of measuring the cluster mass function at a particular 2 renders the param—
eters Qm and 08 degenerate.

In order to break the degeneracy which exists between various parameters we have
to bring in more information from cluster surveys. As an example, the degeneracy
that exists between 9m and 08 can be broken by adding information about the simple
redshift evolution of cluster number counts and the shape of the cluster mass function.
This is done by binning the cluster number counts not only in redshift space but also
in mass Space. Additional information that can be used to break degeneracies is in the
cluster power spectrum. These independent pieces of information can be combined

by adding up the Fisher Matrices corresponding to the each type of data.

2.7.2 LACK OF KNOWLEDGE ABOUT THE MASS-OBSERVABLE RE-

LATIONS

Apart from having a strong theoretical understanding of the cluster mass function,
its evolution and the selection function of the cluster survey, the most important
issue concerning the cluster surveys is having a knowledge of correct cluster mass-
observables or the cluster scaling relations. Uncertainties in cluster scaling relations
and their evolution lead to degradation of constraints and can also lead to biased and
possibly faulty estimation of cosmological parameters, and for our case it might just
masquerade as a possible wrong signal for the growth function which will make these
attempts to measure the growth function” detection pointless if enough care is not

taken into consideration.

35

2.7.3 HANDLING THE UNCERTAINTY IN M — L RELATION: SELF-

CALIBRATE VS. ONLY COSMOLOGY

While modelling a survey design to estimate cosmological parameters, if the cluster
scaling parameters are kept ﬁxed, it means we are assuming perfect knowledge of
cluster structure. This is the case of Only Cosmology, which however can lead to
overly optimistic constraints on cosmological parameters and may well result in biased
estimation of these parameters as well. One way to avoid having to assume perfect
knowledge of cluster structure and mass-observable scaling relations is to solve for
both cosmology and the cluster scaling parameters so that the survey itself Self-
Calibrates the mass-observable scaling relations without us having to impose certain
ﬁxed values for them.

However, adding these additional free parameters will weaken our constraints on
cosmological parameters which however can be improved by combining different pieces

of information from a galaxy cluster survey as also mentioned in Section (2.7. 1) above.

2.8 BEING REALISTIC

The various problems and caveats in ﬁnding constraints using the Fisher formalism as
mentioned above have to be properly taken into account to get realistic estimation of
various parameters and particularly the growth function index 7. The next Chapter
explains how we achieved this, using the following step-by-step method.

1. Model of the Universe: We pick a ﬁducial model to describe the “real” Universe
having cosmological parameters’ values from the best known results in literature.

2. Model of the Cluster Structure: For the cluster structure parameters, we use the
results from the most recent results from observational studies. We also introduce the
realistic estimates for parameters for the evolution of the mass-observable relations

and the parameters for scatter and its evolution with z, from recent observational

36

studies.

3. Redshift Evolution of the Cluster Number Counts: We then ﬁnd the redshift
distribution of cluster number counts in our model Universe based on a given survey
deﬁnition by binning the survey in redshift space.

4. Information from the Shape of the Cluster Mass Function: In addition to ﬁnding
evolution of cluster number counts in redshift space, we also bin in mass-observable
(luminosity) space to see how the cluster mass function evolves with redshift and
mass.

5. Information from the Cluster Power Spectrum: We estimate the cluster power
spectrum and its variance over a wide redshift range to process information from it.

6. Varying the Model Parameters: We then vary the model parameters of our
ﬁducial Universe and see how each parameter affects the above three sources of in-
formation.

7. Finding Constraints: The constraints on various parameters are then found from
the Fisher Information Matrix method, from a given information source, and for the
various cases: from assuming perfect knowledge of galaxy cluster scaling relation,
(Only Cosmology) to admitting the lack of this knowledge (Self-Calibration). -

8. Improving Constraints: Finally we combine the different sources of information

and see how the constraints are improved at each step.

37

 

CHAPTER 3:
THE SURVEY EXPERIMENT

 

We conduct a theoretical experiment to access the statistical power of the next gen-
eration galaxy cluster surveys in ﬁnding constraints on various cosmological as well
as cluster structure parameters. A better understanding of these parameters and how
they govern the structure and evolution of the Universe is needed in order to under-
stand the underlying cosmological framework. A perfect knowledge of galaxy cluster
structure gives tight constraints even for the current survey deﬁnitions [Levine et.
al., 2002]. This, however, is an overly Optimistic assumption due to our incomplete
understanding of galaxy cluster formation and evolution.

Lack of cluster structure knowledge, its evolution with time and the scatter present
in the cluster structure scaling relations as well as its evolution will degrade our
knowledge of underlying cosmology when we admit our insuﬂicient knowledge of clus-
ter structure parameters and let the analysis of a given survey solve, or self-calibrate,
for these parameters itself. We are interested in understanding how this degradation
happens, and given the huge power of the upcoming surveys, whether we will be able
to better our understanding of both, the cosmological as well as cluster structure
parameters.

Since cosmic acceleration is a major mystery of the present times, and one inter-
esting explanation is the nature of underlying gravitational framework [Linder and
Cahn, 2007], the focus of this study will be on constraining the gravitational growth

index parameter 7, which is a parameter describing such a framework. For this study,

38

 

our ﬁducial model will be the GR model with a Dark Energy component, correspond-
ing to 7 ~ 0.55. For the comparative study we will use the DGP Braneworld Gravity
model [Dvali, Gabadadze and Porrati, 2000], with 7 ~ 0.68, and see if the two models
can be distinguished in this experiment.

In this project we intend to determine whether the upcoming galaxy cluster sur-
veys will be able to provide strong enough constraints on 7 to make this distinction.
Constraints degrade when the survey must be self-calibrated, however we can model
the inclusion of additional information by adding priors, which could come from in-
dependent studies such as weak lensing studies of galaxy clusters. In particular, we
intend to see how the interplay between degradation of constraints from insufficient
knowledge of cluster structure parameters, and improvement of constraints from clus—
ter mass function and cluster bias measurements affects our ability to distinguish GR
from non-GR (e.g. DGP) after the evolution of cluster scaling relations, the scat-
ter present in such relations and its evolution have been taken into account. If the
two models cannot be distinguished, we would like to know what priors from other

independent studies will be needed to make a clear distinction for a given survey.

3.1 SURVEY DEFINITION: GALAXY CLUSTER SURVEYS

STUDIED

The force responsible for the acceleration of the Universe affects both the abundance
and the spatial distribution of galaxy clusters. The number of clusters detected is a
strong function of the type of survey deﬁnition used which in turn depends on the
technological parameters of the instrument detecting clusters as well as the detection
technique (e.g. S-Z Detection, X—ray, Weak Lensing, etc.). For X—ray detection of
galaxy clusters, the survey deﬁnition is mainly determined by the ﬂux-limit of the

X-ray survey and the sky area to be covered by it.

39

Various sky surveys are in the process of implementation and / or design and were in-
troduced in Chapter 1. Of these we study the statistical power of the surveys designed
for eROSITA[www.mpe.mpg.de/heg/www/Projects/EROSITA/main.html] and WFXT[wfxt.pha.jhu.edu]
[Murray et. al., 2010]. We build up mock cluster survey catalogue based on survey

parameters characteristic of the surveys to be undertaken by these instruments.

3.1.1 EROSITA

eROSI TA (extended ROentgen Survey with an Imaging Telescope Array) will be
the primary instrument on—board the Russian satellite “Spectrum-Roentgen-Gamma”
(SRG), which will be launched from Baikonur in 2012 and placed in an L2 orbit [ref.:
eROSITA Mission Document].

Based on the ACDM cosmological model, eROSITA will discover about 50, 000 —
100, 000 clusters. The three surveys designed for this mission are the All-Sky Survey,
the Wide-Field Survey and the Deep-Field Survey. The parameters for these surveys
envisaged for galaxy cluster detection by eROSITA are summarised in Table 3.1.

 

 

 

Instrument Survey Deﬁnition ﬂux-limit (erg s—lcm—z) Solid Angle (degz)
eROSITA A11 Sky Survey 16*10-13 42,000
Wide-ﬁeld Survey 3.3’i10-l4 20,000
Deep Survey 8"‘10‘15 200
WFXT Wide-ﬁeld Survey 5"‘10‘15 20,000
Medium Survey 1*10-15 3000
Deep Survey 1*10—l6 100

 

 

 

 

 

 

Table 3.1 Survey parameter values for various surveys to be undertaken by eROSI TA
and WFX T.

3.1.2 WIDE FIELD X-RAY TELESCOPE

The Wide—Field X—ray Telescope WFX T is a proposed NASA mission dedicated to
performing surveys of the sky in the soft X—ray band (0.4-6 keV). Based on the
ACDM cosmological model, the WFXT will discover about 500,000 clusters. The

40

three surveys planned for this mission are the Medium Survey, the Wide—Field Survey
and the Deep-Field Survey. The survey parameters for WFXT are also summarised
in Table 3.1.

We wish to see which survey and which instrument would be most effective in

constraining the parameters studied.

3.2 MODELING THE UNIVERSE

3.2.1 THE COSMOLOGICAL PARAMETERS

The large-scale structure as well as the expansion history of the Universe is essentially
contained in a few cosmological parameters which are given below. For our most
probable model, we use the values of these parameters from the latest WMAP7 results
[Larson et. al., 2010] which gives the most conﬁdent results to date. The values for
the same are given in Table 3.2.

1) Density Parameters give the density of an energy component at present times
in terms of critical density parameter pc.

(a) 52m, This gives the total matter density in the Universe at present and is given
by, Kim = CC + 9b + (In, where QC, (2), and (In are the cold dark matter, baryon and
neutrino density parameters respectively.

(b) (Zr, gives the radiation density at present times.

(c) {2 A is a term to account for the acceleration of the Universe. Based on the latest
WMAP7 results we take our model Universe to be ﬂat. Therefore, (2 A = 1— Sim -— (2,».

2) w is the equation of state for the Dark Energy.

3) 08, gives the root-mean-square ﬂuctuations of overdensity within spheres of
8h-1Mpc radius and is given by Eqn. (1.19). It is used in the normalisation of the
matter power spectrum P(k).

5) Hubble Constant H0, gives the current rate of expansion of the Universe.

41

 

 

6) np, is the index of the primordial power spectrum.

7) Gravitational growth index parameter 7: This parameter has a value of 0.55 for
the GR model and 0.68 for the DGP model.

Models with same expansion history will have the same values for above-mentioned
parameters. We will therefore use the same values of these parameters for the two
models since our main aim is to study the growth history of the Universe, rather than

the xpansion history.

3.2.2 CLUSTER STRUCTURE PARAMETERS

The cluster structure parameters describe the model used to extract mass from some
other observable property of a galaxy cluster. Since we use X—ray luminosity as the
mass-observable in this study, we parameterise the Mass-Luminosity (M - L) relation

as Eqn. (2.7) (see below),

L = Lil-1%.)" (iii-f
The values used for M — L scaling parameters, L0 and a are those given by Reiprich
and Bohringer (2002). For the M - L evolution parameter ,0, we use the value
predicted by the self-Similar models as has been found by recent observational studies
[Pratt et. al., 2009].

The presence of scatter in M — L relation and its evolution is also modelled in our

ﬁducial cluster structure using Eqn. (2.8) (see below),
aml = aml0(1 + z)"

where, the value used for 00 is taken from Pratt et. a1. (2009). We parameterise
the evolution in scatter by parameter 17, as shown above, however for our ﬁducial

model we take it to be zero, meaning that in our model Universe the scatter in M - L

42

 

relation does not evolve with 2. Table 3.2 also describes the values used for these

parameters for building up our experiment.

 

 

 

Model Parameter ﬁducial value
Cosmology w -1
71,, 0.963
0m 0.2660
08 0.801
Ob 0.045
9,, 0.00
9,. 0.00
It A 1 — Sim
H0 71 km s 1 Mpc 1
7 0.55 (GR), 0.68 (DGP)
Cluster Structure (1 1.81
0 0.233
00 0.38
77 0.00
L0(1045erg 8’1) 1.0
M00015 M9) 1.0

 

 

 

 

 

Table 3.2 Model Parameter values used for the Survey Experiment.

3.2.3 PARAMETERS STUDIED IN THIS EXPERIMENT

For the purpose of this experiment, we assume a perfect knowledge of the expansion of
the Universe as well as the primordial power spectrum index np. Also the Universe is
assumed to be ﬂat with Q A value determined entirely by Om value. Hence in the whole
study we keep H0 and 71,, ﬁxed at their WMAP7 values and let (I A to be determined
by the Sim value, since Q,» has a value of zero according to the WMAP7 results.
The parameters studied are 9m, w, 08 and 7. The cluster structure parameters are

unfrozen successively at each step to study how they degrade the constraints.

43

 

3.3 PROGRESSION OF THE EXPERIMENT: FROM ONLY

COSMOLOGY TO SELF-CALIBRATION

When solving the Only Cosmology case for a particular survey, the mass-observable
parameters for a galaxy cluster are given ﬁxed values thereby assuming a perfect
knowledge of cluster structure. This is, however, an overly optimistic assumption and
may well result in a biased estimation of cosmological parameters. One way to avoid
this is to let the survey solve for both cosmology and the cluster parameters or Self-
Calibrate which is more realistic, however, it weakens the constraints progressively as

more and more parameters are allowed to be free.

3.3. 1 ONLY COSMOLOGY:

Only Cosmology: In the case of Only Cosmology (OC), all the cluster structure
parameters are held constant. As a result this case gives very tight constraints on
cosmological parameters. Although highly irrelevant, we study this case for reference

purposes.

3.3.2 SELF-CALIBRATION:

Constraints degrade at each step of unfreezing of the cluster structure parameters.
The different cases under this category are as follows.

(a) Self- Calibration I: When we allow only the normalisation (L0) and the exponent
(or) of the M — L relation to be unknown, we call it the minimal Self-Calibration case,
or SC I.

(b) Self-Calibration II: Admitting total lack of knowledge about the evolution of
the M — L relation and letting the evolution parameter 0 to be free in addition to
L0 and or makes case of self-calibrate II, or SC II

(0) Self- Calibration III: Allowing the scatter present in the M — L relation and its

44

evolution with redshift to be unknown, in addition to the rest of the cluster structure
parameters, forms our full self-calibration case, or SC III, in which all the parameters
used to model mass-observable relation, L0, 0, B, 00 and 77, are unfrozen for the
purpose of ﬁnding constraints on various cosmological as well as cluster structure

parameters.

3.4 INFORMATION GATHERING FROM GALAXY CLUS-

TER SURVEYS

Various bits and pieces of information are needed to prepare for the analysis of the
ﬁnal experiment of obtaining and understanding constraints on different parameters.

These and their implications are described below.

3.4.1 INFORMATION SOURCE 1: CLUSTER NUMBER COUNTS

Distribution of cluster number counts at different z’s is an important source of infor-
mation about the growth history of the Universe because it is sensitive to the growth
of density ﬂuctuations. This redshift distribution of cluster number counts is found
for different surveys. Table 3.3 gives the total number of clusters detected using the
GR Model and the DGP Model for each of the surveys that were mentioned in Section
3.2.

 

 

 

 

 

 

 

Instrument Survey Deﬁnition Cluster Number Counts Cluster Number Counts
GR Model DGP Model

eROSITA All Sky Survey 72,000 78,860
Wide-ﬁeld Survey 1,72,902 1,91,406

Deep Survey 6316 7,039
WFXT Wide-Field Survey 9,48,113 10,58,658
Medium Survey 4,92,728 5,54,342

Deep Survey 61,918 71,931

 

Table 3.3 Total number of galaxy clusters detected by diﬁerent survey deﬁnitions of
eROSI TA and WFX T for the two gravity models.

45

 

The evolution of cluster number count with redshift from the different surveys
is shown and compared in Figure 3.1. The two survey parameters on which the
cluster number count and its evolution depend are its ﬂux-limit fx, and its solid

angle coverage fl.

 

 

 

 

 

 

107 I I I r WI I I I I IIIIIIIII l I I I I I I I I I = = IIIIIIIII l IIIIIIIII I IIIIIIIII ‘
>- 4 P 1
6 ./ -'\.
IO 7 3 F I ‘~\_ '5
: . :,' r " ~ 4 ‘. :
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\ \. :4 E, '\ \ g
l \ \~ 4 J ............. ‘\ \
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U .'..\ I\ q r .l. \~ \..\.‘
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: -. ' -' ‘ \
3 . \., \ . .
10 E x \ 1 E ‘ \ “i
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t " \ ‘ ’\ \ ‘
s \ .\ E ‘ \:
i \ -\ l .- ‘-\ E
\ I .
102 r . ‘ 1 -. ‘ 1
E \ \. E \. a
i , \ : \.:
- . '\ L \4
\ .~‘ ' ]_ <
1 \ .. \‘
1O 111111111 I L I l I 4 I I 1'11; 4 L1 4L I4 I L l l 44 i J L L4 1 1 l 111111111
Z Z
(a) (bl

Figure 3.1 Redshift evolution of cluster number counts based on the GR gravity model,
for (a) the eROSI TA wide-ﬁeld (dot-dashed line), all-sky (dotted line) and deep (dotted
line) surveys and for (b) the WFX T wide-ﬁeld survey (dot-dashed), medium (dashed)
and deep (dotted) ﬁeld surveys. For a given survey DGP has more clusters at a given
2. Among the two surveys, WFX T surveys detects more clusters at all redshifts and at
higher redshifts where none are detected by eROSI TA surveys. Of WFX T, wide-ﬁeld
survey detects most number of clusters in all whereas deep-ﬁeld and medium surveys
detect more clusters at higher .2 ’3 due to their higher flux-limits.

As can be seen from Figure 3.1, the surveys with high ﬂux-limits are considerably
more efficient in detecting not only clusters at all redshifts but they also detect clusters
at highest redshift where low fa; surveys are not able to detect anything. A survey
with lower f; and higher (I is, therefore, most effective for the purpose of counting

the clusters.

46

COMPARING GR AND DGP IN CLUSTER NUMBER COUNT EVOLUTION

Figure 3.2(a) shows the distribution of clusters per unit redshift interval from the
two gravity models, and for two different surveys. For a given survey deﬁnition, the
DGP model contains more clusters at any 2, than the GR model. Also, the relative

proportion between the two increases with z.

 

 

 

 

 

 

 

 

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1O IIIIIIIII I 111111111 I Al-1\1\ L x r A A l LLLLLLLLL I AAAAAAAAA I AAAAAAAAA
O 1 2 3 O l 2 3
Z Z
(a) (b)

Figure 3.2 (a) Distribution of cluster number counts per unit redshift, for the two
gravity models, GR (dotted lines) and DGP (dashed lines). The higher curves are for
the WFX T wide-ﬁeld survey and the lower curves are for eROSI TA wide-ﬁeld survey.
(b) Growth Function plotted as a function of z, for the GR gravity model (dotted line)
and the DGP gravity model (dashed line).

This is an implication of lower growth rate in the DGP model compared to GR
model at a given 2. Figure 2.1 (reproduced here as Figure 3.2(b)) shows growth
function behaviour for the two cosmologies. At a given 2, the growth rate is given
by the slope of the growth function D(z). Since the function is normalised to 1 at
z = 0, lower growth rate results in more clusters at a given 2. The effect is more
pronounced at higher z’s, thereby mapping the similar effect in proportionately more
cluster number counts at high 2. This, therefore, shows a clear distinction in the

growth history resulting from the two models.

47

 

 

PARAMETER SENSITIVITY OF CLUSTER NUMBER COUNT REDSHIFT EVOLUTION

The redshift evolution of cluster number counts is sensitive to various cosmological as
well as cluster structure parameters. We studied how the change in these parameters
gets reﬂected in the redshift cluster number count evolution. This sensitivity is shown
graphically in Figure 3.3, for various parameters for the WFXT wide-field survey
deﬁnition. It shows how the cluster number count per unit redshift varies when we

change a given parameter by 10%.

SENSITIVITY TO THE COSMOLOGICAL PARAMETERS

(a) w: Varying w has a relatively small effect on cluster number counts at low 2 which,
however, increases as we go to higher z’s (See Figure 3.3). The effect is inverse.
Increasing w decreases N (z), which means, as we go to higher z’s proportionately
more clusters form if we have a lower w. A change 6w ~ 10% produces only a small
change 6N(z) ~ —4.5% in total cluster number count. The dependence of cluster
number counts at a given z comes via the redshift at which the dominance of Qm
ends and Dark Energy starts dominating. For lower (more negative) values of w,
the domination era of Dark Energy starts later. This will result in more evolution
of clusters at low z. The redshift distribution of cluster number counts provides
additional information via the expansion history. The cluster number counts in a
given interval reveal the comoving volume component associated with a given interval
dz, which is dependent on w.

(b) 52m: A change 69m ~ 10% produces a signiﬁcant change (from 15% at low z
to 96% at highest z) in cluster number counts and the percent change increases as we
go back in time. The effect is directly proportional. Increasing Qm increases N (z).
Redshift distribution of the cluster number counts is highly sensitive to the matter
density because of the exponential dependence of the cluster mass function on o( M)

and D(z). The dependence of D(z) on 9m was seen in Eqn. (2.1) and the dependence

48

 

 

dN/dz

 

 

dN/dz

 

 

 

 

 

 

Figure 3.3 The sensitivity of redshift distribution of cluster number counts for different
cosmological parameters. The curves show the distribution of cluster number counts
for a 10% increase (dashed lines) or decrease (dotted lines) in the parameter value.
The solid curves are for the ﬁducial value of the respective parameter.

of a(M) on {2m (Eqn. 1.18) comes via dependence of P(k) on the Tfansfer function
T(k).

(c) 083 Change in 08 results in an even more pronounced change, with percent
change in N (z) going from 5% to 614% from lowest to highest 2. Increasing 08
produces more clusters at all redshifts. This is a result of the exponential dependence
of 08 on the cluster mass function.

((1) 7: This has a relatively low effect on change in cluster number counts as
compared to Om and 08. The percent change in cluster number count increases with

z and reaches a high value of 50% at highest z. The dependence of N (z) on 7 comes
via D(z).

49

SENSITIVITY TO THE CLUSTER STRUCTURE PARAMETERS

Of the various cluster structure parameters, the cluster number count evolution with
redshift is most sensitive to a, the index of cluster structure scaling relation, followed
by B, the cluster structure evolution parameter, and to a lesser extent on L0, the

normalisation of the cluster structure scaling relation.

 

 

 

 

 

 

 

 

 

 

 

.
l. 4
101 I mmm A A A I I l ........ l A mmmu mm A

Figure 3.4 The sensitivity of redshift distribution of cluster number counts for diﬁerent
cluster structure parameters. The curves show the distribution of cluster number
counts for a 10% increase (dashed lines) or decrease (dotted lines) in the parameter
value. The solid curves are for the ﬁducial value of the respective parameter.

50

 

The scatter parameters 00 and n have only a marginal effect on the evolution

behaviour of cluster number counts.

3.4.2 INFORMATION SOURCE 2: SHAPE OF THE CLUSTER MASS

FUNCTION

The cluster number density at a given z is a function of mass also as seen in Eqn.
2.2. The cluster number counts are, therefore, different in different mass bins at a
given z, and this behaviour carries information that can be used in addition to their
evolution with redshift to a get better understanding of how the Universe works. The
variation of number density with mass comes in form of the shape of the function
which evolves with 2. In Figure 3.5 we plot the cluster mass function as a function

of luminosity for three different redshifts: 2 ~ 0.0, 0.2, 0.5 and 1.0.

 

 

 

 

-4
10 '
10‘5— -
1O_6 E'\_ d
5.2-:‘\
--.‘._\ ;"*-->."3';3:\
1% 10‘7 7 “ix ;‘>;‘ ix, -
_ \ ‘-.\ '-\.,‘-\
'0 \ \ -.‘.,\ "aux.
\ \ ”-T \“'\~.: \
C 10-8 _ \ \ \ \'_\.\\\ _.
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.\ \ .\\ .\..-\.‘.\\
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IO '- l".\\ ll'.\ _,
\ '. \
.. \ '2‘
-11 \
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44 45 46
10 l O l O

L09 (L)
Figure 3.5 (a) Cluster mass function evolution in mass (luminosity) for GR (dotted
lines) and DGP ( dashed lines) at different 2 ’s. The highest to lowest curves are from

z ~ 0.0, 0.2, 0.5 and 1.0 respectively. The shape of the mass function changes with
2, as well as for the diﬂerent gravity models.

We see that the shape of the mass function changes with z. The Shape also varies

51

 

for the two gravity models, for a given 2, as seen from the same ﬁgure. The difference
between the two models becomes more prominent at higher 2. When cluster number
counts are binned in luminosity space also (which is used as our mass-proxy), the
shape Of the mass function and the way it changes with 2 provides more information
in addition to the redshift evolution of the cluster mass function.

The Cluster Mass Function is a very strong function of mass M of a galaxy clus-
ter. When the information from the shape of the mass function is added to the
information from redshift evolution of cluster number counts, it improves constraints
on cosmological parameters. Information from the evolution of cluster number counts
with mass is therefore very essential in constraining the mass-observable relation and
its evolution which is a key factor in obtaining tight constraints from the redshift

evolution of cluster number counts.

PARAMETER SENSITIVITY OF SHAPE OF CLUSTER MASS FUNCTION

A change in parameter values, thereby, results in the change of the shape of the
cluster mass function. Figure 3.6 shows this change in the shape of the mass function
when a given parameter is varied by 10%. Of the various parameters, 03, 52m, 0 and
L0 are most sensitive to this variation in the decreasing order of variation strength.
The M — L evolution and scatter parameters are relatively less sensitive. Increased
sensitivity of the cluster mass function to the cluster structure parameters results in
better constraints when the cluster parameters a and L0 are allowed to be free in an

experiment.

3.4.3 INFORMATION SOURCE 3: CLUSTER POWER SPECTRUM

Clusters tend to show a spatial bias towards other clusters and this peculiarity can be
exploited to get more information from the cluster survey data. The Cluster Power

Spectrum essentially encodes in it this biasing information and forms a vital ingredient

52

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

_l
C
'0
\
C
'O
: i V
._l
c E
'0 l I
\
C
'0
A : ~ ‘ ‘ s ‘ ‘ a :
E E” \ ‘ N x m. ~. "‘5‘
C .
'O =- ‘ 3
E \ x 1
10'8': "~- E
; " . E : 3
. 4
10'9‘ l l *\x I m l . \
1043 1044 1045 10461043 1044 1045 1046

Log(L) Log(L)

Figure 3.6 The sensitivity of the shape of the cluster mass function for cosmological
and cluster structure parameters. The curves show the change in cluster mass function
evolution for a 10% increase ( dashed lines) or decrease ( dotted lines) in the parameter
value. The solid curves are for the ﬁducial value of the respective parameter.

in our experiment on constraining the growth history Of the Universe. The amplitude
and the shape Of the cluster power spectrum depends on the underlying matter power
spectrum and the bias of galaxy clusters. Figure 3.7 shows the cluster power spectrum
for the WFXT wide-ﬁeld survey and the variance in its calculation. The ﬁrst source

of information from the cluster power spectrum comes from its shape which is deﬁned

by shape Of the underlying matter power spectrum. The Shape reﬂects the Transfer

53

 

 

 

Op(k)/Pc|(kl

   

 

 

 

 

 

 

Axnxl A L A AAAAAI 4 . . 0.001 n.4.1 . 4 A . .I..l
0.01 0.10 0.01 0.10
k (M961) k (MPC'1)
(a) (b)

Figure 3.7 (a) Redshift averaged cluster power spectrum for WFX T wide-ﬁeld sur-
vey. (b) Fractional uncertainties op(k)/Pd(k), in estimating the given cluster power
spectrum.

Function behaviour which is a very strong function of 9m because of its sensitivity
to the redshift of the epoch of matter-radiation equality.

The second source of information is the spatial bias of clusters which is strongly
dependent on the mass of a galaxy cluster. The cluster power spectrum from different
surveys is essentially similar in shape as well as amplitude. However, for a given
survey the power spectrum increases in amplitude as we go from low 2 to high 2,
which is opposite to the behaviour of the underlying matter power spectrum which
decreases in amplitude as we go to high 2. The opposite behaviour of the cluster
power spectrum is a result of the bias parameter b(M, z), which, for a given mass M
increases with z. This Offsets the decreasing amplitude of the matter power spectrum
P(k) and essentially reverses its behaviour in the cluster power spectrum.

The variance in the estimated cluster power spectrum P0109) increases both at
the lowest and the highest k. The increase in uncertainty at the lowest k effectively
shuts Off the contribution to the information from the cluster power spectrum. On
the other hand, the uncertainty at the highest k increases the contribution to this
information. This, however, occurs in the regime where non-linear effects become im-

portant and therefore care must be taken to discard the k values when non-linearities

54

start appearing in the estimation of the cluster power spectrum.

PARAMETER SENSITIVITY OF CLUSTER POWER SPECTRUM

The cluster power spectrum is less sensitive to the variation of parameters except on
Kim and to a lesser extent on a. It is almost insensitive to the variation in remaining

parameters. This insensitivity of the cluster power spectrum is reﬂected in poor

 

 

 

 

 

6_ rrrrr . ......., . .._...rr . s W, . . .‘
1 _ . ,
h 4» q
‘ *” (I ‘
- 4:- <
m .. .
' -4>- ” —————
_ x
————— -. ' x
_— -\ ‘. . x
5 ‘- ~‘~ -
r ‘ —0— —
\ .
10 , .
\ -. dlv -1
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.4
1
.\
I- .l -\ 4
103 ....I . .......I . .. ....I . ......I . . ..
0.01 0.10 0.01 0.10

Figure 3.8 The sensitivity of the cluster power spectrum to Om and a. The curves show
the distribution of cluster number counts for a 10% increase (dashed lines) or decrease
(dotted lines) in the parameter value. The solid curve is for the ﬁducial value of the
respective parameter. The cluster power spectrum is relatively insensitive to the rest
of the cosmological and cluster structure parameters

constraints on those parameters when the cluster power Spectrum is used as the only

source of information of the structure growth history.

3.5 PROCESSING INFORMATION: CONSTRUCTING FISHER

MATRICES

With the above sources of information about structure and evolution of the Universe,
we determine the constraints that can be placed on the model parameters using the

Fisher formalism as was described in Section 2.6.

55

 

3.5.1 INFORMATION FROM THE REDSHIFT-Only EVOLUTION OF

CLUSTER NUMBER COUNT

We survey the redshift space over the range, 2 = 0 — 3, which is divided into 300 bins
each having a width of dz = 0.01. Each bin is scanned for clusters in the luminosity
range of 1040 — 1047 erg S—l. Thus we use the cluster number count information from
each of 300 redshift bins. The Fisher Matrix is then constructed using Eqn. (2.26)
(see below) by summing over 300 redshift bins for each combination of parameter

variation.

The greater the sensitivity of the cluster number counts in a bin to a given param-
eter, the greater the corresponding partial derivative, BN/ddi. The Fisher Element
will therefore be relatively larger for highly sensitive parameters. However, since each
Fisher Element is composed of partial derivatives of two parameters, the product will
therefore be coupled and the two parameters could well be degenerate. The behaviour
of the Fisher Element, therefore, depends on whether the two parameters are coupled

or not, which can be gauged from the corresponding information used in constructing

the matrix. For the cluster number counts, {2m and 08 Show degenerate behaviour.

3.5.2 ADOINC THE CLUSTER MASS EVOLUTION To THE RED-

SHIFT EVOLUTION

TO include the information of the shape Of the mass function to the cluster number
count redshift evolution, we bin the luminosity space into 20 bins in log space, in
addition to, 300 bins in redshift Space. The cluster counts are detected in each
redshift and luminosity bin to construct the Fisher Element Of the corresponding

parameters using,

56

 

BNnm aNnm 1
as,- asj Nnm

 

F5771 = znzm (3.1)

where, n is the number of z bins and In is the number of bins in log(l) space. This
way we include the mass function shape information in calculating the Fisher Matrix

for redshift evolution.

3.5.3 CLUSTER POWER SPECTRUM CALCULATIONS

For the purpose of cluster power spectrum calculations, the k-space is logarithmically
binned into 20 bins. Also the full z—space in a given survey is divided into three wide
z-bins, with each having approximately the same number of clusters. The Fisher

Matrix is then constructed using Eqn. (2.27) (see below),

 

BP (1061—9 (k)Akm
P _ cl cl
Fij _ Ean 691' (993' 0%(1

3.5.4 USING PRIORS FROM OTHER EXPERIMENTS

The prior on a parameter is the information that comes from some other independent
study. For example, we can use priors on cosmological parameters from a Cosmic
Microwave Background experiment to improve constraints on different parameters
from our experiment. When we do not let any parameter vary in the experiment,
it means we are using perfect knowledge of that parameter as will be done here for
the curvature of the Universe, the rate of expansion of the Universe, H0, and the
primordial power spectrum index, np. This means that we have used full priors from
the WMAP 7 results. Priors can also mean that our given parameter lies in a range
of values, e.g. a 10 percent prior on a means we know that (1 lies in this range from
some other way of finding this parameter, such as from Weak Lensing measurements.
Priors are added to improve our knowledge of different parameters. This information

from priors is added by constructing a Prior Fisher Matrix, which has all elements in

57

 

it as zero except the diagonal element corresponding to the given parameter, which

is given by,

1
Fee = —2 (3-2)
‘79

Adding priors may or may not improve our understanding of another parameter.
The next Chapter will focus on ﬁnding constraints on various parameters using dif-
ferent sources of information processed using the Fisher Matrix Formalism described

above and for the different cases of the Survey Experiment.

58

 

CHAPTER 4:
CONSTRAINTS FROM CLUSTER
COSMOLOGY

 

Using simulated galaxy cluster data based on different survey parameters of eROSIT A
and WFXT, we next ﬁnd constraints on various parameters. Various cosmological
and cluster structure parameters govern the information on the growth history which
is gathered by galaxy cluster surveys. The data is processed using the Fisher Matrix
formalism to extract conﬁdence intervals on these parameters. These are plotted in
the form of error ellipses which provide a convenient means of graphically interpreting
the results. In Section 4.1 we will ﬁnd the constraints on cosmological parameters de—
rived from different information sources which were described in the previous Chapter.
In Sections 4.2 and 4.3 we will study constraints on the gravitational growth index
7, and see if the next generation galaxy cluster surveys will have enough power to
rule out either of the two gravity models: the GR and the DGP with 95% and 99%

conﬁdence.

4.1 INFORMATION PROCESSING: CONSTRAININC PA-

RAMETERS

One of our purposes in this study has been to see at what stage of the experiment
the constraints get worse so that we no longer can measure parameter values with

sufﬁcient certainty. Therefore, we start unfreezing the set of parameters one by one

59

and study the degradation (or enhancement for the case of priors) at each step as
we proceed through OC, SC I, SC II and SC III. In this Section we analyse 2o
constraints on the 0m — 0‘8 plane from the above mentioned sources of information,
and study their successive degradation from CC to SC III cases for each individual
information source and dramatic improvement for the case when all the three sources

of information (the redshift and mass evolution of cluster counts and the cluster power

Spectrum) are combined.

4.1.1 CONSTRAINTS FROM REDSHIFT- Only EVOLUTION OF CLUS-

TER NUMBER COUNTS

Figure 4.1 shows 95% conﬁdence contours on the Sim-08 plane from the eROSITA
wide-ﬁeld survey for all the four cases, OC, SC 1, SC II and SC III.

 

 

 

 

 

 

 

 

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0.240 0.250 0.260 0.270 0.280 0.240 0.250 0.260 0.270 0.280
Om 0m

Figure 4.1 Constraints on the Qm-og plane from eROSI TA Wide-ﬁeld Survey. The
ﬁgure shows a step-by-step degradation of constraints from CC (dash-dot line) to SC
I (short-dashed line) to SC II (dotted line) and ﬁnally to the full self-calibrate case,
SC III (long-dashed line) for redshift-only evolution of cluster number counts when 7
is held constant (left-panel) and when it is unfrozen (right-panel).

When 7 is held constant, and our only source of information is the redshift- only

evolution of cluster number counts, the constraints on both parameters, Qm and 08

60

are pretty tight for the OC case, with {2m constrained well within ~ 0.266 :1: 0.004
and 03 having value of 0.801 :1: 0.12.

These constraints degrade successively as we allow for SC I, SC II, and SC III
cases; with am now constrained within ~ 0.266 :t 0.030 for the SC I case and within
~ 0.266 i 0.034 for SC III case. For the redshift-only evolution, the error estimates
increase by the largest percent after SC I (AQm = 0.004 for CC and Aﬂm = 0.03 for
SC I), when the M - L relation parameters, L0 and a are allowed to be free. There is
only a little degradation on conﬁdence contours on Qm-ag plane when the structure
evolution parameter, S and the scatter parameters, 00 and 17 are freed.

When 7 is freed, the constraints for each individual case degrade. The uncertainty

on 9m, Aﬂm increases from 0.004 to 0.01 for the OC case. Figure 4.2 shows the

 

 

 

 

IIIIIIIII "V'7"IYVIII\YYYVIYTVTVYYYYVYIYYYYYYVYY
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0.240 0.250 0.260 0.270 0.280
Om

Figure 4.2 This ﬁgure shows the relative comparison of how constraints on Qm-og

plane degrade after making 7 a free parameter for the two cases of OC (inner set
of ellipses) and SC III (outer set of ellipses). The dotted lines are when 7 is held
constant and dashed lines are for when 7 is unfrozen.

comparison for the OC and SC III, the full self-calibrate case, when 7 is held constant
and when it is freed. The qualitative behaviour remains essentially the same, except

that there is a little change in orientation for the two cases.

61

PERFORMANCE OF DIFFERENT SURVEYS

The WFXT wide-ﬁeld survey will be most effective in constraining parameters pri-
marily because of its combination of low ﬂux-limit and large solid angle. Figure
4.3 compares the constraints in 9m — 08 plane from different surveys when full self-
calibration is allowed. The deep-ﬁeld surveys are not explored here for constraining

parameters owing to their small sky coverage.

 

 

 

 

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0m

Figure 4.3 Comparing constraints that can be obtained from different surveys to be
undertaken by 612051 TA and WFX T for the full self-calibrate case when 7 is held

constant. ( eROSI TA: All-sky survey - long-dashed line, Wide-ﬁeld survey - short-
dashed line; WFX T: Medium survey - dotted line, Wide-ﬁeld survey - dot-dashed

line.

4.1.2 CONSTRAINTS FROM REDSHIFT And MASS EVOLUTION OF
CLUSTER NUMBER COUNTS

Next we include the information about the shape of the cluster mass function by

binning the clusters in luminosity space. We see the same qualitative behaviour of

constraints as we go from the OC case to the SC III case (see Figure 4.4), however the

constraints for SC cases are signiﬁcantly improved, with the constraints on 9m for

62

SC III case improving from Aﬂm = 0.034 (from redshift-only information) to 0.006

(from redshift and mass evolution information) as shown in Figure 4.4.

 

 

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0.255 0.260 0.265 0.270 0.275 0.255 0.260 0.265 0.270 0.275
0,, 0m

Figure 4.4 Constraints for the 9m - 08 plane using redshift and mass evolution of
cluster number counts when 7 is held constant (left panel) and when it is unfrozen
(right panel). This shows a step-by—step degradation of constraints from CC (long-
dashed line ) to SC I ( dotted line) to SC II (short-dashed line) and ﬁnally to the full
self-calibrate case, SC 111 (dash-dotted line)

This huge improvement especially for SC cases is seen for all parameters. The
additional binning in luminosity space limits the degradation that we get after cluster
structure parameters are freed. It, therefore, looks like that this binning in luminosity
space is somehow constraining our lack of cluster structure knowledge.

Thus adding mass function shape information to cluster number redshift evolution
provides much more information in constraining the cosmological as well as the cluster
structure model parameters. Figure 4.5 Shows the comparison of constraints from
redshift- only evolution and how they are improved after adding the information from
cluster mass function evolution to its redshift evolution, when 7 is held constant and

when it is freed.

63

 

 

 

 

 

 

 

 

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om 0m

Figure 4.5 Comparing the constraints from redshift-only ( outer ellipses) and redshift
and mass evolution (inner ellipses) of cluster number counts for CC ( dashed lines)
and SC III cases ( dotted lines) when 7 is constant (a), and when it is freed (b).

4.1.3 CONSTRAINTS FROM CLUSTER POWER SPECTRUM

The cluster power spectrum is not very effective in constraining parameters other
than 9m. In fact the constraints practically get very poor as soon as SC is allowed,
on all parameters except on 9m. Figure 4.6 Shows an illustrative example for CC case
only. As was also discussed in Section (3.4.3), tight constraints on 9m come essentially
from the shape of the cluster power spectrum, thereby reflecting the Transfer Function
T(k) behaviour which is very sensitive to the redshift of the epoch of matter-radiation
equality. The second source of information for improvement in Cm is the bias factor,

which is a strong function of mass of the galaxy cluster.

4.1.4 IMPROVED CONSTRAINTS BY COMBINING INFORMATION SOURCES

Combining information from the cluster power Spectrum and from the redshift and
mass evolution of cluster number counts provides us with improved constraints on all

parameters. Figure 4.7 Shows that this improvement is achieved for all cases, from

64

 

 

 

 

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Figure 4.6 Constraints from the cluster power spectrum only, for CC case when 7 is
constant ( dotted line) and when it is freed ( dashed line).

CC to SC III.

From this ﬁgure we see that the constraints on 0m, for SC 111 case, improve from
Aﬂm = 0.034 (from redshift-only) to 0.006 (from redshift and mass evolution) and
ﬁnally to 0.004 (from cluster power spectrum + redshift and mass evolution of cluster
counts). The constraints improve for all the cases when 7 is held constant as well as
when it is freed. This shows how combining the three sources Of information helps in

improving constraints.

4.1.5 CONCLUSION

In this Section we learned that for a given survey, and for a given information source,
constraints degrade as we go from CC to SC III. For the 0m — 08 plane the M — L
structure parameters L0 and a are responsible for maximum uncertainty. In general,
unfreezing 7 also degrades conﬁdence levels for a given case. Further, redshift-only
evolution of cluster number counts is a very poor source of information in obtaining

constraints. This weakness can be overcome by combining information from the

65

 

 

 

 

 

 

 

 

 

 

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0.255 0.260 0.265 0.270 0.275 0.255 0.260 0.265 0.270 0.275

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Figure 4.7 Improvement in constraints, for CC (top-left), SC I (top-right), SC II
(bottom-left) and SC III (bottom-right) cases, when the information from the red-
shift and mass evolution (dashed-lines) is combined with that from the cluster power
spectrum (dash-dotted lines), 7 is held constant here.

cluster mass function evolution with its redshift evolution information. The cluster
power spectrum is a very poor source of information on all parameters except on 0m,
however, when used in combination with the other two information sources it helps

in improving the information gained about different parameters.

66

 

 

 

 

 

 

 

 

 

 

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0.255 0.260 0.265 0.270 0.275 0.255 0.260 0.265 0.270 0.275

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m m

Figure 4.7 Improvement in constraints, for CC {top-left), SC I (top-right), SC II
(bottom-left) and SC III (bottom-right) cases, when the information from the red-
shift and mass evolution (dashed-lines) is combined with that from the cluster power
spectrum (dash-dotted lines ), 'y is held constant here.

cluster mass function evolution with its redshift evolution information. The cluster
power spectrum is a very poor source of information on all parameters except on Qm,
however, when used in combination with the other two information sources it helps

in improving the information gained about different parameters.

66

 

 

 

 

 

 

 

 

 

 

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0.255 0.260 0.265 0.270 0.275 0.255 0.260 0.265 0.270 0.275

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m

Figure 4.7 Improvement in constraints, for 00’ {top-left), SC I (top-right), SC 11
(bottom-left) and SC III {bottom-right) cases, when the information from the red-
shift and mass evolution (dashed-lines) is combined with that from the cluster power
spectrum (dash-dotted lines ), '7 is held constant here.

cluster mass function evolution with its redshift evolution information. The cluster
power spectrum is a very poor source of information on all parameters except on (2m,
however, when used in combination with the other two information sources it helps

in improving the information gained about different parameters.

66

4.2 THE GRAVITATIONAL GROWTH INDEX: How WELL

Is IT CONSTRAINED?

The most widely accepted theory to explain the cosmic acceleration is General Rel-
ativity, which needs a Dark Energy component. GR directed growth of structure is
different from other gravity models that have been theorised to explain cosmic accel-
eration. The parametric form of the growth function D(z), as is given in Eqn. (2.1)
models the GR directed growth for a 7 value of ~ 0.55 [Linder, 2005]. The other lead-
ing candidate to explain cosmic acceleration is Modiﬁed Gravity. The DGP Model is
one such example and has a 7 value of ~ 0.68. The two models GR and DGP predict
different growth history as was seen in Section (2.1) and in Section (3.4). Observing
structure growth in the Universe will therefore differentiate between the two models
if the cluster survey will have enough power.

We have seen the effect of unfreezing the 7 on the Kim-08 plane in the last Section.
Accepting a lack of complete knowledge about 7 essentially degrades the constraints.
In this Section we will see how well the GR model can be constrained, given the
power of next generation surveys. In the next Section we will return to the question
of distinguishing growth from the two gravity models to see if one or the other of the
these models can be ruled out using information on galaxy clusters that these surveys
will gather, in light of insufficient knowledge of cluster structure including the M — L

scaling relation, its evolution, the scatter present as well as scatter evolution.

4.2.1 CONSTRAINTS ON GR GROWTH

Figure 4.8 shows 20 constraints on the 7 — (2m plane that can be obtained from the
eROSITA wide-field survey, as we proceed from the OC case to the SC III case, using
information from the redshift-mass evolution and combined information from the

cluster mass function and the cluster power spectrum. Constraints degrade from DC

67

to SC cases, as is expected. For the full SC case and using combined information from

 

 

 

 

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0.45 lilllLLIl'OZLlll\L~1_/Ii?lllillllllL14L
0.250 0.255 0.260 0.265 0.270 0.275 0.280
Om

Figure 4.8 Constraints on 7 — 9m plane in the GR Model for cluster mass function
evolution (dotted lines) and cluster mass function evolution + cluster power spectrum
(dashed lines) as we go from 00 (innermost ellipses) to SC III ( outermost ellipses).

the cluster mass function and the cluster power spectrum, GR growth is constrained

well within 0.55 :l: 0.10.

Figure 4.9 shows the performance of different surveys in constraining the GR
growth. The 20‘ contours plotted here are for the SC III case and use combined
constraints from the three information sources. WFXT is expected to constrain the

GR Model twice as strongly than eROSITA, with its wide-ﬁeld survey constraining

7 to well within 0.55 :l: 0.05 on a 95% confidence level.

68

 

 

 

 

I I // I ;/"I \\l x I
/ \ l
/ ll .' - ll l
_ ll /’ .l "1 | l
-— l | I —I
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‘ \\\ [’1 //
0.45.IIII.LIlIEI\.,I’.Hill..lll...l
0.250 0.255 0.260 0.265 0.270 0.275 0.280
mm

Figure 4.9 Combined constraints from cluster mass function evolution and cluster
power spectrum on 7 — 9m plane for the full SC case from different surveys, WFX T:
wide-ﬁeld (dash-dotted line) and medium survey ( dotted line); eROSI TA: wide-ﬁeld

(short-dashed line) and all-sky survey (long-dashed line)
4.3 Is IT GR OR Is IT NOT GR? WILL THE NEXT

GENERATION SURVEYS BE ABLE TO TELL?

In this Section we compare the two gravity models to see if either of them can be
ruled out for the full SC case at the 20 level using the galaxy cluster survey power of
eROSITA and of WFXT. Ruling out one or the other of the gravity models for full
Self- Calibration case is important because the presence of scatter and / or evolution of
scaling relations can masquerade as a different gravity model if the statistical power
of the survey is not enough. We then need to ﬁnd ways to add more information
through the use of priors for the purpose of distinguishing the growth history of the

Universe. For this purpose we conducted an experiment where Fisher Matrices were

69

constructed for two model Universes based on the two gravity models GR and DGP.

4.3. 1 EROSITA ’ PERFORMANCE

Figure 4.10 compares the 20 error ellipses for the two gravity models, GR (lower

ellipses) and DGP (upper ellipses) at each step of information loss.

 

 

 

 

 

 

 

 

 

 

 

 

   

 

 

1.0 v v v v I 1 v v 1 v I v T Y Y 1.0
0.8 * ‘ 0.8
v 0.6 " ‘ 0.6
0.4 ‘ ‘ 0.4
0.2 . 1 I 0.2
1.0 l I I I I I I I \\ 1.0
0.8 ’__,__‘ """" ‘ 0.8
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.' I ’ . ' I
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.._.-...,.1- )3" I, 4
I I“,
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0.4 0.4
0.2....L.Ln-..l..LLI ...- 02...... ..
0.250 0.255 0.260 0.265 0.270 0.275 0.280 0.250 0.255 0.260 0.265 0.270 0.275 0.280
0m 0m

Figure 4.10 Degradation in the ability to distinguish the two gravity models from the
0C case (top-left) to the SC I (top-right) to the SC [I (bottom-left) and to the full
self-calibrate case SC III (bottom-right) for eROSI TA wide-ﬁeld survey. The contours
shown are for redshift-only evolution (solid lines ), redshift and mass evolution (dotted
lines) of cluster number counts and for the combined constraints with cluster power
spectrum (dashed lines).

If redshift-only evolution of cluster number counts is our only source of informa-

70

tion, the two gravity models will not be distinguished, even after we assume perfect
knowledge of cluster structure. Combining redshift-only evolution with other sources
of information allows us to distinguish the two models at the 20 level for the OC
case. Constraints degrade when the structure parameters, L0 and a are allowed to be
free, however the information from cluster mass function evolution will still be able to
differentiate growth from the two models. When the structure evolution parameter
5 is unfrozen, the combined information from cluster mass function evolution and
cluster power spectrum will not be able to completely distinguish growth from the
two models.

Adding Priors: Essentially for SC II and SC III cases, we see that the eROSITA
Wide-ﬁeld Survey is not able to distinguish between the growth from the GR and the
DGP models. In order to improve constraints further, we need to add priors. To see
what more information is needed to distinguish the models when the survey power is
not enough, we decided to study this further by adding artiﬁcial priors on different
parameters in order to see what parameter is the reason behind this degeneracy.

Any knowledge of scatter or its evolution is of little help in constraining growth
further. Only a marginal improvement is seen in constraints after adding even strong
priors either on scatter or on its evolution. Similarly adding priors on M — L scaling
relations cannot constrain gravity further for the purpose of distinguishing the two
models. However, when we add strong priors on the evolution of cluster scaling
relations ﬂ, it is very effective in improving the constraints and for eROSITA wide-
ﬁeld survey it does distinguish growth when strong priors ~ 5% are added on S.

eROSI TA Wide-Field Survey

Figure 4.11 shows constraints on the 7 — Qm plane for the no prior case and how
they it improve after we add ~ 10%, 5% and 3% priors on 5. From this we see that
for eROSITA wide-ﬁeld survey to be able to separate GR physics from DGP physics,

we need to add priors on S better than ~ 5% when full self-calibration is allowed.

71

 

 

 

 

 

 

 

 

 

 

 

 

 

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0.75} { 0.75} «1
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0.250 0.255 0.250 0.265 0.270 0.275 0.280 0.250 0.255 0.250 0.265 0.270 0.275 0.280
Qm Om

Figure 4.11 Indistinguishability of the growth models and the improvement in con-
straints on growth as a result of adding priors on 0, ~ 10% (top-right), ~ 5%
(bottom-left) and N 3% (bottom-right). The top-left panel shows no prior case. The
20 contours shoum are for the combined constraints from the cluster mass function
with the cluster power spectrum for SC III case. The survey deﬁnition used is that
of 612051 TA Wide-ﬁeld Survey. The dash-dotted lines show the improved constraints
when priors are added. The stars show the location for the respective ﬁducial models.
As we see from ﬁgure, the two models are completely distinguishable on 20 level after
adding strong priors on S.

eROSI TA All-Sky Survey

The picture is worse for the case when the survey power of eROSITA All-sky survey
deﬁnition is used. Figure 4.12 shows the result of constraining growth using its survey
parameters.

Thus, we see from this ﬁgure that the growth is not completely distinguished, on

72

 

 

 

 

 

 

 

 

 

_ Y I l f1 ., F # 10j l
0.75} 1 0.75} 3
: : : i
0.70} 1 0.70} 1
: : l i
- -I l- 1
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0.250 0.255 0.260 0.265 0.270 0.275 0.28 0.250 0.255 0.260 0.265 0.270 0.275 0.280
om 0..

Figure 4.12 Indistinguishability of the growth models and the improvement in con-
straints on growth as a result of adding strong (~ 3%) priors on S (right panel) The
left panel shows no prior case. The contours shown are for redshift and mass evolution
( dotted lines) of cluster number counts, for the combined constraints from cluster mass
function with the cluster power spectrum for the SC 111 case. The survey deﬁnition
used is 612051 TA All-sky survey. The dash-dotted lines show the improved constraints
when priors are added. The stars show the location for the respective ﬁducial models.
As we see from ﬁgure, the two models are not completely distinguishable on 20 level
even after adding strong priors on S.

a 20‘ level, even after adding priors as strong as ~ 3%. Again, information in form of

priors from other cluster structure parameters is Of little help in constraining growth.

4.3.2 WFXT DOES THE JOB!

WFXT with its unprecedented ﬂux-limits and large sky coverage, promises to be
unparalleled in constraining growth history of the Universe. Figure 4.13 shows the
effectiveness of the two WFXT surveys to distinguish the two gravity models on a
95% conﬁdence level.

However, the survey power of WFXT medium survey will not be enough to dis-
tinguish growth, and strong priors on S will be needed to be able to completely rule
out either of the two gravity models with a 99% conﬁdence. Figure 4.14 shows 20

and 30 constraints on 'y — Qm plane.

73

 

 

 

 

 

 

 

 

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0.250 0.255 0.260 0.265 0.270 0.275 0.280 0.250 0.255 0.260 0.265 0.270 0.275 0.280
0,, 0m

Figure 4.13 20 constraints on 'y - 0m plane for the two gravity models from cluster
mass function evolution ( dotted lines) and the combined constraints with cluster power
spectrum ( dashed line) when full self-calibration is allowed. WFX T medium survey
( left panel) and wide-ﬁeld survey (right-panel) deﬁnitions are used. Both surveys are
able to distinguish between the two models on a 20 level. The stars show the location

for the respective ﬁducial models.

 

 

 

 

 

 

 

 

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0.250 0.255 0.260 0.265 0.270 0.275 0.280 0.250 0.255 0.260 0.265 0.270 0.275 0.280
0,," 0m

Figure 4.14 20 and 30 constraints on growth from the WFX T medium (left-panel) and
wide-ﬁeld survey (right-panel) for full self-calibrate case, from combined information
from cluster mass function evolution and cluster power spectrum. WFX T wide-ﬁeld
survey will be able to distinguish between CR and DGP model with 99% conﬁdence.
The stars show the location for the respective ﬁducial models.

74

 

 

 

 

 

 

 

 

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0.250 0.255 0.260 0.265 0.270 0.275 0.280 0.250 0.255 0.260 0.265 0.270 0.275 0.280
mm 0m

Figure 4.13 20 constraints on 7 — 0m plane for the two gravity models from cluster
mass function evolution ( dotted lines ) and the combined constraints with cluster power
spectrum (dashed line) when full self-calibration is allowed. WFX T medium survey
( left panel) and wide-ﬁeld survey (right-panel) deﬁnitions are used. Both surveys are
able to distinguish between the two models on a 20 level. The stars show the location,

for the respective ﬁducial models.

 

 

 

 

 

 

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0.250 0.255 0.260 0.265 0.270 0.275 0.280 0.250 0.255 0.260 0.265 0.270 0.275 0.280
0 on,

m
Figure 4.14 20 and 3a constraints on growth from the WFX T medium (left-panel) and
wide-ﬁeld survey (right-panel) for full self-calibrate case, from combined information
from cluster mass function evolution and cluster power spectrum. WFX T wide-ﬁeld
survey will be able to distinguish between GR and DGP model with 99% conﬁdence.
The stars show the location for the respective ﬁducial models.

74

 

 

 

 

 

 

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0 0m

m
Figure 4.13 20 constraints on ”y -— {2m plane for the two gravity models from cluster
mass function evolution ( dotted lines) and the combined constraints with cluster power
spectrum ( dashed line) when full self-calibration is allowed. WFX T medium survey
(left panel) and wide-ﬁeld survey (right-panel) deﬁnitions are used. Both surveys are
able to distinguish between the two models on a 20 level. The stars show the location
for the respective ﬁducial models.

 

 

 

 

 

 

 

 

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0.250 0.255 0.260 0.265 0.270 0.275 0.280 0.250 0.255 0.260 0.265 0.270 0.275 0.280
0m Om

Figure 4.14 20 and 30 constraints on growth from the WFX T medium {left-panel) and
wide-ﬁeld survey (right-panel) for full self-calibrate case, from combined information
from cluster mass function evolution and cluster power spectrum. WFX T wide-ﬁeld
survey will be able to distinguish between GR and DGP model with 99% conﬁdence.
The stars show the location for the respective ﬁducial models.

74

We see from Figure 4.14 that the WFXT wide-ﬁeld survey will thus be carrying
enough information in its galaxy cluster data to be able to tell us with 99% conﬁdence

whether it is GR or not.

75

 

CHAPTER 5:
SUMMARY AND CONCLUSIONS

 

Acceleration of the Universe is one of the biggest mysteries which is haunting the
current generation of cosmologists since the last decade. To explain it, the standard
model needs hitherto unobserved Dark Energy or Einstein’s cosmological constant
A. While the current constraints are consistent with A, the uncertainties are still
enormous. The other alternative is to go beyond Einstein and test the large-scale
structure for deviations from GR, since expansion alone is not sufficient to differentiate
between the different gravity models.

For this we studied the statistical power of next generation galaxy cluster surveys
which will soon be scanning the skys. Their combination of lower flux-limits and
larger sky area to be covered will push the discovery space far beyond the limits
achieved by current surveys. The information from these galaxy cluster surveys in
the form of the evolution of cluster number counts in redshift and mass and in the
form of the cluster power spectrum derived from statistical correlations of galaxy
clusters on the sky, can be used to constrain various cosmological parameters. In
light of the present uncertainty about the galaxy cluster structure and its evolution,
it is practical to let the survey solve for (or self-calibrate) these scaling relations as
well as the scatter present therein.

From this study we found that the statistical power of the next generation surveys
will arm us with better constraints on various cosmological parameters even after

admitting a lack of complete knowledge about the cluster structure, when we com-

76

bine the information from the evolution of cluster number counts’ redshift and mass
evolution together with the information from the cluster power spectrum. Based on
this we studied the ability of different surveys to constrain the growth history of the
Universe. It was found that eROSITA surveys will need strong priors (Z 5%) on clus-
ter structure evolution parameter 5 to rule out, at the 95% conﬁdence level, one or
the other of the two gravity models GR and DGP which were studied here. However,
WFXT surveys do hold the special promise of differentiating growth and telling us
whether it is GR or not, with its wide-ﬁeld survey having the ability to say so even
with a 99% conﬁdence level.

In brief, WFXT will do the job!

77

 

CHAPTER 6:
INTRODUCTION TO QUASARS

 

Discovered in 1963 by Maarten Schmidt [Schimdt, 1963], Quasars form a part of the
larger AGN family as its most luminous member. Their most visible characteristic
is the enormous amount Of luminosity generated, which can be as much as 104 times
that of a typical galaxy. This has earned them the title of the light beacons of the
early Universe. Quasars can be seen out to the farthest reaches of the Universe and
hence they are a powerful source of information about early times in the evolution of
the Universe. Also known as Quasi-stellar objects (QSOS), they appear as point-like
objects in the sky.

However, it is the spectrum of a quasar which is its most distinguishing feature
and contains a wealth of information. The spectrum is unique in the sense that it
extends over the widest range of frequencies, right from the X-ray tO far in the radio
regime. In addition to the continuum, which is roughly constant over thirteen orders
of magnitude in frequency, the most prominent part of a quasar spectrum in the
optical and UV wavelength range is the plethora Of emission lines superimposed on
this continuum.

Quasars and in general active galactic nuclei (AGN) show a very strong cosmolog-
ical evolution. It has been Observed that these Objects were much more numerous at
a redshift (z) ~ 2.5 than they are in the recent Universe. Their luminosity is a strong
function of redshift, which suggests that there is something special about the youthful

galaxies that promotes the creation of AGN. Another interesting connection between

78

quasars and the evolution of the Universe comes from the fact that the intervening gas
clouds in the inter-galactic medium (IGM) absorb the photons coming from quasars,
as a result, their spectrum is changed by galaxies and clusters of galaxies along the

line of sight.

6.1 SALIENT FEATURES

The salient features of quasars include:

Very small angular size: In the night sky, as seen through a telescope, they appear
as star-like objects (hence the name Q80), and their structure is usually unresolved.
This is because they are very far away. Most often they outshine their host galaxies
and hence only the nucleus is seen.

Huge redshifts: While the ﬁrst object identiﬁed as a quasar had a redshift Of 0.158
[Schimdt, 1963], quasars at redshifts z 2 6 are now known [Jiang et. al., 2009].
These are accepted to be cosmological redshifts, indicating that we see QSOs at great
distances and hence at large lookback times. We can ﬁnd the distance to a quasar by
comparing the displacement of emission lines of known atoms and ions to measure its
2: in a given cosmological model.

Very High Luminosity: Given the moderately bright apparent magnitudes Of these
objects, the luminosities must be huge. They produce huge energy output in very
small area, resulting in enormous luminosities.

Characteristic Spectrum: The spectrum of a quasar is its most distinguishing fea-
ture and is unlike that of a star or a galaxy. It has a broad-band continuum emission
on which are superimposed the strong emission lines. Usually the spectrum is variable

in time. Also the light coming out is Often polarized.

79

6.2 THE QUASAR SPECTRUM

Figure A.1 (see Appendix A for ﬁgures) shows a characteristic quasar spectrum from

Sloan Digital Sky Survey (SDSS) [Vanden Berk et. al., 2001].

6.2.1 THE CONTINUUM

The broad-band spectral energy distribution (SED) is one of the deﬁning characteris-
tics of quasars. Tk have been observed in every wavelength. As a result, their spectra
cannot be described in terms of one single physical process. The broad-band SED of
a quasar continuum can be roughly described by a power law, E, = 011—“ where 01 is
the power-law index, C is a constant, and E, is the flux per unit frequency interval.
Several thermal and non-thermal processes have been invoked in an attempt to ex-
plain the continuum emission. The UV and optical region is dominated by the big blue
bump, coming mainly from the thermal emission from an accretion disc surrounding
a black hole. X—ray continuum gets a major contribution from inverse Compton scat-
tering of photons by relativistic electrons. The IR spectrum is generated by the dust
emission whereas the radio emission, if present, is coming from synchrotron emission

in strong magnetic ﬁelds associated with the quasar.

6.2.2 THE EMISSION LINES

The spectral lines in a quasar Spectrum are generally in emission and are a very
prominent feature in the optical, UV and X-ray with equivalent widths (E W) ~100A.
This is in contrast to the spectrum of stars and galaxies, which has very weak lines
that are predominantly in absorption. Another interesting thing about these lines is
their remarkable uniformity from one object to another. The spectrum of very many
objects looks very similar. The formation Of emission lines is governed by basic laws of

atomic physics, which is well studied by the experiments on Earth and hence we can

80

use them with conﬁdence as the diagnostics Of physical conditions in the environments

where these lines are formed.

BROAD AND NARROW EMISSION LINES

The main difference in the emission lines of different quasars comes from the fact that
some have lines with broad wings extending out to many tens of thousands of km/s,
and hence are called Broad Emission Lines (BEL), whereas others have very narrow
widths, called Narrow Emission Lines (NEL), not reaching more than a few hundred
km/s in width. Permitted and semi-forbidden lines are seen in both BELS and NELS.
When there is a broad wing, there is usually a narrow core as well. However, forbidden
lines are only seen in NELs indicating a lower gas density in the region where they are
formed. These emission lines are useful for deducing information about the physical
conditions existing in the gas surrounding the central Black Hole (BH).

Other than the redshifts these emission lines tell us about various other things
such as:

Velocities: By studying the widths Of emission lines, we can deduce how fast the
gas is moving in that region, and hence using kinematics we can ﬁnd the mass of the
central black hole.

Physical size: Studying the variability of the emission lines with respect to the

continuum tells us about the physical size Of the line emitting region.

6.2.3 LINE FORMATION PROCESS

Line formation is a result of atomic transitions. The various transitions occurring in
a region include radiative and collisional transitions. The heating/ cooling balance be-
tween these transitions determine what line is formed and what would be its strength.
This balance between various heating and cooling processes is governed by various

factors.

81

Energy of Photons incident on the Region: The incident photons from the central
engine photoionise the broad emission line region (BELR) gas, which further results
in line formation through radiative recombination and / or collisional de—excitation.

The Critical Densities: The electron densities in the region determine whether
or not forbidden emission lines can be formed. There exists a competition between
radiatively and collisionally de—excited lines in cooling the gas. The density at which
collisional de—excitation starts to dominate is called the critical density. Usually the
densities in the BELR are ~ 109 — 1011 cm‘l. Since critical densities governing
different lines vary, we also see some semi-forbidden lines like CIII] along with mostly
permitted lines. In addition the transition probabilities of different elements and their
abundances as well as the electron temperature in the region are among the deciding

factors in the line-formation process.

6.2.4 ABSORPTION LINES

In addition to the very prominent emission lines, some atomic absorption features are
also present in some quasar Spectra. These absorption features are formed because
of the absorption and/ or scattering of quasar photons by the gas present in the IGM
along the line-of-sight. Usually the further away a quasar is the more absorption
featuras it has. The Lyman a forest ubiquitously present in the quasar spectra iS a

well-known example.

6.2.5 QUASAR ABUNDANOE ANALYSIS USING BROAD EMISSION
LINES

The BELS come from the region just outside of the accretion disk. The gas in this re-

gion is moving very fast ~ 10,000 km / s . The quasar spectrum is dominated by these

lines in the rest-frame Optical and UV regions. Because of the ease of their detection

and measurement in many objects they form a very good source for measuring abun-

82

dances in that region. However many of these lines suffer from the disadvantage Of
severe blending with other nearby emission features. A careful deblending procedure
therefore needs to be followed in deducing abundances from them.

The line-intensity ratios Of different emission lines can be used to determine the
relative abundances Of the elements that enriched that region. However, there exists
a plethora Of lines even in the UV-Optical part, so deciding which lines and more
importantly which line-intensity ratios to use while making any such analysis becomes
important. Flux in the lines depends on the heating vs. cooling balance. Furthermore,
many line-intensity ratios are strongly sensitive to other physical conditions like gas
temperature and ionisation level as well as to metallicity. So just any ratio will not
work. Usually Nitrogen (N) is a good indicator Of the enrichment in the region and
scales directly with metallicity hence different N lines like NV, NIV], NIII] form the
primary source of information on abundances in the BELR.

Over the past decade a technique has been developed to measure the overall metal-
licity (Z) of these BELRs. (Z/ZQ) ~ (O/H) — (O/H)@, where O and H indicate
the abundances of these elements by number. The approach [Hamann and Ferland,
1993; Hamann and Ferland, 1999; Hamann et. al., 2002] is to directly measure the
N/O and N / C line-intensity ratios and then use the strong correlation between these
two ratios and Z that is observed in our own Galaxy [e.g., Pettini et. al., 2002] to
determine Z. The physical origin of the Observed correlation is the build up of N
as a secondary product of hydrogen (H) fusion via the CNO cycle in higher mass
stars. This approach of measuring BELR chemical abundances is needed because it
is impossible to directly measure the O / H or C / H ratios due to the fact that the H
emission lines are primarily recombination lines that record the ionisation and heating
rate in the BELR gas while the lines Of elements heavier than Helium (He), (including
C, N, 0) record the cooling rate; and the heating and cooling rates always adjust to

be in balance. This technique, instead, compares the strengths of emission lines that

83

are competing to carry the cooling load, including lines of C, N and 0. When the
abundance of N is higher relative to C and O, lines of N are able to carry a greater
fraction of the cooling, at the expense of the collisionally excited lines of the other
elements. This makes the N/ O and N / C line-intensity ratios sensitive to the relative
abundances Of these elements.

When connecting the line-intensity ratios to Z we also need a model which relates
these two. Since most of the N is from secondary enrichment in the CNO cycle in
massive stars, it is safe to assume that most Of the stars that enriched the region
were massive ones. The underlying model considered here is the Locally Optimally-
emitting Cloud (LOC) Model of the BELR in a quasar [Baldwin and Ferland, 1995].
The LOC Model considers a stratiﬁed BELR with wide range Of electron densities
and wide range in incident photon flux. Furthermore, it says that each line forms
prefentially wherever its emission is most favoured by the atomic physics and the

Observed spectrum is the sum over many diverse BELR components.

6.3 THE ELEMENTAL ABUNDANOES IN QUASARS

The presence of BELS in the spectrum indicates the presence and abundance of heavy
elements near the central engine of the quasar. This gives a unique measure of the
star formation and chemical evolution in young galactic nuclei, Since the gas emitting
these elemental lines must have undergone some amount of chemical enrichment via
the various processes, mentioned below. The abundance measurements in high 2
quasars put strong constraints on the properties Of star formation in the very early
Universe. One important goal of quasar abundance studies is to develop a better
picture of star formation and galaxy evolution at early times. Quasar abundances
studies also help us to better understand the local physics and environment of quasars

themselves.

84

6.3.1 SITES OF CHEMICAL ENRICHMENT IN A GALAXY

The stars in a galaxy are the primary source of metal enrichment in a galaxy. When
they die, they release the metals formed/locked up in them into the Inter-Stellar
Medium (ISM) [Hamann and Ferland, 1993],

Envelopes of intermediate mass stars (1M9 - 701(9). The envelopes Of these stars
are important sources Of He, N and C. There is no further burning after C is formed
in their cores because of low mass. These stars end their lives as He or CO white
dwarfs.

Type IA SNe: Type IA SNe are assumed to be main source of Iron (Fe) present in
a galaxy.

Ezploding He cores of massive stars as Type II and Type Ib SNe: These are im-
portant contributors Of the major metals found in galaxies.

Envelopes above He cores of massive stars (M 2 7MQ). These contribute to the
enhancement of secondary CN O cycle elements in the ISM Of a galaxy.

Low mass stars: These stars do not contribute much because they live too long

and hence don’t release their locked up metals in the ISM soon enough.

6.4 QUASAR ABUNDANCES AND THE EVOLUTION OF

GALAXIES

The main question we explore in this project in studying the elemental abundances
in quasars is to search for the relationship of the QSO phase to the overall evolution
of massive galaxies. It is well evident from the relation between M 3 M B H — Mgal that
there exists a coupled evolution between spheroids and the Super Massive Black Holes
(SMBHs) [Tremaine et. al., 2002]. The abundance studies help us in exploring this
evolutionary relationship by telling us how much star formation occurs in spheroids

before the quasars are lit. However there exist at least two diverging schools of

85

thought on the nature Of this evolution.

6.4.1 MERGERS Vs. IN-SITU STAR FORMATION
GALAXY MERGERS

Proposed ﬁrst by Toomre (1977) and later expanded upon by Soltan (1982), this
line of thought believes that massive spheroids are formed by major gas-rich galaxy
mergers. The quasar phase is triggered by the merger between two spirals of roughly
the same mass. The quasar is essentially the ﬁnal stage of this merger process at which
the spheroid is largely formed and has begun to relax. The observed relationship
between spheroids and BHS residing in them indicates strong correlation between
them. There are no bulges without Black Holes, and there are no bulge-less systems
with Black Holes. This implies the same origin (common physical trigger) for SMBH
and spheroids. The merger-driven model accurately predicts the Observed excess
(clustering) of quasars as a function Of L and z, i.e., the Observed Sharp rise and fall

Of quasar luminosity density over cosmic time [see e.g., Hopkins et. al., 2007].

IN-SITU STAR FORMATION

The major blow against the merger theory as being the quasar phase trigger comes
from surveys like DEEP2 and GOODS, neither of which shows any evidence Of a
connection between mergers and quasars at 2 ~ 1. DEEP2 [Cooper and Newman,
2003] maps about 20,000 galaxies in the redshift range, 0.4 S 2 S 1.35 and studies
the relationship between the galaxy colour and environment. It concludes that the
fraction of red galaxies depends strongly on local environment out to a z of 1. Red
galaxies favour overdense regions at low 2 relative to their counterparts at high z(2
1.3). This suggests that the build-up of red galaxies has occurred prefentially in
overdense environments at z 3 1.5. Therefore it seems that the correlations between

morphology and colour-density are the result of nurture (environment-driven) rather

86

than being imprinted by nature (e.g. mergers) during their epoch Of formation.

6.4.2 WHAT DOES QUASAR METALLICITY TELL Us ABOUT ANY

OF THIS?

What information can we get about the role Of quasars in the evolution of galaxies
by studying their abundances? The metallicity of a quasar is representative of the
population of stars which were formed in the galaxy sometime back before the cos-
mic time corresponding to the observed 2. The catastrophic events resulting from
explosions and/ or mergers ripped apart the stars and pushed some Of the expelled
gas to the centre of the galaxy toward the BH which grew supermassive as a result.
The BELS we see come mainly from the region which most likely has formed from
the winds of an accretion disk [Peterson, 1988]. A knowledge Of quasar metallicity
therefore points to the stellar population which might have enriched this gas in the
BELR. The typical mass of the gas in BELR is about M B E L R N 103 —104M@ and the
mass of a BH is, M B H ~ IOQMQ. Simple scaling arguments based on normal galactic
chemical enrichment and solar or higher BELR metallicities Show that the minimum
mass of the enriching stellar population is of the order of 10 times the BELR mass,
or more than 104 ~ 105M® [Baldwin et. al., 2003]. This stellar population needed
to enrich this gas should be already there or still rapidly forming, when luminous

quasars become observable.

6.4.3 PREVIOUS RESULTS AND NEW QUESTIONS

Previous studies about the elemental abundances in quasars have found no signiﬁcant
trend in metallicity (Z) and redshift (z) relation. However a stronger trend for larger
N line-intensity ratios and hence high Z is seen in more luminous quasars at every
2 [Hamann and Ferland 1999; Warner et. al., 2003; Nagao et. al., 2006]. Shemmer

and Netzer (2002) ﬁnd that NV/CIV is more strongly correlated with the normalised

87

accretion rate, L/ L E D D, than with Luminosity (L) or the central black hole mass,
M B H: thereby implying that quasars with higher L/ L E D D have higher Z. How-
ever contrary to this, Warner et. al., (2003, 2004, 2007) do not ﬁnd any signiﬁcant
relationship with L/ L E D D but instead with M B H even if the L is constant. This
suggests that more massive BHS reside in more massive spheroids which character-
istically have higher Z. Also, the SIOpe of M B H — Z roughly mimics the galactic
mass-metallicity relation, in that Z is higher in more massive hosts, consistent with
the normal mass-metallicity relation in galaxies.

The metallicity of a quasar, or more speciﬁcally that of the BELR gas is, Zgas ~
1 — 5Z9, implying enrichment by at least a galactic bulge-like population. Also, most
star formation must have happened before the start of the quasar epoch. The SMBH
halts the star formation and thus leads to the Observed M B H — Mgal relation. The
evolutionary sequence proposed by many theoretical models which go with the merger
argument, is: Major merger => Ultra-luminous infrared galaxy (ULIRG)/starburst
=> possible transition Object with declining star formation or partially obscured AGN
=> visible quasar.

QSOS tell us about the ISM metallicity in the centre of massive galaxies. Some of
the questions we can ask are:

Does the metallicity distribution ﬁt with the expected age distribution in galaxy
evolution models? What is presently known about QSO metallicity distributions?
Does BH mass or L / L E D D correlate most directly with Z? There however remains a
paucity of very high metallicity QSOS. Once we have more such Objects we can hope

to have an increased leverage in measuring correlations with metallicity.

88

 

CHAPTER 7:
SAMPLE SELECTION AND DATA
REDUCTION

 

7 . 1 THE PROJECT

The direct goal of this current project is to make improved measurements of the
BELR metallicity in QSOs at the high end of the metallicity distribution, and to
then compare the distribution of metallicities and the dependence of metallicity on
other physical parameters of the QSOs to the predictions of chemical enrichment
models.

In most quasar spectra, the only N line strong enough to be measured is NV.
The strength of this NV A1240 line with respect to CIV A1549 or He II A1640 has
consistently indicated above solar metallicities in the BELR of QSOS. Such high
metallicities are also expected according to the chemical evolution models. However,
it has long been known from reverberation measurements that these different quasar
emission lines are formed in overlapping, but non-identical parts of the BELR [e.g., see
Peterson, 1988]. This emphasizes the fact that a correction for the different ionisation
levels of N (N'l'2, N+3, N+4), He++ and C‘*‘3 is needed in order to properly determine
the relative abundances from the observed line-intensity ratios. These ionisation
corrections are usually made by assuming a model for the radial (relative to the
ionising continuum source) and density distribution of the gas in the BELR, and

then computing how the Observed line-intensity ratios are predicted to change with

89

changing metallicity.

The model normally used for this is the Locally Optimally-emitting Cloud (LOC)
model [Baldwin et. al., 1995]. It assumes that the distributions in internal density
and in the radial distribution of number of gas clouds, both have simple power-
law dependences. For the abundance determinations, the usual power laws used to
describe these distributions are (number of clouds) ~ (internal gas density)’1 and
(number of clouds) ~ (radial position)"1, which satisfactorily reproduces the mean
spectrum of all QSOS, but is not very likely to exactly describe the situation in
any particular QSO. Indeed, the spectra of QSOS with unusually narrow emission
lines Often Show lumpy, complex emission-line proﬁles; demonstrating a non-uniform
distribution of clouds over internal gas density and radial position [Baldwin et. al.,
1996]

Given these uncertainties in the ionisation corrections, it is important to try and
use lines from other ionisation states of N, in addition to NV. Besides providing a check
for errors due to overlooked ionisation / excitation effects, this will also check for errors
in measuring the heavily blended NV line. The ﬁrst Object checked for such a case was
Q0353 — 383, which had been found by Osmer (1980) to have NIII] A1750 and N IV]
A1450 lines that are far stronger than in typical QSOS. Although they are still much
weaker than the strongest BELR lines such as Lya or CIV A1549, the N 111] and NIV]
lines in Q0353—383 are strong enough to be accurately measured, which is not usually
the case. Baldwin et. al. (2003b) obtained new Optical / UV spectra of this luminous
Q80, and showed that line-intensity ratios involving all three measurable ionisation
states of N (N++, N+3 and N+4) all give the same result that N/C' ~ 15(N/C)® and
hence the metallicity Z ~ 15Z® in this particular object. This supported the idea
that the high metallicities determined for other QSOS in which just the NV line can
be measured are also generally correct.

In a follow-up paper [Dhanda et. al., 2007] we studied the validity of the abundance

90

measurements in two additional QSOs which had unusually strong, and therefore
accurately measurable, N III] and NIV] lines. The objects were S DS S J 125414.27 +
0241175 and SDSS J 154651.75 + 5253131. In the ﬁrst of these Objects, the lines of
all the different observed N ionisation states again turned out to imply Similar values
of Z, with Z ~ 1029. However, in the second case the different line-intensity ratios
indicated different metallicities. This implies that in this later object, the standard
LOC model does not correctly describe the structure of the BELR. Thus, two out Of
three of the “N-Loud” QSOs studied to date give results that support the use of the
NV line strength as an abundance indicator, but the third object provides a warning
that this line is not 100% trustworthy.

These results also led us to conclude that many of the quasars with relatively strong
N111] and NIV] lines are representative of very highest metallicity galaxy cores in
the highest redshift Universe. The high metallicity in these quasars raises interesting
questions about the unusual chemical properties of such objects as well. Such quasars
can therefore be used to test chemical enrichment models.

This current project is a study in using the N -line technique for measuring Z in a
larger sample of QSOs with strong NIV] and N III] emission lines, and to map out the
general properties of these super-metal-rich QSOS in order to understand how they

ﬁt into the general picture of the early evolution of massive galaxies.

7.2 SLOAN DIGITAL SKY SURVEY

The observations for this project have been taken from the Sloan Digital Sky Survey
(SDSS).

The Sloan Digital Sky Survey (SDSS)lwww'3dSS'0"9l is one Of the most ambitious
cosmography projects ever undertaken. The SDSS is systematically mapping a quar-
ter of the entire Sky producing a detailed image of it and determining the positions and

absolute brightnesses Of more than 100 million galaxies, giving us a three-dimensional

91

picture of the Universe through a volume one hundred times larger than that explored
to date. The SDSS is also recordng the distances to 100,000 quasars, giving us the
unprecedented knowledge of the distribution of matter to the edge of the visible Uni-
verse. The SDSS uses a dedicated 2.5-meter telescope at Apache Point, New Mexico,
with a 3 degree ﬁeld, and a mosaic CCD camera and two ﬁber fed double spectro-
graphs to carry out the imaging and surveys respectively. A separate 20” photometric
telescope is used for photometric calibration.

The SDSS is obtaining spectra of complete samples of galaxies and quasars. These
spectrOSCOpic targets are selected from the imaging data via various target selection
criteria. Quasar target selection is based on the non-stellar colours of quasars and
matching unresolved sources to the FIRST radio catalogue. The colour selected
quasar candidates are those Objects that lie more than 40 from the stellar locus and
have i-band PSF magnitudes, 15.0 S i S 19.1. The SDSS spectra are taken with
two ﬁber fed spectrographs, covering the wavelength range 3800-9200 A over 4098
pixels. The ﬁbers plug into plates that are the focal plane Of the telescope. Each
plate can hold 640 ﬁbers with a ﬁxed aperture of 3”. The plates are positioned
by a tilting algorithm and ﬁbers are assigned to targets. The ﬁnite diameter of
the ﬁber cladding prevents ﬁbers on any given plate from being placed closer than
55” apart.The resolution varies between, R = 6A/ A ~ 1850 — 2200. The relative
spectrophotometry is accurate to about 20%. Each spectrum is accompanied by
an estimated error per pixel, based on photon statistics and the amplitude of Sky
residuals.

The Spectroscopic data are reduced through the spectroscopic pipelines, Spectrold,
spectro2d and specBS. Spectro2d reduces the two dimensional Spectrograms produced
by the spectrographs to ﬂux and wavelength calibrated spectra, while specBS deter-
mines classiﬁcations and redshifts via a X2 ﬁt to the spectrum in question with series

of rest-frame star, galaxy and quasar templates.

92

7.3 THE SDSS QUASAR CATALOGUE IV

We use the fourth edition of the SDSS Quasar Catalogue as the base sample for our
abundance studies. The catalogue contains a total of 77,429 objects and comes from
the SDSS ﬁfth data release (SDSS DR5) [Schneider et. al., 2007]. It consists of Objects
that have luminosities greater than M, N —22.0 (in a cosmology with H0 = 70 km
sec—1, 0 M = 0.3, Q A = 0.7) and have at least one BEL with FWHM larger than 1000
km sec"1 or have interesting/ complex absorption features, are fainter than i ~ 15.0
and have highly reliable redshifts. This catalogue covers an area of about 5740 degz.
The quasar z’s range from 0.08 to 5.41, with a median value of 1.48 and a 70% of
all detected quasars have z’s below 2.0. The data are presented in tabular form and
were downloaded from the SDSS website. More than 90% of the objects in here were
discovered by the SDSS.

7.3.1 SELECTION EFFECTS IN SDSS QUASAR SAMPLE

This Quasar Catalogue is not a statistically complete sample. There are two reasons
for this. It includes Objects from all categories of target selection in SDSS, not just
those selected as quasar candidates. While the catalogue contains both the TARGET
selection ﬂags used to select spectroscopic targets, and the BEST selection ﬂags ob-
tained by applying the ﬁnal target selection version (sometimes to better photometric
data obtained later during the survey), use of the BEST data produces a different set
of quasar candidates than the TARGET version that was used to deﬁne spectroscopic
plates, even for those parts of the sky that were targeted using the ﬁnal quasar target
selection algorithm described in Richards et. a1. (2002). Secondly, the survey targets

the areas of high galactic latitudes only.

93

7 .4 SAMPLE SELECTION AND DATA REDUCTION

The 77,429 Quasars in the SDSS Quasar Catalogue IV formed the base sample for

this project. Not all spectra are, however, useful for this study.

7 .4. 1 MAIN SAMPLE

As the very ﬁrst step in narrowing down the sample base, we apply a redshift restric-
tion. In this study Of abundance analysis we need to ﬁnd ﬂux-ratios of various ions
present in the BELR of a quasar, such as NIII] /CIII] and NV/CIV. We therefore need
the quasars for which all the emission lines of interest fall within the observed wave-
length range. The CIII] line lies at 1909 A rest wavelength and forms one extreme
of the picture. NV lies at 1215 A rest wavelength and forms the other extreme. In
order to have both these lines of interest present in the spectrum, the quasar should
have, 2.29 S 2 S 3.61. Putting this redshift restriction into use reduces our sample
base to 8122 Objects. This is only about 20% of the total number of quasars in the

base sample.

7.4.2 INITIAL DATA REDUCTION STEPS

Various IRAFlimf'mao'edul routines have been used for the initial data reduction
steps. A random sample of 100 QSOs was checked for spectrum quality, using the
IRAF task SPLOT.

EXTINCTION CORRECTION

The spectra were corrected for Galactic Extinction using the Au values given in the
SDSS Quasar Catalogue, which are based on the maps Of Schlegel, Finkbeiner and
Davis (1998). We used the IRAF task, DEREDDEN, for this purpose.

94

REDSHIFT CORRECTION

The next step is to correct the spectra to rest frame wavelengths. This was done by

applying redshift correction, using 2 values given in the catalogue, using the IRAF

routine, DOPCOR.

SMOOTHING THE SPECTRA

The spectra as downloaded are still noisy and not of much use in the raw form.
In order to process the data further, the IRAF smoothing routine contained in the

SPLOT task was applied to all the spectra, with a seven pixel smoothing.

CONTINUUM SUBTRACTION

All 8122 spectra were continuum subtracted using a polynomial ﬁtting routine with
maximum power law of 3 and applying two rejection iterations of three sigma each,
to allow rejection of spurious signal from atmospheric emission lines, residual cosmic
rays etc. These 8122 reduced quasar Spectra formed the intermediate sample base,

to be used for further data reduction and analysis.

7.4.3 DATA REDUCTION II

This Section explains the narrowing down of the intermediate sample base to 42
Quasars for precise abundance measurements.

SIGNAL-TO-NOISE RATIO

First, all 8122 quasar spectra were examined by eye and ~ 2000 Of them which were
too noisy (e.g., see Figure A.2(a)) for detailed abundance analysis were discarded.

The S / N threshold for this rejection was roughly 5.

95

MISSING LINES OF INTEREST

A F ortran routine was applied to check for any spectrum with no data in the regions
of emission lines we needed for further processing (e.g., see Figure A.2(b)). This step

then eliminated all spectra with missing lines of interest.

CIV ABSORPTION

The CIV A1549 emission line strength is important for our study as it is used in ﬁnding
the line-intensity ratios. Many times this line is absorbed either by intervening gas
clouds or quasar outﬂows. We therefore checked the database for spectra with heavily
absorbed CIV lines, using a Fortran routine to check the fraction of absorbed CIV
emission line ﬂux and rejected spectra where CIV emission line ﬂux is more than 50%

absorbed (see, e.g., Figure A.2(c)).

CHECKING THE AUTHENTICITY OF NIV] AND NIII] LINES

The N111] and NIV] lines are relatively weak in the QSO spectrum. Even when
the lines are unusually strong, it is still quite difﬁcult to be sure that they are real
because they are blended with the broad wings of CIV (for NIV]) and Fe II (for
NIII]) (see e.g., Figure A.2(d)). To check for the authenticity of these N-lines, we
checked to see if they had roughly the same proﬁle as the CIV line. This was done
by automatically measuring ﬂuxes in the NIV], CIV and N111] lines through a wide
velocity window (approximately 10,000 km 3‘1) and then again through a narrower
velocity window (approximately 7000 km s-l). The NIV]/CIV and NIII]/CIV ﬂux
ratios were computed separately for each velocity window size, and then the ratio of
ratios (narrow/ broad) was computed. We discarded cases where this ratio of ratios
fell outside the range: 0.7 — 1.3. In the rejected spectra, the apparent N—lines were

either just noise, or were dominated by blending with other features.

96

7.4.4 AUTOMATED MEASUREMENTS OP INTERMEDIATE SAMPLE

Next we performed automated measurements to calculate the full width at half max-
imum of the CIV emission line (FWHM(CIV)) and the continuum luminosity, L A at
1450 A. using IRAF and FORTRAN routines. This was done for the full intermediate

sample except for the spectra with heavy CIV absorption.

7.4.5 FINAL SAMPLE WITH MEASURABLE NIII] AND NIV] LINES

The rejection steps described in Section 1.4.3 reduced our sample base to about 1000
spectra. We then ordered the surviving spectra by N I V]/ CI V ratio. Of these about
42 quasars had N I V] / CI V ratios stronger than in SDS S J 1254 + 0241. An example
of quasar spectra with strong N lines is shown in Figure A.2(e). Final data reduction

and full abundance analysis was then performed on these 42 quasar spectra.

7.5 FINAL DATA REDUCTION

7 .5. 1 FE SUBTRACTION

After the spectra have been corrected for redshift and continuum subtracted, the next
step is to ﬁt and subtract templates of FeII emission. A grid of such templates based
on the Vestergaard and Wilkes (2001) study of I Zw 1, but broadened in velocity by
different amounts, was kindly provided to us by M. Vestergaard. These particular
templates do not include FeIII. For each QSO further analysed, we used the template
with the broadening which most closely matched the measured widths Of strong and
relatively unblended emission lines (NIV] or C IV). To the extent possible, the ﬁt
was guided by the strength Of the UV bump in the AA2240 — 2650 A rest wavelength
region, where the FeII emission normally is strongest. However a few spectra which
showed no visible Fe emission, were not Fe—subtracted. Also, none of these QSOs for

which it was possible to ﬁt FeII have very strong FeII bumps, so this correction was

97

modest in all cases. The FeII A2450 strengths relative to the continuum are given in

Table B.1 (all Tables for this project are given in Appendix B).

7.5.2 PROFILE FITTING AND FLUX ESTIMATION

We then measured the emission-line strengths by ﬁnding and isolating individual lines
which we could use as template velocity proﬁles for ﬁtting to weak and/ or blended
lines. This is the same technique that was used by Baldwin et. al. (2003b) to measure
the emission line strengths in 620353—383 and recently by Dhanda et. a1. (2007). The
template proﬁles are based on different'emission lines for different QSOS. Table B.2
lists which emission lines served as the template proﬁle in each case. The measured
ﬂuxes Of the emission lines are given in Table B.3, with ﬂuxes in units of the total
ﬂux in the CIV doublet.

The Table B.3 also lists minimum and maximum ﬂuxes for each line that are
based on the best ﬁt with alternate template proﬁles that did not ﬁt as well as the
best ﬁtting template. In this or any other technique for measuring the strengths of
broad and/ or blended QSO emission lines, the errors usually are not due to photon
counting or due to the statistics of the ﬁt, but rather are completely dominated by the
uncertainties in systematic effects such as the true shape Of the line proﬁle, whether
or not additional weak lines should be included in the blend, and the level and shape
Of the underlying continuum. The maximum and minimum ﬂuxes listed in Table B3
are our best estimates of these effects.

This measurement technique has the advantage that it uses empirically determined
line proﬁles, which in real life exhibit a wide variety of non-Gaussian shapes. It has
the disadvantage that different lines in the same QSO can have quite different proﬁles,
so the template proﬁle Often does not provide an exact ﬁt. The initial ﬁts were done
by eye, and then the exact line strengths were ﬁnalized automatically using a )8-

minimisation technique.

98

Apart from the usual lines used in the abundance analysis, mentioned before, OVI
line at 1035 A can also be used for this purpose. Out Of a total of 42 quasar spectra in
the ﬁnal sample, 19 of these also have this OVI line present in their Observed spectra.
These spectra were, therefore, also ﬁtted for the OVI line at 1035 A. This provides us
with two additional line—intensity ratios (NV/OVI and NV/(CIV+OVI)) to be used

for the abundance measurements.

7 .6 ABUNDANCE ANALYSIS

We apply here the same procedure here estimating the abundances, that was used by
Baldwin et. al. (2003b) for Q0353 — 383, and Dhanda et. a1. (2007) for two of the
QSOs from SDSS DRl with strong N linas found by Bentz et. a1. (2004).

7.6.1 LINE-INTENSITY RATIO MEASUREMENT

Line-intensity ratios of various combinations are found Simply by dividing the ﬂux of
the respective ions. Table B.4 lists the diagnostic line-intensity ratios for all 42 QSOs

for which detailed measurements were made.

7.6.2 FROM LINE-INTENSITY RATIO TO METALLICITY

The abundance measurement technique uses the Observed line-intensity ratios of ni-
trogen lines to cooling lines of other elements, and compares them to the ratios
predicted by the LOC model of the BELR for a segmented power law [Hamann et.
al., 2002]. Here we have also adjusted the Hamann et. a1. (2002) predictions to
the revised solar C, O, and Fe abundances found by Allende Prieto et. a1. (2001,
2002) and Holweger (2001). This modiﬁcations means that the same NV (relative
to other strong lines) now occurs at about 30 percent lower Z than before, which

was accounted for by subtracting 0.11 from (Z /Z@) values given by Hamann et. al.

99

(2002). Figure A.3 shows the plot of these measured metallicities, separately for each
QSO, onto the curves of line-intensity ratios versus metallicity predicted by the LOC
Model, for each line-intensity ratio. Table B.5 lists the resulting best metallicity value
for each line-intensity ratio Z for each QSO, along with the corresponding minimum

and maximum values.

7 .7 MASS MEASUREMENTS

The mass Of the SMBH Of each quasar is estimated using the following equation

[Warner et. al., 2004],

 

0.7
FWHM(CIV) 2 AL ,(1450A)
M = 1.4 106M —— 7.1
SMBH X G ( 103km/s ) ( 1044ergS/s ( )
here, the FWHM is the full width at half maximum intensity of the CIV A1549 line.
This equation estimates the SMBH masses by applying the virial theorem, M S M B H =

rv2 / G, to the line-emitting gas [Kaspi et. al., 2000],

RBLR FWHM 2
AI = 1. 1 5M —— —— .
SMBH 5 X 0 Q (llt — day) (103km/sec> (7 2)

where RB L R is the radial distance between the BELR and the central engine and
FWHM applies to the broad emission line proﬁle. The R B L R can be estimated on
the basis of observed relation between R B L R for a particular line and the continuum

luminosity. CI V has been used for the calculation Of FWHM and Luminosity.

100

 

CHAPTER 8:
THE RESULTS

 

8.1 METALLICITY OF QUASARS WITH STRONG NITRO-

GEN LINES

We found the metallicity of 42 QSOs with strong N lines using six (eight for 19

QSOs) line-intensity ratios and the predictions from the LOC model. In our analysis,
we also include the Quasar, SDS S J 125414.27 + 0241175 which was found to have

a metallicity of Z ~ IOZQ, as mentioned in the last Chapter.

8.1.1 BEST METALLICITY ESTIMATE: MEAN Vs. MAXIMUM LIKE-

LIHOOD

The metallicities from different line-intensity ratios for all the QSOs are not exactly
the same. In order to have the best metallicity estimate from all the measurements
we calculated the mean metallicity Zmean, from all the line-intensity ratios as well as

the maximum likelihood estimate of metallicity, Z M L-

MEAN METALLICITY (Zmean)

This is simply the mean of the best estimate of metallicity from the individual line-
intensity ratios. To ﬁnd the error range on mean metallicity estimates, we used the
minimum and maximum estimates of individual line-intensity ratios. This, however,

puts huge error bars on the Zmean and we essentially loose the big picture. This

101

might result from the fact that our minimum and maximum values of metallicities
for individual line-intensity ratios are highly conservative estimates in nature. Using
the standard deviation of the mean (SDOM) also gives a fair representation Of the
error on Zmean values, so ﬁnally we decided to use the SDOM as our error estimate

in Zmean-

MAXIMUM LIKELIHOOD ESTIMATE OF Z (Z M L)

We also used the maximum likelihood method to estimate the best Z using all the
line-intensity ratios. To estimate the error in metallicity from this method we used

the lowest and the highest metallicity values from the individual line-intensity ratios.

COMPARING THE Two METHODS

The metallicity estimates from these two methods are compared in Figure A.4. These
two estimates point towards similar metallicities in QSOS. We ﬁnally decided to use
the mean estimates (Zmean) for our further analysis because of the simplicity Of the

method.

8.1.2 METALLICITY FROM INDIVIDUAL LINE-INTENSITY RATIOS

To see how well the metallicity from individual line-intensity ratios (Zind) compares
with the Zmean we plotted the Zind as a function of Zmean. Figure A.5 illustrates the
comparison graphically. As seen from it, the Zind for all line intensity ratios matches
quite well except those from NIV]/CIV and NV/ He II. Zind(N I V] /CI V) for most
quasars lies well below the Zmean line. This means that this line consistently indicates
lower metallicity when compared to Z from other line-intensity ratios. Likewise,
Zind(N V/ H 61 I ) indicates consistently higher Z when compared to Z from the other

line-intensity ratios.

102

8.1.3 BEST METALLICITY ESTIMATE (Zbest)

Since the metallicity from these two line-intensity ratios (NIV] /CIV and NV/ He II) is
on average very different from that indicated by other line-intensity ratios we decided
not to use them in our best metallicity estimate. The best metallicity estimate (Zbest)
is now simply the mean metallicity of all line-intensity ratios sans the two deviant
ones. Figure A.6 compares the mean metallicity values for all QSOS before and after
we neglect the two line-intensity ratios. We see that that on the average it does
not change the results drastically. However, after removing the two deviant line-
intensity ratios, the new best metallicity estimate, Zbestv agrees quite well with the
metallicities from individual line intensity ratios which have been used to arrive at
the mean value. The SDOM is used to give error in Zbest- Table B.6 lists the best
metallicity estimates, Zbesta and the corresponding error values. Figure A.7 plots the

distribution of Zbest among the N-loud sample, in form of a histogram.

IMPORTANT POINTS ABOUT THE MEASURED METALLICITY TREND

The metallicity values as determined from the individual line-intensity ratios agrees
well with one another except for Zz‘nd(N I V] / CI V) and Zind(N V/ H eI I ), for most
Of the QSOS in our N—Loud sample. Even though there were some cases for which
these metallicities from two these line-intensity ratios matched quite well with others,
e.g. SDSSJ1430 + 4811; based on the statistics we decided to neglect these two lines
to compute our best metallicity estimate. The main points we gathered from our
abundance measurements in N-loud QSO sample are:

l. The line-intensity ratios, except NV] / CIV and NV/ He II, give consistent Z
estimates and can be used as valid metallicity indicators. Table B.7 gives the slopes
and intercepts from all the relation between Zlnds for different line—intensity ratios
and Zmean for quantitative comparison.

2. The mean of metallicity from all these line-intensity ratios sans the two described

103

above, is used as the best metallicity estimate (Zbest)-

3. There are lone cases like SDS S J 1159 + 6638 where none of the line-intensity
ratios agree with one another in metallicity. There were a total of three such QSOS,
which is about 7% of total QSOS in the sample. This might be due to some complex
BELR structure or excitation processes peculiar to that Quasar which are not found
in QSOS in general.

4. On the whole the N IV] / CIV line-intensity ratio shows consistently lower metal-
licities. Here, the metallicities have been derived using the LOC model, which assumes
a very simple distribution of gas clouds. The fact that the Z from this line-intensity
ratio is, in general, not in agreement with Z from other line-intensity ratios suggests
that either the simple distribution of clouds is not a sufﬁciently accurate description
of the structure of the BELR, or that the Z from these line—intensity ratios are not
being correctly predicted by the photoionisation code CLOUDY [Ferland, 1996].

5. Similarly, the NV/ He II line-intensity ratio, which shows on the average higher
metallicities, suggests that the gas distribution might not be accurately described by
the LOC model. Also, there might be errors due to the fact that the NV line is heavily
blended with Lya emission line, however that might not be the reason because the
NV/CIV line-intensity ratio gives reasonable Z estimates.

6. Finally, the Quasars with strong N lines indeed have high Nitrogen abundance
and are super-solar in metallicity, with Z reaching up to a maximum of Z ~ 22Z® in
our N-loud sample. Figure A.7 also shows the distribution of measured Zbe st in the

N—loud sample in log Space.

8.1.4 DISTRIBUTION OF OTHER PHYSICAL PROPERTIES

The redshift distribution of the two sample sets is shown in Figure A.8. Figure A.9
shows the distribution of F WH M (CI V) for the intermediate sample as well as for the

ﬁnal sample, measurements of which are described in Section 2.2.4. The measurement

104

results for the continuum luminosity at A ~ 1450 A, L ,((1450), are shown in Figure
A.10, which shows the distribution of L ,\ for the intermediate sample as well as
the ﬁnal sample of N-Loud Quasars. The CIV Equivalent Width EW(C'I V) was
measured for the N-Loud sample and the Figure A.11 shows its distribution among
the N-loud QSOS sample only. The Mass of the supermassive blackhole (M 5 M B H)
was estimated using the virial theorem as described in the previous Chapter. The
distribution of M S M B H is illustrated in Figure A.12 for the intermediate as well as
for the full sample. Figure A.13 gives the distribution of M S M B H as a function of
redshift (z) for both sample sets. The M S M B H is Of the order of 107M® - 1014M9.

No evolution is seen in mass of the supermassive black hole with redshift.

8.1.5 RELATIONS INVOLVING THE SUPERMASSIVE BLACK HOLE

MASS

We wish to see if there exist any interesting correlations among various measured
physical properties of Quasars in general and the N-Loud Quasars in particular. Also,
we want to see how do the N-Loud Quasars stand in relation to the overall QSO
population in SDSS DR5. We, therefore, compare various measured properties of the
intermediate sample and the N-Loud sample.

From the data of M 3 M B H distribution in the two sample sets, we conclude that the
N—Loud sample has on the average lower masses M 5 M B H, than the general sample of
Quasars. We veriﬁed this using the Student’s t test. We found t ~ 5.3, corresponding
to a probability, P value S 0.0001 that the two samples are drawn from the same

distribution. See also Figure A.14 which shows the comparison graphically.

COMPARING MASS AND METALLICITY

We compare M 5 M B H with the metallicity results Of the ﬁnal sample M 3 M B H as

function of metallicities from individual line-intensity ratios (Zmd) as seen in Figure

105

A.15. A comparison of M S M B H was also made with the best metallicity estimate,
Zbest- This is illustrated in Figure A.16.

The M S M B H showed essentially no trend with most Zind’ as can be seen from
Figure A.15. However, it is interesting to note that the only line-intensity ratio (Zind)
which Showed some correlation with M S M B H was Zmd(N V/ H e] I ), one of the line-
intensity ratios we decided to neglect in our ﬁnal metallicity analysis due to their

deviant behaviour as compared to other line-intensity ratios.

COMPARING MASS AND LUMINOSITY

TO compare the relation between the mass of the supermassive black hole and con-
tinuum luminosity for the N-quiet sample and N-loud sample, M 5 M B H is plotted as

a function of L A in Figure A.17, for the two sample sets.

COMPARING MASS AND FWH M (CI V)

Figure A.18 shows the comparison Of M S M B H as a function Of F WH M (CI V) for
the two sample sets. There is a strong correlation, as is expected from the way in
which M 3 M B H is calculated (see Section 2.5). The lower M 3 M B H for the N-Loud
sample comes mainly from the narrower line widths found in those Objects. Given
the relative weakness of the N-lines, this might in principle be due to a selection
effect where narrower N—lines are easier to detect. However, we identiﬁed the N-
Loud objects using an automated procedure which our tests show are insensitive to
such effects for lines-widths at least up through (FWH M (CI V)) = 3.5, which are
essentially the broadest lines seen in either the Intermediate or the N-Loud Quasar

Sample.

106

COMPARING MASS AND EW(CIV)

Finally, we check for the relation between the mass of the supermassive black hole,
M 5 M B H and the continuum reprocessing efficiency of the BELR for CIV line, quan-
titatively estimated by the equivalent width, EW(CI V) for the N-Loud sample only.
This is shown ﬁguratively in Figure A.19. The relation between continuum luminos-
ity, L A and EW(C'I V) is shown in Figure A.20. For the N-Loud sample, for which
we measured EW(CI V), it seems to follow the often seen Baldwin effect, showing
an anti-correlation between M 5 M B H or L A and EW(CI V). The effect is, however,

better pronounced in L A and EW(CI V) relation.

107

 

CHAPTER 9:
DISCUSSION

 

9.1 METALLICITY AND THE BELR LOC MODEL

In our study of BELR metallicities of N-Loud Quasars in the SDSS DR5, using
different line-intensity ratios and the predictions of the LOC Model, we have found
that all line-intensity ratios except NIV] /CIV and NV / He II imply similar metallicity
values and therefore are valid abundance indicators. The deviant behaviour of the
two ratios which we have come to know from this study suggests that the LOC Model
needs to be reﬁned.

The line-intensity ratios will indicate different metallicities if the parameters in the
LOC model used by Hamann et. a1. (2002) do not correctly describe the QSO in
question. Now because the LOC model gives very different results for the two line-
intensity ratios for the majority Of the N-Loud sample, this implies that something
common is going on in all QSOS as these two different values in Zind is not restricted
to only a few QSOS. Previous papers on metallicity of QSOS have also reported
that Z is signiﬁcantly different as measured by NIV]/CIV [Dietrich et. al., 2003;
Shemmer and Netzer, 2003] and NV/ He II [Dietrich et. al., 2003] as compared to
other line—intensity ratios.

Nagao et. a1. (2006), studied 5344 QSOS from SDSS DR2, by forming composite
spectra in different redshift (z) and luminosity (L) bins. They found no evolution
Of metallicities with z (in range 2.0 S 2 S 4.5), however, some evolution was found

With L. They infer the metallicities for different composite spectra based on the

108

LOC model predictions for various line-intensity ratios and found the average quasar
metallicities in various bins to be 5Z9 in low L bins and reaching up to 10Z© in the
highest L bins. However the line-intensity ratios for Z estimation are not the same
as ours except for NV/CIV and NV/ He II.

Dietrich et. a1. (2003) studied chemical enrichment in 70 high 2(2 3.5) QSOS and
found an average metallicity Of 5.3Z® with highest metallicities reaching upto IOZQ.
They found some positive correlation of Z with L but no trend between Z and 2: was
seen.

Here we have studied the 42 QSOS with the strongest N111] and NIV] lines, sug-
gesting also the highest metallicities. We ﬁnd a Zmedian ~ 6.429, with a third of
them having Z 2 IOZQ and and a highest value of me8 ~ 2220- This is consistent
with our sample representing the upper end of the same Z distributions studied by

Nagao et. a1. (2006) and Dietrich et. al. (2003).

9.2 CHEMICAL EVOLUTION MODELS AND EXTREME

METAL RICH QUASARS

The metallicity of the N-rich sample is super-solar and can reach up to and above
2026. This can be used to constrain the chemical evolutionary history Of the BELR
gas and hence it is possible to rule out certain models of chemical evolution in quasars.

Quasars have been linked to massive galaxies based on several Observational results.
In particular, QSOS are now believed to be a stage in the evolutionary histories of
galaxies. Thus chemical evolution models of galaxies have been used in the study
of BELR abundances in order to understand the physical conditions therein and
its link to the host galaxy. Several models of chemical evolution of galaxies have
been developed over the years. These differ from one another mainly in the input

parameters like Initial Mass Function (IMF) and the gas infall timescales as well as

109

details of the various physical processes going on in the ISM of the galaxy.

An important set of such models were computed by Hamann and Ferland (1993)
(HF93). They are one-zone closed box models of chemical evolution in galaxies in
order to explain the line-intensity ratios observed in the QSOS. Figure 3 in their
paper shows the metallicity (Z) predicted by each of these models as a function of
time (t), Since the beginning of star formation in the galaxy. We reproduce that ﬁgure
here as the main part of our Figure A.21. HF93 start by developing a reference solar
neighborhood model, M1 in order to calibrate the nucleosynthesis contributions from
different types of stars. The three free parameters used in the calculation of chemical
evolution in a given model are, the shape of the IMF, the star formation rate and the
timescale for gas infall which essentially accounts for the mass buildup of the system.
The IMF is normalised and is a power law of the form 43 ~ M ‘5” . The timescale
for gas infall comes in the form of the stellar birthrate function, 2/J(t), which scales
linearly with gas density. It is of the form, w(t) ~ VG (t), where V is a constant input
parameter and is a measure of star formation rate (SFR) and G (t) is the gas density
at time t. The results are mainly sensitive to the timescale of gas infall and star
formation. Finally in all models the chemical evolution is halted when the remaining
gas is less than 3% of the total mass.

In the solar neighborhood model M1, in HF93, the IMF has a slope, 3 ~ 1.1 for
M S 1M@ and is 1: ~ 1.6 for higher mass stars. The timescale of gas infall is taken
to be 3 Gyr. This model has the lowest Z at all epochs and reaches only up to 129.
Model M2 uses a ﬂatter IMF with x ~ 1 for all masses and the timescale for gas
infall remains the same as in model MI. The ﬂatter IMF leads to more processing
by high mass stars leading to higher Z at all epochs compared to M1. However the
metallicities reached are not yet quite as high as those seen in QSOS. The model M3
uses an IMF Similar to that in M1 but with a shorter infall timescale of 0.05 Gyr.

This is also the infall timescale used in the models of massive galaxies. The star

110

formation rate, as a result shoots up to be 20 times higher than that Of M1. Also,
Z rises more quickly here than either in M1 or in M2. and then declines because
star formation is halted when gas fraction reaches 3%. The model M4 combines a
relatively ﬂat IMF (:1: ~ 1.1) with the shorter timescale of 0.05 Gyr. These parameters
are appropriate for the Giant Elliptical galaxies. This model provides a good ﬁt for
the observed metallicities in high 2 QSOS. The metallicity peaks at IOZQ, and then
falls off to about 6Z9, which is the median metallicity of the N-Loud QSOS studied
here. However, this still does not explain the highest metallicity QSOS found in our
study. The last two models Of HF93, put a cut-off limit on miminum mass of stars at
2.5MQ. Model M5 has a slightly higher star formation rate than M4, it has a ﬂatter
IMF, 2: ~ 1, and Shorter infall timescale of 0.05 Gyr, with the minimum mass cut-off
of 2.5M@. The lack of low mass stars leads to much less mass locked up in stars and
stellar remnants and therefore this model reaches even higher Z. Model M6 uses a
steeper IMF of :1: ~ 1.6, yet reaches higher Z because of the minimum mass cutoff
limit. These models do reach a high metallicity of 35 Zg, although they are rather
unphysical owing to absolute lack of low mass stars.

An additional set of chemical evolution models was developed by Friaca and Ter-
levich (1998). They differ from the HF93 models in some important details which
intend to more realistically describe a galactic environment. They are multi-zone mod-
els which follow the dynamical evolution of the gas by including the several episodes
of gas inﬂows and outﬂows and in particular the evolution of a galactic wind; instead
Of the simple one-zone models of HF93. Phrther they do not put a Sharp cut Off
limit of 3% for the remaining gas as the halting point of star formation in the galaxy.
Instead, they include inhibition Of star formation when the gas density is too low or
when the gas is expanding. Finally they adopt the Saltpeter’s IMF with :1: ~ 1.35. In
the example for which they describe results, the evolution in the chemical abundances

is very similar to HF93 model M3 (which uses a similar IMF), with a maximum value

111

of Z ~ [O/H] ~ 4 reached after 1 Gyr.

Romano et. a1. (2002) also discusses the chemical evolution in massive spheroids
at high 7., using one-zone ISM and taking into account the effects of cooling and stellar
feedback. They found a Similar 1 Gyr timescale for reaching the peak metallicity, but
that the peak metallicity reached (Z ~ 1.3ZQ) is much lower than that in the HF93
models. It is also possible that the metal enrichment occurs on more localised scales
closely associated with the AGN central engine [see e.g., Collin and Zahn, 1999].

Based on our ﬁndings we can rule out models where metallicities do not reach the
same as we have found in our study. The HF93 models Mland M2 can most certainly
be ruled out (see Figure A.21 which Shows the qualitative location of Z in the our
N-loud sample set on the chemical evolution models). This cannot be explained based
on the high redshifts of the Quasars where the age of the Universe is considerably
less (~ 1 Gyr) than the time needed for metallicities to reach as high as 20ZQ. The
observed metallicities in N-Loud QSOS can also be used to put constraints on the
IMF favourable to evolution of galaxies resulting in such high metallicities in such
short amount of time.

The only models that predict Z 2 529 are those Of HF 93. These are admittedly
very simpliﬁed models, but they do serve to bring out the interplay between the
shape of the IMF and the maximum metallicity that is reached. It is important to
keep in mind that our metallicity results do not depend on any Of these enrichment
models. They convert measured emission line-intensity ratios to metallicities using
just the physics contained in CLOUDY, and the LOC Model to then describe the
distribution of clouds. While the LOC Model obviously is not quite a rigorously
correct description of the average QSO, and the individual QSOS will be different
from the average, it still does produce the same Z for 6 Of the 8 line-intensity ratios
used here and therefore does seem to be fairely accurate. Our results therefore do

appear to Show that some QSOS do indeed reach high metallicities, with Z 2 10Z®

112

and probably in the neighborhood of 2023. The only way to escape this conclusion
would be to abandon our basic assumption that N is a secondary element, so that
the N/ O abundance ratio, which is what we actually measure, would no longer be
proportional to O / H, which is what we call metallicity, Z.

The model which best explains the high metallicity in quasars is the Giant Elliptical
model. However this model also reaches only up to Z ~ 1026 and then ﬂattens out.
Models M5 and M6 Of HF93 do reach higher metallicities. They put a cut-Off limit on
minimum mass stars that can be formed, that may not be very physical, but they may
still be indicating that a very top-heavy IMF is needed. An alternative explanation
of the extreme metallicity QSOS in the context of Giant Elliptical model is the infall
of gas from the outer regions of the Quasar host galaxy right after it reached its peak,
causing a further burst of star formation not included in the enrichment models.
Mergers of galaxies might also result in enhanced metallicities.

Our sample of 42 N-Loud QSOS has presumably picked off the highest metallicity
end of a broader range in Z among the thousands Of SDSS QSOS. One possible
way to interpret these results is in the context of the proposal by Silk and. Rees
(1998) that QSOS gestate out of sight, enshrouded by dust in the centers of galaxies,
and then only become visible at the very end Of the process of building the massive
black hole, when the luminosity becomes high enough to blow away or evaporate
the remaining dust. This carries with it the implication that in most QSOS we are
seeing the ﬁnal end-state reached in the chemical enrichment process. If so, then the
different metallicities measured here would indicate that different host galaxies shut
Off metal enrichment at different metallicities. One explanation for such differences,
suggested by the HF93 models, would be that there are differences in the IMFS in the
host galaxies in a situation where chemical enrichment is stopped because essentially
all of the gas has been turned into stars as is inherent in the HF93 models.

However, an alternate possibility ﬁtting within the same general picture is that

113

the enrichment is in fact halted by feedback from the QSO, and that L ~ L ED D
is reached at different points in the enrichment process for different QSOS. A third
possibility is that the QSOS are not as enshrouded as was suggested by Silk and
Rees (1998), and that in fact we are seeing similar objects, all of which will reach,
Z ~ 2029, at different moments in their chemical evolution. This could be tested by
converting the predicted Z (t) curves for each model into histograms of the expected
number of QSOS as a function of Z, and seeing if any Of the models come at all close
to ﬁtting the observations. However, that would require a very careful combining
of the distribution of metallicities measured here for our N-Loud sample with the
distribution of metallicities measured for lower-metallicity objects by using just the
NV/CIV ratio, in order to get the widest possible range in Z. Such a test is beyond

the scope of this present work.

114

 

CHAPTER 10:
SUMMARY AND CONCLUSIONS

 

A detailed abundance analysis was done on QSOS with strong nitrogen (N) lines (N-
Loud QSOS) drawn from the SDSS DR5 Quasar Catalogue. A total of 42 such QSOS
were found in the catalogue in the desired redshift range Of 2.29 S z S 3.6, which
ensured the presence of required emission lines (NV A1240, NIV] A1486, NIII] A1750,
CIV A1549, He II A1640, OIII] A1666 and C111] A1909) used in our abundance analysis
method. Of these 42, 19 QSOS also had the OVI A1034 emission line present in the
Observed range and hence that emission line was also used for abundance analysis. We
then carefully deblended the blended regions to ﬁnd the line-intensity ratios and the
corresponding metallicity Z estimates using the predictions from the photoionisation
code CLOUDY. In addition we also measured the F WH M (CI V) and the continuum
luminosity, L ,((1450A), to ﬁnd the mass of the supermassive black hole, M S M B H for
the intermediate sample which consisted Of all QSOS in the desired redshift range as
given above, barring the ones where the CIV line was heavily absorbed or the data
were missing. The Equivalent Width, E W of CIV line was also measured for N—Loud
QSOS. In all above measurements, we used various IRAF and FORTRAN routines.
In order to get the best estimate of metallicity, we averaged the metallicity (Zmean)
from individual line-intensity ratios. However we found that the metallicity from
line-intensity ratio NIV]/CIV shows a consistently lower Z value compared to the
Zmean. Also the line-intensity ratio NV/ He II consistently shows higher values when

compared to Zmean. The fact that Z's from these two line-intensity ratios do not

115

agree with those from the other line-intensity ratios implies that either the gas density
distribution as given in the LOC model is not accurate or the Z from these line-
intensity ratios is not being correctly predicted by CLOUDY. In both cases LOC
model needs to be improved if these two line-intensity ratios are also to be used in
the ﬁnal Z estimate, which is beyond the scope of present work.

We, therefore, decided to drop these two line-intensity ratios from our ﬁnal best
metallicity estimate, Zbest- The error in Zbest is taken to be its SDOM. We found that
these N-LOud QSOS have super—solar metallicities with all Of them having Zbe st Z Z@,
and about a third of these with Zbest 2 102G. The mean of this sample was ~ 8Z9.

We found no evolution in M 5 M B H with z. Also no trend was seen in the relation
of M SM B H and Zbest- While studying the relation between M3 M B H and Z from
individual line-intensity ratios we found no correlation between the two variables as
well. However a weak trend was seen with the two line-intensity ratios which we had
decided to neglect from our best metallicity estimate, (NIV]/CIV and NV/ He II).
The EW(C'IV) showed a weak correlation with MSMBH and L ,(1450A).

To see the implications of the very high metallicities found here, we compared
our results to the predictions of published galactic chemical evolution models. The
Hamann and Ferland (1993) models Show that ﬂat IMFS and rapid gas infall are
needed to reach Z ~ 1029, the value reached by 1 / 3rd of our sample. The highest
metallicity that we found is Z ~ 22ZQ. The HF93 models require an exceedingly top-
heavy IMF to reach such a high metallicity. We suggest the alternative that a recent
starburst due to a merger might have pushed up the metallicity in a host galaxy that
had already reached Z ~ 102G.

116

APPENDICES

117

 

APPENDIX A:
FIGURES FOR THE QUASAR PROJECT

 

The following pages of Appendix A contain the ﬁgures for the Quasar Project of this
thesis. They appear in the order in which they have been mentioned in the text in

the earlier Chapters.

118

 

 

 

 

 

 

 

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2000 4000 6000 8000
Rest Wavelength, A (A)

Figure A.1z Characteristic Quasar Spectrum.

This image is a composite spectrum from SDSS Data Release 1.
Power-law ﬁts to the estimated continuum ﬂux are shown. The
resolution Of the input spectra is R = NA)» ~1800, which gives a
wavelength resolution Of about 1 A in the rest frame (V anden
Berk et. al., 2001).

119

Flux (10'17 ergs/S)

 

 

 

 

 

 

 

 

 

l l l l l l
2 — _
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-3 _ _
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1250 1500 1750 2000 2250 2500
Wavelength (A)

Figure A.2: Quasar Spectrum: An Example

(a) SDSS] l65806.76+611858.9, A Quasar with poor Signal-
tO-Noise ratio.

120

 

 

 

 

 

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Figure A.2 cont’d: Quasar Spectrum: An Example
(b) SDSS] 102753.89+661219.6, A Quasar with missing lines of
interest.

121

 

 

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Figure A2 cont’zl: Quasar Spectrum: An Example
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absorption.

122

 

 

 

 

 

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Figure A.2 cont’d: Quasar Spectrum: An Example

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line.

123

 

 

 

 

 

 

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Figure A.2 cont’al: Quasar Spectrum: An Example

(e) SDSS J164148.19+223225.2, A Quasar with strong Nitrogen
lines.

124

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136

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function of mean metallicity.

I37

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Figure A.5 cont’d: Metallicity from individual line-intensity ratios as
a function of mean metallicity. Note that in the last two graphs,
which use the OVI line in the denominator; we have used the
mean metallicity based on all eight line-intensity ratios.

138

 

0.6 - " -

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0.4 - -

0.2 - _

 

 

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0 0.2 0.4 0.6 0.8 1 1.2 1.4
Log(zmean/Zsun)

 

Figure A6: Comparing Best Metallicity Estimate before
(Zmean) and after (ZbCSL) removing the two deviant line-
intensity ratios (N IV] / CIV and NV/CIV).

139

 

 

 

 

 

 

 

Number of QSOS

 

 

 

 

 

 

 

0 5 10 15 20 85
Zbest(z®)

Figure A.7: Distribution of Best Metallicity Estimate (21m) in the N-Loud
Quasar sample.

140

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Number of QSOS

 

 

 

 

0 0.2 0.4 0.6 0.8 1 1.2 1.4
Log (Zbest/ZGD)

Figure A.7 cont’d: Distribution of Best Metallicity Esu'mate (Zbest) in the
N-Loud Quasar sample in Log space (Log Zbest)’

141

2500 .

 

2000

 

 

1500‘

 

1000‘

Number of QSOS

500

 

 

 

 

 

 

Number of QSOS

 

 

 

2 .25 5 4

3 3.
Redshift (2)

Figure A.8: Redshift (2) Distribution of the Intermediate Quasar Sample
(top) and in the N-Loud Quasar Sample (bottom).

142

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure A.9: Distribution of FWHM (CIV) in the Intermediate Quasar
Sample (top) and N-Loud Quasar Sample (bottom).

143

2500

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Quasar Sample (top) and in the N-Loud Quasar Sample (bottom).

144

Number of QSOS

 

14 I I

 

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O 20 4O 6O 80 100
EW(CIV) (A)

Figure A.11: Distribution of the Equivalent Width (EW) of the CIV
Emission Line in the N-Loud Quasar Sample.

145

 

2000 , T

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Number of QSOS

 

 

 

 

 

 

 

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14

Figure A.12: Distribution of Supermassive Black Hole Mass (MSMBH) for
Intermediate Quasar Sample (top) and N-Loud Quasar Sample (bottom).

146

 

 

 

 

 

 

 

 

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the bottom figure shows the redshift distribution of
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for the two data sets. In the plot A refers to the N-Loud
Sample set and B refers to the Intermediate Sample set.
The dot indicates the mean MSMBH and the error bars
represent the standard deviation

148

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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ratios as a function of Supermassive Black Hole Mass

(Msmbh) '

149

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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2 ° 0 §’ 0 ' o
a - g '
0’ N
3 0.5 " ‘ E 0.5 " . 4

3
o 3 2'23 313:: 1‘2: 221': 0 2 ;l:: CE:: 1.23 23"]:
5 7 8 9 1O 5 7 8 9 10
L09(Msmbh/Msun) LOg(Msmbh/Msun)

Figure A.15 cont’ri: Metallicity from individual line-
intensity ratios as a function of Supermassive Black Hole

Mass (Msmbh.) '

150

 

 

 

 

I I I I

1.4 _ a

g C
O
1.2 ’ -
F . . u .
1 _ C . . . . _
Ag 0 o
(n O
u 3' _
E; 03 .0 : 0. g . CO .
'3‘, o
8’ 06 - . o . -
_l 0 g
0 o
0.4 P . g "
O
0.2 - _
0 I I m I
5 6 7 8 9 10
L09(Msmbh/Msun)

Figure A.16: Best Metallicity Estimate (Zbest) as a function
of Supermassive Black Hole Mass (Msmbh).

151

 

 

 

 

 

 

 

14 T I ﬁ I I I I
A 12 — ‘53:. .7:- -
c . .. .
23 ° i
\f; 10 - i -
{,E, .
E 8 - I: ..
5 ’-.
O .
_J 6 _ q
4 I I I I I I I
14 I T I I I I I
A 12 " -‘
C
23
\§ 10 - . ,. -
(D . f o
g 8 - .... 0° ’ .0 _i
U) .0 g o ' .
O '0 : '
—| 6 r o 0.. . '1
4 I I I I I I I

43.5 44 44.5 45 45.5 46 46.5 47 47.5
L1450 ergs/s

Figure A.17: Supermassive Black Hole Mass (Msmbh)
as a function of Continuum Luminosity (Lx(1450 A».
The top ﬁgure shows the relation for the
intermediate sample whereas the bottom figure
shows for the N-Loud sample.

152

 

LOg(Msmbh/Msun)

 

 

 

L0g(Msmbh/Msun)
‘0'

 

 

 

4 l l 1 l
2.5 3 3.5 4 4.5 5

Log(FWHM(CIV) km/s)

Figure A.18: Supermassive Black Hole Mass (Msmbh) as a
function of FWHM (CIV). The top figure shows the relation for
the intermediate sample whereas the bottom ﬁgure shows for the
N loud sample.

153

 

 

 

 

12 I I I I
11 - 1
1O - ..
o
1% 9 ~ . . .0 ‘
o
g: . . .
g 8 ' . Q 0 O _
E ' 'g. 0
as ' - .
o 7 - 9 ' ' _
_I . . .
9 o
0 o
6 h o o ‘
5 - ' -
4 J I l I
0 20 40 60 80 100

Equivalent Width (CIV) (Angstroms)

Figure A.19: Supermassive Black Hole Mass (Msmbh) as a function
of CIV Equivalent width.

154

46.5

 

 

 

 

l l I l
o
46 - . -
E o o .
m o o
9 no
a) o .
g 45.5 .. g o .0 o g 0 _
=3 .. .
§’ ° 0:. o
' o
o
45 h .‘ . . . . u
o
o
o
44.5 I I l l
O 20 40 60 80 100

Equivalent Width (CIV) (Angstroms)

Figure A.20: Continuum Luminosity (110450 A) plotted as a
function of CIV Equivalent width.

155

 

 

 

.0 510

No. of QSOS
: per 0.2 dex bin

Metallicity Z / Z®

 

 

 

Figure A.21: Models of Chemical Evolution in Quasars (HF93)
and the metallicity distribution in the N -Loud Quasar sample.
The thick dotted line just above Model M4 refers to the Giant
Elliptical model of Hamann and Ferland, (1999).

156

 

APPENDIX B:
TABLES FOR THE QUASAR PROJECT

 

The following pages of the Appendix B contain the tables for the Quasar Project of
this thesis. They appear in the order in which they have been mentioned in the text

in the earlier Chapters.

157

Table B.1

Fe strengths for the N-Loud Quasars. Note that in all our
tables we also include measurement results from N-Loud
Quasar SDSS J125414.27+024117.5.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

QSO Name Fe strength

SDSS JOO3815.92+140304.5 0.57
SDSS J025505.93+001446.7 -

SDSS J074520.21+415725.4 0.40
SDSS J075326.12+403038.6 0.20
SDSS J080025.10+441723.1 0.20
SDSS]084715.16+383110.0 0.20
SDSS 1085220.46+473458.4 0.00
SDSS J085522.87+375425.9 0.30
SDSS J093355.72+084043.0 0.40
SDSS J095027.35+123335.9 0.66
SDSS J095334.95+003724.3 0.14
SDSSJ104229.19+381111.2 0.40
SDSSJ104713.16+353115.6 0.00
SDSS J104713.39+O95711.3 0.14
SDSS J105922.31+663806.2 —

SDSSJ110013.68+030529.8 0.53
SDSS J112127.96+123816.1 0.76
SDSS]115631.40+133714.9 0.20
SDSSJ115911.52+313427.3 1.80
SDSSJIZI913.19+043809.1 0.20

 

 

158

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

QSO Name Fe strength

SDSS J122205.12+034310.3 0.33
SDSS J123450.00+375530.3 0.40
SDSS J124158.18+123059.3 -

SDSSJ125414.27+024117.5 0.07
SDSS J130423.24+340438.1 0.04
SDSS J132827.07+581836.9 0.13
SDSS J133317.41+641718.0 0.54
SDSS J133923.77+632858.4 0.20
SDSS J135604.28+471058.7 0.10
SDSSJ140432.99+072846.9 0.48
SDSS J142915.19+343820.3 0.30
SDSSJ143048.84+481102.7 0.33
SDSS J144241.74+100533.9 0.60
SDSS J144805.84+440806.4 -

SDSS J145615.82+433954.3 0.20
SDSS J154534.59+511228.9 —

SDSS J155007.07+023607.6 0.29
SDSSll 64148.19+223225.2 0.39
SDSS J165023.36+415142.0 0.20
SDSSll70704.87+644303.2 .—

SDSS J171341.05+325045.3 0.30
SDSS]233101.64-010604.1 -

sossiz3393000+0030173 0.69
SDSS J003815.92+140304.5 0.57

 

 

Table B.1 confd.

159

 

Table B.2

Template proﬁles used in deblending various emission lines.
The templates were ﬁrst extracted from the spectrum and
then used for deblending. The different templates used were:
CIV, He II, N IV] and OIII].

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Name Template
Lya N V Si 11 N IV]
21215.67 1.1240 2.1263 11486.50

SDSSJOO38+1403 C IV C IV C IV N IV
SDSS J0255+0014 C IV C IV C IV N IV
SDSSJ0745+4157 C IV He II C IV N IV
SDSS J0753+4030 C IV C IV C IV N IV
SDSS JO800+4417 C IV C IV C IV N IV
SDSS J0847+3831 C IV He II N IV N IV
SDSSJO852+4734 C IV C IV C IV N IV
SDSS J0855+3754 C IV C IV C IV N IV
SDSS J0933+0840 C IV C IV C IV N IV
SDSS J0950+1233 C IV C IV C IV N IV
SDSS J0953+0037 C III C III C III N IV
SDSSJIO42+3811 C IV C IV C IV N IV
SDSSj1047+0957 C IV C IV C IV N IV
SDSSJIO47+3531 C IV C IV C IV N IV
SDSSJ1059+6638 C IV He II C IV N IV
SDSSJIIOO+O305 C IV C IV C IV N IV
SDSSJ1121+1238 C IV C IV C IV N IV
SDSSJ1156+1337 C IV C IV C IV N IV
SDSSJ1159+3134 C IV C IV C IV N IV
SDSSM19+O438 C IV C IV C IV N IV
SDSSJ1222+O343 C IV C IV C IV N IV

 

 

 

 

 

160

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Name Template
Lya N V Si II N IV]
11215.67 1.1240 1.1263 21486.50

SDSSJ1234+3755 C IV C IV C IV N IV
SDSSJ1241+123O C IV C IV C IV N IV
SDSS}1254+0241 C IV C IV C IV N IV
SDSSj1304+3404 C IV He II C IV N IV
SDSSJ1328+5818 C IV C IV C IV N IV
SDSSJ1333+6417 C IV C IV C IV N IV
SDSSJI339+6328 C IV C IV C IV N IV
SDSSJI356+4710 C IV C IV C IV N IV
SDSSJI404+O728 C IV N IV C IV N IV
SDSSJ1429+3438 C IV He II C IV N IV
SDSSJ1430+4811 C IV C IV C IV N IV
SDSSJ1442+1005 He II C IV C IV N IV
SDSSJI448+4408 C IV He II C IV N IV
SDSSll456+4339 C IV C IV C IV N IV
SDSSJIS45+5112 C IV C IV C IV N IV
SDSS]1550+0236 C IV C IV C IV N IV
SDSSJ1641+2232 C IV He II C IV N IV
SDSSJI650+4151 C III He II C III N IV
SDSSJI707+6443 C IV C IV C IV N IV
SDSSJ1713+3250 C IV C IV C IV N IV
SDSSJZ331-0106 C IV C IV C IV N IV
SDSSJ2339+OO3O C IV C IV C IV N IV

 

 

 

 

 

Table B.2 cont’d.

161

 

Table B.2 cont’d.

Template profiles used in deblending various emission lines.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Name Template

C IV He II 0 III] N III]

1.1549 11640.72 1.1665 1.1750
SDSS J0038+1403 C IV He II He II N III
SDSS J0255+0014 C IV He II N IV N III
SDSSJ0745+4157 C IV He II N IV C IV
SDSS J0753+4030 C IV He II 0 III C IV + He II
SDSS J0800+4417 C IV He II N IV N 111
SDSS J0847+3831 C IV He II N IV N IV + He II
SDSS JO852+4734 C IV He II N IV N III
SDSS J0855+3754 C IV He II 0 I C IV
SDSS JO933+0840 C IV He II 0 I N 111
SDSS J0950+1233 C IV He II N IV N IV
SDSS JO953+0037 C III He II N IV C III
SDSSJ1042+3811 C IV He II N IV C IV
SDSSJ1047+O957 C IV He II N IV N 111
SDSSJIO47+3531 C IV He II N IV N IV
SDSSJIOS9+6638 C IV He II C IV N III
SDSSJIIOO+O305 C IV He II N IV He II
SDSSJ1121+1238 C IV He II N IV N III
SDSSJ1156+1337 C IV He II N IV C IV + He II
SDSSJ1159+3134 C IV He II He II He II
SDSS]1219+0438 C IV He II N IV N IV
SDSSJ1222+0343 C IV He II 0 I O I
SDSS]1234+3755 C IV He II C IV 0 I
SDSSJ1241+1230 C IV He II He II 0 I

 

 

 

 

 

162

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Name Template

C IV He II 0 III] N 111]

Ms49 11640.72 M665 M750
SDSS J1254+0241 C IV He II N IV He II
SDSSJ1304+3404 C IV He II N IV N III
SDSSJ1328+5818 c IV He II C IV c IV
SDSSJ1333+6417 C IV He II N IV N IV
SDSS J1339+6328 C IV He II N IV N IV
SDSS J1356+4710 C IV He II He II C IV
SDSS J1404+0728 c IV He II N IV C IV , 111" ’ He
SDSSJ1429+3438 C IV He II c IV c IV
SDSSJI430+4811 c IV He II c IV N IV
SDSS J1442+1005 C IV He II C IV N IV
SDSS J1448+4408 C IV He II C IV He II
soss J1456+4339 C IV He II N IV c IV
SDSS J1545+5112 C IV He II N IV C IV
SDSS J1550+0236 C IV He II N IV N IV
SDSS J1641+2232 c IV He II C IV C IV
SDSS J1650+4151 C III He II c III C III
SDSS J1707+6443 C IV He II He II He II
SDSSJ1713+3250 c IV He II c IV N IV
SDSS 12331—0106 C IV He II C IV N IV
SDSS 12339+0030 C IV He II C IV C IV

Table B.2 cont’a’.

163

 

Table B.2 cont’d.

Template proﬁles used in deblending various emission lines.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Name Template
Fe blend
Al III Si III] C 111]
1.1857 11892.03 11908.73 1.1895,1915,1926

soss JOO38+1403 - c IV C IV i C IV
SDSS J0255+0014 N IV He II C IV C IV
SDSSJO745+4157 N IV He II C IV C IV
SDSS J0753+4030 C IV C IV C IV C IV
SDSS J0800+4417 C IV C IV C IV C IV
SDSSJO847+3831 N IV N IV C IV N IV
SDSS J0852+4734 C IV C IV C IV C IV
SDSSJO855+3754 C IV C IV C IV C IV
SDSS J0933+0840 C IV C IV C IV C IV
SDSS J0950+1233 C IV C IV C IV C IV
SDSS jO953+OO37 N IV C III C III C III
SDSSJ1042+3811 N IV He II C IV C IV
SDSSJ1047+O957 N IV N IV N IV C IV
SDSSJ1047+3531 N IV N IV C IV -

SDSSJIOS9+6638 N IV He II C IV C IV
SDS§11100+0305 He II N IV C IV C IV
SDSSJ1121+1238 He II N IV N IV N IV
SDSSJ1156+1337 C IV N IV C IV -

SDSS]1159+3134 N IV C III C III N IV
SDSSJ1219+0438 C IV C IV C IV C IV
SDSS]1222+O343 C IV C IV C IV C IV
SDSSJ1234+3755 C IV C IV C IV C IV

 

 

 

 

 

164

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Name Template
Fe blend
Al III Si 111] C III]
1.1857 11892.03 11908.73 1.1895,1915,1926

SDSS}1241+1230 C IV OI C IV C IV
SDSSJ1254+0241 C IV N IV C IV C IV
SDSSJ1304+3404 N IV N IV C IV C IV
SDSSJ1328+5818 C IV N IV C IV C IV
SDSS]1333+6417 He II He II C IV C IV
SDSSJ1339+6328 N IV N IV C IV C IV + He II
SDSSJI356+4710 N IV C IV C IV C IV
SDSSJ1404+0728 N IV N IV C IV C IV
SDSSJI429+3438 O I C IV C IV C IV
SDSSJ1430+4811 C IV He II He II -
SDSSJ1442+1005 N IV C IV C IV C IV
SDSSJI448+4408 N IV C IV C IV C IV
SDSSJI456+4339 C IV N IV C IV C IV
SDSS]1545+5112 C IV He II C IV C IV
SDSSJ1550+0236 C IV N IV C IV C IV
SDSSJI641+2232 C IV C IV C IV C IV
SDSSJI650+4151 C III C III C III C III
SDSSJ1707+6443 C IV He II C IV C IV
SDSSJI713+3250 C IV He II 0 III He II
SDSS J2331-0106 C IV N IV C IV C IV
SDSS J2339+OO30 He II C IV C IV C IV

 

 

 

 

 

Table B.2 cont’d.

165

 

Table B.3

Emission line-ﬂux strengths for NV, NIV] and
NIH] in the units of CIV line-ﬂux.

Name NV NIV] NIH]
SDSS Best min max Best min max Best min max
J0038+1403 0.95 0.81 1.04 0.06 0.03 0.09 0.15 0.10 0.20

 

J0255+0014 0.57 0.47 0.66 0.20 0.16 0.23 0.25 0.24 0.27

 

0745+4157 0.75 0.67 0.86 0.08 0.07 0.15 0.15 0.13 0.20

 

0753+4030 0.24 0.17 0.45 0.02 0.01 0.03 0.02 0.01 0.02

 

J0800+4417 1.30 1.51 1.51 0.09 0.09 0.14 0.16 0.17 0.17

 

0847+3831 1.46 1.23 1.79 0.13 0.11 0.16 0.32 0.27 0.40

 

J0852+4734 1.52 1.55 1.54 0.22 0.23 0.34 0.71 0.78 0.84

 

_]0855+3754 0.79 0.61 1.00 0.02 0.01 0.03 0.06 0.05 0.09

 

J0933+0840 1.71 1.12 1.97 0.03 0.02 0.03 0.18 0.15 0.22

 

j0950+1233 1.25 1.20 1.29 0.23 0.23 0.27 0.31 0.29 0.43

 

0953+0037 0.28 0.24 0.27 0.05 0.03 0.07 0.07 0.07 0.08

 

J1042+3811 0.95 0.67 1.24 0.23 0.23 0.24 0.30 0.31 0.32

 

J1047+0957 0.44 0.35 0.53 0.03 0.03 0.05 0.03 0.03 0.03

 

J1047+3531 1.61 1.34 1.56 0.11 0.10 0.12 0.47 0.40 0.46

 

J1059+6638 0.55 0.52 0.60 0.16 0.13 0.16 0.09 0.08 0.09

 

1100+0305 0.56 0.51 0.82 0.12 0.11 0.14 0.28 0.21 0.33

 

11121+1238 0.54 0.40 0.71 0.05 0.04 0.06 0.17 0.17 0.20

 

J1156+1337 0.63 0.43 0.76 0.06 0.06 0.06 0.22 0.19 0.23

 

11159+3134 2.40 2.23 2.54 0.04 0.04 0.04 0.18 0.17 0.19

 

I1219+0438 1.48 0.98 1.79 0.03 0.03 0.03 0.03 0.02 0.05

 

J1222+0343 1.04 0.98 1.18 0.08 0.07 0.10 0.18 0.17 0.21

 

1234+3755 1.05 0.89 1.22 0.08 0.08 0.15 0.24 0.22 0.27

 

J1241+1230 1.75 1.70 1.93 0.10 0.09 0.16 0.38 0.32 0.45

 

11254+0241 1.50 1.44 1.44 0.23 0.23 0.25 0.40 0.37 0.39

 

jl304+3404 1.57 1.19 1.71 0.16 0.17 0.17 0.48 0.45 0.47

 

D328+5818 0.57 0.43 0.68 0.04 0.03 0.04 0.05 0.05 0.05

 

J1333+6417 1.25 1.04 1.63 0.06 0.05 0.07 0.28 0.25 0.30

 

J1339+6328 0.37 0.30 0.45 0.07 0.07 0.08 0.04 0.04 0.05

 

 

 

 

 

 

 

 

 

 

 

J1356+4710 1.52 0.94 1.90 0.05 0.03 0.06 0.16 0.10 0.20

 

 

166

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Name NV NIV] NIH]

SDSS Best min max Best min max Best min max
J1404+0728 1.68 1.23 2.05 0.18 0.19 0.21 0.28 0.29 0.28
JI429+3438 0.45 0.35 0.86 0.03 0.02 0.04 0.05 0.04 0.07
Jl430+4811 1.19 1.11 1.42 0.32 0.28 0.37 0.56 0.50 0.72
114424-1005 0.66 0.48 0.83 0.05 0.04 0.07 0.12 0.09 0.12
JI448+4408 1.85 1.76 2.40 0.37 0.34 0.41 0.32 0.26 0.41
J1456+4339 0.47 0.45 0.43 0.10 0.09 0.11 0.10 0.09 0.11
J1545+5112 1.16 1.15 1.15 0.08 0.07 0.09 0.13 0.13 0.14
J1550+0236 0.72 0.73 0.78 0.38 0.40 0.45 0.39 0.44 0.40
J1641 +2232 1.95 1.63 2.28 0.35 0.34 0.38 0.53 0.51 0.68
116504-4151 0.57 0.46 0.80 0.06 0.05 0.12 0.24 0.21 0.26
Jl707+6443 0.69 0.52 0.79 0.09 0.06 0.09 0.06 0.05 0.07
JI713+3250 0.90 0.64 1.16 0.08 0.06 0.10 0.14 0.13 0.14
J2331-0106 0.48 0.37 0.68 0.05 0.05 0.05 0.10 0.09 0.12
J2339+0030 1.25 1.25 1.34 0.05 0.05 0.06 0.22 0.21 0.23

Table B.3 cont’a’.

167

 

Table B.3 cont’d.

Emission line-ﬂux strengths for CIII], He II and
OIII] in the units of CIV line-ﬂux.

Name CHI] HeII OIII]
SDSS Best min max Best min max Best min max
l0038+1403 0.39 0.34 0.42 0.12 0.11 0.13 0.12 0.09 0.15

 

j0255+0014 0.37 0.32 0.43 0.19 0.18 0.20 0.15 0.12 0.16

 

J0745+4157 0.21 0.16 0.25 0.21 0.20 0.23 0.11 0.09 0.11

 

j0753+4030 0.13 0.08 0.19 0.08 0.07 0.08 0.05 0.05 0.06

 

J0800+4417 0.25 0.30 0.34 0.12 0.15 0.13 0.11 0.14 0.12

 

J0847+3831 0.29 0.27 0.35 0.15 0.14 0.15 0.10 0.10 0.15

 

0852+4734 0.44 0.35 0.53 0.30 0.32 0.35 0.33 0.26 0.38

 

J0855+3754 0.21 0.15 0.25 0.11 0.09 0.12 0.07 0.06 0.08

 

JO933+0840 0.33 0.23 0.42 0.19 0.17 0.20 0.12 0.10 0.14

 

10950+1233 0.24 0.15 0.32 0.24 0.25 0.24 0.12 0.12 0.14

 

J0953+0037 0.24 0.19 0.27 0.10 0.08 0.12 0.08 0.06 0.10

 

le42+3811 0.19 0.14 0.23 0.17 0.18 0.18 0.10 0.11 0.13

 

J1047+0957 0.17 0.13 0.22 0.09 0.06 0.10 0.07 0.06 0.07

 

J1047+3531 0.22 0.18 0.24 0.05 0.05 0.05 0.08 0.06 0.09

 

J1059+6638 0.22 0.18 0.27 0.14 0.14 0.14 0.09 0.09 0.10

 

11100+0305 0.19 0.12 0.42 0.28 0.26 0.27 0.22 0.17 0.26

 

J1121+1238 0.20 0.14 0.27 0.07 0.06 0.09 0.06 0.05 0.07

 

J1156+1337 0.21 0.17 0.24 0.15 0.15 0.15 0.15 0.14 0.15

 

J1159+3134 0.53 0.46 0.59 0.06 0.06 0.05 0.10 0.09 0.11

 

J1219+0438 0.35 0.27 0.43 0.06 0.05 0.07 0.04 0.04 0.05

 

11222+0343 0.51 0.32 0.63 0.11 0.08 0.13 0.08 0.07 0.11

 

11234+3755 0.64 0.45 0.87 0.08 0.07 0.09 0.17 0.13 0.21

 

11241+1230 0.41 0.35 0.48 0.14 0.14 0.17 0.15 0.15 0.18

 

j1254+0241 0.42 0.42 0.42 0.23 0.16 0.21 0.16 0.13 0.15

 

JI304+3404 0.29 0.28 0.27 0.26 0.25 0.24 0.12 0.12 0.12

 

JI328+5818 0.27 0.23 0.32 0.12 0.12 0.13 0.12 0.11 0.12

 

11333+6417 0.50 0.45 0.52 0.14 0.14 0.14 0.11 0.09 0.13

 

 

 

 

 

 

 

 

 

 

 

J1339+6328 0.12 0.07 0.19 0.08 0.08 0.09 0.08 0.07 0.09

 

 

168

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Name CIII] HeII OIII]

SDSS Best min max Best min max Best min max
J1356+4710 0.48 0.35 0.73 0.11 0.10 0.12 0.06 0.03 0.09
J1404+0728 0.27 0.16 0.33 0.17 0.16 0.17 0.08 0.08 0.09

1429+3438 0.23 0.17 0.30 0.10 0.09 0.12 0.07 0.05 0.08
J1430+4811 0.41 0.30 0.46 0.26 0.26 0.34 0.28 0.25 0.32
ll442+1005 0.28 0.25 0.34 0.07 0.05 0.09 0.09 0.09 0.13
J1448+4408 0.36 0.31 0.41 0.21 0.20 0.22 0.17 0.18 0.18
J1456+4339 0.25 0.17 0.28 0.12 0.12 0.12 0.07 0.05 0.09
J1545+5112 0.35 0.30 0.46 0.19 0.21 0.18 0.17 0.19 0.17
J1550+0236 0.29 0.23 0.35 0.21 0.21 0.26 0.22 0.25 0.22
J1641 +2232 0.53 0.38 0.61 0.31 0.28 0.32 0.26 0.25 0.26

1650+4151 0.52 0.38 0.50 0.11 0.11 0.13 0.09 0.08 0.12
J1707+6443 0.16 0.12 0.21 0.09 0.07 0.11 0.08 0.06 0.08
_]1713+3250 0.21 0.11 0.31 0.19 0.18 0.20 0.10 0.09 0.12
J2331-0106 0.25 0.19 0.23 0.10 0.10 0.10 0.09 0.08 0.08
J2339+0030 0.30 0.22 0.44 0.13 0.12 0.15 0.09 0.08 0.11

Table B.3 ront’d.

169

 

Table B.3 cont’d.

Emission line-ﬂux strengths for OVI in the units
of CIV line-ﬂux.

Name OVI

J0038+1403 - — -
J0255+0014 — - -
JO745+4157 0.654 0.587 0.722
JO753+4030 0.248 0.231 0.290
J0800+4417 - - -
J0847+3831 1.715 1.554 1.825
JO852+4734 - - -
JO855+3754 - - -
J0933+084O — - —
10950+1233 0.937 0.879 0.992
JO953+0037 - — —
JIO42+3811 . - - -
11047+0957 - - -
J1047+3531 — — -
J1059+6638 0.378 0.378 0.382
J1100+0305 - — —
J1121+1238 0.117 0.109 0.127
J1156+1337 0.187 0.109 0.193
J1159+3134 - - -
J1219+O438 - - —
J1222+0343 - - -
11234+3755 0.504 0.457 0.570
11241+1230 0.470 0.446 0.605
11254+0241 - - -
J1304+3404 - - -
jl328+5818 0.468 0.445 0.493
j1333+6417 - — -
J1339+6328 - — —

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

170

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Name OVI
Best min max
J1356+4710 0.281 0.250 0.330
J1404+0728 0.386 0.320 0.402
J1429+3438 — - -
jl430+4811 - - -
J1442+1005 0.486 0.478 0.464
J1448+4408 1.336 1.380 1.353
J1456+4339 0.309 0.274 0.310
J1545+5112 - — —
11550+0236 - - -
j1641+2232 - - -
11650+4151 - — —
j1707+6443 0.381 0.356 0.382
j1713+3250 0.632 0.531 0.892
12331-0106 0.230 0.219 0.240
J2339+0030 0.608 0.574 0.711

 

 

 

 

Table B.3 cont’d.

171

 

 

 

Table B.4

Best measurements of line—intensity ratios for
NIII] /CIII] and N111] / OIII] along with their
corresponding minimum and maximum values.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Name NIII/CIII] NIII] /OIII]
SDSS Best min max Best min max
10038+ 1403 -0.410 -0.647 -0.209 0.109 -0.186 0.377
J0255+0014 -0.178 -0.327 -0.015 0.217 0.110 0.398
J0745+4157 -0.150 -0.272 0.096 0.131 0.068 0.361
JO753+4030 -0.927 -1.116 -0.561 -0.530 -0.625 -0.354
J0800+4417 -0.192 -0.489 -0.061 0.157 -0.047 0.277
J0847+3831 0.043 -0.110 0.175 0.485 0.250 0.591
J0852+4734 0.206 0.027 0.531 0.338 0.168 0.654
J0855+3754 -0.522 -0.708 -0.198 -0.044 -0.182 0.180
J0933+0840 -0.253 -0.499 0.021 0.177 -0.033 0.365
J0950+1233 0.110 -0.086 0.485 0.429 0.290 0.601
JO953+0037 -0.537 -0.708 -0.298 -0.075 —0.287 0.206
J1042+ 3811 0.204 0.094 0.386 0.478 0.344 0.514
J1047+0957 -0.747 -0.933 -0.554 -0.320 -0.411 -0.201
J1047+3531 0.322 0.170 0.463 0.792 0.581 0.951
J1059+6638 -0.422 -0.590 -0.256 -0.028 -0.161 0.073
J1100+0305 0.180 -0.320 0.460 0.104 -0.114 0.320
J1 121 +1238 -0.058 -0.227 0.181 0.480 0.358 0.672
J1 156+ 1337 0.011 -0.140 0.172 0.179 0.070 0.247
J1159+3134 -0.462 -0.635 -0.278 0.262 0.102 0.425
J1219+0438 -1.025 -1.339 -0.670 -0.076 -0.362 0.190
J1222+0343 -0.447 -O.598 —0.148 0.342 0.165 0.485
J1234+3755 -0.422 -0.622 -0.200 0.151 -0.003 0.356
J1241 +1230 -0.067 -0.230 0.171 0.446 0.351 0.634
J1254+0241 -0.021 —0.094 0.000 0.398 0.364 0.509
J1304+ 3404 0.222 0.068 0.370 0.592 0.438 0.743
J1328+5818 -0.748 -0.858 -0.619 —0.371 -0.431 -0.298

 

 

 

 

 

 

 

172

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

173

Name NIII/ CIII] NIII] / OIII]

, SDSS Best min max Best min max
J1333+6417 -0.256 -0.374 -0.112 0.385 0.217 0.605
J1339+6328 —0.429 -0.683 -0.174 -0.253 -0.345 -0.167
J1356+4710 -0.491 -0.879 -0.212 0.421 0.053 0.811
J1404+0728 0.007 -0.110 0.290 0.539 0.464 0.613
J1429+3438 —0.669 -0.859 -0.353 -0.118 -0.261 0.169
J1430+4811 0.139 0.033 0.389 0.299 0.190 0.466
J1442+1005 -0.380 -0.667 -0.260 0.139 -0.245 0.217
J1448+4408 -0.045 -0.315 0.228 0.283 0.037 0.477
J1456+4339 -0.380 -0.572 —0.156 0.176 —0.069 0.352
J1545+5112 —0.429 -0.682 -0.204 -0.119 -0.237 —0.010
J1550+0236 0.130 -0.032 0.377 0.262 0.175 0.333
J1641 +2232 -0.063 -0.158 0.145 0.407 0.363 0.600
J1650+4151 -0.339 -0.492 -0.061 0.421 0.137 0.645
J1707+6443 -0.444 -0.700 -0.177 -0.114 -0.299 0.111
J1713+3250 -0.186 -0.389 0.100 0.128 0.037 0.186
J2331-0106 -0.358 -0.450 -0.124 0.097 -0.011 0.254
J2339+0030 -0.132 —0.431 0.129 0.386 0.182 0.603

Table B.4 cont’d.

 

Table B.4 ront’d.

Best measurements of line-intensity ratios for

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

NIV] / OIII] and NIV] / CIV along with their
corresponding minimum and maximum values.
Name NIV] /OIII] NIV] / CIV

SDSS Best min max Best min max
J0038+1403 -0.312 -0.760 0.040 -1.236 -1.600 -1.010
J0255+0014 0.124 -0.071 0.341 -O.699 -O.87O -0.568
J0745+4157 -0.124 -0.187 0.222 —1.092 -1.130 -0.837
JO753+4030 -0.511 -O.624 -0.213 -1.788 -1.843 -1.500
0800+4417 -0.090 -0.302 0.181 -1.035 -1.217 -0.681
J0847+3831 0.095 -0.130 0.184 -0.889 -0.944 -0.800
J0852+4734 -0.172 -0.362 0.258 -0.658 -0.783 -0.327
J0855+3754 -O.647 -0.772 -0.353 —1.797 -1.897 -1.565
J0933+0840 -0.686 -0.900 -0.503 -1.599 -1.745 -1.485
J0950+1233 0.301 0.188 0.397 —0.635 -0.679 —0.533
J0953+0037 -0.219 -O.648 0.154 -1.296 -1 .639 -1068
11042+3811 0.347 0.222 0.387 -0.648 -0.666 -0.591
11047+0957 -O.282 .0409 -0.050 -1.469 -1.585 -1282
J1047+3531 0.162 -0.024 0.370 -0.959 —1.055 -0.865
J1059+6638 0.236 0.040 0.309 -O.808 -0.952 -O.762
J1100+0305 -0.280 -0.391 -0.069 -0.933 -0.977 -0.840
J1121+1238 -0.074 -0.253 0.175 -1.315 -1.407 -1.164
1156+1337 -O.383 -0.425 -0.361 -1.223 -1.256 -1210
11159+3134 -0.387 -0557 -0.217 —1.387 -1 .524 -1.261
J1219+0438 -0097 -0319 0.000 -1.496 -1.658 -1.422
j1222+0343 -0.005 -0233 0.171 -1.086 -1.199 -0.959
J1234+3755 0332 -O.438 0.106 -1099 -1.1 19 -0.793
11241+1230 -O.180 -0.363 0.090 -1015 -1.115 -O.746
11254+0241 0.158 0.158 0.317 -O.638 -0.675 -O.568
11304+3404 0.118 0.019 0.293 -0.790 -0.919 -O.632
J1328+5818 -0.470 -0.589 -0.403 -1.409 -1.510 -1.355
J1333+6417 -O.256 -0.457 -0014 -1200 .1330 -1.080

 

174

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Name NIV] /OIII] NIV] / CIV
SDSS Best min max Best min max
J1339+6328 -0.037 -0.147 0.068 -1.146 -1.214 -1.069
J1356+4710 -0.049 -0.439 0.315 -1.278 -1.506 -1 .170
J1404+0728 0.363 0.284 0.485 -0.737 -0.771 -0.624
J1429+3438 —0.328 -0.600 -0.065 -1.518 -1.726 -1.369
1430+4811 0.060 -0.055 0.176 -0.493 -0.549 -0.430
J1442+ 1005 —0.241 -0.581 -0.006 ~1.307 -1.468 -1.077
J1448+4408 0.343 0.157 0.477 -0.430 -0.577 -0.279
J1456+4339 0.178 -0.063 0.381 -0.982 -1.125 -0.889
J1545+5112 -0.350 -0.518 -0.209 -1.114 -1.296 -0.929
J1 550+ 0236 0.244 0.128 0.377 -0.423 -0.534 -0.220
J1641+2232 0.131 0.118 0.194 -0.459 -0.463 -0.415
J1650+4151 -0.203 -0.519 0.329 -1.248 -1.447 -0.793
J1707+6443 0.060 -0.177 0.236 -1.066 -1.260 -0.981
J1713+3250 -0.086 —0.255 0.051 -1.077 -1.191 ~0.987
J2331—0106 -0.234 -0.342 -0.025 -1.297 -1.421 -1.127
J2339+0030 -0.242 -0.466 0.021 -1.286 -1.438 -1.106
Table B.4 cont’a’.

175

 

Table 3.4 cont’d.

Best measurements of line-intensity ratios for NV/ He
II and NV/CIV along with their corresponding
minimum and maximum values.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Name NV/ He II NV/CIV
SDSS Best min max Best min max
0038+1403 0.896 0.757 1.010 -0.025 -0.118 0.044
J0255+0014 0.489 0.308 0.621 -0.241 -0.397 —0.1 14
0745+4157 0.555 0.475 0.641 -0.124 -0.173 -0.066
J0753+4030 0.487 0.330 0.815 -0.623 -0.773 -0.346
J0800+4417 1.019 0.871 1.198 0.114 -0.003 0.361
J0847+3831 0.996 0.902 1.126 0.165 0.088 0.254
J0852+4734 0.698 0.497 0.823 0.180 0.044 0.332
J0855+3754 0.870 0.684 1.064 -0.102 -0.247 0.031
J0933+0840 0.960 0.696 1.118 0.232 0.000 0.344
J0950+1233 0.713 0.657 0.749 0.095 0.039 0.151
0953 +0037 0.449 0.197 0.663 -0.547 -0.71 9 -0.465
1042+3811 0.752 0.550 0.881 -0.020 -0.208 0.128
J1047 +0957 0.698 0.508 0.972 -0.355 -0.509 -0.232
J1047 +3531 1.521 1.429 1.545 0.206 0.078 0.245
J1059+6638 0.592 0.511 0.689 -0.257 -0.335 -0.172
1100+0305 0.305 0.252 0.522 -0.250 —0.31 5 -0.060
J1121+1238 0.869 0.625 1.112 -0.266 -0.431 -0.121
J1156+1337 0.621 0.420 0.739 -0.204 -0.400 -0.084
J1159+3134 1.631 1.531 1.719 0.380 0.254 0.498
J1219+0438 1.396 1.131 1.587 0.170 -0.057 0.300
J1222+0343 0.995 0.840 1.203 0.018 -0.044 0.104
J1234+3755 1.106 0.953 1.278 0.022 -0.078 0.113
J1241+1230 1.112 0.957 1.203 0.242 0.176 0.339
1254+0241 0.814 0.796 0.992 0.176 0.121 0.196
J1304+3404 0.782 0.546 0.980 0.195 -0.073 0.381
1328+ 581 8 0.670 0.518 0.775 -0.247 -0.382 -0.151
J1333+6417 0.942 0.806 1.134 0.096 -0.040 0.270

 

 

 

 

 

 

 

 

176

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Name NV/ He II NV/CIV

SDSS Best min max Best min max
J1339+ 6328 0.671 0.517 0.802 -0.428 -0.546 -0.316
J1356+4710 1.131 0.880 1.302 0.180 -0.050 0.300
J1404+0728 0.996 0.799 1.159 0.225 0.036 0.366
J1429+ 3438 0.653 0.448 0.989 -0.348 -0.464 -0.053
J1430+4811 0.668 0.512 0.744 0.077 0.046 0.153
J1442+1005 0.976 0.641 1.270 -0.179 -0.397 -0.007
J1448+4408 0.949 0.802 1.196 0.267 0.140 0.487
J1456+4339 0.587 0.507 0.629 -0.329 -0.408 -0.302
J1545+5112 0.786 0.661 0.873 0.064 -0.076 0.196
J1550+0236 0.548 0.320 0.708 -0.142 -0.269 0.022
J1641+2232 0.797 0.713 0.908 0.291 0.212 0.358
J1650+4151 0.734 0.443 0.989 -0.244 -0.457 0.017
J1707+6443 0.907 0.622 1.094 -0.164 -0.331 -0.054
J1713+3250 0.681 0.504 0.819 -0.045 -0.191 0.064
J2331-0106 0.661 0.391 0.991 -0.321 -0.602 0.007
J2339+0030 0.998 0.800 1.154 0.095 -0.016 0.239

Table B.4 ront’a’.

177

 

Table B.4 cont’é.

Best measurements of line-intensity ratios for
NV/OVI and NV/(CIV+OVI) along with their
corresponding minimum and maximum values.

Name NV/ OVI NV/ (CIV+ OVI)

Best min max Best min max
J0038+1403 - - - - - -
J0255+0014 — - - — - -
J0745+4157 0.060 -0.032 0.165 —0.343 -0.409 -0.267
J07 53+4030 -0.018 -0.235 0.289 -0.719 -0.884 -0.437
10800+4417 - - - - - -
J0847+3831 —0.069 -O.l73 0.063 -0.268 -0.363 -0.153
J0852+4734 — - - - - -
lO855+3754 - - - — - -
jO933+0840 - — - — - -
J0950+ 1233 0.124 0.042 0.207 -0.192 -0.260 -0.123
JO953+0037 — - - — - —
J1042+3811 — — — - — —
JIO47+0957 - - - - - -
j1047+3531 - - - - - -
J1059+6638 0.166 0.083 0.251 -0.396 -0.475 -0.311
1100+0305 - - - - - -
J1121+1238 0.665 0.466 0.842 -0.314 -0.483 -0.166
J1156+1337 0.524 0.315 0.878 -0.278 -0.477 -0.129
J1159+3134 - — - - - —
j1219+0438 - - - - - -
J1222+0343 - - - - - -
J1234+3755 0.320 0.166 0.453 -0.155 -0.274 -0.051
£241 + 1230 0.570 0.395 0.690 0.075 -0.029 0.179
J1254+0241 - - - - — -
J1304+3404 - - - - - -
J1328+5818 0.083 -0.076 0.200 -0.414 -0.557 —0.311

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Name NV/ OVI NV/ (CIV+ OVI)
Best min max Best min max

J1333+6417 - - - - - -
J1339+6328 - - - - - —
J1356+4710 0.732 0.432 0.901 0.073 -0.174 0.203
J1404+0728 0.637 0.431 0.860 0.083 -0.111 0.245
J1429+3438 - - — - - -
Jl430+4811 — - - - — —
J1442+1005 0.134 -0.064 0.313 -0.351 -0.562 -0.177

1448+4408 0.141 0.009 0.347 -0.102 -0.232 0.110
J1456+4339 0.181 0.101 0.260 -0.446 -0.525 -0.407
J1545+5112 - - - - - -
J1550+0236 - - - - - -
11641+2232 — - — — - -
J1650+4151 — - — - - —
J1707+6443 0.254 0.087 0.395 -0.305 -0.472 -0.186
J1713+3250 0.154 -0.142 0.339 -0.258 -0.468 -0.121
12331-0106 0.299 0.057 0.612 -0.414 -0.688 -0.089
J2339+0030 0.311 0.132 0.480 -0.111 -0.249 0.042

Table B.4 cont’d.

179

 

Table 3.5

Metallicity Estimates from individual line-intensity ratios.
This table lists the Z estimates from NIII]/CIII] and
NIII]/OIII] line-intensity ratios, the best estimates along
with the corresponding minimum and maximum values.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

NQSO Metallicity Log(Z/zm) Metallicity Leg(Z/zm)
ame N IIIJ/C III] N IIIJ/O III]
Best Best

SDSS Estimate Minimum Maximum Estimate Minimum Maximum
J0038+1403 0.388 0.181 0.584 0.661 0.380 0.952
J0255+0014 0.614 0.469 0.861 0.774 0.662 0.976
J0745+4157 0.641 0.522 1.055 0.682 0.622 0.934
J0753+4030 -0.061 -0.264 0.250 0.119 0.052 0.241
J0800+4417 0.600 0.311 0.762 0.708 0.512 0.841
J0847+3831 0.985 0.680 1.150 1.103 0.811 1.270
J0852+4734 1.187 0.951 1.577 0.909 0.720 1.370
0855+3754 0.282 0.131 0.595 0.515 0.384 0.733
J0933+0840 0.541 0.301 0.938 0.730 0.526 0.939
J0950+1233 1.072 0.709 1.522 1.014 0.856 1.286
J0953+0037 0.270 0.131 0.497 0.486 0.288 0.762
J1042+3811 1.185 1.053 1.403 1.092 0.916 1.148
1047+0957 0.100 -0.068 0.256 0.265 0.202 0.366
1047+3531 1.326 1.144 1.496 1.587 1.254 1.838
J1059+6638 0.376 0.227 0.538 0.530 0.404 0.627
J1100+0305 1.156 0.476 1.492 0.656 0.449 0.889
1121 +1238 0.769 0.566 1.157 1.095 0.931 1.398
1156+1337 0.916 0.651 1.146 0.732 0.624 0.808
J1159+3134 0.337 0.191 0.517 0.824 0.654 1.008
1219+0438 -0.166 -0.504 0.162 0.485 0.236 0.744
J1222+0343 0.352 0.221 0.643 0.913 0.717 1.103
1234+3755 0.376 0.201 0.593 0.701 0.554 0.929
J1241+1230 0.749 0.563 1.145 1.041 0.923 1.338

 

 

 

 

 

 

 

 

180

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

QSO Metallicity Log(Z/Zsun) Metallicity Log(Z/Zsun)
Name N III] /C III] N 1111/0 111]
Best Best
SDSS Estimate Minimum Maximum Estimate Minimum Maximum
J1254+0241 0.848 0.696 0.893 0.976 0.938 1.140
J1304+3404 1.206 1.022 1.384 1.272 1.028 1.510
1328+5818 0.099 0.010 0.204 0.229 0.188 0.280
1333+6417 0.538 0.423 0.678 0.961 0.774 1.292
J1339+6328 0.369 0.152 0.618 0.316 0.248 0.398
1356+4710 0.309 -0.010 0.581 1.002 0.608 1.617
J1404+0728 0.908 0.680 1.288 1.188 1.069 1.305
J1429+3438 0.163 0.009 0.443 0.445 0.309 0.721
1430+4811 1.107 0.964 1.407 0.866 0.744 1.073
1442+1005 0.417 0.165 0.534 0.689 0.324 0.774
J1448+4408 0.796 0.481 1.214 0.848 0.592 1.090
J1456+4339 0.417 0.242 0.636 0.729 0.491 0.924
J1545+5112 0.369 0.152 0.589 0.444 0.331 0.548
J1550+0236 1.096 0.824 1.392 0.824 0.728 0.903
J1641+2232 0.758 0.634 1.114 0.986 0.937 1.284
J1650+4151 0.457 0.308 0.762 1.002 0.688 1.355
J1707+6443 0.355 0.138 0.615 0.449 0.280 0.663
J1713+3250 0.606 0.408 1.060 0.679 0.592 0.740
12331-0106 0.438 0.349 0.667 0.650 0.547 0.816
J2339+0030 0.659 0.367 1.095 0.962 0.736 1.289

 

 

 

 

 

 

 

Table B.5 ront’d.

181

 

Table B.5 cgnt’d.

Metallicity Estimates from individual line-intensity ratios.
This table lists the Z estimates from NIV]/OIII] and
NIV]/CIV line-intensity ratios, the best estimates along

with the corresponding minimum and maximum values.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

QSO Metallicity Log(Z/Zsun) Metallicity Log(Z/ Zsun)
Nam N IV] /0 III] N IV] /C IV
Best Best

SDSS Estimate Minimum Maximum Estimate Minimum Maximum
10038+1403 0.642 -0.397 0.982 0.247 -0.155 0.485
102554-0014 1.080 0.884 1.351 0.772 0.628 0.866
J0745+4157 0.838 0.782 1.202 0.400 0.361 0.662
J0753+4030 0.259 -0.120 0.759 -0.345 -0.396 -0.052
10800+4417 0.868 0.660 1.151 0.459 0.269 0.785
J0847+3831 1.044 0.832 1.155 0.609 0.552 0.700
JO852+4734 0.795 0.551 1.247 0.801 0.712 1.057
10855+3754 -0.183 -0.413 0.567 -0.353 -0.446 -0.119
J0933+0840 -0.289 -0.590 0.289 -0.154 -0.305 -0.036
J0950+1233 1.301 1.160 1.421 0.818 0.786 0.891
109534-0037 0.754 -0.185 1.117 0.178 -0.196 0.425
J1042+3811 1.359 1.202 1.409 0.809 0.796 0.849
J1047+0957 0.696 0.465 0.903 -0.020 ~0.140 0.194
J1047+3531 1.128 0.926 1.388 0.537 0.438 0.633
110594-6638 1.220 0.982 1.311 0.692 0.544 0.727
J1100+0305 0.700 0.498 0.886 0.564 0.518 0.659
J1121+1238 0.882 0.724 1.144 0.156 0.050 0.327
J1156+1337 0.513 0.436 0.553 0.262 0.224 0.277
J1159+3134 0.506 0.086 0.756 0.073 -0.077 0.218
11219+0438 0.862 0.629 0.947 -0.048 -0.215 0.032
i1222+0343 0.943 0.742 1.139 0.407 0.290 0.537
J1234+3755 0.605 0.413 1.058 0.393 0.373 0.705
J1241-+1230 0.802 0.607 1.146 0.463 0.309 0.704

 

 

 

 

 

 

 

 

182

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

QSO Metallicity Log(Z/Zsm) Metallicity Log(Z/Zm)
Name N IV] /0 111] N IV]/C IV
Best Best
SDSS Estimate Minimum Maximum Estimate Minimum Maximum
J1254+0241 1.122 1.122 1.321 0.816 0.789 0.866
jl304+3404 1.072 0.964 1.291 0.707 0.578 0.820
J1328+5818 0.354 -0024 0.476 0.047 -0.062 0.110
jl333+6417 0.721 0.378 0.935 0.289 0.139 0.413
J1339+6328 0.914 0.817 1.010 0.345 0.272 0.424
11356+4710 0.904 0.411 1.319 0.199 -0.058 0.320
11404+0728 1.379 1.280 1.531 0.745 0.721 0.826
jl429+3438 0.613 -0054 0.890 -007 -0.285 0.094
J1430+4811 1.000 0.899 1.145 0.919 0.879 0.964
J1442+1005 0.734 -0003 0.942 0.165 -0019 0.416
J1448+4408 1.354 1.121 1.521 0.964 0.859 1.108
1456+4339 1.148 0.891 1.401 0.513 0.367 0.609
J1545+5112 0.573 0.233 0.763 0.378 0.178 0.568
J1550+0236 1.230 1.085 1.396 0.969 0.890 1.171
j1641+2232 1.211 1.165 1.362 0.944 0.936 0.991
11650+4151 0.768 0.229 1.336 0.233 0.004 0.705
J1707+6443 1.000 0.791 1.220 0.427 0.219 0.514
j1713+3250 0.871 0.722 0.992 0.416 0.299 0.508
j2331-0106 0.741 0.587 0.925 0.176 0.034 0.365
12339+0030 0.734 0.362 0.966 0.189 0.014 0.386
Table B.5 cont’d.

183

 

Table B.5 cont’d.

Metallicity Estimates from individual line-intensity ratios.
This table lists the Z estimates from NV/ He II and
NV/CIV line-intensity ratios, the best estimates along with
the corresponding minimum and maximum values.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

' QSO Metallicity L6g(Z/zm) Metallicity Log(Z/Zsun)
Name N V/He II N V/C IV
Best Best

SDSS Estimate Minimum Maximum Estimate Minimum Maximum
J0038+1403 1.273 1.119 1.400 0.994 0.891 1.096
J0255+0014 0.688 0.498 0.942 0.754 0.570 0.896
0745+4157 0.810 0.674 0.982 0.884 0.830 0.949
J0753+4030 0.686 0.521 1.183 0.297 0.147 0.632
0800+4417 1.410 1.246 1.609 1.201 1.026 1.571
J0847+3831 1.384 1.280 1.529 1.278 1.162 1.411
j0852+4734 1.053 0.697 1.192 1.300 1.096 1.528
J0855+3754 1.244 1.038 1.460 0.909 0.748 1.077
jO933+0840 1.344 1.051 1.520 1.378 1.030 1.546
jO950+1233 1.070 1.008 1.110 1.173 1.089 1.257
J0953+0037 0.646 0.381 1.014 0.389 0.201 0.488
J1042+3811 1.113 0.800 1.257 1.000 0.791 1.222
ﬂO47+0957 1.053 0.716 1.358 0.621 0.435 0.764
j1047+3531 1.968 1.866 1.994 1.339 1.147 1.398
J1059+6638 0.884 0.722 1.043 0.737 0.646 0.831
j1100+0305 0.495 0.439 0.744 0.744 0.670 0.956
J1121+1238 1.243 0.950 1.513 0.727 0.529 0.888
j1156+1337 0.942 0.616 1.099 0.796 0.567 0.929
1159+3134 2.090 1.979 2.188 1.600 1.411 1.777
J1219+0438 1.829 1.534 2.041 1.285 0.959 1.480
1222+0343 1.383 1.211 1.614 1.057 0.973 1.186
J1234+3755 1.507 1.337 1.698 1.063 0.936 1.199
J1241+1230 1.659 1.472 1.796 1.556 1.454 1.630
11254+0241 1.182 1.162 1.380 1.294 1.212 1.324

 

 

 

 

 

 

 

 

184

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

QSO Metallicity Log(Z/Zsun) Metallicity Log(Z/Zm)
Name N V/He 11 N V/C 1v
Best Best
SDSS Estimate Minimum Maximum Estimate Minimum Maximum
J1304+3404 1.147 0.792 1.367 1.322 0.941 1.602
j1328+5818 1.022 0.736 1.139 0.748 0.589 0.854
j1333+6417 1.324 1.173 1.538 1.174 0.978 1.435
J1339+6328 1.023 0.734 1.169 0.533 0.390 0.669
j1356+4710 1.534 1.256 1.724 1.300 0.967 1.480
J1404+0728 1.384 1.166 1.566 1.367 1.084 1.579
J1429+3438 1.003 0.645 1.377 0.630 0.489 0.963
j1430+4811 1.020 0.724 1.104 1.145 1.099 1.260
1442+1005 1.362 0.982 1.689 0.823 0.570 1.020
j1448+4408 1.332 1.169 1.607 1.431 1.240 1.760
jl456+4339 0.874 0.714 0.958 0.653 0.557 0.686
j1545+5112 1.151 1.012 1.248 1.126 0.938 1.324
j1550+0236 0.796 0.511 1.064 0.864 0.723 1.063
j1641+2232 1.292 1.170 1.450 1.554 1.471 1.666
11650+4151 1.093 0.640 1.377 0.751 0.498 1.056
J1707+6443 1.286 0.944 1.493 0.840 0.650 0.962
J1713+3250 1.034 0.708 1.188 0.972 0.810 1.126
J2331-0106 1.012 0.585 1.379 0.662 0.322 1.041
J2339+0030 1.387 1.167 1.560 1.173 1.006 1.388
Table B.5 cont’d.

185

 

Table B.5 cont’d.

Metallicity Estimates from individual line-intensity ratios.
This table lists the Z estimates from NV/OVI and
NV/(CIV+OVI) line-intensity ratios, the best estimates
along with the corresponding minimum and maximum
values.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

QSO Metallicity Log(Z/Zsun) Metallicity Log(Z/Zsun)
Name N V/o VI N V/(C IV+ 0 VI)
Best Best

SDSS Estimate Minimum Maximum Estimate Minimum Maximum
10038+1403 - - - - - -
10255+0014 - - - - - -
10745+4157 - - - - - -
j0753+4030 0.827 0.524 1.299 0.442 0.249 0.790
_10800+4417 0.859 0.859 0.859 1.395 1.395 1.395
J0847+3831 0.737 0.599 0.970 1.030 0.896 1.187
J0852+4734 — - - — — -
jO855+3754 - — - - — -
J0933+0840 - - - - - -
10950+1233 1.063 0.933 1.181 1.134 1.041 1.228
10953+0037 - - - - - -
J1042+3811 - - - - - -
j1047+0957 - - - - - -
J1047+3531 - - - - - -
11059+6638 1.123 1.004 1.244 0.849 0.736 0.970
J1100+O305 - - - - - -
J1121+1238 1.836 1.551 2.089 0.966 0.724 1.169
J1156+1337 1.634 1.336 2.140 1.016 0.733 1.219
J1159+3134 - - - - - -
J1219+0438 — — — — — —
j1222+0343 - - - - - -
11234+3755 1.343 1.123 1.533 1.184 1.022 1.326
j1241+1230 1.851 1.617 1.994 1.645 1.506 1.734

 

 

 

 

 

 

 

186

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

QSO Metallicity Log(Z/ Zsun) Metallicity Log(Z/Zsun)
Nam N V/O VI N V/(C IV+ 0 VI)
Best Best
SDSS Estimate Minimum Maximum Estimate Minimum Maximum

11254+0241 — — — - - -
11304+3404 - - - - - -
J1328+5818 1.004 0.725 1.171 0.823 0.633 0.970
J1333+6417 - - - — - -
J1339+6328 - - - - — —
J1356+4710 1.931 1.503 2.173 1.495 1.158 1.672
J1404+0728 1.796 1.501 2.114 1.509 1.244 1.730
J1429+3438 - — - - - -

1430+4811 - - - - - -
J1442+1005 1.077 0.746 1.333 0.913 0.627 1.154
11448714408 1.087 0.875 1.381 1.256 1.079 1.546
J1456+4339 1.144 1.030 1.257 0.777 0.671 0.833
11545+5112 - - - - - -
j1550+0236 — - — - - -
JI641+2232 - - - - — -
jl650+4151 - - — - - -
J1707+6443 1.249 1.010 1.450 0.979 0.740 1.142
J1713+3250 1.106 0.637 1.370 1.044 0.746 1.230
j2331-0106 1.313 0.959 1.760 0.823 0.479 1.274
J2339+0030 1.330 1.074 1.571 1.244 1.056 1.453

Table B.5 cont’d.

187

 

Table B.6

Best Metallicity Estimates (Log Zbest/Zsun) for the
N-Loud Quasar Sample and their corresponding
error estimates.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

oso Name 2m, .1521“,
SD8810038+1403 0.671 0.108
SDSS J0255+0014 0.805 0.085
SDSSJO745+4157 0.761 0.051
SDSS J0753+4030 0.154 0.07
SDSS J0800+4417 0.844 0.113
SDSS j0847+3831 1.102 0.055
SDSS 10852+4734 1.048 0.102
SDSS J0855+3754 0.381 0.198
SDSS J0933+0840 0.59 0.297
SDSS 10950+1233 1.14 0.054
SDSS 10953+0037 0.475 0.089
SDSS ﬂO42+3811 1.159 0.066
SDSS J1047+0957 0.421 0.123
SDSS j1047+3531 1.345 0.081
SDSS j1059+6638 0.716 0.159
SDSSJ1100+0305 0.814 0.1
SDSS 11121+1238 0.868 0.071
SDSS J1156+1337 0.739 0.073
SDSS J1159+3134 0.817 0.242
SDSSJ1219+0438 0.617 0.266
SDSSj1222+0343 0.816 0.137

 

 

 

188

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

QSO Name Zbcst _AZbﬁst
SDSS J1234+3755 0.686 0.124
SDSS J1241+1230 1.037 0.16
SDSSJ1254+0241 1.06 0.083
SDSS J1304+3404 1.218 0.047
SDSS J1328+5818 0.357 0.121
SDSS J1333+6417 0.849 0.12
SDSS J1339+6328 0.533 0.117
SDSS J1356+4710 0.879 0.18
SDSS J1404+0728 1.211 0.095
SDSS J1429+3438 0.463 0.094
SDSS J1430+4811 1.03 0.054
SDSS J1442+1005 0.666 0.076
SDSS J1448+4408 1.107 0.144
SDSSJ1456+4339 0.737 0.132
SDSSJ1545+5112 0.628 0.148
SDSSL550+0236 1.003 0.083
SDSSJ1641+2232 1.127 0.147
SDSS J1650+4151 0.744 0.097
SDSS j1707+6443 0.661 0.134
SDSSJ1713+3250 0.782 0.073
SDSS J2331-0106 0.623 0.056
SDSSJ2339+0030 0.882 0.101

 

 

 

Table B.6 cont’a’.

189

 

Table B.7

Quantitative comparison of how well the metallicity
from different line-intensity ratios relates to mean
metallicity chm. The values in brackets are the
corresponding error estimates.

Z(line-intensity ratio) Slope (m) Intercept (C) ‘

 

 

 

 

 

 

 

 

 

 

 

 

z (N 111] /c 111]) 1.179 @149) -0341 (0.124)
2 (N III/0111]) 1.073 (0.092) -0.087 (0.077)
2 (N IV] /0111]) 1.030 (0.164) 0.008 (0.137)
2 (N 113/c 119 1.127 (0.137) 0504 (0.114)
2 (N V/He 11) 0.590 (0.193) 0.715 (0.161)
2 (N V/CIV) 1.000 (0.136) 0.211 (0.114)
2 (N V/ov1) 0.805 (0.324) 0.559 (0.299)
2 (N V/(c 1V+o v1)) 1.117 (0.144) 0.081 (0.133)
190

 

Table B.8

Statistics and Student ‘t’ test results for MSMBH for the
two Quasar sample sets.

 

 

 

 

 

 

 

 

 

 

 

Mean Mass 8.32 7.47
Standard deviation 1.05 1.03
Standard error 0.012 0.16
Mass Range (High — Low) 5.10 — 9.66 5.48 — 13.34
Median Mass 8.43 7.51
(AMSNIBH)m_ean 0.8500
Standard error of
difference 0.161
P value < 0.0001
t value 5.2943

 

 

 

The P value for this test is, P value < 0.0001. This indicates
that this difference between the two data sets is extremely
statistically signiﬁcant.

191

 

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