Weak Lensing & Substructure [Elektronische Ressource] / Emilio Pastor Mira
106 pages

Weak Lensing & Substructure [Elektronische Ressource] / Emilio Pastor Mira

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Weak Lensing & SubstructureDissertationzurErlangung des Doktorgrades (Dr. rer. nat.)derMathematisch-Naturwissenschaftlichen FakultatderRheinischen Friedrich-Wilhelms-Universitat Bonnvorgelegt vonEmilio Pastor MiraausAlcoyBonn Dez., 2010Angefertigt mit Genehmigung der Mathematisch-Naturwissenschaftlichen Fakult at derRheinischen Friedrich-Wilhelms-Universit at Bonn1. Gutachter: Prof. Dr. Peter Schneider2.hter: Prof. Dr. Cristiano PorcianiTag der Promotion: 21. 04. 2011Erscheinungsjahr: 2011A tots i cadascu dels profesors he tingut; atotes les persones que de alguna manera m’hanensenyat alguna cosa en ma vida; a tots els queem van ajudar a poder tindre algun orgull en lameua anima, a tots ells est a dedicada aquestatesi. I davant de totes aquestes persones anome-nades, com els millors i els mes antics, li dediquea la meua tesi a:Mar a Dolores Mira Conejero, i aEmilio Pascual Pastor Mart nez.ivContents1 Introduction 11.1 Mathematical notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Basic concepts of cosmology 32.1 Gravitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Fundamental concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.3 Robertson-Walker metric & Friedmann equations . . . . . . . . . . . . . . 62.4 Time & distances in cosmology . . . . . . . . . . . . . . . . . . . . . . . . 72.5 Brief history of the Universe . . . . . . . . . . . . . . . . . . . . .

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Publié le 01 janvier 2011
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Weak Lensing & Substructure
Dissertation
zur
Erlangung des Doktorgrades (Dr. rer. nat.)
der
Mathematisch-Naturwissenschaftlichen Fakultat
der
Rheinischen Friedrich-Wilhelms-Universitat Bonn
vorgelegt von
Emilio Pastor Mira
aus
Alcoy
Bonn Dez., 2010Angefertigt mit Genehmigung der Mathematisch-Naturwissenschaftlichen Fakult at der
Rheinischen Friedrich-Wilhelms-Universit at Bonn
1. Gutachter: Prof. Dr. Peter Schneider
2.hter: Prof. Dr. Cristiano Porciani
Tag der Promotion: 21. 04. 2011
Erscheinungsjahr: 2011A tots i cadascu dels profesors he tingut; a
totes les persones que de alguna manera m’han
ensenyat alguna cosa en ma vida; a tots els que
em van ajudar a poder tindre algun orgull en la
meua anima, a tots ells est a dedicada aquesta
tesi. I davant de totes aquestes persones anome-
nades, com els millors i els mes antics, li dedique
a la meua tesi a:
Mar a Dolores Mira Conejero, i a
Emilio Pascual Pastor Mart nez.ivContents
1 Introduction 1
1.1 Mathematical notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Basic concepts of cosmology 3
2.1 Gravitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Fundamental concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Robertson-Walker metric & Friedmann equations . . . . . . . . . . . . . . 6
2.4 Time & distances in cosmology . . . . . . . . . . . . . . . . . . . . . . . . 7
2.5 Brief history of the Universe . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.6 Random elds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.7 List of cosmological parameters . . . . . . . . . . . . . . . . . . . . . . . . 10
3 Structure formation: theory and computational techniques 13
3.1 Boltzmann equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 Linear Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.3 Transfer function & growth function . . . . . . . . . . . . . . . . . . . . . 16
3.4 Non-linear evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.5 Millennium Run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.6 Substructure in the Millennium Simulation . . . . . . . . . . . . . . . . . . 21
3.7 Semi-analytic catalogues . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.7.1 Basic concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.7.2 Gas accretion and cooling . . . . . . . . . . . . . . . . . . . . . . . 24
3.7.3 Star formation & feedback . . . . . . . . . . . . . . . . . . . . . . . 25
4 Gravitational lensing 27
4.1 Basic theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.1.1 Point mass de ection & thin lens approximation . . . . . . . . . . . 28
4.1.2 The lens equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.2 Lensing potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.3 Observables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.4 Galaxy-galaxy lensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.5 Ray-tracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
5 Substructure & galaxy-galaxy lensing 37
5.1 in clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
5.2 The method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.3 Analyzing the method and the data . . . . . . . . . . . . . . . . . . . . . . 41
5.3.1 Clusters in the Millennium Simulation . . . . . . . . . . . . . . . . 43vi CONTENTS
6 Sub-halos in the Millennium Simulation 45
6.1 Synthetic clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
6.2 Results for the calibration tests . . . . . . . . . . . . . . . . . . . . . . . . 49
6.2.1 Range for measuring . . . . . . . . . . . . . . . . . . . . . . . . 49
6.2.2 Discarding sub-halos . . . . . . . . . . . . . . . . . . . . . . . . . . 51
6.2.3 Main halo center detection . . . . . . . . . . . . . . . . . . . . . . . 53
6.3 Sub-halo pro les for di erent mass bins . . . . . . . . . . . . . . . . . . . . 55
6.4 Evolution of sub-halos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
7 Galaxies in clusters in the Millennium Simulation 63
7.1 Observables in the semi-analytical models . . . . . . . . . . . . . . . . . . 64
7.2 Simulated Surveys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
7.3 Optimal sub-halo mass proxy . . . . . . . . . . . . . . . . . . . . . . . . . 68
7.4 Weak lensing approximation . . . . . . . . . . . . . . . . . . . . . . . . . . 70
7.5 Luminosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
7.6 Stellar mass & morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
7.7 Type-2 galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
8 Summary & conclusions 83
A Shear Pro les 85
A.1 NFW pro les . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
A.2 Truncated NFW pro les . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
A.3 PIEMD pro les . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
B Halo shear signal around any point 88
C Bayes’ theorem and model comparison 90
D Nested Sampling 911. Introduction
This thesis is a feasibility study on applying galaxy-galaxy lensing to galaxies inside
clusters. This method uses gravitational lensing to estimate the average mass pro le of
a sample of galaxies. Galaxy-galaxy lensing requires large cluster samples, which will be
available in the near future.
The main goal of the thesis is to analyze what can be learned about this speci c class
of galaxies using future surveys. For our purpose, we use state-of-the-art cosmological
and gravitational lensing simulations. This allows us to make predictions and arrive
to conclusions in a perfectly controlled environment. We will use one of the largest
cosmological simulations by the time this thesis is written, the Millennium Simulation,
and ray-tracing sim of the gravitational lensing e ect within it.
We shall de ne a precise method to apply galaxy-galaxy lensing to galaxies inside
clusters. Our intention is also to predict the expected signal-to-noise ratios, study how
to optimize the information content and avoid any foreseeable systematic e ect or bias.
We also explore di erent possible analyses that could be compared to our theoretical
predictions and models.
Galaxy clusters are the most massive bound structures known, with estimated masses
14of more than 10 solar masses and hundreds of individual galaxies. They are so large
that they are often assumed to be fair tracers of the composition of the whole Universe.
Their dynamics and composition o er a great amount of cosmological information.
Also, the way in which large galaxy concentrations form and evolve is of great interest for
current cosmological models. The method that we analyze in this thesis can shed some
light on all these topics, and combined with galaxy evolution models, it can help as well
to understand how the mass of galaxies a ects their observables like luminosity, color etc.
The thesis is organized as follows. The rst three chapters are a broad overview of the
basic concepts necessary to develop our work. The rest contain the original work that we
have produced.
We start in Chapter 2 with an introduction to cosmology. We list the essential
points of the current cosmological concordance model which are indispensable for
any work in cosmology.
Chapter 3 is a brief overview about structure growth in the Universe. We illustrate
the theory, and we describe the cosmological simulation on which this thesis is based.
In Chapter 4 we describe gravitational lensing. Gravitational lensing is the tool that
we use to get the mass pro les of galaxies inside clusters. We also describe in here
our gravitational lensing simulations.
The original work and center of this thesis is presented in Chapter 5. Here we make
a thorough description of the method we are going to test.2 Chapter 1. Introduction
We use simulations to make predictions. For a deeper understanding of our results,
we study in detail the output of the simulations in Chapter 6. We also de ne the
limits of our measurements.
In Chapter 7 we use the concepts and conclusions developed before to compute the
predictions we aim for. Here we analyze what is to be expected in di erent lensing
surveys concerning weak lensing on galaxies in clusters. We also suggest di erent
experiments to characterize the mass pro les of satellite galaxies.
Finally we conclude with the summary and conclusions.
1.1 Mathematical notation
To aid the reader and avoid ambiguity on the mathematical expressions, we present the
common notation we maintain throughout the thesis.
Important constants and units (Particle Data Group et al. 2008).
30? Solar Mass: 1 M = (1:98842 0:00001) 10 kg.
22? Megaparsec: 1 Mpc = 3:0856776 10 m.
? The Hubble constantH essential in the de nition of cosmological quantities, is0
1 1often written likeH = 100h km s Mpc . With the constanth we express0
the lack of a precise knowledge of its value.
1? The speed of light 299 792 458 m s (exact) is always represented with the

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