Cosmic shear and the intrinsic alignment of galaxies [Elektronische Ressource] / vorgelegt von Benjamin Joachimi
273 Pages
English
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Cosmic shear and the intrinsic alignment of galaxies [Elektronische Ressource] / vorgelegt von Benjamin Joachimi

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273 Pages
English

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CosmicShearandtheIntrinsicAlignmentofGalaxiesDissertationzurErlangung des Doktorgrades (Dr. rer. nat.)derMathematisch-Naturwissenschaftlichen Fakulta¨tderRheinischen Friedrich-Wilhelms-Universita¨t Bonnvorgelegt vonBenjamin JoachimiausRheineBonn, 2010iiAngefertigtmitGenehmigungderMathematisch-NaturwissenschaftlichenFakulta¨tder Rheinischen Friedrich-Wilhelms-Universita¨t Bonn1. Gutachter: Prof. Dr. Peter Schneider2. Gutachter: Prof. Dr. Andreas EckartTag der Promotion: 04. November 2010Erscheinungsjahr: 2010iiiTo strive,To seek,To find,And not to yield.Lord Alfred Tennyson, UlyssesivAbstractCosmology has recently entered an era of increasingly rich observational data sets, all beingin agreement with a cosmological standard model that features only a small number of freeparameters. One of the most powerful techniques to constrain these parameters and test theaccuracy of the concordance model is the weak gravitational lensing of distant galaxies by thelarge-scale structure, or cosmic shear. This thesis investigates the optimisation of present andfuturecosmicshearsurveyswithrespecttotheextractionofcosmologicalinformationanddealswith the characterisation and control of the intrinsic alignment of galaxies, a major systematicin cosmic shear data.

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CosmicShear
andthe
IntrinsicAlignmentofGalaxies
Dissertation
zur
Erlangung des Doktorgrades (Dr. rer. nat.)
der
Mathematisch-Naturwissenschaftlichen Fakulta¨t
der
Rheinischen Friedrich-Wilhelms-Universita¨t Bonn
vorgelegt von
Benjamin Joachimi
aus
Rheine
Bonn, 2010ii
AngefertigtmitGenehmigungderMathematisch-NaturwissenschaftlichenFakulta¨t
der Rheinischen Friedrich-Wilhelms-Universita¨t Bonn
1. Gutachter: Prof. Dr. Peter Schneider
2. Gutachter: Prof. Dr. Andreas Eckart
Tag der Promotion: 04. November 2010
Erscheinungsjahr: 2010iii
To strive,
To seek,
To find,
And not to yield.
Lord Alfred Tennyson, Ulyssesiv
Abstract
Cosmology has recently entered an era of increasingly rich observational data sets, all being
in agreement with a cosmological standard model that features only a small number of free
parameters. One of the most powerful techniques to constrain these parameters and test the
accuracy of the concordance model is the weak gravitational lensing of distant galaxies by the
large-scale structure, or cosmic shear. This thesis investigates the optimisation of present and
futurecosmicshearsurveyswithrespecttotheextractionofcosmologicalinformationanddeals
with the characterisation and control of the intrinsic alignment of galaxies, a major systematic
in cosmic shear data.
A detailed derivation of the covariance of the weak lensing convergence bispectrum is pre-
sented, clarifying the relation between existing formalisms, providing illustration, and simpli-
fying the practical computation. The results are then applied to forecasts on cosmological
constraints by cosmic shear two- and three-point statistics with the proposed Euclid satellite.
Besides, a novel method to assess the impact of unknown systematics on cosmological parame-
ter constraints is summarised, and several aspects concerning the weak lensing analysis of the
Hubble Space Telescope COSMOS survey are highlighted.
A synopsis of the current state of knowledge about the intrinsic alignment of galaxies is
given, including its physical origin, modelling attempts, simulation results, and existing ob-
servations. Possible corrections to the prevailing model of intrinsic alignments are suggested,
before presenting new observational constraints on matter-intrinsic shear correlations using
several galaxy samples from the Sloan Digital Sky Survey. For the first time a data set with
onlyphotometricredshiftinformationisincluded, afterdevelopingtheformalismforcorrelation
function models that take photometric redshift scatter into account. The intrinsic alignment
signal of early-type galaxies is found to increase with galaxy luminosity and to be inconsistent
with the default redshift evolution of a widely used model, both with high confidence.
Moreover the nulling technique is developed, a method to remove gravitational shear-
intrinsic ellipticity correlations from cosmic shear data by solely relying on the well-known
redshift dependence of the signals, and its performance on realistically modelled cosmic shear
two-point statistics is investigated. Subsequently, the principle of intrinsic alignment boosting,
aninverseandlikewisegeometricalapproachcapableofextractingtheintrinsicalignmentsignal
fromcosmic sheardata, isderived. Bothtechniques areshown torobustlyremove orisolatethe
intrinsic alignment signal, but are subject toasignificant lossofstatistical power caused bythe
similarity between the redshift dependence of the lensing signal and shear-intrinsic correlations
in combination with strict model independence.
As an alternative ansatz, the joint analysis of various probes available from cosmic shear
surveys is considered, including cosmic shear, galaxy clustering, lensing magnification effects,
and cross-correlations between galaxy number densities and shapes. The self-calibration ca-
pabilities of intrinsic alignments and the galaxy bias in the combined data are found to be
excellent for realistic survey parameters, recovering the constraints on cosmological parameters
for a pure cosmic shear signal in presence of flexible parametrisations of intrinsic alignments
and galaxy bias with about a hundred nuisance parameters in total.CONTENTS v
Contents
1 Introduction 1
2 Principles of cosmology 4
2.1 Homogeneous world models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Matter components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 The early Universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4 Structure formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.5 The concordance model and beyond . . . . . . . . . . . . . . . . . . . . . . . . . 19
3 Weak gravitational lensing 24
3.1 Gravitational lens theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 Shear measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.3 Foundations of cosmic shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.4 Measures of cosmic shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.5 The status quo of cosmic shear . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4 Optimisation of cosmic shear surveys 43
4.1 Bispectrum covariance in the flat-sky limit . . . . . . . . . . . . . . . . . . . . . 43
4.1.1 Bispectrum estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.1.2 Averaging over triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.1.3 Bispectrum covariance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.1.4 Equivalence to spherical harmonics approach . . . . . . . . . . . . . . . . 53
4.1.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.2 Forecasting the performance of cosmological surveys . . . . . . . . . . . . . . . . 62
4.2.1 Constraints from the Euclid imaging survey . . . . . . . . . . . . . . . . 62
4.2.2 Functional form filling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.3 Cosmic shear analysis of the HST COSMOS Survey . . . . . . . . . . . . . . . . 74
4.3.1 Cosmic shear tomography with COSMOS . . . . . . . . . . . . . . . . . 74
4.3.2 Modelling the effect of dark energy on structure evolution . . . . . . . . 76
4.3.3 Analytic predictions for the COSMOS analysis . . . . . . . . . . . . . . . 78
5 The intrinsic alignment of galaxies 82
5.1 Introduction to intrinsic alignments . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.1.1 The origin of intrinsic correlations . . . . . . . . . . . . . . . . . . . . . . 83
5.1.2 Models of intrinsic alignments . . . . . . . . . . . . . . . . . . . . . . . . 85
5.1.3 Evidence for intrinsic alignments . . . . . . . . . . . . . . . . . . . . . . 89
5.1.4 Control of intrinsic alignment contamination . . . . . . . . . . . . . . . . 93
5.2 The MegaZ LRG and spectroscopic SDSS samples . . . . . . . . . . . . . . . . . 95
5.3 Modelling galaxy number density-shape correlations . . . . . . . . . . . . . . . . 98
5.3.1 Three-dimensional correlation functions . . . . . . . . . . . . . . . . . . . 98vi CONTENTS
5.3.2 Contribution by other signals . . . . . . . . . . . . . . . . . . . . . . . . 104
5.3.3 Projected correlation functions . . . . . . . . . . . . . . . . . . . . . . . 108
5.4 Measurement details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.4.1 Photometric redshifts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.4.2 Galaxy shape and correlation function measurement . . . . . . . . . . . . 111
5.4.3 Fitting routine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.5.1 Scaling with line-of-sight truncation . . . . . . . . . . . . . . . . . . . . . 114
5.5.2 Galaxy bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.5.3 Intrinsic alignment fits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.6 Implications for cosmology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
6 The nulling technique 129
6.1 Principle of nulling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6.2 Determination of nulling weight functions . . . . . . . . . . . . . . . . . . . . . . 134
6.2.1 Piecewise linear approach . . . . . . . . . . . . . . . . . . . . . . . . . . 135
6.2.2 Chebyshev series approach . . . . . . . . . . . . . . . . . . . . . . . . . . 136
6.2.3 Simplified analytical approach . . . . . . . . . . . . . . . . . . . . . . . . 137
6.2.4 Resulting nulling weights . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
6.2.5 Higher order weights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
6.3 Information loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
6.4 Towards an efficient nulling transformation . . . . . . . . . . . . . . . . . . . . . 152
6.5 Modelling cosmic shear data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
6.5.1 Redshift distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
6.5.2 Lensing power spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
6.5.3 Intrinsic alignment signal . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
6.6 Improving the nulling performance . . . . . . . . . . . . . . . . . . . . . . . . . 161
6.6.1 Optimising the nulling weights . . . . . . . . . . . . . . . . . . . . . . . . 161
6.6.2 Cosmology dependence of the nulling weights . . . . . . . . . . . . . . . 164
6.7 Influence of redshift information on nulling . . . . . . . . . . . . . . . . . . . . . 165
6.7.1 Redshift binning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
6.7.2 Minimum information loss . . . . . . . . . . . . . . . . . . . . . . . . . . 167
6.7.3 Intrinsic alignment contamination from adjacent bins . . . . . . . . . . . 168
6.8 Influence of photometric redshift uncertainty . . . . . . . . . . . . . . . . . . . . 169
6.8.1 Photometric redshift errors . . . . . . . . . . . . . . . . . . . . . . . . . . 169
6.8.2 Analysing optimal nulling redshifts . . . . . . . . . . . . . . . . . . . . . 171
6.8.3 Catastrophic outliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
6.8.4 Uncertainty in redshift distribution parameters . . . . . . . . . . . . . . 178
6.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
7 Intrinsic alignment boosting 186
7.1 Principle of boosting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
7.1.1 Basic relations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
7.1.2 Signal transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
7.1.3 Solving for the weight function . . . . . . . . . . . . . . . . . . . . . . . 189
7.2 Construction of weights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
7.3 Modelling the boosting transformation . . . . . . . . . . . . . . . . . . . . . . . 193
7.4 Performance of intrinsic alignment boosting . . . . . . . . . . . . . . . . . . . . 195CONTENTS vii
7.4.1 Boosted signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
7.4.2 Parameter constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
7.5 Relation to the nulling technique . . . . . . . . . . . . . . . . . . . . . . . . . . 201
7.5.1 Signal transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
7.5.2 Construction of weights . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
7.5.3 Nulled signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
7.5.4 Information content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
7.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
8 Self-calibration of intrinsic alignments 209
8.1 Two-point correlations from cosmological surveys . . . . . . . . . . . . . . . . . 210
8.2 Modelling two-point statistics in cosmological surveys . . . . . . . . . . . . . . . 217
8.2.1 Matter power spectrum & survey characteristics . . . . . . . . . . . . . . 217
8.2.2 Galaxy luminosity function . . . . . . . . . . . . . . . . . . . . . . . . . 218
8.2.3 Galaxy and intrinsic alignment bias . . . . . . . . . . . . . . . . . . . . . 220
8.2.4 Parameter constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
8.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
8.3.1 Dependence on intrinsic alignments and galaxy bias . . . . . . . . . . . . 228
8.3.2 Dependence on characteristics of the redshift distribution . . . . . . . . . 232
8.3.3 Dependence on nuisance parameter priors . . . . . . . . . . . . . . . . . 234
8.3.4 Information content in the individual signals . . . . . . . . . . . . . . . . 235
8.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
9 Conclusions & Outlook 242
Acknowledgements 247
Bibliography 248
Appendix 258
A Parameter estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
B Fisher matrix for a parameter-dependent data vector . . . . . . . . . . . . . . . 261
C Validity of the bias formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263viii1
Chapter 1
Introduction
Cosmology is targeted on a physical description of the Universe as a whole and takes a special
place among the disciplines of physics, as there exists only a single ‘object’ of interest from
which one can collect empirical data. Yet, the ensembles studied to infer properties of the
large-scale structure of the cosmos are among the largest in physics and comprise billions of
constituents. To arrive at a consistent picture of the Universe, physical laws have to be applied
to the largest possible scales, and to unveil its origin, the physics on scales smaller than those
reached hitherto by laboratory experiments have to be probed. Fundamental cosmological
questions drive some of the most forefront research in modern physics but were also posed at
the very beginnings of man’s rational understanding of nature, playing a relevant part in the
evolution of human society over the past centuries.
These dichotomiesunderline thecomprehensiveness aswell asthechallenges inherent tothe
taskofestablishingageneralmodeloftheUniverse. Inaddition,cosmologistsfacetheproblems
of being restricted to essentially a single point in space and time, and of receiving cosmological
information almost entirely in the form of electromagnetic radiation. As a consequence, only a
very limited part of the Universe is in principle accessible through observations, which in turn
are only available for cosmological objects that emit or absorb photons.
In spite of these intricacies, a concordance model of the cosmos has emerged in the past
two decades whose success is comparable to the feats of the standard model of elementary
particle physics. At the end of the twentieth century, after a long time of ‘data starvation’,
cosmology entered a prosperous era of immense and rich data sets, provided by novel, both
ground- and space-based observational facilities. To date, all major observations by various
mutually independent cosmological probes are consistent with this standard model, featuring
only six free parameters which could already be constrained with fair precision.
However, despite the success of the concordance model, it remains deeply unsatisfactory as
regards the requirements of a comprehensive physical theory because – again not unlike the
standard model of elementary particle physics – central elements remain unexplained. The
most important issue is the fact that according to the concordance model only about 5% of
the total energy budget of the Universe today are composed of matter whose existence has
been confirmed in laboratory experiments, including protons, neutrons, electrons, neutrinos,
and photons. Astronomical observations agree that another 20% of this budget are covered
by dark matter, supposedly massive elementary particles that interact only gravitationally and
via weak nuclear forces, and that in particular do not emit light. The remaining 75% are made
up of the even more exotic dark energy, a component which causes the late-time acceleration
of the expansion of the Universe but which is otherwise obscure.
Not only are thus 95% of the energy content of the cosmos of unknown nature, but in
addition the concordance model rests on two fundamental constituent theories which have not2 Chapter 1. Introduction
been verified by cosmological observations (yet), namely the validity of general relativity on
cosmological scales and the inflationary paradigm, setting the initial conditions for structure
formation.
One of the main challenges for cosmology in the near future is therefore to pin down the
properties of dark matter and dark energy with high precision, test general relativity and mod-
ified theories of gravity on large scales, and possibly collect evidence for one of the various
models of inflation by exploiting upcoming new data sets of unprecedented richness. Comple-
mentary to established methods probing anisotropies of the cosmic microwave background, the
large-scale galaxy distribution, or indicators of the cosmological distance ladder, weak gravi-
tational lensing on cosmological scales, or cosmic shear in short, has recently emerged as the
potentially most powerful technique to shed light on the issues listed above.
Gravitational lensing refers to the general relativistic effect of the bending of light paths in
gravitational potentials. Regarding cosmological scales, the light of distant galaxies is conti-
nously deflected by the large-scale matter distribution along the line of sight to an observer on
Earth, causing very small distortions or shears on the shapes of the galaxy images. Correlating
millions of these background galaxies, the shear signal can be extracted and used to infer sta-
tistical properties of the intervening matter distribution. This in turn allows one to constrain
cosmological parameters by probing both the geometry of the Universe and the growth of the
large-scale structure.
The smallness of the cosmic shear effect on the shape of a galaxy image is an observa-
tional challenge wherefore the first detections were reported only a decade ago. Since then the
method hasbeen rapidly maturing, with variousground- and space-based weak lensing surveys
upcoming or in advanced planning stages. Among the central issues for cosmic shear research
are therefore the optimisation of future surveys and moreover, with the increasing statistical
accuracy of measurements, the control of systematic effects potentially jeopardising cosmolog-
ical parameter estimates. Of particular importance in this respect is the intrinsic alignment
of galaxies which can mimic a cosmic shear signal and which has been identified as the major
astrophysical source of systematic errors.
It is the scope of this thesis to investigate both of these aspects, i.e. the optimisation
of cosmic shear surveys and their analysis as well as the elimination of systematics due to
intrinsic alignments, aiming at a contribution to prepare cosmic shear for the upcoming era of
high-precision cosmology, which in turn is going to have a significant share in constraining and
consolidating the standard model of cosmology. The thesis is organised as follows:
We begin with a brief overview on cosmology in Chap.2, outlining the central ingredients
of the concordance model such as the metric structure and the different matter components
populating the cosmos. The important processes in the early phases of the Universe as well
as the formation and evolution of structure are summarised. We also highlight the current
knowledge about the free parameters in the concordance model and the main probes used to
constrainthem,beforedetailingpotentialshortcomingsinthestandardpictureandthepossible
extensions or modifications that could eventually resolve them.
In Chap.3 the basic theory of weak gravitational lensing is presented, focusing on its ap-
plication to the large-scale structure of the Universe via the cosmic shear effect. We elucidate
how the gravitational shear can be inferred from galaxy images and derive the statistics used
to extract information from the shear field, as well as their dependence on cosmology. Finally,
the status quo of cosmic shear measurements is discussed by reviewing the observations of the
past ten years and providing an outlook on the surveys of the coming decade.
Chapter 4 is dedicated to various aspects concerning the optimisation of cosmic shear sur-
veys, beginning with an in-depth study of the covariance of the weak lensing bispectrum.
Subsequently, detailed forecasts of the performance of the cosmic shear survey by the planned