Probing Cosmic Dark Matter and Dark Energy with Weak Gravitational Lensing Statistics

144 Pages·2016·3.91 MB·English

by  Masato Shirasaki (auth.)

Springer Theses
Recognizing Outstanding Ph.D. Research
Masato Shirasaki

Probing Cosmic
Dark Matter and Dark
Energy with Weak
Gravitational Lensing
Statistics
Springer Theses
Recognizing Outstanding Ph.D. Research
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Masato Shirasaki
Probing Cosmic Dark
Matter and Dark Energy
with Weak Gravitational
Lensing Statistics
Doctoral Thesis accepted by
The University of Tokyo, Tokyo, Japan
123
Author Supervisor
Dr. Masato Shirasaki Prof. NaokiYoshida
TheUniversity of Tokyo TheUniversity of Tokyo
Tokyo Tokyo
Japan Japan
ISSN 2190-5053 ISSN 2190-5061 (electronic)
SpringerTheses
ISBN978-981-287-795-6 ISBN978-981-287-796-3 (eBook)
DOI 10.1007/978-981-287-796-3
LibraryofCongressControlNumber:2015950028
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’
Supervisor s Foreword
Observations of the spatial distribution of galaxies suggest that our universe is
approximatelyhomogeneousandisotropicatverylargelengthscales.Galaxies are
not distributed randomly, however. There are patterns and prominent “structures”
that extend over millions of light years. The origin of such a large-scale structure
oftheuniversehasattractedmuchattentionnotonlyfromprofessionalastronomers
but also from the general public.
The standard theory of cosmic structure formation posits that the structure is
formed through nonlinear gravitational growth of tiny density fluctuations gener-
ated in the very early universe. A broad range of astronomical observations have
provided a consistent picture overall with the above notion, but there remain
important questions regarding the source of gravity that enabled the formation
ofthelarge-scalestructure.Thenatureoftheso-calleddarkmatter,whichamounts
tonearly80%ofthetotalmattercontentintheuniverse,holdsakeytounderstand
the evolution of the universe and the formation of the rich structure we see today.
Gravitationallensingprovidesadirectphysicalmethodtoprobethedistribution
of matter in the universe. Collective information of distorted images of distant
galaxiescanbeutilizedtomapoutthedistributionofinterveningmatter.Recently,
wide-area surveys by large ground-based telescopes have begun providing an
enormousamountofdatafromwhichwecanstudyindetailthematterdistribution
in and around galaxies and galaxy clusters.
Dr.Shirasakiexplorednovelmethodsforrevealingthenatureofdarkmatterand
the evolution of the universe using primarily gravitational lensing observations.
Alargesetofnumericalsimulationsofcosmicstructureformationwasalsousedto
derive crucial statistical quantities for precision cosmology. The contents of this
thesisaretimelyinthatthemainresultscanbereadilyappliedtothedatafromthe
v
vi Supervisor’sForeword
ongoing large observational program Subaru Hyper Suprime-Cam survey.
A promising example of cross-correlation analysis is also presented. Altogether,
this doctoral thesis lays out the foundation for weak lensing cosmology.
Tokyo, Japan Naoki Yoshida
May 2015
Acknowledgments
Iamgratefultomysupervisor,ProfessorNaokiYoshida,forhiscontinuoussupport
and encouragement. Through fruitful discussions with him, I have learned many
things in cosmology, astrophysics, data analysis, and computational skills. He
originally led me to the interesting research area observational cosmology. I also
would like to express special thanks to my collaborators Takashi Hamana and
Shunsaku Horiuchi. If it had not been for their kind support and our useful dis-
cussions, I could not have completed this thesis. I would like to thank Masahiro
Takada, Chiaki Hikage, Masayuki Tanaka, Kazuhiro Nakazawa, and Zoltan
Haiman for useful and helpful discussions. Masanori Sato kindly providedus with
their ray-tracing simulations data. I am thankful to all of members at the Kavli
Institute for Physics and Mathematics of the Universe (Kavli IPMU), The
UniversityofTokyoTheoreticalAstrophysicsGroup(UTAP),andResearchCenter
for the Early Universe (RESCEU).
My graduate research was supported by Research Fellowships of the Japan
Society for the Promotion of Science (JSPS) for Young Scientists. Numerical
computationspresentedinthisthesiswereinpartcarriedoutonthegeneralpurpose
PC farm at the Center for Computational Astrophysics, CfCA, of the National
Astronomical Observatory of Japan. The analysis presented in this thesis is based
onobservationsobtainedwith MegaPrime/MegaCam,ajointprojectofCFHT and
CEA/IRFU, at the Canada–France–Hawaii Telescope (CFHT), which is operated
by the National Research Council (NRC) of Canada, the Institut National des
Sciences del’UniversoftheCentreNationaldelaRechercheScientifique(CNRS)
of France, and the University of Hawaii. The research used the facilities of the
Canadian Astronomy Data Centre operated by the National Research Council of
Canada with the support of the Canadian Space Agency. CFHTLenS data pro-
cessing was made possible and thanks to significant computing support from the
NSERC Research Tools and Instruments grant program.
Finally, I wish to thank my father, mother, and sister and all my friends who
have supported me.
vii
Contents
1 Introduction to Observational Cosmology . . . . . . . . . . . . . . . . . . . 1
1.1 Cosmic Acceleration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Type Ia Supernovae. . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.2 Baryon Acoustic Oscillations. . . . . . . . . . . . . . . . . . . . . 2
1.2 Astrophysical Evidence of Dark Matter. . . . . . . . . . . . . . . . . . . 3
1.2.1 Rotation Curves of Galaxies . . . . . . . . . . . . . . . . . . . . . 4
1.2.2 Mass Estimate of Clusters of Galaxies . . . . . . . . . . . . . . 4
1.2.3 Global Energy Budget of Universe. . . . . . . . . . . . . . . . . 5
1.3 Cosmology with Gravitational Lensing. . . . . . . . . . . . . . . . . . . 6
1.4 Objective of This Thesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Structure Formation in the Universe. . . . . . . . . . . . . . . . . . . . . . . 15
2.1 The Standard Cosmological Model. . . . . . . . . . . . . . . . . . . . . . 15
2.1.1 Friedmann Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.2 Cosmological Redshift and Angular-Diameter Distance. . . 18
2.2 Growth of Matter Density. . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.1 Evolution of Density Fluctuations . . . . . . . . . . . . . . . . . 20
2.2.2 Linear Perturbation. . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.3 Non-linear Perturbation. . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3 Statistics of Matter Density Perturbation . . . . . . . . . . . . . . . . . . 25
2.3.1 Two Point Statistics. . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3.2 Mass Function and Halo Bias . . . . . . . . . . . . . . . . . . . . 27
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3 Weak Gravitational Lensing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.1 Basic Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 Observable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3 Statistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3.1 Two Point Correlation Function. . . . . . . . . . . . . . . . . . . 36
3.3.2 Lensing Mass Reconstruction . . . . . . . . . . . . . . . . . . . . 41
3.3.3 Minkowski Functionals. . . . . . . . . . . . . . . . . . . . . . . . . 42
ix
x Contents
3.4 Numerical Simulation of Weak Lensing . . . . . . . . . . . . . . . . . . 46
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4 Weak Lensing Morphological Analysis . . . . . . . . . . . . . . . . . . . . . 53
4.1 Impact of Masked Region. . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.1.1 Estimation of Lensing MFs from Cosmic Shear Data. . . . 54
4.1.2 Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.1.3 Bias Due to Masking Effect . . . . . . . . . . . . . . . . . . . . . 58
4.1.4 Impact of Masking on Cosmological
Parameter Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.1.5 Application to Subaru Suprime-Cam Data. . . . . . . . . . . . 61
4.2 Statistical and Systematic Error of Minkowski Functionals . . . . . 63
4.2.1 Mock Weak Lensing Catalogs. . . . . . . . . . . . . . . . . . . . 63
4.2.2 Realistic Forecast of Cosmological Constraints . . . . . . . . 66
4.2.3 Possible Systematics. . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.3 Application to CFHTLenS. . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.3.1 Data Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.3.2 Likelihood Analysis of Lensing MFs . . . . . . . . . . . . . . . 76
4.3.3 Breaking Degeneracies. . . . . . . . . . . . . . . . . . . . . . . . . 77
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5 Cross Correlation with Dark Matter Annihilation Sources. . . . . . . 85
5.1 Dark Matter Annihilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.1.1 Relic Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.1.2 Gamma-Ray Intensity. . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.2 Extragalactic Gamma-Ray Background. . . . . . . . . . . . . . . . . . . 89
5.2.1 Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.3 Cross Correlation of Extragalactic Gamma-Ray Background
and Cosmic Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.3.1 Theoretical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.3.2 Cross-Correlation Estimator and Covariance . . . . . . . . . . 100
5.4 Application to Real Data Sets . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.4.1 Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.4.2 Result. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.5 Constraint and Forecast. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.5.1 DM Annihilation Constraint . . . . . . . . . . . . . . . . . . . . . 107
5.5.2 Future Forecast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
6 Summary and Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6.1 Lensing Minkowski Functionals. . . . . . . . . . . . . . . . . . . . . . . . 115
6.1.1 Subaru Suprime-Cam. . . . . . . . . . . . . . . . . . . . . . . . . . 115
6.1.2 Canada-France-Hawaii Telescope Lensing Survey . . . . . . 116
6.1.3 Future Work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117