Weak lensing mass determination of eight X-ray selected galaxy clusters from the 400d survey [Elektronische Ressource] / vorgelegt von Holger Israel

Holger Israel

Sujets

• Astronomie

Informations

• Publié par: rheinische_friedrich-wilhelms-universitat_bonn
• Publié le: 01 janvier 2011
• Nombre de lectures: 14
• Langue: English
• Poids de l'ouvrage: 21 Mo

Extrait

Weak Lensing Mass Determination
of
Eight X-ray Selected Galaxy Clusters
from the 400d Survey
Dissertation
zur
Erlangung des Doktorgrades (Dr. rer. nat)
der
Mathematisch–Naturwissenschaftlichen Fakulta¨t
der
Rheinischen Friedrich–Wilhelms–Universita¨t Bonn
vorgelegt von
Holger Israel
aus
Got¨ tingen
Bonn, 2010Angefertigt mit Genehmigung der
Mathematisch–Naturwissenschaftlichen Fakulta¨t der
Rheinischen Friedrich–Wilhelms–Universita¨t Bonn
1. Referent: Prof. Dr. Thomas H. Reiprich
2. Referent: Prof. Dr. Peter Schneider
Tag der Promotion: 17. Dezember 2010
Erscheinungsjahr: 2011
iiAbstract
Evolution in the mass function of galaxy clusters sensitively traces both the expansion history
of the Universe and cosmological structure formation. Hence, measuring the number density of
galaxy clusters as a function of redshift provides constraints to cosmological parameters, indepen-
dent of other methods. Current results from these probes, including clusters of galaxies, are found
to agree on a cosmological model dominated by Dark Energy and Cold Dark Matter. Investigating
the unknown physical nature of Dark Energy ranks among the foremost questions in current cos-
mology. In particular, the presence or absence of evolution in Dark Energy density is expressed
by the equation-of-state parameter.
This thesis presents the first results from the 400d Galaxy Cluster Survey Weak Lensing
Programme, in which optical follow-up observations for a sample of relatively distant (0:35< z<
0:90) X-ray selected galaxy clusters are analysed and presented. Mass determination by weak
gravitational lensing uses minute distortions in the images of background galaxies, caused by the
relativistic curvature of space-time, to infer the mass of the intervening cluster. The weak lensing
follow-up project aims at measuring reliable weak lensing masses for 36 clusters, for which a
mass function and resulting cosmological constraints using Chandra X-ray observations have been
published. Determining cluster masses by weak lensing makes possible a cross-calibration of the
assumptions and systematics related to both the X-ray and weak lensing methods.
As the initial phase of the 400d weak lensing programme project, observations of eight clus-
ters were obtained with the Megacam instrument at the 6:5 m MMT telescope, which we demon-
strated to be well-suited for weak lensing. In this thesis, the successful weak lensing detections of
these eight clusters are reported, leading to weak lensing mass estimates which then are compared
to X-ray masses. For the pilot object, CL 0030+2618, the data analysis is described in great detail,
focussing in particular on the construction of a catalogue of lensed background galaxies by using
photometry in three passbands. In a synopsis involving several optical and X-ray methods, the
identity of the brightest cluster galaxy is established and found to be consistent with both X-ray
and weak lensing cluster centres for CL 0030+2618. Cluster masses are obtained by fitting the
tangential weak lensing shear measured as a function of separation from the cluster centre with a
profile function derived from the Navarro-Frenk-White Dark Matter density profile.
Performing a similar analysis for the seven further clusters and investigating the spatial dis-
tribution of the lensing signal, multiple shear peaks and/or clusters are detected in three cases. In a
comparison between the weak lensing and hydrostatic X-ray mass estimates for the eight clusters,
good agreement and a power-law relation with remarkably small scatter are found. Preliminary
scaling relations between the weak lensing masses and published X-ray observables of the eight
clusters indicate the potential of the weak lensing survey, once observations are available for the
complete 36 cluster sample. The completion of the 400d weak lensing survey is concluded to be
feasible and promising in terms of improved cosmological constraints from galaxy clusters.
iii“We have no need of other worlds. We need mirrors.
We don’t know what to do with other worlds.”
Stanisław Lem, Solaris
ivContents
0 Introduction 1
1 Concepts of Cosmology 3
1.1 The Concordance Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.1 Expansion and Big Bang, H and CMB . . . . . . . . . . . . . . . . . . 30
1.1.2 Friedmann Equation and Energy Densities . . . . . . . . . . . . . . . . . 4
1.1.3 Redshift and Distance Measures . . . . . . . . . . . . . . . . . . . . . . 7
1.1.4 Dark Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2 Structure Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.1 Growth of Inhomogeneities . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.2 Spherical Collapse and Halo Mass Function . . . . . . . . . . . . . . . . 11
1.2.3 Galaxy Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3 TheΛCDM Universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3.1 Values of the Density Parameters . . . . . . . . . . . . . . . . . . . . . 12
1.3.2 The Case for Dark Energy . . . . . . . . . . . . . . . . . . . . . . . . . 14
2 Clusters of Galaxies 15
2.1 Basic Properties and Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.1 Optical Cluster Detection . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.2 The X-ray View on Clusters . . . . . . . . . . . . . . . . . . . . . . . . 16
2.1.3 The Sunyaev-Zel’dovich Effect . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Clusters as Cosmological Probes . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.1 The Cluster Mass Function . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.2 Mass Proxies and Scaling Relations . . . . . . . . . . . . . . . . . . . . 19
3 Gravitational Lensing 23
3.1 Concepts of Lensing Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.1.1 Deflection Angle and Lens Equation . . . . . . . . . . . . . . . . . . . . 23
3.1.2 Gravitational Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 Weak Lensing Observables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2.1 Shear, Shape, and Ellipticity . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2.2 Tangential Shear Around Galaxy Clusters . . . . . . . . . . . . . . . . . 30
3.2.3 Mass Reconstruction of Galaxy Clusters . . . . . . . . . . . . . . . . . . 31
vCONTENTS CONTENTS
4 The 400d Survey 33
4.1 The 400d X-ray Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.1.1 The Rosat–Based 400d Sample . . . . . . . . . . . . . . . . . . . . . . 33
4.1.2 The Chandra Cluster Cosmology Project and Subsample . . . . . . . . . 34
4.2 The Weak Lensing Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2.2 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.2.3 Observing Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.2.4 Megacam Data Analysed for the 400d Survey . . . . . . . . . . . . . . . 41
5 Data Reduction 43
5.1 Data Reduction for MMT/Megacam . . . . . . . . . . . . . . . . . . . . . . . . 43
5.1.1 TheTHELI “Run Processing” Stage . . . . . . . . . . . . . . . . . . . . 43
5.1.2 TheTHELI “Set Processing” Stage . . . . . . . . . . . . . . . . . . . . . 45
5.1.3 Coaddition Post Production . . . . . . . . . . . . . . . . . . . . . . . . 47
5.2 Photometric Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.2.1 The Calibration Technique . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.2.2 Photometric Calibration of CL 0809+2811 . . . . . . . . . . . . . . . . 52
5.2.3 Indirect Photometric Calibration of CL 0030+2618 . . . . . . . . . . . . 52
5.2.4 Indirect Photometric Calibration of CL 0230+1836 . . . . . . . . . . . . 53
5.3 Frame Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.3.1 Measuring the PSF Anisotropy . . . . . . . . . . . . . . . . . . . . . . . 54
5.3.2 Selection for the 400d Cluster Fields . . . . . . . . . . . . . . . . . . . . 56
5.4 KSB Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.4.1 The KSB Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.4.2 Measuring Shear from Cluster Lenses . . . . . . . . . . . . . . . . . . . 61
5.4.3 The KSB Catalogue and Galaxy Shape Catalogue . . . . . . . . . . . . . 63
5.4.4 The PSF Properties of MMT/Megacam . . . . . . . . . . . . . . . . . . 65
viCONTENTS CONTENTS
6 CL 0030+2618: The Pilot Study 69
6.1 Aperture Mass Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.1.1 Outline of Background Selection . . . . . . . . . . . . . . . . . . . . . . 70
6.1.2 Background Selection by Galaxy Colours . . . . . . . . . . . . . . . . . 71
6.1.3 Detection of the Shear Signal . . . . . . . . . . . . . . . . . . . . . . . 74
6.1.4 Verification of the Shear Signal . . . . . . . . . . . . . . . . . . . . . . 74
6.2 Photometric Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
6.2.1 The Red Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
6.2.2 Comparison to Photometric Redshift Surveys . . . . . . . .