The Colours of Galaxies in Intermediate X-ray Luminosity Galaxy Clusters

The Colours of Galaxies inIntermediate X-ray Luminosity

Galaxy Clusters

By

Peter Christian Jensen

A thesis submitted to the University of Queenslandin partial fulfilment of the Degree of Bachelor of Science (Honours)

Department of PhysicsJune 2008

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Abstract

Recent cluster studies have found radial and density colour gradients in the modal coloursof the elliptical galaxies from the high density cores of clusters. This effect has been widelyinterpreted as being a manifestation of star formation truncation for galaxies falling intoclusters. Colour gradients are also implicated in the morphology-density relation whichshows that the fraction of elliptical galaxies is a sharply decreasing function of density. Ourknowledge of the relationships between cluster environment and galaxy evolution, however,have tended to focus on the most massive, X-ray luminous clusters in isolation to theirlarge-scale structure. In comparison to what has been previously done, the intermediate-LXregime is relatively unexplored and by going wide-field, we probe all galaxy environmentsfrom the dense cluster core out to the field. In this thesis we report that colour gradients forintermediate-LX clusters are consistent with ones reported for high-LX clusters. The criticalradius (which demarcates the cluster environment from the field environment) has movedinward from ∼ 4 Mpc for high-LX clusters to (1.7 ± 0.5) Mpc for intermediate-LX clusters.We also report a critical local galaxy density of (1.5 ± 0.5) Mpc−2 which is consistent withhigh-LX studies. We argue that the mechanism responsible for galaxy evolution is universaland only depends on local galaxy density. This rules out mass-dependent mechanisms suchhalo gas starvation and ram-pressure stripping and makes galaxy “harassment” the mostlikely candidate.

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iv Abstract

Acknowledgments

I dedicate this thesis to my long-suffering partner, Sofie Ham. Without her love, support,and patience, I doubt that I could have survived the four and half years it has taken to get tothis point. I also wish to thank my family who have been my other pillar of support. Theirmoral support has kept me going through the hard times and their financial support haskept me going through the lean times. Finally, I wish to thank my supervisor, Dr. KevinPimbblet, from whom I have learned so much about astronomy and about myself in thepast year. Kevin’s ability as a supervisor and dedication to his students is second to none.I feel honoured to have been his student and he has inspired me to continue my career inastronomy.

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vi Acknowledgments

Declaration

Except where acknowledged in the customary manner, the material presented in this thesisis, to the best of my knowledge, original and has not been submitted in whole or part for adegree in any university. The SDDS colours and magnitudes, redshifts, equivalent widths,k-corrections, right ascensions, declinations and photometric images used throughout thisthesis were downloaded from the Sloan Digital Sky Survey (SDSS). I acknowledge the hardwork of the SDSS team in making their data publically available. I also acknowledge theNASA/IPAC Extragalactic Database (NED) from whom I obtained Bautz-Morgan type datafor the majority of the galaxy clusters in this thesis. I also used NED and SDSS photometricimages to visually inspect clusters in a number of instances. Finally, I acknowledge editorialwork and suggestions made by my supervisor, Dr. Kevin Pimbblet. Editorial work by Dr.Kevin Pimbblet did not change the meaning or content of this thesis.

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viii Declaration

Contents

Abstract iii

Acknowledgments v

Declaration vii

List of Figures xi

List of Tables xix

1 Introduction 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 History and background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2.2 Clusters and Large Scale Structure . . . . . . . . . . . . . . . . . . . 7

1.3 Galaxy evolution in clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.3.1 The colour-magnitude relation . . . . . . . . . . . . . . . . . . . . . . 111.3.2 The Butcher-Oemler effect . . . . . . . . . . . . . . . . . . . . . . . . 131.3.3 The morphology-density relation . . . . . . . . . . . . . . . . . . . . 151.3.4 Star formation in cluster galaxies . . . . . . . . . . . . . . . . . . . . 171.3.5 Gas-stripping mechanisms . . . . . . . . . . . . . . . . . . . . . . . . 21

1.4 This study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2 Constructing and Qualifying the Dataset 272.1 Cluster selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.2 Bias in the cluster selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.3 Constructing the galaxy catalogue . . . . . . . . . . . . . . . . . . . . . . . . 332.4 Discordant points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382.5 Calculating projected radii and local galaxy densities . . . . . . . . . . . . . 402.6 Calculation of r200 and concentration index . . . . . . . . . . . . . . . . . . . 422.7 Mass and morphology degeneracy . . . . . . . . . . . . . . . . . . . . . . . . 432.8 Substructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3 Evolution of the Red Galaxies 473.1 The cluster luminosity function . . . . . . . . . . . . . . . . . . . . . . . . . 473.2 Fitting the colour-magnitude relations . . . . . . . . . . . . . . . . . . . . . 50

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3.3 Dependence of the colour-magnitude relation on global cluster properties . . 583.3.1 Slope of the CMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583.3.2 Colour of the CMR at M∗ . . . . . . . . . . . . . . . . . . . . . . . . 59

3.4 The composite cluster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613.4.1 Stacking the clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . 623.4.2 Colour distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633.4.3 Dependence of the modal colour on cluster environment . . . . . . . . 64

4 Discussion 73

5 Conclusion 775.1 Key results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 775.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

References 81

A Cluster Characterisation and Colour-Magnitude Diagrams 87

B Dependence of the Colour-Magnitude Relation on Cluster Global Proper-ties: Supplementary Figures 179

C Composite Cluster: Supplementary Figures 201

D SQL Queries 231D.1 The Galaxy Catalogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231

D.1.1 Identification, Positional and Photometric Data . . . . . . . . . . . . 231D.1.2 Spectroscopic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232

D.2 Other Queries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233D.2.1 The Cluster Catalogue . . . . . . . . . . . . . . . . . . . . . . . . . . 233D.2.2 Number of Galaxies in Each Cluster . . . . . . . . . . . . . . . . . . 233D.2.3 Overlapping Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

List of Figures

1.1 X-ray luminosity-redshift parameter space diagram. The grey squares rep-resent XBACS, BCS, and eBCS clusters while the dashed line boxes showthe region of parameter space probed by recent X-ray selected cluster stud-ies. Note that CNOC, MACS and Wake et al. studies select clusters fromcatalogues other than XBACS, BCS, and eBCS. . . . . . . . . . . . . . . . . 2

1.2 Hubble’s tuning-fork diagram (source: http://commons.wikimedia.org). . . . 51.3 Example clusters showing different Bautz-Morgan types. From top to bottom,

the inner 0.5 h−1 Mpc × 0.5 h−1 Mpc of Abell 2199 (BMI), Coma (BMII)and Virgo (BMIII) (source: Sloan Digital Sky Survey). . . . . . . . . . . . . 9

1.4 Large-scale structure in the 2dF Galaxy Redshift Survey (source: Collesset al., 2001). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.5 The (g-i) versus i colour-magnitude diagram for Abell 2199. The solid line isthe CMR and the vertical dashed line is the i-band fiducial magnitude. . . . 12

1.6 The (V-I) vs I colour-magnitude diagram for Abell 1703. Scatter about theCMR is evident at faint magnitudes (source: Stott, 2007). . . . . . . . . . . 13

1.7 The evolution of cluster galaxies on the colour-magnitude plane. The left-mostcolour-magnitude diagrams in each row correspond to actual observations ofgalaxy clusters. Subsequent diagrams to the right are generated by N-bodycomputer simulations. The dotted and dashed lines correspond to the Butcher& Oemler (1984) criteria of MV = −20 and ∆(B-V) = -0.2 (source: Kodama& Bower, 2001). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.8 The evolution of (V-I) vs I red sequence slope. The solid and dotted linesrepresent model predictions with ± 1 σ errors (source: Stott, 2007). . . . . . 15

1.9 The Butcher-Oemler effect is the name given to the phenomenon where thefraction of blue galaxies increases with redshift (source: Pimbblet, 2003). . . 16

1.10 The morphology-density relation for a composite cluster composed of 55 clus-ters (source: Dressler, 1980). . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

1.11 The morphology-radius and morphology-density relations for a compositecluster composed of six irregular clusters (source: Dressler, 1980). . . . . . . 18

1.12 The SFR-R and SFR-Σ relations. This figure clearly shows that [OII] lumi-nosity (which traces ongoing star-formation) is truncated more abruptly inthe SFR-Σ relation than in the SFR-R relation (source: Pimbblet et al., 2006). 19

1.13 The MORPHS spectral classification system (source: Dressler et al., 1999). . 201.14 Galaxy spectral types on the colour-magnitude plane (source: Pimbblet et al.,

2006). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

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xii List of Figures

1.15 Evolutionary sequence in the harassment model. Spiral galaxies are effectivelystripped of their star-forming gas and are transformed into dwarf ellipticalgalaxies after 4 – 5 close encounters. The time steps shown here are ∼ 0.5Gyr and the whole process occurs over 2 – 3 Gyr (source: Moore et al., 1996). 23

2.1 Projection of the celestial sphere, showing spectroscopic sky coverage of theDR6 Sloan Digital Sky Survey. RA and Dec have units of degrees (source:http://www.sdss.org/dr6/). “Whisker” regions are the long, narrow stripes ofspectroscopically-sampled sky near the celestial equator, below RA ∼ 60degand above RA ∼ 300deg. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.2 Redshifts, X-ray luminosities and cluster morphology in the intermediate-LXcluster catalogue. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.3 Bautz-Morgan type fraction histograms for the XBACS, BCS, and eBCS cat-alogues (462 clusters) and the intermediate-LX cluster sample (45 clusters). . 33

2.4 Redshift histograms for clusters in XBACS and BCS by Bautz-Morgan type.The solid horizontal line represents the average fraction of clusters taken acrossall redshift bins. The dashed horizontal lines represent the 3σ uncertainty levelin the average fraction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.5 LX histograms for clusters in XBACS and BCS by Bautz-Morgan type. Thesolid horizontal line represents the average fraction of clusters taken across allLX bins. The dashed horizontal lines represent the 3σ uncertainty level in theaverage fraction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.6 Redshift histograms in the intermediate-LX cluster sample by Bautz-Morgantype. The solid horizontal line represents the average fraction of clusterstaken across all redshift bins. The dashed horizontal lines represent the 3σuncertainty level in the average fraction. . . . . . . . . . . . . . . . . . . . . 36

2.7 LX histograms in the intermediate-LX cluster sample by Bautz-Morgan type.The solid horizontal line represents the average fraction of clusters taken acrossall LX bins. The dashed horizontal lines represent the 3σ uncertainty level inthe average fraction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.8 Discordant point on the (g-i) versus i colour-magnitude diagram for Abell1767. A blue spiral galaxy in the line-of-sight of the target red elliptical galaxyconfuses the photometric measurements, causing the i band to be much fainterthan the other bands. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.9 Discordant point on the (u-g) versus g colour-magnitude diagram for Abell971. A star nearby to the target galaxy saturates the photometric measure-ments, causing the u band to be much fainter than the other bands. . . . . . 39

2.10 Discordant points on the (u-g) versus g colour-magnitude diagram for Abell1809. The source of bias is unknown but is suspected to be due to dust-reddening. The discordant galaxies congregate around 4.5 degrees of dec-lination on the RA-Dec diagram. No bad pixel rows or nearby sources ofphotometric contamination suggest that the reddening may be caused by thepresence of a dust lane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

List of Figures xiii

2.11 X-ray luminosity versus velocity dispersion. There is no trend between X-ray luminosity and velocity dispersion, however, the velocity distributionsare normally distributed about 600 km s−1, indicative of an homogeneousintermediate-mass cluster sample. . . . . . . . . . . . . . . . . . . . . . . . . 44

2.12 Bautz-Morgan type versus concentration index. There is no trend betweenBautz-Morgan type and concentration index which indicates that they quan-tify different and independent aspects of cluster morphology. . . . . . . . . . 45

3.1 Magnitude distributions for the u, g, r, i, and z′ bands with line of bestfit for the log n distribution. The vertical dashed lines represent the 90%completeness limit in each band. . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.2 Absolute magnitude luminosity functions for the u, g, r, i, and z′ bands. Thesolid curves are our Schechter function model fits. The vertical dashed linesmark the position of M∗. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

3.3 The composite cluster colour-magnitude diagram in (g-i)′ colour versus i′ mag-nitude. The vertical dashed line shows the position of M∗i at median redshiftz ∼ 0.09 while the solid horizontal line shows the median (g-i) colour at M∗ifor all 45 clusters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

3.4 The composite cluster colour distribution with double Gaussian fits. Thevertical dashed lines show the positions of the colour cuts for single Gaussianfitting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

3.5 The composite cluster colour distribution – continued. . . . . . . . . . . . . . 69

3.6 Modal colour (bottom panel) and width (top panel) of the CMR versus pro-jected radius in (g-i)′ colour. . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.7 Modal colour (bottom panel) and width (top panel) of the CMR versus logprojected radius in (g-i)′ colour. . . . . . . . . . . . . . . . . . . . . . . . . . 71

3.8 Modal colour (bottom panel) and width (top panel) of the CMR versus loglocal galaxy density in (g-i)′ colour. . . . . . . . . . . . . . . . . . . . . . . . 72

4.1 Comparison of (g-r)/log rp colour gradients from recent X-ray selected clusterstudies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

A.1 Abell 602 - The top left panel shows an SDSS image of the inner 0.5×0.5Mpc2 of the cluster core. The top right panel is the RA-Dec diagram forthis cluster. The inner circle represents the r200 projected radius, the outercircle represents the 3r200 projected radius, and the borders have been tightlycropped to 10 Mpc in projected radius. The bottom left panel is the redshifthistogram plot for this cluster. The bottom x-axis is velocity dispersion whilethe top x-axis is redshift. The superimposed Gaussian fit is the one we usedto estimate the clustercentric redshift and velocity dispersion for this cluster.The bottom right panel is the projected radius-local galaxy density plot forthis cluster. The vertical dashed line on the left represents the r200 projectedradius while the outer vertical dashed line represents the the 3r200 projectedradius. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

xiv List of Figures

A.2 Abell 602 - Colour-magnitude diagrams. The solid sloping lines represent ourbest estimate of the CMR, the vertical solid lines represent fiducial magni-tudes, and the vertical dashed lines represent M∗ in apparent magnitude. . . 89

A.3 Abell 671 - The same as figure A.1 except these diagrams characterise Abell671. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

A.4 Abell 671 - Same as figure A.2 except these colour-magnitude diagrams arefor Abell 671. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

A.5 Abell 743 - Same as figure A.1 except these diagrams characterise Abell 671. 92A.6 Abell 743 - Same as figure A.2 except these colour-magnitude diagrams are

for Abell 743. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93A.7 Abell 744 - Same as figure A.1 except these diagrams characterise Abell 744. 94A.8 Abell 744 - Same as figure A.2 except these colour-magnitude diagrams are







for Abell 971. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107A.21 Abell 1035 - Same as figure A.1 except these diagrams characterise Abell 1035.108A.22 Abell 1035 - Same as figure A.2 except these colour-magnitude diagrams are

for Abell 1035. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109A.23 Abell 1045 - Same as figure A.1 except these diagrams characterise Abell 1045.110A.24 Abell 1045 - Same as figure A.2 except these colour-magnitude diagrams are



for Abell 1361. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115A.29 Abell 1446 - Same as figure A.1 except these diagrams characterise Abell 1446.116

List of Figures xv

A.30 Abell 1446 - Same as figure A.2 except these colour-magnitude diagrams arefor Abell 1446. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

A.31 Abell 1691 - Same as figure A.1 except these diagrams characterise Abell 1691.118A.32 Abell 1691 - Same as figure A.2 except these colour-magnitude diagrams are














for Abell 2124. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

xvi List of Figures

A.59 Abell 2141 - Same as figure A.1 except these diagrams characterise Abell 2141.146












A.71 RXJ0820.9+0751 - Same as figure A.1 except these diagrams characteriseRXJ0820.9+0751. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

A.72 RXJ0820.9+0751 - Same as figure A.2 except these colour-magnitude dia-grams are for RXJ0820.9+0751. . . . . . . . . . . . . . . . . . . . . . . . . . 159











A.83 ZwCl 1478 - Same as figure A.1 except these diagrams characterise ZwCl 1478.170

List of Figures xvii

A.84 ZwCl 1478 - Same as figure A.2 except these colour-magnitude diagrams arefor ZwCl 1478. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

A.85 ZwCl 4905 - Same as figure A.1 except these diagrams characterise ZwCl 4905.172A.86 ZwCl 4905 - Same as figure A.2 except these colour-magnitude diagrams are

for ZwCl 4905. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173A.87 ZwCl 6718 - Same as figure A.1 except these diagrams characterise ZwCl 6718.174A.88 ZwCl 6718 - Same as figure A.2 except these colour-magnitude diagrams are

for ZwCl 6718. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175A.89 ZwCl 8197 - Same as figure A.1 except these diagrams characterise ZwCl 8197.176A.90 ZwCl 8197 - Same as figure A.2 except these colour-magnitude diagrams are

for ZwCl 8197. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

B.1 Evolution of the slope of the CMR with redshift. . . . . . . . . . . . . . . . . 180B.2 Evolution of the slope of the CMR with redshift – continued. . . . . . . . . . 181B.3 Mass dependence of the slope of the CMR with X-ray luminosity. . . . . . . 182B.4 Mass dependence of the slope of the CMR with X-ray luminosity – continued. 183B.5 Mass dependence of the slope of the CMR with velocity dispersion. . . . . . 184B.6 Mass dependence of the slope of the CMR with velocity dispersion – continued.185B.7 Morphology dependence of the slope of the CMR with concentration index. . 186B.8 Morphology dependence of the slope of the CMR with concentration index –

continued. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187B.9 Morphology dependence of the slope of the CMR with Bautz-Morgan type. . 188B.10 Morphology dependence of the average slope of the CMR with Bautz-Morgan

type – continued. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189B.11 Evolution of the colour of the CMR at M∗ with redshift. . . . . . . . . . . . 190B.12 Evolution of the colour of the CMR at M∗ with redshift – continued. . . . . 191B.13 Mass dependence of the colour of the CMR at M∗ with X-ray luminosity. . . 192B.14 Mass dependence of the colour of the CMR at M∗ with X-ray luminosity –

continued. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193B.15 Mass dependence of the colour of the CMR at M∗ with velocity dispersion. . 194B.16 Mass dependence of the colour of the CMR at M∗ with velocity dispersion –

continued. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195B.17 Morphology dependence of the colour of the CMR at M∗ with concentration

index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196B.18 Morphology dependence of the colour of the CMR at M∗ with concentration

index – continued. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197B.19 Morphology dependence of the average colour of the CMR at M∗ with Bautz-

Morgan type. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198B.20 Morphology dependence of the average colour of the CMR at M∗ with Bautz-

Morgan type – continued. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

C.1 Composite cluster colour-magnitude diagrams. . . . . . . . . . . . . . . . . . 202C.2 Composite cluster colour-magnitude diagrams – continued. . . . . . . . . . . 203C.3 Modal colour and width of CMR versus projected radius in (u-g)′ colour. . . 204C.4 Modal colour and width of CMR versus projected radius in (u-r)′ colour. . . 205

xviii List of Figures

C.5 Modal colour and width of CMR versus projected radius in (u-i)′ colour. . . 206C.6 Modal colour and width of CMR versus projected radius in (u-z′)′ colour. . . 207C.7 Modal colour and width of CMR versus projected radius in (g-r)′ colour. . . 208C.8 Modal colour and width of CMR versus projected radius in (g-z′)′ colour. . . 209C.9 Modal colour and width of CMR versus projected radius in (r-i)′ colour. . . . 210C.10 Modal colour and width of CMR versus projected radius in (r-z′)′ colour. . . 211C.11 Modal colour and width of CMR versus projected radius in (i-z′)′ colour. . . 212C.12 Modal colour and width of CMR versus log projected radius in (u-g)′ colour. 213C.13 Modal colour and width of CMR versus log projected radius in (u-r)′ colour. 214C.14 Modal colour and width of CMR versus log projected radius in (u-i)′ colour. 215C.15 Modal colour and width of CMR versus log projected radius in (u-z′)′ colour. 216C.16 Modal colour and width of CMR versus log projected radius in (g-r)′ colour. 217C.17 Modal colour and width of CMR versus log projected radius in (g-z′)′ colour. 218C.18 Modal colour and width of CMR versus log projected radius in (r-i)′ colour. . 219C.19 Modal colour and width of CMR versus log projected radius in (r-z′)′ colour. 220C.20 Modal colour and width of CMR versus log projected radius in (i-z′)′ colour. 221C.21 Modal colour and width of CMR versus log local galaxy density in (u-g)′ colour.222C.22 Modal colour and width of CMR versus log local galaxy density in (u-r)′ colour.223C.23 Modal colour and width of CMR versus log local galaxy density in (u-i)′ colour.224C.24 Modal colour and width of CMR versus log local galaxy density in (u-z′)′ colour.225C.25 Modal colour and width of CMR versus log local galaxy density in (g-r)′ colour.226C.26 Modal colour and width of CMR versus log local galaxy density in (g-z′)′ colour.227C.27 Modal colour and width of CMR versus log local galaxy density in (r-i)′ colour.228C.28 Modal colour and width of CMR versus log local galaxy density in (r-z′)′ colour.229C.29 Modal colour and width of CMR versus log local galaxy density in (i-z′)′ colour.230

List of Tables

2.1 Intermediate-LX cluster sample . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.1 Completeness limits in the intermediate-LX cluster sample . . . . . . . . . . 483.2 Schechter function fit parameters . . . . . . . . . . . . . . . . . . . . . . . . 533.3 CMR fit coefficients I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563.4 CMR fit coefficients II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.5 Scatter in the CMR slopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603.6 Spearman rank correlation coefficients for the slope of the red sequence versus

cluster global properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603.7 Linear fit coefficients for the colour of the CMR at M∗ versus redshift. . . . . 613.8 Scatter in the colour of the CMR at M∗ . . . . . . . . . . . . . . . . . . . . . 623.9 Spearman rank correlation coefficients for the colour of the CMR at M∗ versus

cluster global properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623.10 Composite cluster colour distribution double Gaussian fit coefficients and

colour cuts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653.11 Projected radius colour gradients and critical radii . . . . . . . . . . . . . . . 663.12 Log projected radius colour gradients and critical radii . . . . . . . . . . . . 673.13 Log local galaxy number density colour gradients and critical number densities 67

4.1 Comparison of colour gradients in projected radius and log local galaxy density. 76

xix

xx List of Tables

1Introduction

1.1 Motivation

How do galaxies evolve in intermediate-mass galaxy clusters? The short answer is that no-body knows because the question has never been addressed adequately. Presumably theprocess is similar to how galaxies evolve in better-studied high-mass clusters. A more in-sightful question is the following. What can we learn about the general properties of galaxyevolution based on the differences between evolution in high and intermediate-mass clusters?This is the overarching question motivating this work.

Much effort has been devoted to understanding how galaxies evolve in clusters. Most ofthe attention has been placed on the highest-mass clusters because these are the easiest onesto locate at high-redshift, and thus lend themselves to longitudinal redshift studies. Recentexamples include Yee et al. (1996), Balogh et al. (1999), Ebeling et al. (2001), Wake et al.(2005) and Pimbblet et al. (2006). In comparison, intermediate and low-mass clusters are arelatively unexplored region of parameter space and thus merit our attention. InterpretingX-ray luminosity, LX , as a proxy for cluster mass, the bias toward high mass is immedi-ately apparent in a diagram of X-ray luminosity-redshift parameter space. In figure 1.1,we present the regions of parameter space explored by four recent X-ray luminosity-selectedgalaxy cluster studies – the Las Campanas/Anglo-Australian Telescope Rich Cluster Survey(LARCS, see Pimbblet et al., 2002, 2006), the Canadian Network for Observational Cosmol-ogy (CNOC) Cluster Redshift Survey (see Yee et al., 1996; Balogh et al., 1999), the MassiveCluster Survey (MACS, see Ebeling et al., 2001) and the work of Wake et al. (2005) – aswell as the region explored by this work. Note that clusters are not distributed evenly acrossparameter space, only the brightest clusters are observed at high redshift. As a first approx-imation, redshift, z, is proportional to distance so the cluster distribution is the result ofthe minimum flux limit imposed by the X-ray detector. This selection effect, which is calledMalmquist bias (Carroll & Ostlie, 1996), occurs whenever an astronomer uses a flux-limited

1

2 Introduction

0 0.1 0.2 0.3 0.4 0.5 0.6

0.1

1

10

MACS

LARCSCNOC

Wake et al.

This work

Redshift, z

L X /

1044

erg

s-1

Figure 1.1: X-ray luminosity-redshift parameter space diagram. The grey squares representXBACS, BCS, and eBCS clusters while the dashed line boxes show the region of parameter spaceprobed by recent X-ray selected cluster studies. Note that CNOC, MACS and Wake et al. studiesselect clusters from catalogues other than XBACS, BCS, and eBCS.

sample of objects.

Given that all luminosity-selected cluster surveys are subject to Malmquist bias, a numberof observational strategies are possible. The MACS and CNOC studies opted for a high-LX ,longitudinal redshift strategy whereas the LARCS study focused on creating a homogeneoussample at low-redshift. In contrast, Wake et al. probes a wide range of X-ray luminositiesat intermediate redshift by selecting clusters from a variety of surveys with different fluxlimits. A drawback of selecting clusters from multiple sources though, is that unforeseenbiases may be introduced into the sample. Furthermore, the work by Wake et al. does nottell us very much about intermediate-mass clusters because it only looks at 12 clusters, ofwhich only 4 are found within the LX limits of this work. Since we are interested in selectinga large, homogeneous, intermediate-LX cluster sample, we are constrained to low-redshiftaround z ∼ 0.1.

1.2 History and background 3

In addition to filling in a blank piece of parameter space, there are a number of otherexciting reasons why we should be interested in intermediate-mass clusters. We may be ableto deduce the physical mechanism(s) driving galaxy evolution in clusters. At the very least,we should be able to discriminate between mechanisms which depend on cluster mass frommechanisms which are independent of cluster mass. An exciting prospect of this work is thatwe may be able to obtain “smoking gun” evidence of galaxy evolution in progress. There is acritical radius/density where galaxy star-formation is “switched off” in clusters (Lewis et al.,2002; Gomez et al., 2003; Pimbblet et al., 2006). In high-mass clusters the star-formationrate, SFR, gradient around the critical radius/density is too steep to find transition objects.However, if the mechanism driving star-formation suppression is dependent on cluster mass,then the SFR gradient may be shallower in intermediate-mass clusters and we might findtransition objects like the ones reported by Moran et al. (2007). Some of the transitionobjects we might hope to find are post-starburst galaxies1, S0 galaxies2, or anaemic spirals3.

In contrast to earlier studies, we implement the following innovations which will help usstudy galaxy evolution in intermediate-mass clusters. Our first innovation is in scope. Thisstudy is by far the largest study ever performed on intermediate-mass regime - 45 galaxyclusters between 0.7 × 1044 < LX < 4 × 1044 erg s−1 and 0 < z < 0.2. Our second innovationis to use a 10 Mpc radius aperture around each galaxy cluster. Most earlier studies haveonly focused on the central few Mpc around the core regions of galaxy clusters. By goingwide-field we ensure that we sample a wide range of galaxy environments, not just the over-dense regions. The final innovation, exploring a new region of parameter space, has alreadybeen discussed.

The rest of this chapter has been structured as follows. In section 1.2 we present a briefoutline of the history of observational cosmology and discuss the nature of galaxies andclusters of galaxies. In section 1.3 we review the literature on the subject of galaxy evolutionin clusters. Finally, in section 1.4 we list the research questions we wish to answer, discusstechnical, introductory information relating to this study and overview the structure of therest of this thesis.

1.2 History and background

The history of modern observational cosmology begins in 1923 when Edwin Hubble (1889-1953) observed Cepheid variable stars4 in Andromeda. Prior to 1923, the astronomicalcommunity was divided on the issue of whether spiral “nebulae” were part of the Milky Way

1Galaxies falling into the cluster potential might undergo a sudden, short burst of intense star-formationimmediately before the onset of star-formation suppression Post-starburst galaxies thus represent a transitionspecies between star-forming and quiescent galaxies.

2S0 is a type of galaxy morphology, intermediate between spiral and elliptical morphologies. Spiralgalaxies may be transformed into elliptical galaxies by way of S0 morphology on their descent into thecluster core.

3In comparison to regular spiral galaxies, anaemic spirals tend to have reduced star-formation rates andare uncharacteristically red in colour van den Bergh (1976).

4Cepheids are a class of star whose luminosity varies periodically with time. A relation exists betweena Cepheid’s luminosity and period thus they can be used as a standard candle to measure astronomicaldistances.

4 Introduction

or whether they in fact represented “island universes”. Hubble answered the question insupport of the latter option when he found that the Cepheids he discovered in Andromedawere many magnitudes fainter than any observed in the Milky Way. Despite underestimatingthe distance to the spiral nebula by about a factor of 3, the distance he calculated still safelyplaced it outside the Milky Way (Carroll & Ostlie, 1996).

In 1929, Hubble demonstrated a relationship between distance and recessional velocityamong galaxies. It had been noted by Vesto Slipher (1875-1969) as early as 1914 that theradial velocities of spiral “nebulae” were not random - most exhibited redshifted spectrademonstrating that they were receding from the Earth. Hubble (1929) and Hubble & Hu-mason (1931) correlated Slipher’s results with their own distance measurements using theCepheid method to show a linear relation between recessional velocity and distance. Thisrelation is now called Hubble’s Law and is given by:

vr = H0 d (1.1)

where vr is the recessional velocity, d is the distance to the galaxy and H0 is Hubble’sconstant. Hubble obtained a value of 500 km/s/Mpc for H0, however modern astronomersbelieve H0 to be somewhere between 50-100 km/s/Mpc. Because of the uncertainty in H0

and to make results directly comparable, many authors use the parametric form:

H0 = 100hkm s−1 Mpc−1 (1.2)

where h is a unitless parameter between 0.5 and 1. The latest results from the WilkinsonMicrowave Anisotropy Probe (WMAP) render this somewhat unnecessary, narrowing thevalue down to 73.2+3.1

−3.2 km/s/Mpc (Spergel et al., 2007). Recessional velocities can be calcu-lated very accurately by obtaining a galaxy’s spectrum and measuring the Doppler redshift,z, of prominent spectral features. The z parameter is defined as:

z =λoλe− 1 (1.3)

where λo is the observed wavelength of the spectral feature and λe is the rest frame wave-length. Because of the finite speed of light, when we look at distant galaxies we are alsolooking back in time. Not only is the z parameter a measure of velocity and distance, it isalso a measure of look-back time. In summary, Hubble’s law provides a convenient, and insome cases the only method of determining extragalactic distances.

The interpretation of equation 1.1 is unambiguous - the Universe is expanding. Even in1929, the idea of an expanding Universe was not without precedent. Willem de Sitter (1872-1935) used Einstein’s theory of general relativity in 1917 to describe an expanding universe,albeit a Universe devoid of matter. Hubble was aware of de Sitter’s work and noted in his1929 paper that the velocity-distance relation might be a manifestation of the “de Sittereffect”. Albert Einstein (1879-1955) originally preferred a static Universe, incorporatinga cosmological constant, Λ, in his field equations to offset gravitational contraction in hisUniverse. Einstein was obliged to abandon the idea of a static Universe in 1930 and latercalled the cosmological constant the “biggest blunder” of his life. Today, Hubble’s Law isconsidered to be a cornerstone of the big bang theory.


Figure 1.2: Hubble’s tuning-fork diagram (source: http://commons.wikimedia.org).

The progress Hubble made to observational cosmology was revolutionary. Within theperiod of 6 years he showed that the Universe was expanding and was composed of notone, but billions of galaxies. Since the time of Hubble, one of the main aims of observationalcosmology has been to describe and account for the pantheon galaxies we see in the Universe.

1.2.1 Galaxies

After determining the extragalactic nature of the spiral nebulae, Hubble again played akey role in classifying the galaxies by morphology. Hubble’s classification system is bestunderstood in terms of the tuning-fork diagram, shown in figure 1.2. The diagram classifiesgalaxies as being either elliptical (E’s), spiral (S’s and SB’s), lenticular (S0) or irregular(Irr). Hubble interpreted the tuning-fork diagram as an evolutionary sequence for galaxies.He erroneously postulated that galaxies evolved from left to right along the tuning-forkdiagram. Today, astronomers still use the terms early-type for ellipticals and late-type forspirals and irregulars. Ironically, much of the evidence we will outline in section 1.3 indicatesthat galaxy evolution moves from right to left along the tuning-fork diagram.

The ellipticals are organised on the left-hand side of the tuning-fork diagram and followthe sequence E0 through to E7. The number next to the E represents the galaxy’s ellipticity,ε, with E0 corresponding to a spherical system with ε = 0 and E7 corresponding to a highlyelliptical system with ε = 0.7. Elliptical galaxies with ε > 0.7 have never been observed(Hubble, 1936). Elliptical galaxies generally have a homogeneous red colour, indicating theabsence of massive, short-lived stars, a characteristic r1/4 surface luminosity profile and theyare typically found at the centers of galaxy clusters Dressler (1980).

6 Introduction

On the right-hand side of the tuning-fork diagram are 2 sequences of spiral galaxies. TheS’s represent the normal spirals while the SB’s represent the barred spirals. All spiral galaxiesare composed of 3 stellar populations - a red central bulge population, a circumstellar diskpopulation and a tenuous halo population. Barred spirals are similar to normal spirals but,as the name and digram suggest, have a bar-like structure in the bulge. In the tuning-forkdiagram, the lower case letter next to the S and SB describes the prominence of the centralbulge, the pitch angle of the spiral arms and the integrated colour. Sa’s and SBa’s havethe most prominent bulges, tightest wound arms and are the reddest of the spirals whilethe Sc’s and the SBc’s have the least prominent bulges, most loosely wound arms and arethe bluest of the spirals. Spirals tend to be among the larger galaxies in the Universe, withmasses between 109 - 1012 M. Giant elliptical cD galaxies are a special case, residing only inthe centers of galaxy clusters, these are the largest galaxies in the universe (Hubble, 1936).Spiral galaxies are generally bluer than elliptical galaxies indicating the presence of massive,short-lived stars and ongoing star formation. Most importantly, spiral galaxies tend to avoidthe centers of galaxy clusters Dressler (1980).

Irregular galaxies, as the name suggests, are amorphous and usually lack a discerniblebulge or disk. Archetypal examples of irregular galaxies are the large and small Magellanicclouds which are visible in the southern skies. Irregular galaxies are not shown in figure1.2, but they would appear to the right of the spiral galaxies because they are generallybluer than Sc’s. Some authors insert an additional spiral class between Sc/SBc and Irr toaccount for irregular galaxies which show some hint of organised structure. These so-calledSd/SBd galaxies along with the truly irregular galaxies are much smaller than galaxies onthe conventional spiral sequence and are sometimes referred to as dwarf spirals.

At the bifurcation point between the ellipticals and the spirals is a class of galaxy knownas the lenticulars or S0s. Lenticular galaxies have features in common with both ellipticalsand spirals. Like spiral galaxies, lenticulars are composed of a bulge and a disk. The bulgeis very prominent in S0s and there is no apparent spiral structure in the disk. Like ellipticalgalaxies, lenticulars have a homogeneous red colour and don’t appear to have active star-formation (Hubble, 1936). S0s may represent an evolutionary stepping stone between spiraland elliptical galaxies and the fraction of S0s in galaxy clusters may evolve with redshift(Dressler et al., 1997).

No classification system is perfect, but Hubble’s tuning-fork diagram does capture muchof the detail. In the case of late-type galaxies, the Hubble types correspond well withmany physical parameters and as a result Hubble’s classification scheme has proven to bevery useful. On the other hand, Hubble’s classification scheme for early-type galaxies hasbeen virtually useless since galaxy ellipticity has no correlation with fundamental physicalparameters. Since the 1980’s, new elliptical galaxy classification systems have been developedto address the unsatisfactory nature of the Hubble system. Some of the new morphologicalclasses for elliptical classes include cD galaxies, normal ellipticals, dwarf ellipticals (dE’s),dwarf spheroidals (dSph’s), blue compact dwarfs (BCD’s) and ultra-compact dwarfs (UCD’s)(Drinkwater et al., 2003).


1.2.2 Clusters and Large Scale Structure

Galaxies are not distributed randomly across the sky. Instead, most galaxies reside in enor-mous gravitationally bound entities. The largest of these systems are called rich galaxyclusters and may have up to 10,000 galaxies distributed about a common redshift and setof celestial coordinates in a region about 6 h−1 Mpc in diameter. The smaller systems arecalled groups or poor galaxy clusters and usually have fewer than 50 members in a regionabout 1.4 h−1 Mpc in diameter. The mass of a typical galaxy cluster is of the order 1014

- 1015 M while groups are of the order 1013 M. These values are easily obtained fromthe virial theorem which is a statement of conservation of energy in a gravitationally-boundequilibrium system. The virial theorem is given by:

2K + U = 0 (1.4)

where K and U are respectively the kinetic and gravitational potential energy of the system(Carroll & Ostlie, 1996). In our case, the kinetic energy can be directly calculated from theradial velocity dispersion, σz, of the galaxies inside the cluster. Typical values for σz are300 - 1200 km/s (Fabian, 1994). Assuming a spherical density distribution, and substitutingappropriate expressions for K and U into the virial theorem gives the following relationbetween σz and the virial mass, mvir:

σ2z ≈

Gmvir

5rvir(1.5)

where G is the universal gravitation constant and rvir is the virial radius. In practice, rvir isoften taken to be r200 which is the radius at which the matter density is 200 times the criticaldensity5(Balogh et al., 1999). The virial tells us the size of the cluster core (everything withinrvir is in hydrostatic equilibrium and the region is said to be virialised), however, the infallregion of these systems extend out to at least 3 – 4 rvir (Gomez et al., 2003).

An early result from the study of clusters was that the virial mass of most clustersgreatly exceeds the sum of the masses of the individual galaxies. The problem of the missingmass was first discovered by Fritz Zwicky (1898-1974) in 1933 while measuring the velocitydispersion of galaxies in the nearby Coma cluster. Some of Zwicky’s missing mass wasaccounted for in 1977 when the High Energy Astronomical Observatory (HEAO) satellitesdiscovered that many galaxy clusters are strong X-ray emitters (Riegler et al., 1977). X-ray luminosity, LX , ranges between 1044 – 1045 erg s−1 for galaxy clusters and 1043 erg s−1

for galaxy groups. The source of the X-ray emission is thermal bremsstrahlung from hotintracluster gas, called the intracluster medium (ICM). The ICM fills the virialised regions ofgalaxy clusters and usually exceeds the combined mass of the galaxies (Ebeling et al., 1996).For the ICM to remain in hydrostatic equilibrium, the gas must have a velocity dispersionof similar magnitude to the velocity dispersion of the galaxies in the cluster. The virialtemperature of the ICM is therefore of the order 107 - 108 K which is consistent with X-rayspectrum measurements (Fabian, 1994). The rest of the missing mass is believed to be inthe form of non-baryonic cold dark matter.

5The critical density is the matter density which is required for the universe not to contract back in uponitself.

8 Introduction

Given that galaxy clusters are among the brightest extragalactic X-ray sources in theUniverse, X-ray selection is an ideal method to find clusters. Furthermore, LX is proportionalto the square of the mass of the ICM, a fact which can be exploited to select galaxy clusters bymass. One possible drawback of the X-ray selection method is that it may be biased towardselecting clusters which have already formed deep gravitational potential wells (Andreonet al., 2008; Gilbank et al., 2004). X-ray selection is by no means the only method tofind clusters. Other methods include searching for galaxy overdensities at optical and IRwavelengths (e.g. Gilbank et al., 2004), exploiting the Sunyaev-Zeldovich effect (see Sunyaev& Zeldovich, 1980)6 and gravitational lensing7 (e.g. Clowe et al., 2006).

Many classification systems have been devised to assist in the study of galaxy clusters.The simplest scheme is that of Abell (1965) where clusters are identified as being eitherregular or irregular. In this scheme, regular clusters are defined as those clusters having ahigh degree of spherical symmetry and strong central concentration. All regular clusters arerich clusters. Irregular clusters do not have marked spherical symmetry, have little or nocentral concentration and have an amorphous appearance. An earlier scheme by Zwicky et al.(1961) also classified clusters by degree of central concentration. In this scheme, clusters areinspected by eye and are said to be either compact, medium compact or open8. Clusterscan also be classified by the brightness of their core galaxies. In a scheme proposed byBautz & Morgan (1970), clusters are divided into three classes depending on the nature ofthe brightest galaxy. Type I (BMI) clusters contain one centrally located cD galaxy whichis much brighter than all the others (e.g. Abell 2199). Type II (BMII) clusters have oneor a few galaxies that are intermediate in appearance between cD and giant elliptical (e.g.Coma cluster) and Type III (BMIII) clusters have no dominant galaxies (e.g. Virgo cluster).Bautz-Morgan type examples are shown in figure 1.3. Other systems are also in commonuse (e.g. Rood & Sastry, 1971).

Butcher & Oemler (1984) propose a more quantitative approach to cluster classification.They define a concentration index, C, which is defined as:

C = log10(r60/r20) (1.6)

where r20 and r60 are the projected radii containing 20% and 60% of the clusters galaxies.In terms of the Abell classification system, irregular clusters typically have a concentrationindex of the order C ∼ 0.3 while regular cluster typically have C & 0.4.

Just as galaxies are not distributed randomly across the sky, galaxy clusters also congre-gate together in superclusters, forming the largest known structures in the Universe. Unlikegalaxies in clusters, clusters are not gravitationally bound to each other inside superclus-ters and these giant systems may never become virialised. Evidence from the 2dF GalaxyRedshift Survey (Peacock, 2002; Pimbblet et al., 2004) as well as other redshift surveys hasshown that the large-scale structure of the Universe is foamy. The universe is composed of

6In the Sunyaev-Zeldovich effect, photons from the cosmic microwave background (CMB) are scatteredby hot ICM electrons. The effects on the observed CMB are noticeable at some radio frequencies.

7The presence of massive galaxy clusters can be inferred by the bending of background light by thecluster’s gravitational potential well.

8The Zwicky classification scheme is analogous to a commonly used scheme which classifies star clustersas being either compact, medium compact or open.


Figure 1.3: Example clusters showing different Bautz-Morgan types. From top to bottom, theinner 0.5 h−1 Mpc × 0.5 h−1 Mpc of Abell 2199 (BMI), Coma (BMII) and Virgo (BMIII) (source:Sloan Digital Sky Survey).

10 Introduction

Figure 1.4: Large-scale structure in the 2dF Galaxy Redshift Survey (source: Colless et al.,2001).

filaments of galaxies interspersed with large regions of low galaxy density which are calledvoids. Galaxy clusters are found at the intersections of filaments where the galaxy density ishighest. Voids and filaments are evident in figure 1.4 which shows the large-scale structureof the local universe.

1.3 Galaxy evolution in clusters

Rich galaxy clusters are hotbeds of galaxy evolution research. Cluster galaxies are thought toform coevally at high redshift (z & 2), thus rich galaxy clusters present large, homogeneouscollections of similar-aged galaxies (Bower et al., 1992). The galaxies are morphologicallydiverse, extending from the most massive elliptical galaxies through to lenticular galaxies,spirals and irregulars (Dressler, 1980). The galaxies also inhabit a broad range of environ-ments, from the high-density cluster core out to the field9.

Many researchers have suggested and shown numerous relationships exist between theobservable properties that result from galaxy evolution. Some of the major, well-studiedrelationships include colour versus magnitude (Visvanathan & Sandage, 1977; Bower et al.,1992; Kodama & Bower, 2001; Terlevich et al., 2001; Pimbblet et al., 2002; de Propris et al.,2004; Wake et al., 2005; Pimbblet et al., 2006; Stott, 2007), colour versus projected localgalaxy density10, Σ, or projected clustercentric radius, rp (Bower et al., 1992; Abrahamet al., 1996; Terlevich et al., 2001; Pimbblet et al., 2002; Wake et al., 2005; Pimbblet et al.,2006), galaxy morphological type, T, versus Σ or rp (Dressler, 1980; Whitmore et al., 1993;

9The field distribution of galaxies is the background galaxy distribution outside of clusters.10Σ is the surface density of galaxies projected onto the celestial sphere, consequently it should have units

of length−2.

1.3 Galaxy evolution in clusters 11

Abraham et al., 1996; Dressler et al., 1997; Kodama & Bower, 2001; Pimbblet et al., 2002;Smith et al., 2005), fraction of blue galaxies, fb, versus Σ or rp (Butcher & Oemler, 1984;Abraham et al., 1996; Kodama & Bower, 2001; Pimbblet et al., 2002; Wake et al., 2005),fb versus z (Butcher & Oemler, 1984; Smail et al., 1998; Ellingson et al., 2001; Kodama& Bower, 2001; Margoniner et al., 2001; Pimbblet et al., 2002; Pimbblet, 2003; de Propriset al., 2004; Wake et al., 2005) and star-formation rate, SFR, versus Σ, galaxy density11, ρ,or rp (Balogh et al., 2000; Lewis et al., 2002; Gomez et al., 2003; de Propris et al., 2004;Pimbblet et al., 2006).

Other relationships which have been studied to a lesser extent include T versus z (Smithet al., 2005; Stott, 2007), fb versus magnitude (Butcher & Oemler, 1984; Kodama & Bower,2001; de Propris et al., 2004), fb versus ρ (de Propris et al., 2004), line-of-sight velocitydispersion, σz, versus rp (Bower et al., 1992; Pimbblet et al., 2006), σz versus colour andmagnitude (Bower et al., 1992), magnitude versus Σ (Wake et al., 2005), SFR versus z(Madau et al., 1996; Kodama & Bower, 2001), SFR versus colour (Abraham et al., 1996)and SFR versus magnitude (de Propris et al., 2004).

In this section we will focus on how galaxy evolution in clusters is evident in the rela-tionships between colour and magnitude, blue fraction and redshift, galaxy morphology andprojected radius/local galaxy density, and star-formation rate and projected radius/localgalaxy density. We will conclude the section with a discussion of the physical mechanismswhich may be responsible for galaxy evolution in clusters.

1.3.1 The colour-magnitude relation

On the colour-magnitude plane, there are two distinct galaxy populations residing in galaxyclusters. The first population is mainly composed of E and S0 galaxies which form a tight,linear relation extending to the brightest magnitude galaxies on the colour-magnitude plane.This population is known as the red sequence and the ridge line upon which the red sequencegalaxies lie is known as the colour-magnitude relation (CMR; Visvanathan & Sandage 1977).Subsequent studies (e.g. Bower et al. 1992) have demonstrated the universal existence of ared sequence in all clusters. At faint magnitudes, the red sequence is observed to fan out onthe colour-magnitude plane. This effect has been interpreted by (Pimbblet et al., 2002) interms of the age-metallicity relation – the increasing spread of galaxy colours is the resultof an increasing spread of galaxy metallicities and ages. The second population is mainlycomposed of bluer, fainter-magnitude, galaxies which lie underneath the CMR (Kodama &Bower, 2001). This second population is henceforth referred to as the blue cloud. A recentspectroscopic study by Pimbblet et al. (2006) confirmed that the majority of red sequencegalaxies have spectra similar to those of passive, early-type galaxies, whereas blue cloudgalaxies have spectra consistent with actively star-forming, late-type galaxies.

An example of a cluster with a typical colour-magnitude diagram from this work is Abell2199, shown in figure 1.5. A strong red sequence is evident a the top of the figure and anobvious blue cloud is apparent below the red sequence. Faint end scatter is not observedin this diagram due to a relatively high flux limit imposed by selecting cluster members

11de Propris et al. (2004) use 2dF Galaxy Redshift Survey data to re-create the three-dimensional galaxydistribution to calculate volume densities, ρ. Consequently, ρ has units of length−3.

12 Introduction

12 13 14 15 16 17 18-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

i

(g -

i)

Figure 1.5: The (g-i) versus i colour-magnitude diagram for Abell 2199. The solid line is theCMR and the vertical dashed line is the i-band fiducial magnitude.

spectroscopically. An example of a colour-magnitude diagram with faint-end scatter fromanother study is shown in figure 1.6. Stellar astronomers may recognise the colour-magnitudediagram as an Hertzsprung-Russell diagram drawn on its side.

Red sequence galaxies have reached the end of their star forming history, their integratedcolours become redder with time as their short-lived, bright, blue stars die out. As timeprogresses, these galaxies accumulate an increasing proportion of long-lived, faint, red starswhose evolution as a whole is well understood (Kodama & Bower, 2001; Bruzual & Charlot,2003). These galaxies are said to be evolving passively. On the other hand, blue cloudgalaxies have ongoing star formation and stay blue as long as they have a constant supply ofstar-forming material (mainly H and He gas). These galaxies are said to be evolving actively.Observations of clusters spanning a few Gyr (Butcher & Oemler, 1984; Ellingson et al., 2001;Margoniner et al., 2001) as well as N-body computer simulations (Kodama & Bower, 2001)have shown that galaxies evolve from the blue cloud onto the red sequence, presumably dueto the removal of star-forming material from blue cloud galaxies. An example of galaxyevolution on the colour-magnitude plane is shown in figure 1.7. The evolution of blue cloudgalaxies onto the red sequence is evident since the size of the blue cloud diminishes as zapproaches 0. Passive evolution can also be seen since the position of the CMR movesredward with decreasing z.

Studies by Stott (2007) and Pimbblet et al. (2002) find that the slope of the CMRbecomes steeper (more negative) with redshift (see figure 1.8). A likely explanation is star-formation “downsizing”. Downsizing is the phenomenon where peak star formation occurs


Figure 1.6: The (V-I) vs I colour-magnitude diagram for Abell 1703. Scatter about the CMRis evident at faint magnitudes (source: Stott, 2007).

in the largest (brightest) galaxies at high redshift and in the smallest (faintest) galaxiesat low redshift (Cowie et al., 1996; Heavens et al., 2004; Thomas et al., 2005; Treu et al.,2005). Consequently, the brightest galaxies should evolve onto the CMR first after their star-formation subsides, followed by intermediate-magnitude and faint galaxies. This hierarchicalbuild-up of red sequence galaxies has been reported by de Lucia et al. (2004) and Stott (2007).As the red sequence builds up, the colour of the faint galaxies catches up to the colour ofthe bright galaxies, thereby flattening the slope of the CMR at low redshift.

In summary, colour-magnitude diagrams are powerful tools to analyse the evolution ofgalaxies in clusters. The CMR of each cluster can be found using linear regression tech-niques. It is then a simple procedure to find the dependence of the slope and interceptcoefficients on parameters such as redshift or X-ray luminosity. Furthermore, the position ofthe CMR defines which galaxies lie on the red sequence and in the blue cloud. This allowsone to calculate the fraction of blue galaxies12, fb, in a cluster and to find its dependence onparameters such as z, LX , Σ and rp. The relationship between fb and z has been the focusof many studies since Butcher & Oemler (1984) discovered a positive correlation betweenthem.

1.3.2 The Butcher-Oemler effect

The Butcher-Oemler effect describes the observed phenomenon that the blue fraction ofgalaxy clusters was higher in the past than it is today (Butcher & Oemler, 1984; Pimbblet,2003). Blue fractions are defined as the fraction of galaxies inside a given projected radiuswhich lay underneath the CMR and are brighter than a given fiducial magnitude. Butcher& Oemler (1984) define fb using r30

13 as their given radius, MV = −20 as their absolutefiducial magnitude and (B-V) colour 0.2 mag bluer than the CMR. The choice of parameters

12Alternatively, one could calculate the fraction of red galaxies in a cluster, however, fb is conventionallyused in the literature.

13r30 is the radius projected on the sky containing 30% of the cluster’s galaxies.

14 Introduction

Figure 1.7: The evolution of cluster galaxies on the colour-magnitude plane. The left-mostcolour-magnitude diagrams in each row correspond to actual observations of galaxy clusters. Sub-sequent diagrams to the right are generated by N-body computer simulations. The dotted anddashed lines correspond to the Butcher & Oemler (1984) criteria of MV = −20 and ∆(B-V) = -0.2(source: Kodama & Bower, 2001).


Figure 1.8: The evolution of (V-I) vs I red sequence slope. The solid and dotted lines representmodel predictions with ± 1 σ errors (source: Stott, 2007).

is somewhat arbitrary and other authors (e.g. Ellingson et al. 2001 and Margoniner et al.2001) have demonstrated that the calculation of fb crucially depends on cut-off radius andfiducial magnitude. Figure 1.9 demonstrates the Butcher-Oemler effect since z = 0.5. Theblue fraction appears to increase with redshift, albeit with a large scatter14 about the lineof best fit. Negative blue fractions are an artifact resulting from subtracting field galaxiesfrom the cluster sample.

The Butcher-Oemler effect has been interpreted as evidence for a rapid decline in the starformation rates of cluster galaxies since at least z ∼ 0.5 (Kodama & Bower, 2001; Pimbblet,2003). With blue galaxies being associated with active star formation, the decrease in fbshows a transition from active to passive galaxy evolution in clusters in the past few Gyr.Referring back to figure 1.7, we can understand the evolution of cluster galaxies on thecolour-magnitude plane as being a manifestation of the Butcher-Oemler effect. At highredshift, there is a large blue cloud underneath the CMR on the colour-magnitude planewhich results in a corresponding large fb whereas at low redshift most of the galaxies havemigrated onto the red sequence, resulting in a small fb.

1.3.3 The morphology-density relation

Dressler (1980) was the first to show the existence of a morphology-density (T-Σ) relation byplotting galaxy morphological type fraction versus local galaxy surface density. In a sampleof ∼ 6000 galaxies in 55 clusters at z ∼ 0.04, Dressler (1980) found that the fraction of spiraland irregular galaxies decreases strongly with local density, whereas the fraction of ellipticalgalaxies increases strongly with local density. The fraction of lenticular galaxies tends to

14Ellingson et al. (2001) and Margoniner et al. (2001) find less scatter about the line of best fit betweenz ∼ 0.1 and z ∼ 0.2 than Butcher & Oemler (1984), Smail et al. (1998) and Pimbblet et al. (2002), however,their results are not directly comparable because they do not use the r30 aperture.

16 Introduction

Figure 1.9: The Butcher-Oemler effect is the name given to the phenomenon where the fractionof blue galaxies increases with redshift (source: Pimbblet, 2003).

increase more slowly with local density, having a larger population fraction than ellipticalsat low densities, but falling off slightly in regions of high galaxy density. The original T-Σrelation from Dressler (1980) is reproduced in figure 1.10.

While the morphology-density relation is closely mirrored by the morphology-radius (T-R) relation for radially symmetric galaxy density distributions, Dressler (1980) discoveredthat the T-Σ and T-R relations are not degenerate in general. Taking a subsample of sixirregular clusters, Dressler (1980) showed that the T-Σ relation of the subsample was notsignificantly different from that of the parent sample. On the other hand, the T-Σ andT-R relations of the subsample were significantly different from each other (see figure 1.11)indicating that Σ is the fundamental parameter determining galaxy morphology. Conversely,a re-analysis of the same data by Whitmore et al. (1993) showed that spiral galaxies areabundant everywhere except in the cluster core. They concluded that the T-R relation ismore fundamental than the T-Σ relation.

Other research has looked at the evolution of the T-Σ relation with redshift and hastended to support the view that the T-Σ relation is more fundamental than the T-R relation(Dressler et al., 1997; Smith et al., 2005). These evolutionary studies suggest that while thefraction of elliptical galaxies has not changed much with time, the fractions of lenticular andspiral galaxies have changed significantly - the proposed explanation being the transformationof spirals into lenticular galaxies. There appears to be some link between the high-redshiftT-Σ relation and the Butcher-Oemler effect - an increase in spiral galaxy population at highredshift may account for the increase in fb. However, it is unlikely that the high-redshift T-Σ


Figure 1.10: The morphology-density relation for a composite cluster composed of 55 clusters(source: Dressler, 1980).

relation is the sole cause of the Butcher-Oemler effect because the T-Σ relation was weakerin the past with no obvious trend in irregular clusters (Dressler et al., 1997; Smith et al.,2005). The link between a morphology relation and the Butcher-Oemler effect is still anopen question, though the question of whether rp or Σ is the more fundamental independentparameter in a morphology relation remains controversial but tends to be favoured by a T-Σrelation (e.g. Pimbblet et al., 2006).

1.3.4 Star formation in cluster galaxies

Star formation gradients

Star formation in galaxies is closely related to colour and morphology. Active star formationis mainly associated with blue spiral galaxies whereas passive stellar evolution tends to beassociated with red elliptical galaxies. Recent studies have been mainly concerned with therelationship between SFR and Σ or rp (Balogh et al., 2000; Lewis et al., 2002; Gomez et al.,2003; Pimbblet et al., 2006). Analogous to the T-R and T-Σ relations, these authors findstrong evidence for the existence of SFR-R and SFR-Σ relations describing star formationgradients inside clusters. In these relations, star formation is systematically suppressedinside clusters in comparison to the field population, with the lowest levels being found nearthe high-density cluster centers and the highest levels being where the cluster populationmeets the field. Gomez et al. (2003) and Pimbblet et al. (2006) also find evidence for a

18 Introduction

Figure 1.11: The morphology-radius and morphology-density relations for a composite clustercomposed of six irregular clusters (source: Dressler, 1980).

critical radius and density where star formation is switched off, with rcrit ∼ 4 h−1 Mpc andΣcrit ∼ 2 h2 Mpc−2. The truncation of star formation is more abrupt in the SFR-Σ relationand is evidence that the SFR-Σ relation is more fundamental than the SFR-R relation.

Kodama & Bower (2001) note that the difference between SFRs in cluster centers andthe field is significantly smaller at high redshift than in recent times. They propose a spec-troscopic Butcher-Oemler effect where the SFR inside clusters has a different evolutionaryhistory to that of the field. They performed an N-body simulation and were able to repro-duce the SFR histories from the CNOC and MORPHS cluster surveys (see Balogh et al.1999; Poggianti et al. 1999). They found that star-formation suppression depends stronglyon cluster accretion history. An accretion model with intense starburst followed by abruptSFR truncation matches the MORPHS data quite well but fails to reproduce [OII] emissiongalaxies. A benign accretion model with an exponential decay in SFR due to starvationmatches the CNOC data well but does not reproduce the fraction of Hδ emission galaxiesseen in MORPHS.

Classifying galaxies by spectral type

In addition to morphology, galaxies can be classified by their spectral type. The MORPHSspectral classification system is used widely in the literature (e.g. Dressler et al. 1999;Poggianti et al. 1999; Pimbblet et al. 2006) and describes six different galaxy types: k, k+a,


Figure 1.12: The SFR-R and SFR-Σ relations. This figure clearly shows that [OII] luminosity(which traces ongoing star-formation) is truncated more abruptly in the SFR-Σ relation than inthe SFR-R relation (source: Pimbblet et al., 2006).

a+k, e(c), e(b) and e(a). Galaxies of type k have spectra are reminiscent of K stars15. Theyare characterised by metal absorption lines and very weak emission lines (EW([OII]) < 5A and EW(Hδ) < 3 A). Galaxies of type k+a and a+k are spectroscopically similar to A andK stars and are characterised by metal absorption lines and weak emission lines (EW([OII])< 5 A). Unlike k type galaxies, however, k+a galaxies have moderate Balmer absorptionlines (EW(Hδ) = 3-8 A) and a+k has even stronger Balmer absorption (EW(Hδ) > 8 A). Hδ

is used in the MORPHS system because it is an indicator of recent star formation in the past1-2 Gyr (Poggianti et al., 1999), hence k+a and a+k galaxies fall under the classification ofpost-starburst galaxies. The e type galaxies are emission line galaxies and are characterisedby high EW([OII]) which means that they are undergoing active star-formation. Type e(c)galaxies have moderate emission (EW([OII]) = 5-40 A), weak Balmer absorption (EW(Hδ)< 4 A) and are generally associated with continuous star formation. Type e(b) galaxieshave strong emission (EW([OII]) > 40 A) and are associated with starbursts. Type e(a)galaxies are similar to e(c) galaxies but they have stronger Balmer absorption (EW(Hδ) >4 A) (Pimbblet et al., 2006). The classification scheme is summarised in figure 1.13.

The galaxy spectral types also have morphological and colour analogues. The k typegalaxies are dominated by E and S0 morphologies, however, they also include a small fractionlate-type galaxies all the way out to Sd/Irr (Dressler et al., 1999). The e(a) and e(c) typesare mainly composed of a wide variety of spirals from Sa to Sd/Irr while e(b) type galaxiesare predominantly Sc to Sd/Irr (Poggianti et al., 1999). The a+k type galaxies have similar

15Stars on the main sequence are classified according to colour. The sequence is O,B,A,F,G,K,M with themassive, short-lived O stars being the bluest and low-mass, long-lived M stars being the reddest (Stromgren,1933).

20 Introduction

Figure 1.13: The MORPHS spectral classification system (source: Dressler et al., 1999).

Figure 1.14: Galaxy spectral types on the colour-magnitude plane (source: Pimbblet et al.,2006).


morphologies to the the e(a) and e(c) galaxies while the k+a types are evenly distributedfrom E to Sc (Poggianti et al., 1999). In figure 1.14, Pimbblet et al. (2006) plot galaxiesfrom the LARCS composite cluster by spectral type on the colour-magnitude plane. Broadlyspeaking, the majority of the k type galaxies have colours consistent with the CMR, the e(a)and e(c) type galaxies have colours which are consistent with the blue cloud, while thea+k/k+a types span intermediate colours.

1.3.5 Gas-stripping mechanisms

The evolutionary phenomena described in the previous sections (i.e. CMR, Butcher-Oemlereffect, T-Σ, T-R, SFR-Σ and SFR-R relations) are all manifestations star-formation quench-ing with environment and redshift. In order to explain star-formation quenching in galaxyclusters we require one or more mechanisms which can spirit away the star-forming gas fromcluster galaxies. Gas stripping mechanisms fall into three general categories (Combes, 2004):

1. Intra-cluster medium - inter-stellar medium (ICM-ISM) interactions such as ram-pressure stripping, halo gas starvation and thermal evaporation.

2. Tidal interactions such as galaxy mergers and “harassment”.

3. Outflows due to violent events such as starbursts or Active Galactic Nuclei (AGN)activity.

The effectiveness of gas stripping mechanisms in the first category depend on the densityand temperature of the ICM, hence they should be dependent on cluster mass. Gas strip-ping mechanisms in the other categories are independent of cluster mass. To account forstar-formation quenching and colour-gradients, gas-stripping mechanisms have to be bothlong-range and slow-acting. The mechanism must be long-range, because star-formationquenching and colour-gradients have been observed far out into the cluster infall region.Mechanism must also be slow-acting, operating on a timescale comparable to the time ittakes for a galaxy to fall into the cluster core – a few Gyr.

Ram-pressure stripping

In the ram pressure stripping scenario we imagine infalling spiral galaxies careering into theICM at several thousand kilometres per second. These galaxies experience a violent windcapable of stripping away the star forming gas from the galactic disk. The ram pressure, Pr,experienced by the galaxy is given by:

Pr = ρev2 (1.7)

where ρe is the external, intra-cluster gas density and v is the galaxy’s velocity (Gunn &Gott, 1972). For a typical spiral galaxy, the restoring force per unit area, F, holding the starforming gas into the plane of the disk is given by:

F = 2πGσsσg (1.8)

22 Introduction

where σs is the star surface density and σg is the gas surface density on the galactic disk(Gunn & Gott, 1972). A typical spiral galaxy has a mass ∼ 1011 M, a disk radius ∼ 10 kpc,a gas layer ∼ 200 pc thick and an average gas density ∼ 1 atom cm−3. These values yield σs∼ 0.06 g cm−2 and σg ∼ 10−3 cm−2. Thus if our typical spiral galaxy falls into the clustercentre at a velocity ∼ 1000 km s−1, then it will be stripped of its star-forming gas if the gasdensity of the ICM exceeds ∼ 1.5× 10−4 atoms cm−3 (Gunn & Gott, 1972). This strippingoccurs on a relatively short timescale ∼ 10 Myr (Combes, 2004) and it is only effective inregions where the ICM is dense (e.g. near the cluster core). Hence ram-pressure stripping isunlikely to be responsible for the evolution of galaxies in clusters.

Halo gas starvation

In cases where the ICM is not sufficiently dense (e.g. far from the cluster core), a processsimilar to ram-pressure stripping may be able to remove gas from the galactic halo whereit is less tightly bound than in the disk. The halo is a likely candidate for the source ofgas replenishment in spiral galaxies, so, as the name suggests, galaxies are slowly starved ofstar-forming material in the halo gas starvation mechanism. N-body simulations by Bekkiet al. (2002) demonstrated the slow transformation of spirals into S0s over a time periodof a few Gyr. One strength of this model is that it is able to explain the stripping ofgas from galaxies far away from the cluster core. The model also predicts the existence of apopulation of passive spiral galaxies intermediate between active spiral galaxies and red S0s -spiral galaxies do not evolve immediately into S0s when star-formation is quenched. Passivespiral galaxies produced in the simulation have spectral properties similar to “anaemic”spirals found in the Virgo cluster and may also be spectroscopically similar to k-type spiralsin distant clusters (Bekki et al., 2002).

Halo gas starvation operates over a timescale comparable to the time it takes for galaxiesto fall into the cluster core from the field. Unlike ram-pressure stripping, halo gas starvationis not limited to the cluster core – the mechanism is effective out the infall region. Thushalo gas starvation is a viable mass-dependent mechanism which may be responsible galaxyevolution in clusters.

Thermal evaporation

In the thermal evaporation scenario, galaxies embedded in the high-temperature ICM losetheir cooler ISM primarily through evaporative processes. For an ICM with T ∼ 108 Kand n ∼ 10−4 atoms cm−3 the thermal evaporation rate in the order of 10-100 M yr−1

(Cowie & Songaila, 1977). Using our values from the ram-pressure stripping calculation, weestimate that the initial mass of the ISM before evaporation of a typical spiral galaxy is∼ 109 M. This gives an approximate thermal evaporation timescale around 10-100 Myr.Given the brevity of the timescale, it is unlikely that thermal evaporation is responsible forstar-formation gradients and colour gradients.


Figure 1.15: Evolutionary sequence in the harassment model. Spiral galaxies are effectivelystripped of their star-forming gas and are transformed into dwarf elliptical galaxies after 4 – 5 closeencounters. The time steps shown here are ∼ 0.5 Gyr and the whole process occurs over 2 – 3 Gyr(source: Moore et al., 1996).

Galaxy mergers

Galaxy-galaxy collisions are cataclysmic events which usually results in the complete tidaldisruption of at least one galaxy. These events seem to be associated with the formationof large elliptical galaxies, in particular central dominant (cD) elliptical galaxies which arefound in the cores of most rich clusters (Hubble, 1936). Galaxy mergers were more prevalentin the past - the collision rate dropping from 8 to 2 Gyr−1 over a typical cluster lifetime(Combes, 2004). The large ellipticals were most likely formed by the accretion of smallergalaxies, a process which may even predate cluster formation (Merritt, 1984; Combes, 2004).In comparison to other mechanisms, galaxy-galaxy collisions only play a minor role in galaxyevolution, mainly affecting the large elliptical galaxies in the cluster core.

Galaxy harassment

N-body simulations by Moore et al. (1996) have shown that perturbations from high-speedgalaxy fly-bys are an effective method of stripping gas from galaxies and inducing morpholog-ical change. Dubbed “harassment”, spiral galaxies are stripped of their star-forming materialafter a few (. 5) strong encounters with ∼ M∗ magnitude galaxies (see figure 1.15). Insidethe virial radius, spiral galaxies up to the size of the Milky Way are transformed into dwarfelliptical (dE) galaxies over a 2 – 3 Gyr timescale. Images of disturbed blue spirals in distantclusters and the subsequent lack of them in nearby clusters is evidence that harassment maybe responsible for the transformation of blue, star-forming spirals into passive, red E andS0 galaxies (Moore et al., 1996). The frequency of galaxy fly-bys increases with local galaxydensity, so we expect harassment to be a density dependent mechanism. Tidal interactionswith the cluster’s gravitational potential also have the ability to augment the harassmentmechanism by disturbing or completely disrupting galaxies which are in the process of beingharassed (Moore et al., 1996; Combes, 2004).

Galaxy harassment operates over a timescale comparable to the time it takes for galaxiesto fall into the cluster core from the field. Moreover, galaxy harassment is long-range –the effectiveness of the mechanism depends only on the number of nearby galaxies Thusgalaxy harassment is a viable density-dependent mechanism which may be responsible galaxyevolution in clusters.

24 Introduction

Outflows

Finally, gas can be stripped from galaxies in outflows caused by violent events. Subpopu-lations of disturbed, star-forming galaxies, known as starburst galaxies, have been observedto exist in distant clusters (Poggianti et al., 1999). These starburst galaxies, which arefalling into the cluster or being harassed for the first time, undergo an epoch of intensestar-formation. The subsequent stellar winds and supernovae result in outflows that may bepowerful enough to strip galaxies of their star-forming material (Combes, 2004). The factthat the Fe content of the ICM is about twice as great as the Fe content of most galaxies(Renzini, 2004) and the prevalence of post-starburst galaxies in clusters in comparison totheir almost non-existence in the field (Poggianti et al., 1999) are pieces of evidence thatsuggest starburst outflows play an important role in stripping gas from galaxies. Anotherpossible source of outflows may be due to nuclear activity. When a galaxy suffers tidalinteractions with other galaxies or the cluster potential, the galaxy’s gas reservoir may loseangular momentum and plunge into the galactic nucleus providing fuel for AGN outflows(Moore et al., 1996; Combes, 2004). Outflow stripping is a fairly constant process, perhapspeaking around z ∼ 2 and is most effective at quenching star formation in the smaller galax-ies (Combes, 2004). While outflows might provide some base load amount of star-formationquenching, it is unlikely that this mechanism is responsible for star-formation gradients andcolour gradients.

1.4 This study

Now that we have reviewed the literature, we have enough insight to pose some specificquestions relating to galaxy evolution in intermediate-mass clusters. In this thesis, thespecific questions we wish to address are:

1. How do the red sequence galaxies evolve? Do the CMR fit parameters depend onredshift, cluster mass and cluster morphology? How do the colours of the red sequencegalaxies depend on environment? How do these results compare to what we knowabout red sequence galaxy evolution in high-mass clusters?

2. How do the blue galaxies evolve? Does fb depend on redshift, cluster mass and clustermorphology? How do these results compare to what we know about the evolution ofblue galaxies in high-mass clusters?

3. How does the the star formation rate in cluster galaxies evolve? Does the SFR dependon redshift, cluster mass and cluster morphology? Is there a critical radius or densityfor star-formation suppression? How is the SFR related to the evolution of red sequenceand blue galaxies? How do these results compare to what we know about the evolutionof the SFR in high-mass clusters?

4. What is the nature of the physical mechanism/s behind galaxy evolution in clusters?

The rest of this thesis has been structured as follows. In chapter 2 we will discuss howwe selected our galaxy clusters and how we constructed the dataset. We will also talk about

1.4 This study 25

the various sources of bias in the dataset, mass and morphology degeneracy, and clustersubstructure. In chapter 3 we will look at the evolution of the colours of galaxies in ourdataset. We will discuss how we fit CMRs to each of the 45 clusters and how the CMRfit coefficients depend on global cluster properties. Most importantly, we will examine theevolution of galaxy colours in the composite cluster as a function of environment. In chapter 4we will discuss the implications of our results. We will compare our intermediate-LX resultsto the literature on high-LX clusters and discuss the implications for galaxy evolution inclusters across the entire mass spectrum. In chapter 5 we will summarise the major findingsof this thesis and conclude with a discussion of the future work which needs to be done tofill in the pieces of the galaxy evolution puzzle.

Throughout this thesis we adopt a flat, WMAP cosmology with parameter values takenfrom Spergel et al. (2007). The values quoted by Spergel et al. are h = 0.732+0.031

−0.032 andΩmh

2 = 0.1277+0.0080−0.0079 which correspond to H0 = 73.2+3.1

−3.2 km s−1 Mpc−1, Ωm = 0.238± 0.026and ΩΛ = 1 − Ωm = 0.762 ± 0.026. Here we have assumed a flat universe with Ωk = 0,consistent with WMAP results. Ωm, ΩΛ and Ωk are dimensionless density parameters whichrespectively correspond to the amount matter-energy, dark-energy and space-time curvatureenergy Ωk in the Universe. These values are used to calculate distances to clusters andangular separations between objects in our dataset.

26 Introduction

2Constructing and Qualifying the Dataset

In this chapter we discuss a number of details relating to our dataset. In section 2.1 wewill discuss how we selected appropriate galaxy clusters for this study and how we obtainedvelocity dispersions and better redshift estimates for our clusters. In section 2.2 we willcompare the XBACS, BCS, and eBCS catalogue to our intermediate-LX cluster sample anddiscuss biases in both samples. In sections 2.3 and 2.4 we will talk about the particular datawe obtained from the Sloan Digital Sky Survey (SDSS) database to construct our galaxycatalogue and we will discuss discordant points in galaxy catalogue. In sections 2.5 and2.6 we will discuss additional calculations we made to obtain projected radii, local galaxydensities, virial radii, and cluster concentration indices. In section 2.7 we will talk aboutmass and morphology degeneracy and in section 2.8 we discuss the prevalence of substructurein intermediate-LX cluster sample.

2.1 Cluster selection

Galaxy clusters were selected from the X-ray Brightest Abell Cluster Survey (XBACS),the ROSAT1 Brightest Cluster Sample (BCS) and the ROSAT Extended Brightest ClusterSurvey (eBCS) catalogues (see Ebeling et al., 1996, 1998, 2000). Briefly, the XBACS, BCSand eBCS catalogues list many extended, extragalactic X-ray sources from ROSAT All-SkySurvey data. Clusters were detected in the soft X-ray band between 0.1 – 2.4 keV. In total,the catalogues contain 462 unique galaxy clusters of which 214 satisfy 0.7 × 1044 erg s−1 <LX < 4 × 1044 erg s−1 and 0 < z < 0.2.

In the XBACS, BCS and eBCS catalogues, the right ascension, RA, and declination, Dec,coordinates give the positions of the cluster X-ray centers2. Rather than derive their ownredshift estimates, Ebeling et al. collate cluster redshifts from a multitude of sources. In the

1ROSAT is short for Rontgensatellit, a German, X-ray satellite telescope.2On the celestial sphere, right ascension is the azimuthal angle and declination is the polar angle.

27

28 Constructing and Qualifying the Dataset

cases where no redshift reference was given, we supplemented the catalogues with redshiftstaken from the NASA/IPAC Extragalactic Database (NED). A few of the clusters in XBACS,BCS and eBCS catalogues have multiple X-ray centers. In the cases where we encounteredmultiple cluster cores, we used the mean RA, Dec and redshift values so that we would onlyhave one database entry per cluster. In the case of multiple cores, X-ray luminosities wereadded. Bautz-Morgan type data were also obtained from NED to supplement the clustercatalogue. In the cases where no data were available, the Bautz-Morgan type was manuallyestimated by visual inspection of NED and SDSS images.

We performed preliminary cluster member searches about the nominal RA, Dec, andredshift coordinates given in XBACS, BCS and eBCS. We searched for all galaxies within ±0.02 of the nominal clustercentric redshift and out to 10 Mpc in projected radius from thenominal RA and Dec. Next, we fitted Gaussians to the redshift histograms of each cluster. Inmost cases, the fitting algorithm converged on a prominent peak in the redshift distributionclose to the nominal redshift value. Using the position of the peak of the Gaussian asthe updated clustercentric redshift, we iterated the procedure two more times searching forgalaxies within 3σz/c of the updated clustercentric redshifts and out to 10 Mpc in projectedradius. This procedure yielded better redshift estimates than the ones given in XBACS,BCS and eBCS and also gave us velocity dispersions and preliminary cluster candidates. Weconsider σz as being roughly equivalent to a line-of-sight rvir, thus by selecting selectingall galaxies within ± 3σz/c in redshift we selected all galaxies from the cluster core out tothe edge of the cluster infall region in the line-of-sight direction. A naıve calculation of thecluster redshift bounds as being ± 10 Mpc in Hubble flow about the clustercentric redshifttypically yields values ∼ σz/c which are too small. This is because the galaxies in clusterstypically have large peculiar velocities due to the accelerations they experience from nearbygalaxies and from the global cluster potential.

Gaussian fit coefficients for the redshift histograms were estimated iteratively by perform-ing χ2 minimisations on the histogram data points. One hundred iterations were performedfor each cluster with new random bin sizes on each iteration. The best fit Gaussian coef-ficients and their associated errors were calculated from the mean and standard deviationvalues of the coefficients over 100 iterations. By randomising the bin sizes, we ensuredthat our best fit Gaussians were independent of binning bias. The redshift distributionsand the best fit Gaussians are shown for all clusters in the intermediate-LX sample in fig-ures in appendix A. Updated estimates of the clustercentric redshifts are given in table 2.1corresponding to our best updated estimates the positions of the Gaussian redshift peaks.The velocity dispersions given in table 2.1 are the standard deviations of best-fit Gaussiansmultiplied by c in units of km s−1.

A cluster search like the one described above typically returns a mixture of usable andunusable clusters. Examples of unusable clusters are ones with fewer than 50 members,clusters located in the “whisker” regions3 of the DR6 SDSS spectroscopic survey, and over-lapping clusters. Clusters with fewer than 50 members were excluded because they do notsatisfy the Abell richness criterion and, furthermore, they generally do not have enoughdata points to which we can fit CMRs on their colour-magnitude diagrams. Clusters located

3The “whisker” regions of the SDSS spectroscopic survey are long, narrow stripes of spectroscopically-sampled sky near the celestial equator, and roughly located below RA ∼ 60deg and above RA ∼ 300deg.

2.1 Cluster selection 29

Figure 2.1: Projection of the celestial sphere, showing spectroscopic sky coverage of the DR6Sloan Digital Sky Survey. RA and Dec have units of degrees (source: http://www.sdss.org/dr6/).“Whisker” regions are the long, narrow stripes of spectroscopically-sampled sky near the celestialequator, below RA ∼ 60deg and above RA ∼ 300deg.

in the “whisker” regions were excluded because they were likely to be cropped by stripeboundaries. We define overlapping clusters as clusters which have their 10 Mpc projectedradius search areas overlap with the search areas of other clusters. Removing the overlappingclusters simplified our analysis because it meant that we did not have to worry about how toassign cluster membership to galaxies located in the overlap regions. We were also concernedthat cluster properties might be contaminated by overlapping neighbours. For example, anoverlapping neighbour might manifest itself as a second red sequence in a colour-magnitudediagram. We note that by excluding overlapping clusters we introduce a selection bias intoour cluster samples. We will discuss this type of selection bias in section 2.8.

After performing our database search and excluding clusters with fewer than 50 members,clusters in the “whisker” regions, and overlapping clusters, we obtained an homogeneoussample of 45 clusters. The 45 clusters in our intermediate-LX sample have X-ray luminositiesranging between 0.77 and 3.93 × 1044 erg s−1 at a median redshift 0.0897. Cluster propertiesare summarised in table 2.1 and a redshift-LX parameter space plot of our cluster sampleis shown in figure 2.2. Further cluster characterisation is given in appendix A. Our richestcluster is Abell 2199 which contains 1,344 spectroscopically-confirmed members. Our poorestcluster is Abell 1814 with 54 members. In table 2.1, the values we give for RA, Dec, and LXare taken directly from XBACS, BCS, and eBCs and we have made no attempt to updatethese values. Bautz-Morgan entries are mainly taken from NED, but the ones marked withan asterisk indicate that the value was manually estimated by visual inspection of NED andSDSS images by PCJ. The values we give for the redshifts and velocity dispersions and theirassociated errors have been previously discussed. In table 2.1, we also give values for r200,concentration index and say whether the cluster has substructure. We will discuss how wecalculated r200 and concentration index in section 2.6. We will discuss how we determinedcluster substructure in section 2.8.

30Const

ructing

and

Qualifying

theDatase

tTable 2.1: Intermediate-LX cluster sample

Cluster Name LX B-M Type RA Dec Redshift σz r200 Concentration Substructure[1044 erg/s] [deg] [deg] [km/s] [Mpc]

Abell 602 1.14 III 118.351 29.366 0.06195 ± 0.00006 1080 ± 40 2.39 ± 0.01 0.53 ± 0.01 yesAbell 671 0.9 II-III 127.17 30.432 0.04926 ± 0.00003 600 ± 10 1.339 ± 0.005 0.636 ± 0.007 ?Abell 743 2.71 III 136.614 10.345 0.1361 ± 0.0003 500 ± 200 0.93 ± 0.08 0.34 ± 0.01 noAbell 744 0.77 II 136.857 16.654 0.07298 ± 0.00009 240 ± 40 0.53 ± 0.02 0.65 ± 0.01 noAbell 757 0.9 III 138.357 47.687 0.05108 ± 0.00003 390 ± 10 0.883 ± 0.004 0.419 ± 0.007 noAbell 763 2.34 II-III 138.124 15.943 0.08924 ± 0.00008 380 ± 50 0.81 ± 0.02 0.43 ± 0.01 noAbell 923 2.07 II 151.666 25.924 0.11700 ± 0.00005 420 ± 30 0.88 ± 0.01 0.40 ± 0.01 noAbell 957 0.78 I-II 153.458 -0.904 0.04546 ± 0.00005 850 ± 30 1.91 ± 0.01 0.55 ± 0.01 noAbell 961 3.14 II-III 154.085 33.641 0.1270 ± 0.0001 690 ± 40 1.43 ± 0.01 0.45 ± 0.01 noAbell 971 1.44 II 154.98 40.996 0.09320 ± 0.00002 762 ± 9 1.631 ± 0.004 0.777 ± 0.007 noAbell 1035 0.92 II-III 158.059 40.247 0.06721 ± 0.00005 720 ± 30 1.59 ± 0.01 0.61 ± 0.01 ?Abell 1045 3.47 II-III 158.743 30.695 0.1378 ± 0.0007 600 ± 100 1.28 ± 0.05 0.28 ± 0.01 noAbell 1126 1.15 I-II 163.453 16.842 0.08433 ± 0.00007 350 ± 50 0.75 ± 0.02 0.46 ± 0.01 noAbell 1361 3.59 I-II 175.917 46.374 0.11549 ± 0.00005 640 ± 20 1.333 ± 0.008 0.448 ± 0.007 noAbell 1446 1.3 II-III 180.516 58.041 0.1028 ± 0.0001 710 ± 60 1.51 ± 0.02 0.52 ± 0.01 noAbell 1691 0.89 II 197.771 39.222 0.07176 ± 0.00002 650 ± 8 1.423 ± 0.003 0.523 ± 0.007 yesAbell 1728 1.29 I-II* 200.876 11.296 0.08965 ± 0.00002 940 ± 10 2.020 ± 0.004 0.337 ± 0.007 yesAbell 1767 2.47 II 204.032 59.211 0.07112 ± 0.00002 700 ± 20 1.532 ± 0.007 0.543 ± 0.007 ?Abell 1773 1.53 III 205.528 2.233 0.07727 ± 0.00003 790 ± 40 1.72 ± 0.01 0.53 ± 0.01 yesAbell 1809 1.61 II 208.275 5.158 0.07938 ± 0.00001 808 ± 7 1.755 ± 0.003 0.762 ± 0.007 ?Abell 1814 2.82 II 208.499 14.924 0.12673 ± 0.00009 330 ± 50 0.68 ± 0.02 0.72 ± 0.01 noAbell 1831 1.9 III 209.802 27.978 0.06311 ± 0.00003 480 ± 10 1.062 ± 0.005 0.520 ± 0.007 yesAbell 1885 2.4 II-III 213.432 43.661 0.092 ± 0.002 1100 ± 500 2.4 ± 0.2 0.8 ± 0.0 ?Abell 1925 1.56 II 217.135 56.879 0.10570 ± 0.00007 580 ± 30 1.22 ± 0.01 0.34 ± 0.01 ?Abell 1927 2.14 I-II 217.765 25.628 0.09506 ± 0.00003 520 ± 20 1.117 ± 0.008 0.366 ± 0.007 noAbell 2033 2.57 III 227.848 6.319 0.07828 ± 0.00003 1049 ± 9 2.280 ± 0.004 0.513 ± 0.007 yesAbell 2108 1.97 III 235.038 17.878 0.09033 ± 0.00008 750 ± 30 1.60 ± 0.01 0.51 ± 0.01 noAbell 2110 3.93 I-II 234.952 30.716 0.09728 ± 0.00005 630 ± 40 1.35 ± 0.02 0.42 ± 0.01 noAbell 2124 1.35 I 236.25 36.066 0.06723 ± 0.00002 740 ± 10 1.621 ± 0.006 0.676 ± 0.007 noAbell 2141 3.89 II 239.436 35.497 0.1590 ± 0.0003 900 ± 300 1.8 ± 0.1 0.8 ± 0.0 noAbell 2148 1.39 III* 240.759 25.404 0.08843 ± 0.00005 570 ± 20 1.223 ± 0.007 0.571 ± 0.007 ?Abell 2149 0.83 II-III* 240.399 53.918 0.06503 ± 0.00003 280 ± 20 0.610 ± 0.006 0.346 ± 0.007 noAbell 2175 2.93 II 245.128 29.892 0.09646 ± 0.00004 780 ± 10 1.654 ± 0.005 0.435 ± 0.007 noAbell 2199 3.7 I 247.165 39.55 0.030549 ± 0.000003 681.2 ± 0.6 1.558 ± 0.001 0.426 ± 0.007 yesAbell 2228 2.81 I-II 251.974 29.943 0.10102 ± 0.00004 980 ± 20 2.092 ± 0.006 0.412 ± 0.007 noRXJ0820.9+0751 2.09 I-II* 125.248 7.854 0.11032 ± 0.00007 560 ± 30 1.17 ± 0.01 0.54 ± 0.01 noRXJ1000.5+4409 3.08 III* 150.13 44.154 0.1531 ± 0.0003 700 ± 100 1.33 ± 0.05 0.82 ± 0.01 ?RXJ1053.7+5450 1.04 III* 163.449 54.85 0.07291 ± 0.00004 580 ± 20 1.274 ± 0.009 0.623 ± 0.007 yesRXJ1423.9+4015 0.94 III* 215.976 40.261 0.08188 ± 0.00005 460 ± 10 0.994 ± 0.005 0.536 ± 0.007 ?RXJ1442.2+2218 2.66 II* 220.573 22.301 0.09613 ± 0.00007 470 ± 70 1.01 ± 0.03 0.42 ± 0.01 ?RXJ1652.6+4011 2.85 III* 253.166 40.193 0.1480 ± 0.0002 750 ± 90 1.52 ± 0.03 0.45 ± 0.01 yesZwCl 1478 2.38 II-III* 119.919 53.999 0.1030 ± 0.0008 400 ± 200 0.82 ± 0.08 0.35 ± 0.01 noZwCl 4905 1.2 I-II* 182.571 5.392 0.07641 ± 0.00003 480 ± 20 1.036 ± 0.008 0.482 ± 0.007 noZwCl 6718 1.24 II* 215.401 49.544 0.0722 ± 0.0002 400 ± 200 0.85 ± 0.09 0.55 ± 0.01 noZwCl 8197 2.89 II* 259.548 56.671 0.1132 ± 0.0001 830 ± 100 1.74 ± 0.04 0.31 ± 0.01 no

2.2 Bias in the cluster selection 31

2.2 Bias in the cluster selection

In this section we attempt to see if there is any bias in the X-ray luminosity, redshift andmorphology distributions of our clusters. In figure 2.3 we compare Bautz-Morgan fractionhistograms for the XBACS, BCS, and eBCS catalogues to our intermediate-LX cluster subset.Assuming Poissonian statistics, and the uncertainty in the cluster fractions which define theerror bars, is given by:

∆fi =

√ni∑ni

(2.1)

where ni is the frequency and ∆fi is the error in the fraction in the ith bin. In comparison tothe full X-ray spectrum, intermediate-LX clusters appear to have a lower prevalence of BMI and slightly higher prevalence of BM II types. The fraction of B-M III and intermediateBautz-Morgan types appear to be similar in both populations. Despite this, the differencesbetween the histograms are not significant at the 3σ level.

We now move our attention to the full X-ray spectrum to see how the XBACS, BCS,and eBCS clusters are distributed by redshift and LX . In figure 2.4 we present the redshiftdistribution and in figure 2.5 we present the LX distribution. The clusters in the histogramplots are divided into 5 bins and the y-error bars are again assumed to be Poissonian.Horizontal solid lines are superimposed on the histograms to show the mean cluster fractionacross all bins. The parallel dashed lines show the 3σ significance levels above and belowthe mean cluster fraction The clusters are clearly not distributed evenly across redshift andLX . For all Bautz-Morgan types, the first, fourth and fifth redshift bins all deviate fromthe mean by more than 3σ. The second redshift bin also deviates by more than 3σ for allBautz-Morgan types except for BM I clusters. In the LX distribution, the first bin deviatesby more than 3σ for all Bautz-Morgan types, the second bin also deviates by more than 3σfor all Bautz-Morgan types except for BM I clusters and the fourth bin deviates by more than3σ for BM I-II, BM II-III and BM III clusters. These results demonstrate that the XBACS,BCS, and eBCS catalogues are collectively biased toward low redshift and intermediate tohigh-LX .

Next we performed the same analysis on our intermediate-LX clusters. In figure 2.6we present the redshift distribution and in figure 2.7 we present the LX distribution. Thistime the histogram plots have 3 bins and the horizontal solid and dashed lines have thesame interpretation as before. Unlike the full X-ray spectrum, the intermediate-LX clustersmainly follow a flat redshift and LX distribution. Excluding the second bin in the BM I-IILX distribution, all of the intermediate-LX clusters are within 3σ of having flat redshift andLX distributions.

We performed Kolmogorov-Smirnov (K-S) tests to test the likelihood of the intermediate-LX cluster sample being drawn from the same underlying continuous cluster populationas the XBACS, BCS, and eBCS clusters. At the 3σ significance level we found that theredshift distributions of the intermediate-LX cluster samples and the XBACS, BCS, andeBCS clusters are drawn from the same continuous underlying population. Conversely, wefound that the X-ray luminosity distributions of the intermediate-LX cluster samples and theXBACS, BCS, and eBCS clusters are drawn from different underlying populations. Theseresults are entirely consistent with the parameter space plot in figure 1.1 and the redshift


0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

0.7

0.8

0.9

1

2

3

4

Redshift, z

L X /

1044

erg

/s

BM IBM I-IIBM IIBM II-IIIBM III

Figure 2.2: Redshifts, X-ray luminosities and cluster morphology in the intermediate-LX clustercatalogue.

and LX diagrams in figures 2.4 – 2.7. The XBACS, BCS, and eBCS clusters are biased tolow-redshift, thus, by selecting only low-redshift clusters for the intermediate-LX sample,the two samples have qualitatively similar redshift distributions. However, the XBACS,BCS, and eBCS clusters are also biased to intermediate to high-LX , thus by selecting onlyintermediate-LX clusters for the intermediate-LX sample, the two samples have qualitativelydifferent X-ray luminosity distributions.

We interpret the K-S test results in conjunction with our previous results to concludethat the XBACS, BCS, and eBCS clusters are biased toward low redshift and intermedi-ate to high-LX across the full X-ray spectrum. Despite this, our intermediate-LX clustersample is located in an unbiased region of parameter space. Our intermediate-LX clustersample has a similar redshift distribution to the XBACS, BCS, and eBCS redshift distribu-tion, but because we are exclusively selecting intermediate-LX clusters, the X-ray luminositydistributions are significantly different from each other.

2.3 Constructing the galaxy catalogue 33

I I-II II II-III III0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4XBACS, BCS and eBCS clusters

Bautz-Morgan type

Fra

ctio

n of

clu

ster

s


0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Intermediate-LX cluster sample

Bautz-Morgan typeF

ract

ion

of c

lust

ers

Figure 2.3: Bautz-Morgan type fraction histograms for the XBACS, BCS, and eBCS catalogues(462 clusters) and the intermediate-LX cluster sample (45 clusters).

2.3 Constructing the galaxy catalogue

Galaxies were selected from the DR6 SDSS database according to the criteria discussed insection 2.1. For each galaxy, we obtained the following data:

• a unique photometric object ID

• a unique spectroscopic object ID

• the spectroscopic object type

• the celestial coordinates RA, Dec and z with errors

• u, g, r, i, and z′ 4 band magnitudes with errors, corrected for dust extinction

• K-correction terms

• equivalent widths with errors for the Hα, Hβ, Hγ, Hδ, Hε, [OII] and [OIII] spectral linesas well as the 4000 A break

Our galaxy catalogue contains 10,529 galaxies of which 175 are identified as being low-redshiftQSOs5 from their spectroscopic object type. The SQL queries required to compile the galaxy

4We will always denote z′ band magnitude with the prime symbol to avoid confusion with the unrelatedredshift parameter, z.

5A QSO, or quasistellar object, is a type of galaxy with similar photometric properties to a star. Thestar-like appearance is due to overwhelming emission from the central region of the galaxy which is thoughtto be powered by a supermassive blackhole. QSOs can be identified spectroscopically by their emission lineswhich are much broader than those of regular galaxies.


0 0.1 0.2 0.3 0.4

I

I-II

II

II-III

III

Redshift, z

Bau

tz-M

orga

n ty

pe

XBACS, BCS and eBCS clusters

0 0.1 0.2 0.3 0.4

0

0.05

0.1

Redshift, zF

ract

ion

of c

lust

ers

BM I

0 0.1 0.2 0.3 0.4

0

0.05

0.1

0.15

Redshift, z

Fra

ctio

n of

clu

ster

s

BM I-II

0 0.1 0.2 0.3 0.4

0

0.05

0.1

0.15

Redshift, z

Fra

ctio

n of

clu

ster

s

BM II

0 0.1 0.2 0.3 0.4

0

0.05

0.1

0.15

Redshift, z

Fra

ctio

n of

clu

ster

s

BM II-III

0 0.1 0.2 0.3 0.4

0

0.05

0.1

0.15

Redshift, z

Fra

ctio

n of

clu

ster

s

BM III

Figure 2.4: Redshift histograms for clusters in XBACS and BCS by Bautz-Morgan type. Thesolid horizontal line represents the average fraction of clusters taken across all redshift bins. Thedashed horizontal lines represent the 3σ uncertainty level in the average fraction.


0.1 1 10

I

I-II

II

II-III

III

LX / 1044 erg s-1

Bau

tz-M

orga

n ty

pe

XBACS, BCS and eBCS clusters

0.1 1 10

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

LX / 1044 erg s-1

Fra

ctio

n of

clu

ster

s

BM I

0.1 1 10

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

LX / 1044 erg s-1

Fra

ctio

n of

clu

ster

s

BM I-II

0.1 1 10

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

LX / 1044 erg s-1

Fra

ctio

n of

clu

ster

s

BM II

0.1 1 10

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

LX / 1044 erg s-1

Fra

ctio

n of

clu

ster

s

BM II-III

0.1 1 10

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

LX / 1044 erg s-1

Fra

ctio

n of

clu

ster

s

BM III

Figure 2.5: LX histograms for clusters in XBACS and BCS by Bautz-Morgan type. The solidhorizontal line represents the average fraction of clusters taken across all LX bins. The dashedhorizontal lines represent the 3σ uncertainty level in the average fraction.


0.05 0.1 0.15

I

I-II

II

II-III

III

Redshift, z

Bau

tz-M

orga

n ty

pe


0.05 0.1 0.15-0.05

0

0.05

0.1

0.15

0.2

Redshift, z

Fra

ctio

n of

clu

ster

s

BM I

0.05 0.1 0.15-0.05

0

0.05

0.1

0.15

0.2

Redshift, z

Fra

ctio

n of

clu

ster

s

BM I-II

0.05 0.1 0.15-0.05

0

0.05

0.1

0.15

0.2

Redshift, z

Fra

ctio

n of

clu

ster

s

BM II

0.05 0.1 0.15-0.05

0

0.05

0.1

0.15

0.2

0.25

Redshift, z

Fra

ctio

n of

clu

ster

s

BM II-III

0.05 0.1 0.15-0.05

0

0.05

0.1

0.15

0.2

0.25

Redshift, z

Fra

ctio

n of

clu

ster

s

BM III

Figure 2.6: Redshift histograms in the intermediate-LX cluster sample by Bautz-Morgan type.The solid horizontal line represents the average fraction of clusters taken across all redshift bins.The dashed horizontal lines represent the 3σ uncertainty level in the average fraction.


1 2 3 4

I

I-II

II

II-III

III

LX / 1044 erg s-1

Bau

tz-M

orga

n ty

pe


1 2 3 4-0.05

0

0.05

0.1

0.15

0.2

LX / 1044 erg s-1

Fra

ctio

n of

clu

ster

s

BM I

1 2 3 4-0.05

0

0.05

0.1

0.15

0.2

LX / 1044 erg s-1

Fra

ctio

n of

clu

ster

s

BM I-II

1 2 3 4-0.05

0

0.05

0.1

0.15

0.2

LX / 1044 erg s-1

Fra

ctio

n of

clu

ster

s

BM II

1 2 3 4-0.05

0

0.05

0.1

0.15

0.2

LX / 1044 erg s-1

Fra

ctio

n of

clu

ster

s

BM II-III

1 2 3 4-0.05

0

0.05

0.1

0.15

0.2

LX / 1044 erg s-1

Fra

ctio

n of

clu

ster

s

BM III

Figure 2.7: LX histograms in the intermediate-LX cluster sample by Bautz-Morgan type. Thesolid horizontal line represents the average fraction of clusters taken across all LX bins. The dashedhorizontal lines represent the 3σ uncertainty level in the average fraction.


catalogue can be found in appendix D. Due to size constraints, a tabular representation ofthe galaxy catalogue has been omitted from the body of this thesis, however the RA-Decdiagrams, redshift histograms, and colour-magnitude diagrams in appendix A reproducemost of the galaxy catalogue data in diagrammatic form.

2.4 Discordant points

While the vast majority of galaxies have photometric data consistent with the red sequenceand the blue cloud galaxies, some glaringly anomalous points are apparent in the colour-magnitude diagrams. These so-called discordant points are instantly recognisable becausethey are either much redder than the red sequence or much bluer than the blue cloud andhence they warrant a brief discussion.

The majority of the discordant points appear to be caused by photometric saturationfrom other objects nearby to the target galaxy. The most common source of colour bias isdue to superpositions of line-of-sight galaxies. A typical example is the discordant point onthe (g-i)/i colour-magnitude diagram for Abell 1767 (see figure 2.8). The same discordantpoint also lies far below the blue cloud in the (u-i)/i and (r-i)/i colour-magnitude diagramsand far above the red sequence in the (i-z′)/z′ colour-magnitude diagram because the i bandmagnitude is much brighter than the other bands.

The next most common source of colour bias appears to be due to dust-reddening (seefigure 2.10). In the case of Abell 1809, 10 of the 11 discordant points above the red sequencetend to congregate around 4.5 degrees of declination in the RA-Dec cluster diagram. Visualinspection of these extremely red galaxies showed no evidence of a bad row of pixels or photo-metric contamination from nearby stars or line-of-sight galaxies. In this case we tentativelyconclude that the relationship between position and redness is due to the presence of a dustlane but we add the caveat that none of these galaxies visually betray the presence of a dustlane. In comparison, an example of a strongly dust-reddened galaxy with visible dust lanesis #587731521735295245 which is a member of Abell 2141.

After line-of-sight galaxy effects and dust extinction, photometric saturation by nearbybright stars is the next most common cause of colour bias. A typical example is the discordantpoint on the (u-g)/g colour-magnitude diagram for Abell 971 (see figure 2.9). The samediscordant point also lies far above the red sequence in the (u-r)/r, (u-i)/i and (u-z′)/z′

colour-magnitude diagrams because the u band magnitude is much fainter than the otherbands.

The amount of contamination in the photometric galaxy catalogue is very small. Of the10,529 galaxies, only 46 galaxies or 0.4% have colours which are 3σ above or 5σ below themean galaxian colour of their host cluster. Of these 46 discordant points, 13 are due toline-of-sight galaxy effects, 12 are suspected to be due to dust reddening, and 11 are due tosaturation from nearby stars. The majority of the left-over discordant points appear to begenuinely blue galaxies. Of the 7 genuinely blue galaxy, 4 are low-redshift QSOs detectedonly in (g-r) colour. There were also 2 genuinely red galaxies and 1 galaxy which wasbifurcated by the edge of a sampling stripe.

2.4 Discordant points 39

14 16 18 20-5

-4

-3

-2

-1

0

1

2

i

(g -

i)

Figure 2.8: Discordant point on the (g-i) versus i colour-magnitude diagram for Abell 1767. Ablue spiral galaxy in the line-of-sight of the target red elliptical galaxy confuses the photometricmeasurements, causing the i band to be much fainter than the other bands.

16 16.5 17 17.5 18 18.5

1

2

3

4

5

6

7

g

(u -

g)

Figure 2.9: Discordant point on the (u-g) versus g colour-magnitude diagram for Abell 971. Astar nearby to the target galaxy saturates the photometric measurements, causing the u band tobe much fainter than the other bands.


16 17 18 19

1

2

3

4

5

6

7

8

9

10

g

(u -

g)

207 208 209 210

3.5

4

4.5

5

5.5

6

6.5

7

RA / deg

Dec

/ de

g

Figure 2.10: Discordant points on the (u-g) versus g colour-magnitude diagram for Abell 1809.The source of bias is unknown but is suspected to be due to dust-reddening. The discordant galaxiescongregate around 4.5 degrees of declination on the RA-Dec diagram. No bad pixel rows or nearbysources of photometric contamination suggest that the reddening may be caused by the presenceof a dust lane.

2.5 Calculating projected radii and local galaxy densi-

ties

After obtaining RA and Dec data from SDSS, we calculated projected radii, rp, from thecluster core and local galaxy surface densities, Σ, for each galaxy. However, before we candiscuss the the calculation of rp and Σ, we need to give a brief discussion of how to calculatethe separation between two arbitrary points on the surface of the celestial sphere. Theseparation, s, between 2 points on the surface of a sphere is given by:

s = DA θ (2.2)

where DA is the angular scale and θ is the angular separation. According to Sinnott (1984),an effective formula for calculating the angular separation between 2 points on the surfaceof a sphere is the haversine or half-versed sine formula. In terms of celestial coordinates RAand Dec on the unit sphere, the haversine formula is given by:

haversin(θ) = haversin(dec1 − dec2) + cos(dec1) cos(dec2)haversin(ra1 − ra2) (2.3)

where the haversin and haversin−1 functions are defined as:

haversin(θ) = sin2(θ/2) (2.4)

haversin−1(x) = 2 sin−1(√x) (2.5)

2.5 Calculating projected radii and local galaxy densities 41

The haversine formula is only valid for points on the same spherical surface, so we implicitlyassume all galaxies are situated at the clustercentric redshift when applying this formula.Equation 2.3 is valid for RA and Dec values with units of radians, giving the haversine ofthe angular separation, θ, also in units of radians.

The angular scale is a function of redshift. According to Hogg (1999), the angular scalefor a flat space-time geometry 6 is given by:

DA =DC

1 + z(2.6)

where DC , the comoving or line-of-sight distance, is given by the integral:

DC =c

H0

∫ z

0

dξ√ΩM(1 + ξ3) + ΩΛ

(2.7)

In the case where c has units of km/s and H0 has units of km/s/Mpc, the angular scale, DA,has the desired units of Mpc/radian.

The error in the separation between 2 points on the surface of a sphere, ∆s, is adaptedfrom the general case by Taylor (1997) and is given by:

∆s

s=

√(∆DA

DA

)2

+

(∆θ

θ

)2

(2.8)

where ∆DA and ∆θ are the errors in the angular scale and angular separation respectively.We use the partial differential method of Taylor (1997) to estimate ∆DA and ∆θ. Accordingto equation 2.3, θ is a function of ra1, ra2, dec1, and dec2 so ∆θ is given by:

∆θ =

√(∂θ

∂ra1

∆ra1

)2

+

(∂θ

∂ra2

∆ra2

)2

+

(∂θ

∂dec1

∆dec1

)2

+

(∂θ

∂dec2

∆dec2

)2

(2.9)

where ∆ra1, ∆ra2, ∆dec1, and ∆dec2 are the errors in ra1, ra2, dec1, and dec2 respectively.According to equations 2.6 and 2.7, DA is a function of H0, z, c, ΩM , and ΩΛ. Ignoring theerror term in c (which is assumed to be negligible), ∆DA is given by:

∆DA =

√(∂DA

∂H0

∆H0

)2

+

(∂DA

∂z∆z

)2

+

(∂DA

∂ΩM

∆ΩM

)2

+

(∂DA

∂ΩΛ

∆ΩΛ

)2

(2.10)

where ∆H0, ∆z, ∆ΩM , and ∆ΩΛ are the errors in H0, z, ΩM , and ΩΛ respectively. In thiswork, we use the errors quoted by Spergel et al. (2007) for ∆H0, ∆ΩM , and ∆ΩΛ.

Projected radii, rp and the errors in the the projected radii, ∆rp, were calculated for eachgalaxy on a cluster-by-cluster basis using the method described above. In equations 2.3 and2.9 we assign ra1 and dec1 to the RA-Dec coordinates of the cluster center. Since XBACSand BCS do not quote errors for the RA-Dec clustercentric coordinates, we set ∆ra1 and∆dec1 equal to zero. We assign ra2, dec2, ∆ra2, and ∆dec2 to the RA-Dec coordinates of the

6A flat space-time geometry is characterised by Ωk=0.


galaxy whose projected radius we are calculating. The values of ra2, dec2, ∆ra2, and ∆dec2

are the ones we obtained from the DR6 SDSS database. In equations 2.6, 2.7, and 2.10we use the clustercentric values for z and ∆z from table 2.1 so that all galaxies in a givencluster are projected onto the clustercentric redshift plane. We are confident that projectedradii values calculated using this technique are accurate because every calculated value fallsbetween 0 and 10 Mpc in agreement with the 10 Mpc radius search algorithm used by SDSS.

Using a similar method, local galaxy surface densities, Σ, were calculated for each galaxyon a cluster-by-cluster basis. The projected local galaxy number density is defined by theequation:

Σn =n+ 1

πs2n

(2.11)

where n is the number of galaxies we use to estimate the local galaxy density and sn isthe separation between the galaxy whose local galaxy density we are calculating and itsnth nearest neighbour galaxy. Σn is therefore the number density of galaxies in the areaof a circle projected out to the nth nearest neighbour galaxy. In this work we use n=10and henceforth drop the subscript n. Computationally, Σ was obtained by calculating theseparations between every galaxy in a given cluster and then sorting to find the 10th near-est neighbour. We note that this procedure can be computationally intensive because thenumber of calculations goes as N2 where N is the number of cluster members. As before, weuse the clustercentric values of z and ∆z in equations 2.6, 2.7, and 2.10 so that the surfacedensities are all evaluated on the same plane. The errors in the local galaxy densities werecalculated using the partial differential method. Because Σ is only a function of s10, theerror in the local galaxy density, denoted as ∆Σ, is given by:

∆Σ =

∣∣∣∣ ∂Σ

∂s10

∆s10

∣∣∣∣ =22

πs310

∆s10 (2.12)

where ∆s10 is the error in s10 which can be calculated using equation 2.8.

2.6 Calculation of r200 and concentration index

Assuming that galaxy clusters are singular, isothermal spheres, Carlberg et al. (1997) derivean equation for r200:

r200 =

√3σz

10H(z)(2.13)

where σz is the velocity dispersion of the cluster and H(z) is the Hubble constant at redshiftz which is given by:

H(z) = H20 (1 + z)2(1 + ΩMz)2 (2.14)

Using equations 2.13 and 2.14 we calculated r200 for each cluster. The values of r200 areshown in table 2.1 and are also represented as the inner circles on the RA-Dec plots inappendix A. We consider r200 as the demarcating radius between the cluster core and thecluster infall region. Using the method of Taylor (1997), the errors in r200, represented by

2.7 Mass and morphology degeneracy 43

∆r200, were calculated according to the formula:

∆r200 =

√(∂r200

∂H∆H

)2

+

(∂r200

∂σz∆σz

)2

(2.15)

where ∆H and ∆σz are the errors in H(z) and σz respectively. The error ∆H which goesinto equation 2.15 warrants further explanation. Using the partial differential method ofTaylor (1997), we calculated ∆H(z) as:

∆H =

√(∂H

∂H0

∆H0

)2

+

(∂H

∂z∆z

)2

+

(∂H

∂ΩM

∆ΩM

)2

(2.16)

where ∆H0, ∆ΩM , and ∆z are the errors in H0, ΩM , and z respectively. For ∆H0 and ∆ΩM

we used the uncertainties given by Spergel et al. (2007), and for ∆z we used the values givenin table 2.1.

Using our calculated values of r200, we then proceeded to calculate the concentrationindex, C, of each cluster. Equation 1.6 defined C in terms of r20 and r60, the projected radiiout to the 20th and 60th percentile galaxies. Assuming that the distribution of galaxies inclusters is Gaussian in projected radius and has a standard deviation of rvir, a suitable valuefor the cut-off radius, r100, containing 100% of with cluster members is:

r100 = 3rvir ≈ 3r200 (2.17)

where we have used the fact that r200 is numerically similar to the virial radius. Circlesof radius r100 are represented as the outer circles on the RA-Dec plots in appendix A. Weconsider r100 to be the demarcating radius between the cluster infall region and the field.Next, we counted the number of galaxies in each cluster within r100 and sorted the galaxiesby projected radius from the cluster center to obtain estimates for projected radii out to the20th and 60th percentile galaxies. Plugging the estimates for r20 and r60 into equation 1.6yielded the concentration indices given in Table 2.1. The concentration values in 2.1 appearto be consistent with the the range of values predicted by Butcher & Oemler (1984), rangingfrom ∼ 0.3 up to ∼ 0.8. The errors in the concentration indices, represented by ∆C, werecalculated according to the equation:

∆C =

√(∂C

∂r20

∆r20

)2

+

(∂C

∂r60

∆r60

)2

(2.18)

where ∆r20 and ∆r60 are the errors in the projected radii of the 20th and 60th percentilegalaxies. We note that errors calculated in this way may underestimate the true error inthe concentration. A more rigorous error analysis would also incorporate the error in r100,Poissonian counting error in the number of galaxies within r100. Discretisation errors inclusters with few members also needs to be considered.

2.7 Mass and morphology degeneracy

In this section we explore LX-σz mass-degeneracy and Bautz-Morgan type-concentrationindex morphology-degeneracy. A priori, we expect a trend between LX and σz because


0.7 1 2 3 40

200

400

600

800

1000

1200

1400

1600

LX / 1044 erg s-1

σ z / km

s-1

Figure 2.11: X-ray luminosity versus velocity dispersion. There is no trend between X-rayluminosity and velocity dispersion, however, the velocity distributions are normally distributedabout 600 km s−1, indicative of an homogeneous intermediate-mass cluster sample.

they both depend on cluster mass. From virial theorem we know that the virial mass,mvir, is proportional to σ2

z (see equation 1.5). Furthermore, the number of X-ray photonsemitted from the intracluster medium is proportional to the square of the number of gasparticles, so the intracluster gas mass, mI , is proportional to L

1/2X . Despite theoretical

evidence that LX and σz should be positively correlated a Spearman rank test yields acorrelation coefficient of 0.2252 for the intermediate-LX cluster sample. The interpretationis that there is no significant correlation between LX and σz and hence these parameters arenot mas-degenerate. Figure 2.11 is a plot of LX versus σz demonstrating nothing but scatterbetween the two variables. A Lilliefors’ test confirms that σz is normally distributed at the5% significance level, hence the standard deviation of σz is a good measure of the amountof scatter in figure 2.11. We report a standard deviation of 200 km/s. Despite the lack oftrend between LX and σz, the mean velocity dispersion of 600 km/s is consistent with anhomogeneously-selected intermediate-mass cluster sample.

We also consider the possibility of there being a morphology degeneracy between con-centration index and Bautz-Morgan type. We suspected that there could be a negativecorrelation between Bautz-Morgan type and concentration index (i.e. concentration indexshould decrease with increasing Bautz-Morgan type), however a Spearman rank test yieldeda correlation coefficient of only 0.105 which is not only insignificant, but also the wrongsign. We conclude therefore that there is no relationship between concentration index andBautz-Morgan type. Intuitively this makes sense because concentration index is a measure

2.8 Substructure 45


0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Bautz-Morgan type

Con

cent

ratio

n

Figure 2.12: Bautz-Morgan type versus concentration index. There is no trend between Bautz-Morgan type and concentration index which indicates that they quantify different and independentaspects of cluster morphology.

of central tendency, extending into the cluster infall region whereas the Bautz-Morgan clas-sification scheme is concerned with the luminosity distribution of dominant galaxies in thecluster core. In other words, Bautz-Morgan type and concentration index are completelyindependent morphological classification schemes. Figure 2.12 is a plot of Bautz-Morgantype versus concentration index demonstrating nothing but scatter between the two vari-ables. A Lilliefors’ test confirms that concentration index is normally distributed at the 5%significance level, hence the standard deviation of C provides a good measure of the amountof scatter in figure 2.12. We report a standard deviation of 0.1 in concentration index.

2.8 Substructure

Many of the clusters in intermediate-LX sample display evidence of substructure. The ex-istence of substructure in galaxy clusters can be betrayed in at least three different ways:multiple X-ray centers, visual galaxy overdensities and multiply-peaked redshift distribu-tions. In XBACS, BCS, and eBCS, many clusters have been noted as having multipleX-ray cores. While none of the multiple X-ray core clusters have been inherited into ourintermediate-LX sample, at least 9 out of 45 clusters or 20% have visual galaxy overdensitiesand/or multiply-peaked redshift distributions.

To detect substructure, we constructed projected radius-local galaxy density diagrams


for each of our clusters, inspecting them visually alongside their corresponding redshift dis-tribution histograms. All galaxy clusters exhibit strong Σ peaks in the their cores near rp∼ 0, however, many clusters also exhibit secondary and multiple Σ peaks outside of thecluster core. We attribute the property of having substructure to a cluster if the cluster hasat least one non-core Σ peak within 3r200 and/or one redshift distribution peak not corre-sponding to the Gaussian peak. By looking at the redshift distribution we are probing forgalaxy overdensities in the line-of-sight direction. Plots of rp versus Σ as well as the red-shift distribution histograms are presented in appendix A for each cluster. Abell 1831 (seefigure A.43) is characteristic of a cluster with substructure - it contains a strong secondaryΣ peak at rp ∼ 2 Mpc which is presumably a similar-mass cluster undergoing a mergerwith Abell 1831. Since the analysis of substructure is not a primary goal of this thesis, wehave opted for the quick, simple, visual method outlined above. Computational methods totest for substructure (e.g. Dressler & Shectman, 1988) are time-consuming and beyond thescope of this work, however, we recognise that a more rigorous analysis of substructure inintermediate-LX is needed in future work.

If we also consider clusters which we have tentatively marked as having substructure intable 2.1, then 19 out of 45 clusters or ∼ 40% of intermediate-LX show evidence of substruc-ture. The true percentage of clusters with substructure could be even higher, because weremoved the overlapping intermediate-LX clusters during the cluster selection process. Thefraction of clusters with substructure in our intermediate-LX sample is directly comparableto the fraction given by Lacey & Cole (1993). They place lower and upper limits of 20%and 40% on the fraction of rich clusters having substructure. More recently, Burgett et al.(2004) report that > 80% of poor clusters in 2dFGRS exhibit substructure which is at leasttwice the value we calculated. We note that our results are not directly comparable to Bur-gett et al. (2004) because all of our clusters contain more than 50 members, thus satisfyingAbell’s richness criterion.

Analysing the fraction of galaxies with substructure is of interest because it leads toestimates of cluster merger rates and lifetimes. Reading off the CDM model panel with Ω0

∼ 0.24 in figure 13 of Lacey & Cole (1993), we estimate that intermediate-LX clusters haveaccreted approximately 50% of their total mass in the past 0.5 t0, where t0 is the presentage of the universe7.

7Modern cosmological models place the present age of the universe at ∼ 13.7 Gyr.

3Evolution of the Red Galaxies

In this chapter we will present the major results of this thesis and discuss the methodologyused to obtain them. In section 3.1 we will present the distribution of magnitudes andluminosity function of the intermediate-LX cluster sample. We will use the results of thissection to define photometric completeness limits and to obtain the characteristic magnitude,M∗. In section 3.2 we will discuss how we fitted colour-magnitude relations to the clusters andin section 3.3 we will present results on the redshift evolution of the slope and zero point ofthe colour-magnitude relation. We will also examine how the CMR depends on cluster massand cluster morphology. In section 3.4 we will explain how we evolved individual clustersto a common redshift to construct colour-magnitude diagrams of the composite cluster.In this section we will also explain how we used the composite cluster colour-magnitudediagrams to find colour gradients in projected radius and local galaxy density. Finally, wewill explain how we calculated the critical radius1 and critical galaxy density2 for clusters inthe intermediate-LX sample.

3.1 The cluster luminosity function

In this section we present the magnitude distributions and luminosity functions for galaxies inthe intermediate-LX cluster sample. The purpose of this analysis is to extract characteristicmagnitudes which we will use later in this chapter to fit the colour-magnitude relations andto stack our clusters together to create a composite cluster.

The u, g, r, i, and z′ band magnitude distributions are shown in figure 3.1. The galaxycounts are binned in 0.1 magnitude bins and the errors are assumed to be Poissonian, so the

1The critical radius, rcrit, is the value of the projected radius which characterises the onset of the colour-projected radius relation.

2The critical galaxy density, Σcrit, is the value of the local galaxy density which characterises the onsetof the colour-local galaxy density relation.

47

48 Evolution of the Red Galaxies

Table 3.1: Completeness limits in the intermediate-LX cluster sample

band fiducial magnitudeu 19.4 ± 0.1g 18.2 ± 0.1r 17.2 ± 0.2i 16.7 ± 0.2z′ 16.2 ± 0.1

error bars are given by the square root of the number of galaxies in each bin. The magnitudedistribution is expected to be linear in log n, where n is the number of galaxies in each bin.We fitted linear relations to the log n distributions as shown in figure 3.1. We performed100 ordinary least squares linear regressions on the log n distributions, randomising the binsizes on each new iteration. On each iteration we also calculated completeness as a functionof magnitude. All points on the log n line of best fit are said to be 100% complete, and thecompleteness fraction, ci, in the ith bin is given by:

ci =nine,i

(3.1)

where ni is the number of galaxies in the ith bin and ne,i is the expected number of galaxiesgiven by the line of best fit in the ith bin. The best linear fit coefficients are calculated bytaking the mean of the linear fit coefficients over the 100 iterations and the resultant bestfit linear relation is shown as the solid sloping lines in figure 3.1. We also calculate the bestestimate of the 90% completeness limit by taking the mean of the 90% completeness limitsfor each of the 100 iterations. The error in the 90% completeness limit was calculated bytaking the standard deviation of the 100 iterations. The 90% completeness limits in u, g,r, i, and z′ bands are given in table 3.1 and they are represented in figure 3.1 using verticaldashed lines.

Next we present the u, g, r, i and z′ luminosity functions of the intermediate-LX clustersample in figure 3.2. We are interested in luminosity functions because they provide uswith a robust method for identifying a characteristic magnitude galaxy in each cluster. Thepurpose of defining a characteristic magnitude is so that we can make our clusters (which areall at different redshifts) directly comparable with each other, ultimately allowing us stackour cluster together to make a composite cluster.

Luminosity functions are similar to the magnitude distributions except that the galaxycounts are binned by absolute magnitude3 rather than by apparent magnitude. The galaxycounts are binned in 0.2 magnitude bins and, as before, we assume Poissonian countingstatistics for the error bars. Absolute magnitudes were calculated according to the formula

M = m− d(z)− k(z) (3.2)

3The absolute magnitude of an object is the apparent magnitude it would have if it were placed at adistance of 10 pc from the observer.

3.1 The cluster luminosity function 49

where m is the galaxy’s apparent magnitude, d(z) is the distance modulus and k(z) is theK-correction term. The distance modulus is given by

d(z) = 5 log10

[(1 + z)

DC(z)

10

](3.3)

where Dc(z) is the comoving distance in units of pc. The K-correction is a small correctionterm which accounts for the fact that sources observed at different redshifts are, in general,compared with each other at different rest-frame wavelengths (Hogg et al., 2002). TheK-correction is defined as:

k(z) = −2.5 log

[1

1 + z

∫dλo λo fλ(λo)R(λo)∫

dλe λe fλ([1 + z]λe)R(λe)

](3.4)

where λ is wavelength, fλ is the spectral flux density, R is the bandpass filter and the sub-script o and e represent the observed and emitted frames respectively. Instead of calculatingthe K-corrections for each galaxy, we use the K-corrections given in the Photoz table in theSDSS DR6 database (see http://cas.sdss.org/astro/en/help/browser/browser.asp?n=Photoz-&t=U). While this saves us an incredible amount of time, it does come with the followingcaveat. The K-corrections in the Photoz table are calculated using photometric redshiftsrather than spectroscopic redshifts. The errors associated with the photometric redshifts are1–2 orders of magnitude larger than the errors associated with the spectroscopic redshifts,thus increasing the total error in the k-correction. Despite this, the redshift contributionto the total error is insignificant in comparison to error contributions from the flux densitywhich is rarely known to better than a few percent (Hogg et al., 2002). Moreover, Thek-correction errors are not given in the DR6 SDSS database, hence we calculated the errorsin absolute magnitude, denoted by ∆M, as being given by:

∆M =√

∆m+ ∆d(z) (3.5)

where ∆m and ∆d(z) are the errors in the apparent magnitude and distance modulus respec-tively. We note that errors calculated using equation 3.5 may underestimate the true errorsbecause there is no error term for the K-correction. Using the partial differential method ofTaylor (1997), the uncertainty in the distance modulus is given by:

∆d(z) =

√(∂d

∂z∆z

)2

+

(∂d

∂DC

∆DC

)2

(3.6)

where ∆z is the error in redshift, ∆DC is the error in the comoving distance, and the partialderivatives are calculated with respect to equation 3.3. The values of z and ∆z which go intoequations 3.3 and 3.6 are the clustercentric values given in table 2.1. We use clustercentricredshifts rather than the redshifts of the individual galaxies. This is because the individualgalaxy redshifts have large peculiar velocity components due to line-of-sight motion withintheir host clusters.

After having successfully converted magnitudes into absolute magnitudes, Schechter func-tion models (see Schechter 1976) were fitted to the binned data. Colless (1989) gives theform of the Schechter function in terms of absolute magnitude as:

n(M)dM = kN∗ exp k(α + 1)(M ∗ −M)− exp[k(M∗ −M)] dM (3.7)


where M∗ is the characteristic absolute magnitude at the ‘knee’ of the function, N∗ is thecharacteristic number of galaxies per magnitude at M∗, α is a power law exponent whichgives the faint-end slope of the function and k = log(10)/2.5. To correct for the effects offinite bin size, ∆M , a correction term needs to be added to equation 3.7. The correctedSchechter function is given by

Ne,i = n(Mi)∆M + n′′(Mi)∆M3/24 (3.8)

where Ne,i is the expected number of galaxies in the ith bin, Mi is absolute magnitude at thecenter of the ith bin and n′′(Mi) is the second derivative of equation 3.7 with respect to Mi

(Schechter, 1976). The Schechter functions were fitted to our binned data using the usualordinary least squares method. In the ordinary least squares method, the best fit parametersare the ones which minimise the χ2 statistic, which in this case is given by

χ2 =∑i

(Ni −Ne,i)2

Ne,i

(3.9)

where Ni is the observed number of galaxies in the ith bin. For each absolute magnitudeband, the Schechter functions were fit from the brightest magnitude bin up to a cut-offmagnitude. The luminosity functions and Schechter function fits are shown in figure 3.2.One hundred χ2 minimisations were performed with M∗, N∗ and α as free parameters andwith randomised bin sizes between 0.05 and 0.5 mag. The fit parameters and their associatederrors were calculated as being the mean and standard deviation of the 100 runs. The valuesare shown in table 3.2 and the positions of the M∗ values are represented by vertical dashedlines in figure 3.2.

While the Schechter function models appear to fit the knee of the luminosity functionswell around M∗, they are less than ideal at the bright end. Recently, some authors (e.g. Stott2007; Dahlen et al. 2004; Thompson & Gregory 1993) have advocated fitting combinationGaussian/Schechter functions or double Schechter functions to provide a better descriptionof the luminosity function. Likewise, the single Schechter function fits are inadequate de-scriptions of the luminosity function at the faint end which is why we have cropped ourSchechter functions in figure 3.2 close to the knee. In our case, however, we are interestedonly in the position of M∗ and thus the Schechter function fits shown in figure 3.2 are ade-quate for the purposes of this study. As a characteristic magnitude, M∗ is the ideal choicebecause it has been shown to not vary with redshift out to at least z ∼ 0.3 (Mobasher et al.,2003). Moreover, Schechter functions are widely used in the literature which makes ourresults directly comparable to other studies.

3.2 Fitting the colour-magnitude relations

In this section we will describe the method we used to fit linear relations to the red se-quence galaxies on the colour-magnitude planes of our clusters. Colour magnitude diagramswere constructed for each of our 45 clusters in all 10 possible colour combinations of SDSSpassbands. These colours span all possible colour combinations of the SDSS passbands. Toincrease the amount of degeneracy in our diagrams, we used the redder of the passbands as

3.2 Fitting the colour-magnitude relations 51

16 18 20 2210

0

101

102

103

u-band magnitude distribution

u

Num

ber

of g

alax

ies

14 16 18 2010

0

101

102

103

g-band magnitude distribution

gN

umbe

r of

gal

axie

s

14 16 18 2010

0

101

102

103

r-band magnitude distribution

r

Num

ber

of g

alax

ies

12 14 16 1810

0

101

102

103

i-band magnitude distribution

i

Num

ber

of g

alax

ies

12 14 16 1810

0

101

102

103

z′-band magnitude distribution

z′

Num

ber

of g

alax

ies

Figure 3.1: Magnitude distributions for the u, g, r, i, and z′ bands with line of best fit for thelog n distribution. The vertical dashed lines represent the 90% completeness limit in each band.


-22 -20 -18 -16 -1410

0

101

102

103

u-band luminosity function

Mu

Num

ber

of g

alax

ies

-24 -22 -20 -18 -1610

0

101

102

103

g-band luminosity function

Mg

Num

ber

of g

alax

ies

-24 -22 -20 -18 -1610

0

101

102

103

r-band luminosity function

Mr

Num

ber

of g

alax

ies

-24 -22 -20 -18 -1610

0

101

102

103

i-band luminosity function

Mi

Num

ber

of g

alax

ies

-24 -22 -20 -18 -1610

0

101

102

103

z′-band luminosity function

Mz′

Num

ber

of g

alax

ies

Figure 3.2: Absolute magnitude luminosity functions for the u, g, r, i, and z′ bands. The solidcurves are our Schechter function model fits. The vertical dashed lines mark the position of M∗.


Table 3.2: Schechter function fit parameters

band M∗ N∗ αMu -18.29 ± 0.04 13,200 ± 200 0.27 ± 0.07Mg -20.35 ± 0.05 12,500 ± 200 -0.39 ± 0.07Mr -21.09 ± 0.05 12,000 ± 200 -0.36 ± 0.07Mi -21.53 ± 0.04 11,400 ± 200 -0.40 ± 0.06Mz -21.81 ± 0.04 11,200 ± 200 -0.28 ± 0.06

the abscissa. For example, (g-r) was plotted versus r and (i-z′) was plotted versus z′. Whenfitting CMRs to the red sequence, the colour-magnitude plane was divided into two halves.Data points brighter than the fiducial magnitude for the passband were included in the linearfit, while points fainter than (to the right of) the fiducial magnitude were excluded. In thisthesis, we have used the 90% completeness limits listed in table 3.1 as our fiducial magni-tudes. Completeness limits are an appropriate choice for fiducial magnitude because we canbe confident that galaxies brighter than the completeness limit do not suffer from selectionbias. As the name suggests, galaxies fainter than the completeness limit form an incompletedata subset which may suffer from selection bias. By imposing a fiducial magnitude we alsoreduce the effect of faint-end scatter which would otherwise bias our CMR fits.

Since there are two overlapping galaxy populations on the colour-magnitude plane (redsequence and blue cloud), ordinary least squares fitting techniques were inadequate to fitthe CMRs. Typically, ordinary least squares fitting yields slopes which are too steep andintercepts which are too high - the faint end of the CMR being dragged blueward by the bluecloud. Ideally, one would like to remove the blue cloud galaxies and perform an ordinaryleast squares fit to the remaining red sequence galaxies. However, identifying blue cloudgalaxies without already knowing the position of the CMR is a non-trivial exercise. Amore straightforward approach is to perform a robust linear fit which effectively weights redsequence galaxies higher than blue sequence galaxies. If we parameterise our straight lineequation in the form

y(x) = mx+ c (3.10)

then our ith residual, ri, is simply given by

ri = yi −mxi − c (3.11)

where m and c are the slope and zero-point of our straight line and (xi,yi) are the coordinatesof the ith data point. A linear fit to the data is obtained my finding m and c which minimisethe merit function ∑

i

f(riσi

) (3.12)

where 1/σi is the weighting term. In the case of an ordinary least squares linear regression,the merit function is χ2, however, a minimising set of m and c can be found for almostany sane choice of f (Press et al., 1992). While some authors (e.g. Pimbblet et al. 2002)use a merit function which minimises the sum of the absolute values of the residuals, we


break with tradition and use the Lorentzian function suggested by Press et al. (1992). TheLorentzian merit function is defined as∑

i

log (1 + r2i /2)

∆yi(3.13)

where ∆yi is magnitude of the error in y. In comparison to the absolute deviation minimisingmerit function, the Lorentzian merit function visually appears to converge at least as wellor closer to the apparent red sequence. The merit function was minimised using the Nelder-Mead downhill simplex algorithm (Press et al., 1992). The Nelder-Mead algorithm requiresinitial guess values for the linear fit coefficients - we use ordinary least squares regression fitcoefficients as our starting points.

We do not know of any analytical functions to calculate the error in the fit parametersfor the Nelder-Mead algorithm. Instead, error bars in the slope and intercept of the fittedCMRs were calculated using a shotgun approach. Each CMR was fitted 100 times using themethod described above. Before fitting the CMR on each iteration, 10% of the data pointsbrighter than the fiducial magnitude were randomly removed. For each CMR, the standarddeviations of the slope and intercept of the 100 trials were calculated. These values arepresumed to be good estimates of the error in the slope and intercept.

The CMR fitting process was automated and the resultant colour-magnitude diagramswere visually inspected for goodness-of-fit before continuing into further analyses. In mostcases, our fitting algorithm successfully located the CMR in each diagram, however, some-times the algorithm failed for clusters with few members. In cases where the fitting algorithmfailed to automatically fit the CMR, arbitrary colour envelopes were applied about the sus-pected position of the CMR to help the algorithm hone in on the CMR on a second run.Visual inspection of the colour-magnitude diagrams in appendix A shows that the CMRfitting algorithm and subsequent fit updates (where necessary) provide good estimates ofthe CMR fit parameters in most cases. Of the few colour-magnitude diagrams in appendixA with poor CMR fits, the main cause of badness-of-fit is not enough data points brighterthan the fiducial magnitude. We make no further attempt to improve poorly fitted CMRs.In addition to colour and magnitude data, the colour-magnitude diagrams also show thefitted CMRs (sloped solid lines), fiducial magnitudes (vertical solid lines) and characteristicM∗ magnitudes converted to apparent magnitude, m∗, at the clustercentric redshift (verticaldashed lines). We convert from M∗ absolute magnitude to m∗ apparent magnitude using thefollowing equation:

m∗ = M∗ + d(z) + k(z) (3.14)

For the K-correction terms in equation 3.14 we identify the k, k+a, and a+k spectral-typegalaxies (see Poggianti et al., 1999) in each cluster from the equivalent widths of their Hδ

and [OII] lines and take the mean K-correction value of these galaxies as the K-correction forthe entire cluster. Pimbblet et al. (2006) showed that the red sequence is mainly composedof k, k+a, and a+k type galaxies, thus the mean K-correction method is expected to givethe mean K-correction of the red sequence galaxies which is the population of interest. Theerror in the m∗ apparent magnitude, denoted ∆m∗, is given by:

∆m∗ =√

∆M∗ + ∆d(z) + ∆k(z) (3.15)


where ∆M∗, ∆d(z), and ∆k(z) are the errors in M∗, d(z) and k(z) respectively. We use thestandard deviation of the K-correction values of the k, k+a, and a+k galaxies as the error inthe K-correction for the entire cluster. Methods for calculating d(z) and ∆d(z) are discussedin section 3.1.

The linear fit parameters are presented in tables 3.3 and 3.4. Due to the amount of data,the fit coefficients have been separated into two tables. Table 3.3 contains the fit parametersfor the (u-g) versus g, (u-r) versus r, (u-i) versus i, (u-z′) versus z′, and (g-r) versus r CMRs.Table 3.4 contains the remaining CMR fit parameters. The columns of the tables are labeledin the format mab and cab, where mab and cab are the slope and zero point (at b = 0) of the(a-b) versus b CMR for generic passbands a and b.

56EvolutionoftheRed

Galaxies

Table 3.3: CMR fit coefficients ICluster Name mug cug mur cur mui cui muz cuz mgr cgrAbell 602 -0.099 ± 0.005 3.65 ± 0.08 -0.143 ± 0.007 5.2 ± 0.1 -0.172 ± 0.008 6.1 ± 0.1 -0.17 ± 0.01 6.2 ± 0.2 -0.038 ± 0.006 1.57 ± 0.09Abell 671 -0.060 ± 0.002 2.94 ± 0.03 -0.104 ± 0.005 4.47 ± 0.08 -0.123 ± 0.006 5.14 ± 0.08 -0.143 ± 0.006 5.71 ± 0.08 -0.032 ± 0.003 1.41 ± 0.05Abell 743 -0.10 ± 0.02 3.8 ± 0.3 -0.06 ± 0.04 4.2 ± 0.7 -0.09 ± 0.06 5.2 ± 0.9 -0.1 ± 0.2 5 ± 3 -0.08 ± 0.06 2 ± 1Abell 744 -0.04 ± 0.02 2.6 ± 0.3 -0.09 ± 0.02 4.4 ± 0.3 -0.06 ± 0.03 4.3 ± 0.5 -0.02 ± 0.04 4.1 ± 0.6 -0.014 ± 0.001 1.19 ± 0.02Abell 757 -0.072 ± 0.006 3.1 ± 0.1 -0.12 ± 0.03 4.7 ± 0.4 -0.16 ± 0.02 5.6 ± 0.4 -0.16 ± 0.03 5.9 ± 0.4 -0.022 ± 0.008 1.2 ± 0.1Abell 763 -0.069 ± 0.009 3.2 ± 0.2 -0.05 ± 0.06 4 ± 1 -0.06 ± 0.02 4.4 ± 0.3 -0.09 ± 0.02 5.2 ± 0.3 -0.007 ± 0.008 1.1 ± 0.1Abell 923 -0.086 ± 0.010 3.5 ± 0.2 -0.123 ± 0.008 5.1 ± 0.1 -0.121 ± 0.009 5.5 ± 0.1 -0.11 ± 0.03 5.7 ± 0.5 -0.01 ± 0.01 1.3 ± 0.2Abell 957 -0.052 ± 0.007 2.8 ± 0.1 -0.092 ± 0.006 4.24 ± 0.10 -0.09 ± 0.02 4.6 ± 0.2 -0.086 ± 0.008 4.9 ± 0.1 -0.016 ± 0.003 1.15 ± 0.05Abell 961 -0.01 ± 0.04 2.1 ± 0.7 -0.03 ± 0.08 3 ± 1 -0.07 ± 0.03 4.6 ± 0.6 -0.08 ± 0.06 5 ± 1 -0.007 ± 0.010 1.2 ± 0.2Abell 971 -0.027 ± 0.008 2.4 ± 0.1 -0.07 ± 0.02 4.0 ± 0.4 -0.061 ± 0.006 4.33 ± 0.10 -0.03 ± 0.04 4.2 ± 0.7 -0.005 ± 0.008 1.1 ± 0.1Abell 1035 -0.05 ± 0.02 2.7 ± 0.4 -0.13 ± 0.01 4.8 ± 0.2 -0.138 ± 0.005 5.32 ± 0.07 -0.13 ± 0.01 5.5 ± 0.2 -0.040 ± 0.008 1.5 ± 0.1Abell 1045 -0.08 ± 0.03 3.3 ± 0.6 -0.17 ± 0.05 5.8 ± 0.8 -0.15 ± 0.04 5.9 ± 0.6 -0.16 ± 0.04 6.4 ± 0.6 -0.019 ± 0.009 1.4 ± 0.2Abell 1126 -0.048 ± 0.009 2.8 ± 0.1 -0.07 ± 0.01 4.1 ± 0.2 -0.03 ± 0.03 3.9 ± 0.5 -0.08 ± 0.03 5.0 ± 0.5 0.002 ± 0.009 0.9 ± 0.1Abell 1361 -0.10 ± 0.05 3.6 ± 0.9 -0.15 ± 0.05 5.4 ± 0.8 -0.17 ± 0.04 6.2 ± 0.7 -0.17 ± 0.04 6.5 ± 0.6 -0.01 ± 0.02 1.3 ± 0.3Abell 1446 -0.02 ± 0.02 2.4 ± 0.4 -0.08 ± 0.02 4.2 ± 0.3 -0.06 ± 0.04 4.4 ± 0.6 -0.06 ± 0.05 4.7 ± 0.8 -0.021 ± 0.007 1.3 ± 0.1Abell 1691 -0.025 ± 0.009 2.4 ± 0.2 -0.096 ± 0.003 4.36 ± 0.04 -0.097 ± 0.004 4.74 ± 0.06 -0.09 ± 0.02 5.0 ± 0.2 -0.017 ± 0.001 1.18 ± 0.02Abell 1728 -0.04 ± 0.01 2.7 ± 0.2 -0.09 ± 0.02 4.4 ± 0.3 -0.06 ± 0.02 4.3 ± 0.3 -0.05 ± 0.01 4.4 ± 0.2 0.00 ± 0.01 0.9 ± 0.2Abell 1767 -0.046 ± 0.004 2.68 ± 0.07 -0.11 ± 0.02 4.6 ± 0.3 -0.12 ± 0.02 5.1 ± 0.4 -0.13 ± 0.01 5.5 ± 0.2 -0.029 ± 0.003 1.37 ± 0.04Abell 1773 -0.040 ± 0.002 2.64 ± 0.04 -0.062 ± 0.009 3.9 ± 0.2 -0.071 ± 0.006 4.42 ± 0.09 -0.073 ± 0.009 4.8 ± 0.1 -0.0063 ± 0.0009 1.02 ± 0.01Abell 1809 -0.026 ± 0.005 2.39 ± 0.08 -0.068 ± 0.006 3.96 ± 0.09 -0.057 ± 0.009 4.2 ± 0.1 -0.11 ± 0.02 5.3 ± 0.4 -0.015 ± 0.006 1.19 ± 0.10Abell 1814 -0.00 ± 0.09 2 ± 2 -0.1 ± 0.2 4 ± 3 -0.2 ± 0.1 6 ± 2 -0.1 ± 0.2 6 ± 2 -0.00 ± 0.03 1.2 ± 0.6Abell 1831 -0.054 ± 0.003 2.81 ± 0.06 -0.09 ± 0.01 4.2 ± 0.2 -0.098 ± 0.009 4.7 ± 0.1 -0.077 ± 0.009 4.7 ± 0.1 -0.020 ± 0.002 1.21 ± 0.03Abell 1885 -0.01 ± 0.02 2.1 ± 0.4 -0.05 ± 0.06 4 ± 1 -0.00 ± 0.06 3.3 ± 0.9 -0.03 ± 0.05 4.1 ± 0.9 0.00 ± 0.02 0.9 ± 0.4Abell 1925 -0.069 ± 0.008 3.2 ± 0.1 -0.09 ± 0.01 4.4 ± 0.2 -0.11 ± 0.02 5.1 ± 0.3 -0.113 ± 0.009 5.5 ± 0.1 -0.009 ± 0.002 1.15 ± 0.03Abell 1927 -0.080 ± 0.006 3.43 ± 0.10 -0.15 ± 0.02 5.5 ± 0.3 -0.18 ± 0.02 6.3 ± 0.3 -0.15 ± 0.02 6.2 ± 0.4 -0.031 ± 0.003 1.52 ± 0.05Abell 2033 -0.009 ± 0.010 2.1 ± 0.2 -0.06 ± 0.01 3.8 ± 0.2 -0.07 ± 0.01 4.4 ± 0.2 -0.06 ± 0.01 4.7 ± 0.2 -0.005 ± 0.001 1.05 ± 0.02Abell 2108 -0.038 ± 0.008 2.6 ± 0.1 -0.023 ± 0.010 3.3 ± 0.2 -0.03 ± 0.01 3.8 ± 0.2 -0.00 ± 0.01 3.9 ± 0.2 0.001 ± 0.007 1.0 ± 0.1Abell 2110 -0.09 ± 0.01 3.5 ± 0.2 -0.11 ± 0.02 4.8 ± 0.4 -0.15 ± 0.03 5.8 ± 0.5 -0.14 ± 0.07 6 ± 1 -0.04 ± 0.02 1.7 ± 0.3Abell 2124 -0.035 ± 0.003 2.51 ± 0.05 -0.045 ± 0.006 3.6 ± 0.1 -0.077 ± 0.007 4.5 ± 0.1 -0.13 ± 0.01 5.6 ± 0.2 -0.019 ± 0.004 1.24 ± 0.07Abell 2141 -0.07 ± 0.05 3.5 ± 0.8 -0.24 ± 0.07 7 ± 1 -0.21 ± 0.06 7 ± 1 -0.28 ± 0.08 9 ± 1 -0.04 ± 0.02 1.9 ± 0.3Abell 2148 -0.049 ± 0.006 2.9 ± 0.1 -0.083 ± 0.005 4.50 ± 0.08 -0.078 ± 0.008 4.9 ± 0.1 -0.09 ± 0.01 5.5 ± 0.2 -0.023 ± 0.007 1.4 ± 0.1Abell 2149 -0.046 ± 0.004 2.71 ± 0.06 -0.099 ± 0.003 4.38 ± 0.05 -0.112 ± 0.005 4.97 ± 0.07 -0.116 ± 0.003 5.33 ± 0.05 -0.033 ± 0.002 1.41 ± 0.03Abell 2175 -0.013 ± 0.010 2.3 ± 0.2 -0.05 ± 0.02 3.9 ± 0.4 -0.08 ± 0.03 4.8 ± 0.5 -0.07 ± 0.04 4.9 ± 0.6 -0.04 ± 0.02 1.8 ± 0.4Abell 2199 -0.066 ± 0.002 2.86 ± 0.03 -0.152 ± 0.003 4.87 ± 0.04 -0.162 ± 0.003 5.35 ± 0.04 -0.162 ± 0.005 5.61 ± 0.08 -0.035 ± 0.001 1.33 ± 0.02Abell 2228 -0.03 ± 0.02 2.5 ± 0.4 -0.10 ± 0.04 4.6 ± 0.6 -0.11 ± 0.05 5.4 ± 0.9 -0.14 ± 0.04 6.1 ± 0.7 -0.018 ± 0.009 1.3 ± 0.1RXJ0820.9+0751 -0.03 ± 0.03 2.6 ± 0.5 -0.09 ± 0.04 4.5 ± 0.6 -0.08 ± 0.03 4.7 ± 0.5 -0.18 ± 0.06 6.6 ± 0.9 -0.021 ± 0.004 1.40 ± 0.06RXJ1000.5+4409 0.0 ± 0.2 2 ± 3 -0.15 ± 0.08 6 ± 1 -0.17 ± 0.06 6.5 ± 1.0 -0.3 ± 0.1 9 ± 2 -0.045 ± 0.007 1.9 ± 0.1RXJ1053.7+5450 -0.053 ± 0.006 2.8 ± 0.1 -0.073 ± 0.005 4.00 ± 0.08 -0.086 ± 0.008 4.6 ± 0.1 -0.081 ± 0.005 4.82 ± 0.08 -0.02 ± 0.01 1.3 ± 0.2RXJ1423.9+4015 -0.064 ± 0.008 3.0 ± 0.1 -0.094 ± 0.009 4.4 ± 0.1 -0.107 ± 0.008 5.0 ± 0.1 -0.120 ± 0.007 5.48 ± 0.10 -0.022 ± 0.001 1.29 ± 0.02RXJ1442.2+2218 0.05 ± 0.08 1 ± 1 -0.00 ± 0.06 3 ± 1 -0.01 ± 0.05 3.6 ± 0.7 -0.05 ± 0.07 4 ± 1 -0.01 ± 0.02 1.1 ± 0.4RXJ1652.6+4011 -0.16 ± 0.04 5.0 ± 0.7 -0.15 ± 0.04 5.7 ± 0.7 -0.09 ± 0.05 5.2 ± 0.8 -0.14 ± 0.08 6 ± 1 -0.032 ± 0.007 1.7 ± 0.1ZwCl 1478 -0.03 ± 0.07 2 ± 1 -0.30 ± 0.09 8 ± 1 -0.20 ± 0.04 6.8 ± 0.7 -0.4 ± 0.1 10 ± 2 -0.09 ± 0.02 2.6 ± 0.4ZwCl 4905 -0.04 ± 0.02 2.7 ± 0.3 -0.09 ± 0.02 4.3 ± 0.4 -0.09 ± 0.03 4.7 ± 0.4 -0.13 ± 0.01 5.6 ± 0.2 -0.0190 ± 0.0009 1.23 ± 0.01ZwCl 6718 -0.072 ± 0.004 3.16 ± 0.06 -0.09 ± 0.01 4.3 ± 0.2 -0.131 ± 0.007 5.3 ± 0.1 -0.129 ± 0.008 5.6 ± 0.1 -0.027 ± 0.001 1.35 ± 0.02ZwCl 8197 -0.07 ± 0.02 3.2 ± 0.4 -0.09 ± 0.04 4.5 ± 0.6 -0.09 ± 0.04 4.9 ± 0.7 -0.12 ± 0.02 5.8 ± 0.4 -0.025 ± 0.003 1.47 ± 0.06

3.2

Fitting

thecolour-m

agnituderelations

57Table 3.4: CMR fit coefficients II

Cluster Name mgi cgi mgz cgz mri cri mrz crz miz cizAbell 602 -0.05 ± 0.01 2.2 ± 0.2 -0.05 ± 0.02 2.6 ± 0.3 -0.0104 ± 0.0010 0.62 ± 0.02 -0.013 ± 0.002 1.01 ± 0.03 -0.008 ± 0.010 0.5 ± 0.2Abell 671 -0.046 ± 0.005 2.06 ± 0.09 -0.056 ± 0.009 2.5 ± 0.1 -0.023 ± 0.002 0.79 ± 0.03 -0.030 ± 0.008 1.3 ± 0.1 -0.010 ± 0.003 0.49 ± 0.05Abell 743 0.04 ± 0.02 1.1 ± 0.3 0.0 ± 0.1 2 ± 2 -0.008 ± 0.006 0.62 ± 0.09 -0.00 ± 0.03 1.0 ± 0.5 -0.03 ± 0.01 0.8 ± 0.2Abell 744 -0.01 ± 0.02 1.6 ± 0.3 -0.03 ± 0.02 2.2 ± 0.3 -0.009 ± 0.005 0.63 ± 0.08 0.001 ± 0.009 0.8 ± 0.1 -0.002 ± 0.009 0.4 ± 0.1Abell 757 -0.02 ± 0.01 1.5 ± 0.2 -0.08 ± 0.05 2.7 ± 0.7 -0.015 ± 0.005 0.64 ± 0.08 -0.026 ± 0.006 1.11 ± 0.09 -0.013 ± 0.006 0.50 ± 0.09Abell 763 -0.04 ± 0.02 2.1 ± 0.3 -0.01 ± 0.06 2.0 ± 0.8 -0.009 ± 0.006 0.59 ± 0.10 -0.031 ± 0.007 1.3 ± 0.1 -0.010 ± 0.005 0.51 ± 0.07Abell 923 -0.07 ± 0.03 2.7 ± 0.5 -0.07 ± 0.06 3.0 ± 0.9 -0.017 ± 0.002 0.75 ± 0.03 -0.01 ± 0.02 1.0 ± 0.3 -0.007 ± 0.004 0.52 ± 0.07Abell 957 -0.03 ± 0.01 1.7 ± 0.2 -0.039 ± 0.008 2.3 ± 0.1 -0.016 ± 0.002 0.69 ± 0.03 -0.026 ± 0.001 1.16 ± 0.02 -0.014 ± 0.001 0.56 ± 0.02Abell 961 -0.00 ± 0.04 1.6 ± 0.6 -0.02 ± 0.03 2.2 ± 0.5 0.001 ± 0.006 0.4 ± 0.1 -0.00 ± 0.02 0.9 ± 0.3 -0.002 ± 0.005 0.41 ± 0.07Abell 971 -0.026 ± 0.009 1.8 ± 0.1 -0.00 ± 0.02 1.8 ± 0.2 -0.009 ± 0.009 0.6 ± 0.1 -0.002 ± 0.002 0.80 ± 0.03 -0.017 ± 0.004 0.61 ± 0.07Abell 1035 -0.052 ± 0.006 2.10 ± 0.10 -0.064 ± 0.005 2.59 ± 0.08 -0.016 ± 0.004 0.67 ± 0.07 -0.018 ± 0.003 0.99 ± 0.04 -0.013 ± 0.001 0.51 ± 0.02Abell 1045 -0.03 ± 0.02 2.0 ± 0.3 -0.06 ± 0.01 2.8 ± 0.2 0.004 ± 0.003 0.39 ± 0.04 -0.022 ± 0.005 1.14 ± 0.07 -0.02 ± 0.01 0.7 ± 0.2Abell 1126 -0.01 ± 0.02 1.6 ± 0.4 -0.03 ± 0.05 2.1 ± 0.8 -0.012 ± 0.004 0.63 ± 0.06 -0.037 ± 0.006 1.34 ± 0.09 -0.022 ± 0.004 0.67 ± 0.06Abell 1361 -0.06 ± 0.01 2.4 ± 0.2 -0.07 ± 0.03 3.0 ± 0.5 -0.003 ± 0.009 0.5 ± 0.1 -0.02 ± 0.03 1.2 ± 0.4 -0.026 ± 0.004 0.78 ± 0.06Abell 1446 -0.033 ± 0.007 2.0 ± 0.1 -0.01 ± 0.03 2.0 ± 0.5 -0.001 ± 0.007 0.5 ± 0.1 -0.01 ± 0.02 0.9 ± 0.3 -0.010 ± 0.005 0.50 ± 0.08Abell 1691 -0.021 ± 0.003 1.66 ± 0.04 -0.032 ± 0.005 2.15 ± 0.08 -0.008 ± 0.001 0.55 ± 0.02 -0.013 ± 0.002 0.95 ± 0.03 -0.013 ± 0.001 0.53 ± 0.02Abell 1728 -0.003 ± 0.010 1.5 ± 0.2 -0.01 ± 0.01 1.9 ± 0.2 0.0003 ± 0.0008 0.44 ± 0.01 0.00 ± 0.01 0.7 ± 0.2 -0.008 ± 0.003 0.47 ± 0.05Abell 1767 -0.031 ± 0.006 1.82 ± 0.09 -0.050 ± 0.006 2.43 ± 0.09 -0.016 ± 0.002 0.67 ± 0.03 -0.019 ± 0.005 1.04 ± 0.07 -0.007 ± 0.005 0.43 ± 0.07Abell 1773 -0.021 ± 0.009 1.7 ± 0.1 -0.02 ± 0.01 2.0 ± 0.2 -0.0136 ± 0.0010 0.66 ± 0.02 -0.011 ± 0.006 0.96 ± 0.09 -0.001 ± 0.002 0.36 ± 0.02Abell 1809 -0.032 ± 0.002 1.88 ± 0.03 -0.03 ± 0.02 2.2 ± 0.3 -0.002 ± 0.001 0.47 ± 0.02 -0.001 ± 0.003 0.80 ± 0.04 -0.000 ± 0.002 0.34 ± 0.03Abell 1814 -0.00 ± 0.04 1.6 ± 0.7 -0.00 ± 0.03 2.0 ± 0.4 0.001 ± 0.006 0.4 ± 0.1 -0.03 ± 0.02 1.2 ± 0.4 -0.02 ± 0.02 0.6 ± 0.3Abell 1831 -0.018 ± 0.004 1.59 ± 0.05 -0.020 ± 0.001 1.95 ± 0.02 -0.0090 ± 0.0006 0.559 ± 0.009 -0.016 ± 0.005 0.99 ± 0.07 -0.011 ± 0.001 0.49 ± 0.02Abell 1885 -0.00 ± 0.04 1.4 ± 0.6 -0.04 ± 0.06 2.3 ± 1.0 -0.017 ± 0.003 0.67 ± 0.04 -0.01 ± 0.03 0.9 ± 0.5 -0.000 ± 0.010 0.3 ± 0.2Abell 1925 -0.04 ± 0.02 2.0 ± 0.3 -0.037 ± 0.003 2.40 ± 0.05 -0.010 ± 0.002 0.60 ± 0.03 -0.029 ± 0.005 1.27 ± 0.07 -0.005 ± 0.003 0.44 ± 0.05Abell 1927 -0.047 ± 0.002 2.21 ± 0.03 -0.060 ± 0.006 2.77 ± 0.09 -0.009 ± 0.001 0.60 ± 0.02 -0.031 ± 0.004 1.30 ± 0.07 -0.019 ± 0.003 0.66 ± 0.05Abell 2033 -0.011 ± 0.009 1.6 ± 0.1 -0.028 ± 0.006 2.2 ± 0.1 -0.0037 ± 0.0007 0.51 ± 0.01 -0.012 ± 0.005 1.01 ± 0.07 -0.006 ± 0.006 0.45 ± 0.09Abell 2108 -0.03 ± 0.01 1.9 ± 0.2 -0.005 ± 0.005 1.92 ± 0.08 -0.020 ± 0.004 0.78 ± 0.07 -0.007 ± 0.006 1.0 ± 0.1 -0.001 ± 0.002 0.40 ± 0.04Abell 2110 -0.04 ± 0.02 2.1 ± 0.2 -0.06 ± 0.03 2.7 ± 0.4 -0.020 ± 0.001 0.78 ± 0.02 -0.028 ± 0.003 1.27 ± 0.04 -0.0119 ± 0.0008 0.55 ± 0.01Abell 2124 -0.026 ± 0.002 1.79 ± 0.03 -0.05 ± 0.01 2.4 ± 0.2 -0.010 ± 0.002 0.59 ± 0.03 -0.034 ± 0.004 1.28 ± 0.06 -0.013 ± 0.002 0.54 ± 0.03Abell 2141 -0.04 ± 0.03 2.4 ± 0.5 -0.07 ± 0.02 3.2 ± 0.4 -0.03 ± 0.01 0.9 ± 0.2 -0.03 ± 0.02 1.3 ± 0.3 -0.00 ± 0.01 0.5 ± 0.2Abell 2148 -0.04 ± 0.02 2.3 ± 0.3 -0.06 ± 0.03 2.8 ± 0.5 -0.014 ± 0.005 0.72 ± 0.08 -0.022 ± 0.004 1.27 ± 0.06 -0.01 ± 0.01 0.6 ± 0.2Abell 2149 -0.046 ± 0.002 2.01 ± 0.04 -0.059 ± 0.003 2.53 ± 0.05 -0.010 ± 0.002 0.58 ± 0.04 -0.027 ± 0.002 1.17 ± 0.03 -0.011 ± 0.001 0.49 ± 0.01Abell 2175 -0.04 ± 0.03 2.2 ± 0.4 -0.06 ± 0.02 2.9 ± 0.3 -0.007 ± 0.008 0.6 ± 0.1 -0.023 ± 0.008 1.2 ± 0.1 -0.01 ± 0.01 0.5 ± 0.2Abell 2199 -0.052 ± 0.004 1.95 ± 0.07 -0.059 ± 0.005 2.35 ± 0.06 -0.0217 ± 0.0005 0.712 ± 0.008 -0.033 ± 0.003 1.17 ± 0.04 -0.0134 ± 0.0005 0.497 ± 0.007Abell 2228 -0.05 ± 0.01 2.4 ± 0.2 -0.07 ± 0.02 3.0 ± 0.3 -0.043 ± 0.003 1.15 ± 0.04 -0.043 ± 0.003 1.51 ± 0.05 -0.001 ± 0.002 0.40 ± 0.02RXJ0820.9+0751 -0.08 ± 0.01 2.7 ± 0.2 -0.08 ± 0.02 3.0 ± 0.3 -0.003 ± 0.006 0.5 ± 0.1 -0.003 ± 0.006 0.86 ± 0.09 -0.006 ± 0.002 0.45 ± 0.03RXJ1000.5+4409 -0.12 ± 0.04 3.5 ± 0.7 -0.0 ± 0.1 2 ± 2 -0.02 ± 0.04 0.7 ± 0.7 -0.10 ± 0.07 3 ± 1 -0.01 ± 0.02 0.5 ± 0.3RXJ1053.7+5450 -0.02 ± 0.02 1.6 ± 0.3 -0.06 ± 0.02 2.5 ± 0.2 -0.0113 ± 0.0006 0.597 ± 0.009 -0.015 ± 0.005 0.97 ± 0.07 -0.014 ± 0.003 0.53 ± 0.05RXJ1423.9+4015 -0.034 ± 0.003 1.90 ± 0.05 -0.05 ± 0.01 2.4 ± 0.2 -0.019 ± 0.002 0.73 ± 0.03 -0.029 ± 0.003 1.20 ± 0.05 -0.014 ± 0.002 0.55 ± 0.02RXJ1442.2+2218 -0.05 ± 0.03 2.3 ± 0.4 -0.08 ± 0.02 3.1 ± 0.3 -0.019 ± 0.007 0.8 ± 0.1 -0.025 ± 0.003 1.23 ± 0.05 -0.004 ± 0.003 0.43 ± 0.05RXJ1652.6+4011 -0.041 ± 0.007 2.3 ± 0.1 -0.036 ± 0.007 2.6 ± 0.1 -0.015 ± 0.006 0.72 ± 0.09 -0.008 ± 0.008 1.0 ± 0.1 0.003 ± 0.005 0.34 ± 0.08ZwCl 1478 -0.13 ± 0.01 3.7 ± 0.2 -0.167 ± 0.010 4.6 ± 0.2 -0.04 ± 0.03 1.1 ± 0.4 -0.018 ± 0.007 1.2 ± 0.1 -0.028 ± 0.006 0.83 ± 0.09ZwCl 4905 -0.027 ± 0.004 1.77 ± 0.06 -0.032 ± 0.007 2.2 ± 0.1 -0.0092 ± 0.0009 0.58 ± 0.01 -0.012 ± 0.005 0.95 ± 0.08 -0.006 ± 0.002 0.42 ± 0.03ZwCl 6718 -0.04 ± 0.01 2.0 ± 0.2 -0.05 ± 0.01 2.4 ± 0.2 -0.010 ± 0.001 0.58 ± 0.02 -0.023 ± 0.005 1.11 ± 0.07 -0.012 ± 0.001 0.51 ± 0.02ZwCl 8197 -0.04 ± 0.01 2.2 ± 0.2 -0.05 ± 0.03 2.7 ± 0.5 -0.008 ± 0.007 0.6 ± 0.1 -0.02 ± 0.02 1.2 ± 0.3 0.005 ± 0.004 0.29 ± 0.06


3.3 Dependence of the colour-magnitude relation on

global cluster properties

In this section we examine the relationship between the CMR fit parameters and clusterglobal properties. Our analysis is divided into two sections. In the first section we look athow the slope of the CMR depends on redshift, cluster mass and cluster morphology. In thesecond section we perform the same analysis on the colour of the CMR at M∗.

3.3.1 Slope of the CMR

Redshift evolution

We correlated CMR slope data from tables 3.3 and 3.4 with cluster redshifts to producethe plots shown in figures B.1 and B.2. To check for correlations between CMR slope andredshift, Spearman rank tests were performed between these two parameters. We obtainedSpearman correlation coefficients between -0.1427 and 0.2 (see table 3.6), a strong indicationthat there is no correlation between the slope of the CMR and redshift in the intermediate-LXcluster sample. This is a surprising result because slope evolution has been demonstrated inobservations by Stott (2007) and Lopez-Cruz et al. (2004) and in cosmological simulations byBower et al. (2006) and Kodama & Arimoto (1997). Despite the lack of a formal correlationbetween redshift and the slope of the CMR, the slope-redshift relation qualitatively appearsto demonstrate a kink around z ∼ 0.1 with the effect being most noticeable in (u-i) colour.

Reading the values off figure 4.2 in Stott (2007), we estimate that Bower et al. (2006)predict d(J-K)/dK ≈ (-0.02 ± 0.10) at z = 0.14. We also estimate that Stott (2007) andBower et al. (2006) obtain d(V-I)/dI ≈ (0.022 ± 0.007) at z = 0.1 by reading the values offfigure 4.3 in Stott (2007). To make our results directly comparable to Stott (2007) and Boweret al. (2006), we convert our results into (J-K) colour using the transformations of Bilir et al.(2008) and into (V-I) colour using the transformations of Smith et al. (2002). Averagingover the slopes of all 45 intermediate-LX clusters, we obtain d(J-K)/dK = (-0.01 ± 0.01)and d(V-I)/dI = (-0.03 ± 0.02) which are both in perfect agreement with Stott (2007) andBower et al. (2006). Interestingly, the model of Bower et al. (2006) predicts kinks in the (J-K) and (V-I) slope-redshift relations at z = 0.1 similar to the ones we qualitatively observedaround z ∼ 0.1. We suggest that our results are simultaneously correct with the results ofStott (2007) and Bower et al. (2006) and that the lack redshift evolution in our study is aconsequence of having a narrow redshift range.

Our CMR slopes are significantly different to the slopes found by Lopez-Cruz et al.(2004) and Kodama & Arimoto (1997). Converting our (g-r)/r slopes to (B-R)/R using thetransformations of Smith et al. (2002), we obtain a median value of d(B-R)/dR = -0.032.In comparison, the (B-R) slope-redshift relation cited by Kodama & Arimoto (1997) andobservationally verified by Lopez-Cruz et al. (2004) predicts values of d(B-R)/dR between-0.051 and -0.057 for the interquartile redshift range of our study. We suggest that the

4We read off values at z = 0.1 because it is close to the median redshift of our intermediate-LX clustersample.

3.3 Dependence of the colour-magnitude relation on global clusterproperties 59

discrepancy may be the due to the fact that Kodama & Arimoto obtained their (B-R) slope-redshift relation using Coma Cluster (Abell 1656) as the low-redshift anchor. Reading offfigure 4.2 in Stott (2007), we note that Coma cluster has a (J-K)/K slope which is almost0.02 steeper than the mean (J-K)/K slope predicted by Bower et al. (2006). While the(J-K)/K slope is not directly comparable to the (B-R)/R slope, it does suggest that theslope of the CMR in other colours could be overestimated by using Coma as the anchor fora slope-redshift relation.

Mass and morphology dependence

After looking at the dependence of the slope of the CMR with redshift, we turned our atten-tion to possible correlations with other cluster global properties. To check for correlationsbetween CMR slope and cluster global properties, Spearman rank tests were performedbetween the CMR slope and LX , σz, concentration index, and Bautz-Morgan type. Nosignificant correlations were found with correlation coefficients ranging between -0.2217 and0.1417 for LX , -0.0306 and 0.4204 for σz, -0.1183 and 0.3523 for C, and -0.1493 and 0.2356for Bautz-Morgan type. The correlation coefficients with CMR slope are summarised intable 3.6. Our results confirm Stott’s (2007) results, who also found no slope dependence onLX , σz and degree of brightest cluster galaxy (BCG) dominance5.

Plots of CMR slope versus LX , σz, C, and Bautz-Morgan type are presented in figures B.3– B.10. Unlike slope-redshift relations shown in figures B.1 and B.2, CMR slope versus LX ,σz, C, and Bautz-Morgan type result in true scatter plots. We performed Lilliefors’ tests (seeLilliefors, 1967) on our slope distributions to see if they were normally distributed. At the5% confidence level we found that the (u-g)/g, (u-i)/i, (g-r)/r, (g-z′)/z′, (r-i)/i, and (g-z′)/z′

are normally distributed. Thus we can equate the scatter in these slopes with their standarddeviations. For the (u-r)/r, (u-z′)/z′, (g-i)/i, and (r-z′)/z′ slopes, we equate the scatterusing the mean absolute deviation (MAD). The scatter in the CMR slopes are summarisedin table 3.5. Interpreting LX and σz as proxies for cluster mass and concentration index,Bautz-Morgan type, and degree of BCG dominance as proxies for cluster morphology, weconclude that there is no mass or morphology dependence on the slope of the CMR.

3.3.2 Colour of the CMR at M∗

We calculated the colour of the CMR at M∗ from the data in tables 3.3 and 3.4 and correlatedthe results against redshift, cluster mass and cluster morphology. Analysing the colour ofthe CMR at M∗ has a nicer physical interpretation than simply analysing the intercept, cab,because it tells us about the colour evolution of M∗ galaxies on the red sequence. To find thecolour of the CMR at M∗, we first converted M∗ to apparent magnitude at the clustercentricredshift using equation 3.2 and substituted for b in the linear equation

(a− b)M∗ = mab bM∗ + cab

= mab[M∗ + d(z) + k(z)] + cab (3.16)

5Degree of BCG dominance is a measure of cluster morphology quantifying the luminosity gap between theBCG and the next most luminous cluster member. In this sense it is more closely related to Bautz-Morgantype than concentration index.


Table 3.5: Scatter in the CMR slopes

slope scatterd(u-g)/dg 0.0347d(u-r)/dr 0.0360d(u-i)/di 0.0492d(u-z′)/dz′ 0.0476d(g-r)/dr 0.0193d(g-i)/di 0.0193d(g-z′)/dz′ 0.0304d(r-i)/di 0.0092d(r-z′)/dz′ 0.0111d(i-z′)/dz′ 0.0077

Table 3.6: Spearman rank correlation coefficients for the slope of the red sequence versus clusterglobal properties

slope z LX σz C B-M typed(u-g)/dg 0.0088 -0.0369 0.1457 0.3523 -0.0314d(u-r)/dr -0.0387 -0.0796 0.0776 0.1602 0.1032d(u-i)/di -0.0551 -0.2145 0.1412 0.1181 0.0271d(u-z′)/dz′ -0.1427 -0.2701 0.1273 0.0510 0.1687d(g-r)/dr 0.0158 -0.1347 0.0802 0.0672 -0.1493d(g-i)/di -0.1394 -0.2217 0.0593 0.1584 0.1576d(g-z′)/dz′ 0.0361 -0.1148 0.0827 0.2430 0.2356d(r-i)/di 0.2000 0.0333 -0.0306 -0.1183 -0.0545d(r-z′)/dz′ 0.1250 -0.1044 0.2080 0.1163 0.2285d(i-z′)/dz′ 0.1300 0.1417 0.4204 0.0675 0.0753

for fictitious passbands a and b.

Redshift evolution

Plots of CMR colour at M∗ versus cluster redshift are shown in figures B.11 and B.12. Thefigures appear to show linear relations between M∗ colour and redshift with the M∗ galaxiesbecoming redder with increasing redshift. Excluding the (u-g) colour, all colours have corre-lation coefficients between 0.5228 and 0.8972 indicating intermediate to strong dependenceon redshift (see table 3.9). Given the strength of the correlations, we performed ordinaryleast squares linear regressions on the relations with correlation coefficients > 0.5. The datapoints were weighted by their error bars and the resultant fits have been superimposed onfigures B.11 and B.12. The linear fit coefficients for the colour-redshift relation are shown intable 3.7. Wake et al. (2005) and Lopez-Cruz et al. (2004) have also demonstrated a positivecorrelation between redshift and colour. Whereas we evaluate the colour of the CMR at M∗,

3.4 The composite cluster 61

Table 3.7: Linear fit coefficients for the colour of the CMR at M∗ versus redshift.

colour slope intercept(u-r) 3.3 ± 0.5 2.59 ± 0.04(u-i) 3.8 ± 0.5 2.98 ± 0.03(u-z′) 3.5 ± 0.7 3.33 ± 0.04(g-r) 2.3 ± 0.2 0.75 ± 0.01(g-i) 2.8 ± 0.3 1.15 ± 0.02(g-z′) 3.4 ± 0.3 1.43 ± 0.02(r-i) 0.47 ± 0.10 0.396 ± 0.007(r-z′) 0.5 ± 0.2 0.74 ± 0.02(i-z′) 0.61 ± 0.07 0.292 ± 0.005

Wake et al. (2005) evaluate the colour of the CMR at a fixed absolute magnitude of MV =-21.2 while Lopez-Cruz et al. (2004) consider the colour at a fixed apparent magnitude of R= 17. Because of this, none of the results of these studies are directly comparable, howeverit does go to show that a colour-redshift relation is not without precedent. The positiveslope in the colour-redshift relation tells us that the characteristic M∗ galaxies were redderin the past than they are today.

Mass and morphology dependence

After looking at the colour dependence of the M∗ galaxies with redshift, we turned ourattention to possible correlations with other cluster global properties. Again we performedSpearman rank tests between the colour of the CMR at M∗ and LX , σz, concentrationindex, and Bautz-Morgan type. Some intermediate strength correlations with LX werefound, however a colour-LX relation is a far from universal – only 4 colours have correlationcoefficients > 0.5. No significant correlations were found for σz, C, and Bautz-Morgan type.The correlation coefficients with CMR colour at M∗ are summarised in table 3.9.

Plots of CMR colour at M∗ versus LX , σz, C, and Bautz-Morgan type are presented infigures B.13 – B.20. Unlike colour-redshift relations shown in figures B.11 and B.12, CMRslope versus LX , σz, C, and Bautz-Morgan type result in true scatter plots. We performedLilliefors’ tests on our colour distributions to see if they were normally distributed. At the5% confidence level we found that all the colours are normally distributed. Thus we canequate the scatter in the colours with their standard deviations. The scatter in the CMRcolours at M∗ are summarised in table 3.8. It is interesting to note that the scatter inthe colours increases with passband separation. We interpret the results of this section asevidence there is no mass or morphology dependence on the colour of the CMR at M∗.

3.4 The composite cluster

In this section we will describe how we stacked the clusters together to make a compositecluster. We will discuss the bimodal colour distribution of the composite cluster and how we


Table 3.8: Scatter in the colour of the CMR at M∗

colour scatter(u-g) 0.0476(u-r) 0.0907(u-i) 0.1173(u-z′) 0.1292(g-r) 0.0708(g-i) 0.0960(g-z′) 0.1187(r-i) 0.0208(r-z′) 0.0467(i-z′) 0.0246

Table 3.9: Spearman rank correlation coefficients for the colour of the CMR at M∗ versuscluster global properties.

colour z LX σz C B-M type(u-g)M∗g 0.1104 -0.1086 0.0381 0.1866 -0.0665

(u-r)M∗r 0.5935 0.3741 0.0823 -0.1203 0.0963(u-i)M∗i 0.6324 0.3806 0.1129 -0.1864 0.1095(u-z′)M ′z 0.5812 0.3851 0.1640 -0.2787 0.0906(g-r)M∗r 0.8972 0.6248 0.0784 -0.1692 -0.0001(g-i)M∗i 0.8242 0.6228 0.0910 -0.2473 0.0858(g-z′)M ′z 0.8162 0.5785 0.0839 -0.1837 0.1152(r-i)M∗i 0.5228 0.2930 -0.0607 -0.2025 0.2263(r-z′)M ′z 0.5294 0.3904 0.0892 -0.2383 0.0720(i-z′)M ′z 0.6698 0.5124 0.1796 -0.1939 0.0713

used it to obtain colour cuts separating the red sequence from the blue cloud. After that, wewill describe how we divided the composite cluster colour-magnitude diagram up into radiusand density bins and how we found the modal colour of each bin. Finally we will discusshow the modal colours of the composite cluster CMR depend on radius and density.

3.4.1 Stacking the clusters

To stack the clusters together, we applied colour and magnitude transformations to thecolour magnitude diagrams of each of our clusters. Transformations were a two-step processto remove the trend from the CMR and to evolve the individual clusters to a commonredshift. First we will discuss how we removed the trend from the CMRs.

For each cluster we identify a pivot point which we define to be the intersection of theCMR with the m∗ apparent magnitude at the clustercentric redshift. With respect to thecolour-magnitude diagrams shown in appendix A, the pivot is the intersection of the sloping


solid line (the CMR) with the vertical dashed line (the m∗ apparent magnitude). Afteridentifying the pivot, we rotate every point on the colour-magnitude diagram by the angleα, where α is the angle the CMR makes with the horizontal. This rotates all points on thecluster colour-magnitude diagram in such a way that the new colour magnitude ridge line ishorizontal, thus removing the trend in the CMR.

After removing the trend from the CMRs, we evolved the individual clusters to a commonredshift. We chose the median redshift of the intermediate-LX cluster sample (z = 0.0897)to be the redshift of the composite cluster. The median redshift of the cluster sample is anappropriate choice for the redshift of the composite cluster because it minimises the amountof evolution we need to apply to the low and high-redshift outliers. Small transformationsare preferable to large transformations, because it means that the transformed colours andmagnitudes are close to the observed colours and magnitudes which we trust. Moreover, themedian is preferable to the mean because it is less sensitive to bias caused by outliers. Aswe mentioned earlier, M∗ has been shown to be relatively constant to at least z ∼ 0.3, thuswe use the m∗ apparent magnitude at z = 0.0897 as the characteristic magnitude of ourcomposite cluster. For the characteristic colour of the composite cluster CMR, we use themedian colour of the individual CMRs at M∗. The argument for using the median colourfollows directly from the argument for using the median redshift. Finally, for each individual,de-trended cluster colour-magnitude diagram, we perform a linear translation on all the datapoints such that the pivot points of the individual clusters are translated to the characteristiccolour and magnitude of the composite cluster.

Figure 3.3 shows the colour-magnitude diagram of the composite cluster in (g-i)′ colourversus i′ magnitude. We add a prime to the colours and magnitudes to remind us that theyare transformed colours and magnitudes. A very strong CMR ridge line is evident in figure3.3 which reassures us that the cluster stacking method described above produces convincingcomposite cluster colour-magnitude diagrams. The CMR diagrams for the other transformedcolours also display similarly strong CMR ridge lines (see figures C.1 and C.2).

3.4.2 Colour distribution

Colour histograms of the composite clusters are shown in figures 3.4 and 3.5. Many of thecomposite cluster colour distributions show clear bi-modality and are well described by thedouble Gaussian fits shown as the solid curve in figures 3.4 and 3.5. The double Gaussianmodel is parameterised according to:

f(x) = a1 exp

(−(x− b1)2

2c21

)+ a2 exp

(−(x− b2)2

2c22

)(3.17)

where colour is represented by x. The best fit parameter coefficients were obtained byperforming 100 fitting iterations with randomised bin sizes. We take the mean and standarddeviation of the 100 iterations to be the best fit parameter coefficients. The results are givenin table 3.10.

We are interested in the colour-distributions because they allow us to identify colour cutsseparating the CMR galaxies from the blue cloud galaxies. We use the position of the localminimum between the blue and red peaks of the double Gaussian fits to define the colour


Figure 3.3: The composite cluster colour-magnitude diagram in (g-i)′ colour versus i′ magni-tude. The vertical dashed line shows the position of M∗i at median redshift z ∼ 0.09 while the solidhorizontal line shows the median (g-i) colour at M∗i for all 45 clusters.

cuts. Intermodal local minima are observed in all colour distributions except for (r-i)′, (r-z′)′,and (i-z′)′. For the colour distributions without distinct local minima, we apply arbitrarycolour cuts corresponding to the position of the kink in the Gaussian fit. The colour cutsare represented as the vertical dashed lines in figures 3.4 and 3.5 and their values have beentabulated in table 3.10.

3.4.3 Dependence of the modal colour on cluster environment

Armed with colour-magnitude diagrams for the composite cluster and appropriate colourcuts, we explored the dependence of the modal colour of the CMR as a function of clusterenvironment. We define modal colour here to mean the colour corresponding to the peak ofa Gaussian fitted to the colour histogram of the CMR. To probe modal colour dependenceas a function of cluster environment, we employ a method similar to the one described inPimbblet et al. (2002) and Pimbblet et al. (2006). In particular we refer the reader to figures5 and 6 in Pimbblet et al. (2002) for diagrammatic representations of the method we usedto obtain the modal colours in projected radius and local galaxy density bins.

In this thesis, we separated the composite CMRs into projected radius, log projectedradius and log local galaxy density bins. In projected radius, we used equal size 0.15 Mpcbins with 0 < (rp/Mpc) < 10; in log projected radius, we used 30 equal size bins with -1< (log10(rp/Mpc)) < 1; and in log local galaxy density, we used 30 equal size bins with 2


Table 3.10: Composite cluster colour distribution double Gaussian fit coefficients and colourcuts.

colour cut a1 b1 c1 a2 b2 c2(u-g)′ 1.6302 7650 ± 20 1.412 ± 0.003 0.250 ± 0.003 19500 ± 200 1.9164 ± 0.0007 0.113 ± 0.001(u-r)′ 2.5242 4920 ± 20 2.242 ± 0.008 0.438 ± 0.007 15500 ± 300 2.8908 ± 0.0006 0.129 ± 0.002(u-i)′ 2.9294 4440 ± 10 2.656 ± 0.004 0.494 ± 0.004 14100 ± 200 3.3331 ± 0.0006 0.139 ± 0.002(u-z′)′ 3.2247 3880 ± 10 2.925 ± 0.003 0.560 ± 0.003 13100 ± 200 3.6745 ± 0.0008 0.152 ± 0.003(g-r)′ 0.8447 12150 ± 80 0.748 ± 0.003 0.179 ± 0.001 48000 ± 1000 0.9706 ± 0.0006 0.041 ± 0.001(g-i)′ 1.2173 8970 ± 30 1.146 ± 0.002 0.242 ± 0.001 34000 ± 600 1.4052 ± 0.0004 0.058 ± 0.001(g-z′)′ 1.5091 6750 ± 40 1.430 ± 0.004 0.320 ± 0.001 26100 ± 400 1.7592 ± 0.0004 0.076 ± 0.002(r-i)′ 0.385 32200 ± 300 0.4135 ± 0.0004 0.0730 ± 0.0006 81500 ± 700 0.4419 ± 0.0001 0.0222 ± 0.0003(r-z′)′ 0.665 14500 ± 100 0.688 ± 0.001 0.153 ± 0.001 44600 ± 400 0.7856 ± 0.0002 0.0434 ± 0.0007(i-z′)′ 0.27 22000 ± 200 0.2759 ± 0.0004 0.0922 ± 0.0007 71600 ± 700 0.3458 ± 0.0002 0.0296 ± 0.0004

> (log10(Σ/Mpc−2)) > -1. The binning is arbitrary, and the only reason for choosing thesevalues is because they offer an acceptable balance between resolution and scatter. For eachrp or Σ bin, we fitted a single Gaussian to the colour distribution of the CMR. To obtainunbiased estimates of the modal colours in each rp or Σ bin, we performed 100 Gaussianfitting iterations with randomised colour bins. Data points bluer than the colour cuts givenin table 3.10 were excluded in the Gaussian fitting process. By using the colour cuts, weensured that the fitting algorithm always converged on the red sequence and that the modalcolours were not systematically dragged blueward by the blue cloud. We take the mean andstandard deviation of the position of the Gaussian colour peaks as being the best estimatesof the modal colour and associated error in each rp or Σ bin. We are also interested in thewidth or dispersion of the modal colours as a function of cluster environment. We take themean and standard deviation of the Gaussian colour standard deviations as being the bestestimates of the modal colour dispersion and associated error in each rp or Σ bin.

We present the dependence of the modal (g-i)′ colour and modal (g-i)′ colour dispersionas functions of projected radius, log projected radius and log local galaxy density in figures3.6, 3.7, and 3.8 respectively. Similar figures were produced for the other colours and theseare presented in appendix C. Strong colour gradients are observed in the modal colour-log rpand modal colour-log Σ relations out to ∼ 1.5-2 Mpc in projected radius and ∼ 1-2 Mpc−2

in local galaxy density in all colours. Weaker, but still significant, colour gradients are alsoobserved in the modal colour-rp relations. The gradients are negative in projected radius andlog projected radius and positive in log local galaxy density. In other words, mean galaxycolours become redder with increasing local galaxy density and decreasing distance from thecluster center.

The modal colour dispersions tend to steadily increase with projected radius and steadilydecrease with local galaxy density, flattening out at roughly 1.5-2 Mpc in projected radiusand 1-2 Mpc−2 in local galaxy density. This literally means that there is a wider distributionof galaxy colours in the field than in regions of high galaxy density and in the cores ofclusters. We interpret this result as an age-metallicity effect (see Kodama & Arimoto, 1997;Kodama & Bower, 2001). Older stellar populations tend to be more metal-rich and haveredder colours than younger stellar populations because they have had more time to build-uptheir metallicity content through stellar nucleosynthesis. Thus the wide spread of coloursin the field is indicative of a wide spread of galaxian ages. The colour distribution narrowswith increasing local galaxy density and decreasing projected radius which means that the


Table 3.11: Projected radius colour gradients and critical radii

gradient value [Mpc−1] rcrit [Mpc]d(u-g)′/drp -0.08 ± 0.01 1.2+0.5

−0.3

d(u-r)′/drp -0.07 ± 0.01 1.3+0.4−0.3

d(u-i)′/drp -0.07 ± 0.02 1.2+0.7−0.4

d(u-z′)′/drp -0.07 ± 0.01 1.5+0.7−0.5

d(g-r)′/drp -0.019 ± 0.003 1.2+0.4−0.3

d(g-i)′/drp -0.032 ± 0.002 1.5+0.2−0.1

d(g-z′)′/drp -0.048 ± 0.002 1.20+0.10−0.09

d(r-i)′/drp -0.009 ± 0.002 1.3+0.6−0.4

d(r-z′)′/drp -0.018 ± 0.002 1.4+0.3−0.2

d(i-z′)′/drp -0.017 ± 0.002 1.3+0.3−0.2

galaxies become more coeval as we move closer to the cluster core.We performed weighted linear regressions on all the colour gradients and the slope values

we obtained are summarised in tables 3.11, 3.12, and 3.13. For illustrative purposes, we plotthe best fit linear relations (sloping solid lines) and field values (horizontal solid lines) onfigures 3.6, 3.7, and 3.8. We use the lines to demonstrates that galaxy colours are, on average,consistently blue in field, however, on crossing the critical radius or critical galaxy density(which we interpret as the kink in the solid line), galaxy colours are systematically reddenedwith increasing local galaxy density and decreasing distance from the cluster center. Thefield values were calculated by taking the weighted average colour across all bins in the non-gradient region of the diagrams. Interpreting the kinks in the solid lines as rcrit and Σcrit,we obtained values for the critical radius and critical galaxy density of the composite clusterby finding the intersection of the two lines. Errors were calculated by finding the maximumand minimum position of the intersection when the slope and intercept of the linear relationfitted to the gradient region were allowed to vary up to their error limits. We summarise thevalues we obtained for rcrit, Σcrit, and their associated errors in tables 3.11, 3.12, and 3.13.

We argue that we obtain a better estimate of the critical radius using log projected radiusthan just projected radius. The error bars on the critical radii are smaller using log projectedradius than projected radius because the log projected radius colour gradients are betterconstrained. Comparison of the values of the critical radii in tables 3.11 and 3.12 suggeststhat using projected radius underestimates the values of the critical radii. Visual inspectionof the modal colour-rp relations, confirm that the use of projected radius systematicallyunderestimates the position of the critical radius. The effect is most noticeable in the (g-r)′ and (g-i)′ modal colour-rp relations with a handful of data points form something of ablue blip underneath the field value just past the kink in the fitted relation. Using onlythe values of the critical radii from the modal colour-log rp relations, the mean value of thecritical radius across all 10 colours is rcrit = (1.7 ± 0.5) Mpc. The mean value of the criticalgalaxy density across all 10 colours is Σcrit = (1.5 ± 0.5) Mpc−2.


Table 3.12: Log projected radius colour gradients and critical radii

gradient value rcrit [Mpc]d(u-g)′/d(log rp) -0.069 ± 0.007 2.0+0.3

−0.2

d(u-r)′/d(log rp) -0.099 ± 0.008 1.9+0.2−0.2

d(u-i)′/d(log rp) -0.13 ± 0.02 1.6+0.2−0.2

d(u-z′)′/d(log rp) -0.13 ± 0.01 1.6+0.2−0.1

d(g-r)′/d(log rp) -0.031 ± 0.003 1.4+0.2−0.1

d(g-i)′/d(log rp) -0.049 ± 0.004 1.7+0.2−0.2

d(g-z′)′/d(log rp) -0.073 ± 0.006 1.36+0.11−0.09

d(r-i)′/d(log rp) -0.018 ± 0.002 1.01+0.10−0.07

d(r-z′)′/d(log rp) -0.035 ± 0.004 1.6+0.3−0.2

d(i-z′)′/d(log rp) -0.015 ± 0.002 2.8+1.0−0.6

Table 3.13: Log local galaxy number density colour gradients and critical number densities

gradient value Σcrit [Mpc−2]d(u-g)′/d(log Σ) 0.025 ± 0.004 0.7+0.3

−0.3

d(u-r)′/d(log Σ) 0.041 ± 0.004 1.8+0.2−0.2

d(u-i)′/d(log Σ) 0.043 ± 0.006 1.1+0.2−0.2

d(u-z′)′/d(log Σ) 0.048 ± 0.007 1.4+0.3−0.3

d(g-r)′/d(log Σ) 0.012 ± 0.002 1.7+0.4−0.4

d(g-i)′/d(log Σ) 0.020 ± 0.003 1.7+0.3−0.3

d(g-z′)′/d(log Σ) 0.024 ± 0.005 1.4+0.4−0.4

d(r-i)′/d(log Σ) 0.007 ± 0.001 2.3+0.4−0.5

d(r-z′)′/d(log Σ) 0.017 ± 0.002 1.9+0.3−0.3

d(i-z′)′/d(log Σ) 0.009 ± 0.001 1.1+0.3−0.3


0.5 1 1.5 2 2.510

1

102

103

(u - g)′

Num

ber

of G

alax

ies

1 2 3 410

1

102

103

(u - r)′N

umbe

r of

Gal

axie

s

1 2 3 410

1

102

103

(u - i)′

Num

ber

of G

alax

ies

1 2 3 4 510

1

102

103

(u - z′)′

Num

ber

of G

alax

ies

0 0.5 110

1

102

103

(g - r)′

Num

ber

of G

alax

ies

0.5 1 1.5 210

1

102

103

(g - i)′

Num

ber

of G

alax

ies

Figure 3.4: The composite cluster colour distribution with double Gaussian fits. The verticaldashed lines show the positions of the colour cuts for single Gaussian fitting.


0.5 1 1.5 2 2.510

1

102

103

(g - z′)′

Num

ber

of G

alax

ies

0.2 0.3 0.4 0.5 0.6 0.710

1

102

103

(r - i)′

Num

ber

of G

alax

ies

0.2 0.4 0.6 0.8 1 1.210

1

102

103

(r - z′)′

Num

ber

of G

alax

ies

0 0.2 0.4 0.610

1

102

103

(i - z′)′

Num

ber

of G

alax

ies

Figure 3.5: The composite cluster colour distribution – continued.


0 1 2 3 4 5

0

0.05

0.1

rp / Mpc

σ (g

- i)

′

0 1 2 3 4 51.35

1.36

1.37

1.38

1.39

1.4

1.41

1.42

1.43

1.44

1.45

rp / Mpc

Pea

k (g

- i)

′

Figure 3.6: Modal colour (bottom panel) and width (top panel) of the CMR versus projectedradius in (g-i)′ colour.


-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 10.02

0.04

0.06

0.08

0.1

0.12

log (rp / Mpc)

σ (g

- i)

′

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 11.37

1.38

1.39

1.4

1.41

1.42

1.43

1.44

1.45

1.46

1.47

log (rp / Mpc)

Pea

k (g

- i)

′

Figure 3.7: Modal colour (bottom panel) and width (top panel) of the CMR versus log projectedradius in (g-i)′ colour.


-1-0.500.511.52

0.04

0.06

0.08

0.1

0.12

0.14

log (Σ / Mpc-2)

σ (g

- i)

′

-1-0.500.511.52

1.37

1.38

1.39

1.4

1.41

1.42

log (Σ / Mpc-2)

Pea

k (g

- i)

′

Figure 3.8: Modal colour (bottom panel) and width (top panel) of the CMR versus log localgalaxy density in (g-i)′ colour.

4Discussion

In this chapter we bring together all our major results and discuss their full implications. Wewill also address the questions that we posed at the beginning of this thesis. To recapitulate,the questions we posed in section 1.4 were:

1. How do the red sequence galaxies evolve? Do the CMR fit parameters depend onredshift, cluster mass and cluster morphology? How do the colours of the red sequencegalaxies depend on environment? How do these results compare to what we knowabout red sequence galaxy evolution in high-mass clusters?

2. How do the blue galaxies evolve? Does fb depend on redshift, cluster mass and clustermorphology? How do these results compare to what we know about the evolution ofblue galaxies in high-mass clusters?

3. How does the the star formation rate in cluster galaxies evolve? Does the SFR dependon redshift, cluster mass and cluster morphology? Is there a critical radius or densityfor star-formation suppression? How is the SFR related to the evolution of red sequenceand blue galaxies? How do these results compare to what we know about the evolutionof the SFR in high-mass clusters?

4. What is the nature of the physical mechanism/s behind galaxy evolution in clusters?

Given the results presented in chapters 2 and 3, we are well-positioned to answer the firstand last questions in detail. Our dataset contains sufficient data to answer the second andthird questions but we need to perform further analysis before we can make any defini-tive conclusions regarding the evolution of the blue galaxies and the star formation rate inintermediate-LX cluster. Questions relating to the evolution of the blue galaxies and starformation rates are priorities for future work which will guided by the results of this thesis.

In section 3.3 we looked at how the CMR fit parameters depended on redshift, clustermass and cluster morphology. The results we obtained told us that the slope of the CMR was

73

74 Discussion

independent of redshift, cluster mass and cluster morphology, while the colour of the CMR atM∗ depends weakly on redshift but is independent of cluster mass and cluster morphology.Despite the lack of formal correlation with redshift, as a point estimate around z ∼ 0.1,our cluster CMR slopes agree almost perfectly with the observations of Stott (2007) andthe simulation predictions of Bower et al. (2006). The lack of correlation with redshift cantherefore be accounted by the fact that we simply don’t have a long enough redshift baselineto see any significant slope evolution.

In comparison to our intermediate-LX cluster sample, Stott (2007) only looks at high-LXclusters (between 4.8 – 27.4 × 1044 erg s−1), thus we draw the conclusion that CMR slopesare, on average, the same in intermediate and high-LX clusters. This conclusion is furthersupported by the fact that we observed no LX-dependence in the slope of the CMR in theintermediate-LX cluster sample. Longitudinal redshift studies of intermediate-LX clustersare required, however, we tentatively suggest that the red sequence builds up in the sameway in intermediate-LX clusters as it does in high-LX clusters.

We briefly discussed the correlation between the colour of the CMR at M∗ and redshiftin section 3.3. The characteristic M∗ galaxies residing on the CMR were redder in the pastthan they are today. This evidence suggests M∗ galaxies have enjoyed a modest increasein their star-formation rates since z ∼ 0.2. This is consistent with the galaxy downsizingscenario which was first discussed by Cowie et al. (1996). Galaxy downsizing describes thephenomenon that star-formation has been increasing in successively smaller, less massive,and less luminous galaxies over time.

The lack of colour bimodality in the (r-i)′, (r-z′)′, and (i-z′)′ composite cluster colourdistributions is intriguing. These colours are exclusively located down in the near infrared(NIR) and is obviously a contributing factor to the lack of colour bimodality. We suggest thatstar-forming galaxies which form the bulk of the blue cloud are indistinguishable from thequiescent galaxies which form the bulk of the red sequence in infrared colours. This is likelyto be true if the NIR continuum spectra of the quiescent galaxies are, on average, similar tothe NIR continuum spectra of the star-forming galaxies. If this is the case, then we predictthat mid–far infrared colours are more likely to show colour bimodality than NIR colours.This is because the mid–far infrared corresponds to the blackbody temperature of interstellardust that has been heated by nearby star-formation. Thus mid–far infrared colours shouldbe better at distinguishing between star-forming and non-star forming galaxies.

In section 3.4, we briefly discussed how the width of the modal colours is wider in the fieldthan in the centers of clusters. We interpreted this as an age-metallicity effect, saying thangalaxies in the centers of clusters are more coeval than field galaxies. If this interpretationis correct, then it also has something to say about cluster formation. Coeval galaxies in thecenters of clusters supports the theory that the cores of galaxy clusters were formed fromgroups of galaxies which pre-date the cluster. As pointed out by Combes (2004), the galaxymerger rate in clusters is too small to account for the numbers of elliptical galaxies we see inthe cores of galaxies. However, galaxy groups have higher merger rates than cluster so it ispossible that the elliptical galaxies which we find in the centers of low-redshift clusters wereactually formed over a relatively short period of time in high redshift galaxy groups.

In section 3.4 we reported rcrit = (1.7 ± 0.5) Mpc and Σcrit = (1.5 ± 0.5) Mpc−2. Typicalvalues for rcrit in high-LX clusters are ∼ 5.7 Mpc (Lewis et al., 2002), ∼ 4.3 Mpc (Gerken

75

100

101

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

LX / 1044 erg s-1

d(g-

r) /

d(lo

g r p)

0 0.1 0.2 0.3 0.4-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

Redshift, z

d(g-

r) /

d(lo

g r p)

Abraham et al. (1996)Terlevich et al. (2001)Pimbblet et al. (2002)Wake et al. (2005)This work

Figure 4.1: Comparison of (g-r)/log rp colour gradients from recent X-ray selected clusterstudies.

et al., 2004), and ∼ 4 Mpc (Gomez et al., 2003). Likewise, typical values for Σcrit are ∼ 2Mpc−2 (Kodama et al., 2001), ∼ 1.5 Mpc−2 (Lewis et al., 2002), and ∼ 1 Mpc−2 (Gomezet al., 2003). In comparison to the literature, the critical radius has moved inward by atleast 2.3 Mpc and this shift is significant at the 3σ confidence level. Our value for the criticalgalaxy density is comparable to the values cited in the literature. This is strong evidencethat local galaxy density is a more fundamental parameter than projected radius. We notethat the only result to which which we can make a direct comparison is that of Kodama et al.(2001). The other studies cited here rely on star-formation rate gradients to estimate thevalues of rcrit and Σcrit. Despite the caveat, it seems likely that changes in the star-formationrate should manifest themselves as changes in galaxy colour at similar radii and local galaxydensities.

The radial and density colour gradients we report in this thesis are consistent the gra-dients reported in other recent cluster studies. In figure 4.1 we plot the (g-r)/log rp colourgradients reported by Abraham et al. (1996), Terlevich et al. (2001), Pimbblet et al. (2002),and Wake et al. (2005) together with our (g-r)/log rp colour gradient versus the median X-ray luminosities and redshifts of the studies. While our (g-r)/log rp colour gradient is flatterthan the gradients reported by Abraham et al. (1996), Pimbblet et al. (2002), and Wakeet al. (2005), it is steeper than the value reported by Terlevich et al. (2001). Moreover, thereis no dependence of the (g-r)/log rp colour gradient with median X-ray luminosity. This isconfirmed by a Spearman rank test which gives a correlation coefficient of 0.3. If anything,the (g-r)/log rp colour gradient depends on redshift. The Spearman rank correlation coef-ficient between redshift and d(g-r)/dlog rp is -1 which implies a perfect anti-correlation. Inother words, the (g-r)/log rp colour gradient becomes more negative with redshift.

76 Discussion

Table 4.1: Comparison of colour gradients in projected radius and log local galaxy density.

Study d(g-r)/drp d(g-r)/dlog ΣPimbblet et al. (2002) -0.014 ± 0.003 0.047 ± 0.006Pimbblet et al. (2006) -0.007 ± 0.002 0.039 ± 0.006This work -0.019 ± 0.003 0.012 ± 0.002

We also compare our (g-r)/rp and (g-r)/log Σ colour gradients with the (B-R)/rp and(B-R)/log Σ colour gradients reported by Pimbblet et al. (2002) and Pimbblet et al. (2006).Using the colour transformations of Smith et al. (2002), we converted the (B-R)/rp and(B-R)/log Σ colour gradients of Pimbblet et al. (2002) and Pimbblet et al. (2006) into (g-r)/rp and (g-r)/log Σ colour gradients. The values are summarised in table 4.1. The valuewe obtained for the (g-r)/rp colour gradient is not significantly different from the gradientreported by Pimbblet et al. (2002), but there is a larger than 3σ discrepancy when comparedto the slope reported in Pimbblet et al. (2006). Our (g-r)/log Σ colour gradients are notcomparable with either study. We don’t have a definitive answer to why this is the case, butwe suspect that it may be related to the fact that our log Σ bins only range from -1 to 2whereas Pimbblet et al. (2002) and Pimbblet et al. (2006) have log Σ bins ranging from -1 to3. The intermediate-LX regime just doesn’t probe the highest density bins that are probed byPimbblet et al. (2002) and Pimbblet et al. (2006) and hence this may be the entire reason forthe discrepancy. While there are abundant studies to which we can compare our radial colourgradients, there is a distinct lack of papers reporting local galaxy density colour gradients.This means that it is impossible to make definitive conclusions regarding differences in localgalaxy density colour gradients between intermediate and high-LX clusters.

We have established that radial colour gradients in this study are consistent with radialcolour-gradients in high-LX cluster studies. The radial blueing effect is universal acrossintermediate and high-LX clusters and thus we argue that the mechanism driving the effectmust also be universal and independent of cluster mass. This interpretation is consistentwith our conclusions relating to the slope of the CMR - specifically that the slope of theCMR is independent of cluster mass. We have also established that local galaxy density is amore fundamental parameter than projected radius. Thus we conclude that the mechanismresponsible for galaxy evolution in galaxy clusters is universal, independent of cluster massand only depends on local galaxy density. Of the mechanisms we discussed in section 1.3,the only one which satisfies all these criteria is the galaxy harassment mechanism. Galaxyharassment is independent of cluster mass, its efficacy only depends local galaxy density.Ram-pressure stripping and halo gas starvation models of galaxy evolution are not supportedby our results because their efficacies depend on the gas density of the ICM, which scaleswith cluster mass and X-ray luminosity.

5Conclusion

In conclusion, we successfully created an homogeneous composite cluster constructed from45 intermediate-LX clusters and 10,529 galaxies at a median redshift of z ∼ 0.09. Wecalculated colour gradients in all 10 possible SDSS colours in projected radius, log projectedradius and log local galaxy density. The colour gradients are consistent with previous studiesand indicate that the mechanism driving galaxy evolution is universal and independent ofcluster-mass. We conclude that the most likely mechanism is galaxy harassment.

5.1 Key results

The main results of our analysis are:

1. Radial colour gradients are consistent with other studies. We get a radial colour gradi-ent of d(g-r)/d(log rp) = (-0.031 ± 0.003). The radial colour gradients are independentof mass, but are suspected to depend of redshift.

2. We report rcrit = (1.7 ± 0.5) Mpc and Σcrit = (1.5 ± 0.5) Mpc−2. In comparison tohigh-LX clusters rcrit has moved inward by ∼ 2 Mpc but there is no significant changein Σcrit. This implies that local galaxy density is a more fundamental parameter thanprojected radius.

3. The slope of the CMR does not evolve with redshift in our cluster sample, however,as a point estimate around z ∼ 0.1, our slopes are consistent with Stott (2007) andBower et al. (2006).

4. The colour of the CMR at M∗ evolves with redshift. M∗ galaxies tend to become redderwith increasing redshift, consistent the star-formation downsizing scenario.

77

78 Conclusion

5. The slope of the CMR and the colour of the CMR at M∗ are independent of clustermass and morphology.

6. Galaxies in the core-regions of clusters are more coeval than field galaxies. This isconsistent with the monolithic collapse scenario, where the core regions of clusters arecreated by galaxy mergers at high redshift.

7. Substructure is evident in at least 20% of intermediate-LX clusters. This value isconsistent with values cited in Lacey & Cole (1993).

8. X-ray luminosity is not degenerate with velocity dispersion and Bautz-Morgan type isnot degenerate with concentration index in our cluster sample.

5.2 Future work

The study of clusters of galaxies is a wide and varied field and almost all the anlyses thathave been performed on high-LX clusters could potentially be performed on intermediate-LX clusters. Here we provide a short summary concerning the avenues that we think futurework should pursue.

The calculation of SFR-rp and SFR-Σ relations are required to confirm the values of rcritand Σcrit we found in this thesis. The best estimates of rcrit and Σcrit in high-LX clusterstudies come from the positions of abrupt star-formation truncation in the SFR-rp and SFR-Σ relations. As pointed out in chapter 4, our intermediate-LX estimates of rcrit and Σcrit arenot directly comparable to the high-LX estimates because we have performed the analysisusing colour gradients rather than SFR gradients. Furthermore, our main conclusion (thatlocal galaxy density rather than projected radius is the fundamental parameter) criticallydepends on the values of rcrit and Σcrit. Thus it is of paramount importance that we calculatethe SFR-rp and SFR-Σ relations to confirm the values of rcrit and Σcrit in intermediate-LXclusters.

The next logical step would be to extend analysis down to low-LX clusters or groups.Intermediate-LX clusters are an order of magnitude less X-ray luminous than their high-LXcounterparts, whereas low-LX are a further order of magnitude less X-ray luminous again.The colour gradients of low-LX clusters are of particular interest. Colour gradients compara-ble to those of intermediate and high-LX clusters would provide even stronger evidence thatthe mechanism driving galaxy evolution in clusters is universal and independent of clustermass.

The Butcher-Oemler effect in our intermediate-LX cluster sample is of some interest.Referring back to figure 1.9, we see that the fraction of blue galaxies has a tentative kinkaround z ∼ 0.1 which is close to the median redshift of our intermediate-LX cluster sample.By calculating the blue fractions of each of our clusters, we are poised to add many new datapoints in this region of interest. Given that we have already divided galaxies on the colour-magnitude plane into a red population and blue population according to their positionsrelative to the CMR, the Butcher-Oemler effect should literally fall out of our dataset withlittle effort.

5.2 Future work 79

The morphology-density relation in intermediate-LX clusters is another avenue that needsto be explored. We have omitted the morphology-density relation from this thesis for anumber of reasons. The first reason is that the analysis is labour-intensive and does noteasily permit automation. In practice, we would have to visually inspect images of all 10,000galaxies in our sample one-by-one to determine their morphology. The second reason is thatthe photometric precision of the SDSS images is not of sufficient quality to discriminatebetween morphologies. While the photometric precision is sufficient to broadly separateelliptical galaxies from spiral galaxies, it is unlikely that we would be able to discriminateamong the various sub-classifications of spiral galaxies or between elliptical and S0 galaxieswith SDSS photometry. The new 2-m PILOT telescope which is to built at Dome C inAntarctica will offer sub-arcsecond seeing and would be an ideal instrument to obtain high-precision photometry images. HST imaging would be even better, but realistically it wouldbe very hard to get time on this telescope. Mathematical Morphology (MM, see Moore et al.,2006) is a new technique which we could also use to help ascertain galaxy morphologies.

Finally, we envisage the possibility of extending the analysis of intermediate-LX galaxiesout to higher redshifts. This study is confined to z < 0.2 because of the flux limit imposedon XBACS and BCS by the detector sensitivity on ROSAT. XMM-Newton, the latest X-raytelescope satellite, has a much smaller flux limit than ROSAT and thus could be used tofind intermediate-LX clusters out to higher redshifts.

80 Conclusion

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Zwicky, F., Herzog, E., & Wild, P. 1961, Catalogue of Galaxies and of Clusters of Galaxies,Vol. 1 (Pasadena, California: California Institute of Technology), p. 3

86 References

ACluster Characterisation andColour-Magnitude Diagrams

In this appendix we present characteristic and diagnostic plots on a cluster-by-cluster basis.We include 0.5×0.5 Mpc2 images of the cluster core, RA-Dec plots out to 10 Mpc fromthe cluster core, galaxy redshift histograms, clustercentric radius versus local galaxy densityplots and colour-magnitude diagrams in all 10 possible SDSS colours. The dashed line circleson the RA-Dec plots indicate the positions of r200 (which is numerically similar to rvir) and3r200 which define the core and infall regions of our clusters. The RA-Dec plots have allbeen tightly-cropped at the 10Mpc radius, thus showing the complete galaxy sample foreach cluster and indicating the relative scale of r200. The redshift histograms are calculatedfor galaxies laying within 3σz/c of the clustercentric redshift and 3r200 of the cluster centreon the RA-Dec plane. We have superimposed the Gaussian fits which we used to estimateclustercentric redshifts and velocity dispersions for illustrative purposes. The motivationfor including the rp-Σ10 diagrams is for identifying sub-structure in our cluster sample. Onthe colour-magnitude diagrams, we indicate fiducial magnitudes (90% completeness limits)with solid vertical lines and M∗ magnitudes with dashed vertical lines, again, for illustrativepurposes. Error bars are generally small so we omit them for visual clarity, however, itmust be noted that a few galaxies (especially ones that lie far away from the CMR) havelarge errorbars. These anomalous galaxies are discussed in section 2.3. The CMR linear fitcoefficients for all 45 clusters in all 10 colours can be found in tables 3.3 and 3.4.

87

88 Cluster Characterisation and Colour-Magnitude Diagrams

118.302118.327118.351118.375118.400

29.317

29.342

29.366

29.390

29.415

RA / deg

Dec

/ de

g

116 117 118 119 120 12127

27.5

28

28.5

29

29.5

30

30.5

31

31.5

RA / deg

Dec

/ de

g

-4000 -2000 0 2000 40000

10

20

30

40

50

60

70

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.05 0.055 0.06 0.065 0.07 0.075

z

0 2 4 6 8 100

5

10

15

20

25

30

35

40

rp / Mpc

Σ 10 /

Mpc

-2

Figure A.1: Abell 602 - The top left panel shows an SDSS image of the inner 0.5×0.5 Mpc2

of the cluster core. The top right panel is the RA-Dec diagram for this cluster. The inner circlerepresents the r200 projected radius, the outer circle represents the 3r200 projected radius, and theborders have been tightly cropped to 10 Mpc in projected radius. The bottom left panel is theredshift histogram plot for this cluster. The bottom x-axis is velocity dispersion while the top x-axisis redshift. The superimposed Gaussian fit is the one we used to estimate the clustercentric redshiftand velocity dispersion for this cluster. The bottom right panel is the projected radius-local galaxydensity plot for this cluster. The vertical dashed line on the left represents the r200 projected radiuswhile the outer vertical dashed line represents the the 3r200 projected radius.

89

Figure A.2: Abell 602 - Colour-magnitude diagrams. The solid sloping lines represent our bestestimate of the CMR, the vertical solid lines represent fiducial magnitudes, and the vertical dashedlines represent M∗ in apparent magnitude.


127.110127.140127.170127.200127.230

30.372

30.402

30.432

30.462

30.492

RA / deg

Dec

/ de

g

124 126 128 130

28

29

30

31

32

33

RA / deg

Dec

/ de

g

-2000 -1000 0 1000 20000

10

20

30

40

50

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.045 0.05 0.055

z

0 2 4 6 8 100

50

100

150

200

rp / Mpc

Σ 10 /

Mpc

-2

Figure A.3: Abell 671 - The same as figure A.1 except these diagrams characterise Abell 671.

91

Figure A.4: Abell 671 - Same as figure A.2 except these colour-magnitude diagrams are forAbell 671.


136.590136.602136.614136.626136.638

10.321

10.333

10.345

10.357

10.369

RA / deg

Dec

/ de

g

135.5 136 136.5 137 137.5

9.5

10

10.5

11

11.5

RA / deg

Dec

/ de

g

-1000 0 10000

2

4

6

8

10

12

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.132 0.134 0.136 0.138 0.14 0.142

z

0 2 4 6 8 100

2

4

6

8

10

rp / Mpc

Σ 10 /

Mpc

-2

Figure A.5: Abell 743 - Same as figure A.1 except these diagrams characterise Abell 671.

93

17 18 19

1

1.5

2

2.5

3

g

(u -

g)

16 17 181

1.5

2

2.5

3

3.5

4

r

(u -

r)

16 17 181.5

2

2.5

3

3.5

4

4.5

i

(u -

i)

15 16 17 18

2

3

4

5

z′

(u -

z′)

16 17 180.4

0.6

0.8

1

1.2

1.4

r

(g -

r)

16 17 180.8

1

1.2

1.4

1.6

1.8

2

i

(g -

i)

15 16 17 18

1

1.5

2

2.5

z′

(g -

z′)

16 17 18

0.3

0.4

0.5

0.6

i

(r -

i)

15 16 17 180

0.2

0.4

0.6

0.8

1

1.2

z′

(r -

z′)

15 16 17 180

0.1

0.2

0.3

0.4

0.5

z′

(i -

z′)



136.815136.836136.857136.878136.899

16.612

16.633

16.654

16.675

16.696

RA / deg

Dec

/ de

g

135 136 137 138 139

15

15.5

16

16.5

17

17.5

18

18.5

RA / deg

Dec

/ de

g

-500 0 5000

2

4

6

8

10

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.07 0.072 0.074 0.076

z

0 2 4 6 8 100

5

10

15

20

25

30

rp / Mpc

Σ 10 /

Mpc

-2


95

16 17 18 19

1

1.5

2

g

(u -

g)

15 16 17 18

1.5

2

2.5

3

r

(u -

r)

14 16 18

1.5

2

2.5

3

3.5

i

(u -

i)

14 16 181.5

2

2.5

3

3.5

4

z′

(u -

z′)

15 16 17 18

0.4

0.6

0.8

1

r

(g -

r)

14 16 18

0.6

0.8

1

1.2

1.4

1.6

i

(g -

i)

14 16 180.5

1

1.5

2

z′

(g -

z′)

14 16 180.2

0.3

0.4

0.5

0.6

i

(r -

i)

14 16 18

0.4

0.6

0.8

1

z′

(r -

z′)

14 16 18

0.1

0.2

0.3

0.4

z′

(i -

z′)



138.299138.328138.357138.386138.415

47.629

47.658

47.687

47.716

47.745

RA / deg

Dec

/ de

g

136 138 140 142

45

46

47

48

49

50

RA / deg

Dec

/ de

g

-1000 0 10000

5

10

15

20

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.046 0.048 0.05 0.052 0.054 0.056

z

0 2 4 6 8 100

5

10

15

20

25

30

35

40

rp / Mpc

Σ 10 /

Mpc

-2


97

16 17 180

0.5

1

1.5

2

g

(u -

g)

15 16 17 18

1.5

2

2.5

3

r

(u -

r)

14 15 16 17

1.5

2

2.5

3

3.5

i

(u -

i)

14 15 16 17

1.5

2

2.5

3

3.5

4

z′

(u -

z′)

15 16 17 180.2

0.4

0.6

0.8

1

r

(g -

r)

14 15 16 170.4

0.6

0.8

1

1.2

1.4

1.6

i

(g -

i)

14 15 16 17

0.5

1

1.5

2

z′

(g -

z′)

14 15 16 17

0.2

0.3

0.4

0.5

i

(r -

i)

14 15 16 170.2

0.4

0.6

0.8

1

z′

(r -

z′)

14 15 16 17

0

0.1

0.2

0.3

0.4

z′

(i -

z′)



138.089138.107138.124138.141138.159

15.908

15.926

15.943

15.960

15.978

RA / deg

Dec

/ de

g

137 138 139

14.5

15

15.5

16

16.5

17

17.5

RA / deg

Dec

/ de

g

-1000 0 10000

2

4

6

8

10

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.086 0.088 0.09 0.092 0.094

z

0 2 4 6 8 100

1

2

3

4

5

rp / Mpc

Σ 10 /

Mpc

-2


99

16 17 18 19

1

1.2

1.4

1.6

1.8

2

2.2

g

(u -

g)

16 17 18

1.5

2

2.5

3

r

(u -

r)

15 16 17

2

2.5

3

3.5

i

(u -

i)

15 16 17

2

2.5

3

3.5

4

z′

(u -

z′)

16 17 180.4

0.6

0.8

1

r

(g -

r)

15 16 17

0.8

1

1.2

1.4

1.6

i

(g -

i)

15 16 17

1

1.5

2

z′

(g -

z′)

15 16 17

0.3

0.35

0.4

0.45

0.5

0.55

i

(r -

i)

15 16 17

0.4

0.5

0.6

0.7

0.8

0.9

1

z′

(r -

z′)

15 16 170.1

0.2

0.3

0.4

0.5

z′

(i -

z′)



151.639151.652151.666151.680151.693

25.897

25.910

25.924

25.938

25.951

RA / deg

Dec

/ de

g

150.5 151 151.5 152 152.5 153

25

25.5

26

26.5

27

RA / deg

Dec

/ de

g

-1000 0 10000

2

4

6

8

10

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.112 0.114 0.116 0.118 0.12 0.122

z

0 2 4 6 8 100

2

4

6

8

10

rp / Mpc

Σ 10 /

Mpc

-2


101

16 17 18 19

1

1.5

2

g

(u -

g)

15 16 17 18

1.5

2

2.5

3

3.5

r

(u -

r)

15 16 17

2

2.5

3

3.5

4

i

(u -

i)

14 15 16 17

2

2.5

3

3.5

4

z′

(u -

z′)

15 16 17 180.4

0.6

0.8

1

1.2

r

(g -

r)

15 16 17

0.5

1

1.5

i

(g -

i)

14 15 16 17

1

1.2

1.4

1.6

1.8

2

2.2

z′

(g -

z′)

15 16 17

0.4

0.5

0.6

0.7

i

(r -

i)

14 15 16 17

0.5

0.6

0.7

0.8

0.9

1

z′

(r -

z′)

14 15 16 17

0.15

0.2

0.25

0.3

0.35

0.4

0.45

z′

(i -

z′)



153.393153.426153.458153.490153.523

-0.969

-0.936

-0.904

-0.872

-0.839

RA / deg

Dec

/ de

g

151 152 153 154 155 156-4

-3

-2

-1

0

1

2

RA / deg

Dec

/ de

g

-2000 0 20000

5

10

15

20

25

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.035 0.04 0.045 0.05 0.055

z

0 2 4 6 8 100

20

40

60

80

100

120

140

rp / Mpc

Σ 10 /

Mpc

-2


103



154.060154.072154.085154.098154.110

33.616

33.628

33.641

33.654

33.666

RA / deg

Dec

/ de

g

153 153.5 154 154.5 155 155.5

32.5

33

33.5

34

34.5

RA / deg

Dec

/ de

g

-2000 -1000 0 1000 20000

2

4

6

8

10

12

14

16

18

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.12 0.125 0.13 0.135

z

0 2 4 6 8 100

2

4

6

8

10

rp / Mpc

Σ 10 /

Mpc

-2


105

17 18 19

0.5

1

1.5

2

g

(u -

g)

16 17 18

1.5

2

2.5

3

3.5

r

(u -

r)

15 16 17

2

2.5

3

3.5

4

i

(u -

i)

15 16 17

2

2.5

3

3.5

4

4.5

z′

(u -

z′)

16 17 18

0.6

0.8

1

1.2

r

(g -

r)

15 16 17

0.8

1

1.2

1.4

1.6

1.8

i

(g -

i)

15 16 17

1

1.2

1.4

1.6

1.8

2

2.2

z′

(g -

z′)

15 16 170.2

0.3

0.4

0.5

0.6

i

(r -

i)

15 16 17

0.5

0.6

0.7

0.8

0.9

1

1.1

z′

(r -

z′)

15 16 17

0.1

0.2

0.3

0.4

0.5

z′

(i -

z′)



154.947154.963154.980154.997155.013

40.963

40.979

40.996

41.013

41.029

RA / deg

Dec

/ de

g

153 154 155 156 157

39.5

40

40.5

41

41.5

42

42.5

RA / deg

Dec

/ de

g

-2000 0 20000

5

10

15

20

25

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.085 0.09 0.095 0.1

z

0 2 4 6 8 100

10

20

30

40

50

60

70

80

rp / Mpc

Σ 10 /

Mpc

-2


107

16 17 18 19

1

1.5

2

g

(u -

g)

15 16 17 181

1.5

2

2.5

3

r

(u -

r)

14 16 18

1.5

2

2.5

3

3.5

i

(u -

i)

14 16 181.5

2

2.5

3

3.5

4

z′

(u -

z′)

15 16 17 18

0.4

0.6

0.8

1

r

(g -

r)

14 16 18

0.6

0.8

1

1.2

1.4

1.6

i

(g -

i)

14 16 18

1

1.5

2

z′

(g -

z′)

14 16 18

0.2

0.3

0.4

0.5

0.6

i

(r -

i)

14 16 18

0.4

0.6

0.8

1

z′

(r -

z′)

14 16 180

0.1

0.2

0.3

0.4

0.5

z′

(i -

z′)



158.014158.037158.059158.081158.104

40.202

40.225

40.247

40.269

40.292

RA / deg

Dec

/ de

g

156 157 158 159 160 16138

38.5

39

39.5

40

40.5

41

41.5

42

RA / deg

Dec

/ de

g

-2000 -1000 0 1000 20000

5

10

15

20

25

30

35

40

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.06 0.065 0.07 0.075

z

0 2 4 6 8 100

20

40

60

80

100

rp / Mpc

Σ 10 /

Mpc

-2


109



158.719158.731158.743158.755158.767

30.671

30.683

30.695

30.707

30.719

RA / deg

Dec

/ de

g

157.5 158 158.5 159 159.5 160

30

30.5

31

31.5

RA / deg

Dec

/ de

g

-2000 -1000 0 1000 20000

1

2

3

4

5

6

7

8

9

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.13 0.135 0.14 0.145

z

0 2 4 6 8 100

1

2

3

4

5

rp / Mpc

Σ 10 /

Mpc

-2


111

17 18 19

1

1.5

2

g

(u -

g)

15 16 17 181

1.5

2

2.5

3

3.5

r

(u -

r)

15 16 17 18

1.5

2

2.5

3

3.5

4

i

(u -

i)

15 16 17 18

1.5

2

2.5

3

3.5

4

4.5

z′

(u -

z′)

15 16 17 18

0.4

0.6

0.8

1

1.2

r

(g -

r)

15 16 17 180.6

0.8

1

1.2

1.4

1.6

1.8

i

(g -

i)

15 16 17 18

1

1.5

2

z′

(g -

z′)

15 16 17 180.25

0.3

0.35

0.4

0.45

0.5

0.55

i

(r -

i)

15 16 17 18

0.4

0.6

0.8

1

z′

(r -

z′)

15 16 17 18

0.1

0.2

0.3

0.4

z′

(i -

z′)



163.416163.435163.453163.471163.490

16.805

16.824

16.842

16.860

16.879

RA / deg

Dec

/ de

g

162 163 164 165

15.5

16

16.5

17

17.5

18

18.5

RA / deg

Dec

/ de

g

-1000 -500 0 500 10000

2

4

6

8

10

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.08 0.082 0.084 0.086 0.088

z

0 2 4 6 8 100

5

10

15

rp / Mpc

Σ 10 /

Mpc

-2


113

17 18 19

0.5

1

1.5

2

g

(u -

g)

16 17 18 19

0

1

2

3

r

(u -

r)

15 16 17 18

1

1.5

2

2.5

3

3.5

4

i

(u -

i)

15 16 17

1.5

2

2.5

3

3.5

4

4.5

z′

(u -

z′)

16 17 180.2

0.4

0.6

0.8

1

1.2

r

(g -

r)

15 16 17 18

0.6

0.8

1

1.2

1.4

1.6

1.8

i

(g -

i)

15 16 170.5

1

1.5

2

z′

(g -

z′)

15 16 170.2

0.3

0.4

0.5

0.6

i

(r -

i)

15 16 17

0.4

0.6

0.8

1

z′

(r -

z′)

15 16 170

0.1

0.2

0.3

0.4

z′

(i -

z′)



175.889175.903175.917175.931175.945

46.346

46.360

46.374

46.388

46.402

RA / deg

Dec

/ de

g

174 175 176 17745

45.5

46

46.5

47

47.5

RA / deg

Dec

/ de

g

-2000 -1000 0 1000 20000

5

10

15

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.11 0.115 0.12

z

0 2 4 6 8 100

1

2

3

4

5

rp / Mpc

Σ 10 /

Mpc

-2


115

16 17 18 190

0.5

1

1.5

2

2.5

g

(u -

g)

16 17 18

0.5

1

1.5

2

2.5

3

3.5

r

(u -

r)

15 16 17 18

1

2

3

4

i

(u -

i)

15 16 17 18

1

2

3

4

z′

(u -

z′)

16 17 18

0.2

0.4

0.6

0.8

1

1.2

r

(g -

r)

15 16 17 18

0.6

0.8

1

1.2

1.4

1.6

i

(g -

i)

15 16 17 180.5

1

1.5

2

z′

(g -

z′)

15 16 17 18

0.25

0.3

0.35

0.4

0.45

0.5

0.55

i

(r -

i)

15 16 17 18

0.4

0.5

0.6

0.7

0.8

0.9

1

z′

(r -

z′)

15 16 17 18

0

0.1

0.2

0.3

0.4

0.5

z′

(i -

z′)



180.485180.501180.516180.531180.547

58.010

58.026

58.041

58.056

58.072

RA / deg

Dec

/ de

g

178 179 180 181 182 183

57

57.5

58

58.5

59

59.5

RA / deg

Dec

/ de

g

-2000 -1000 0 1000 20000

5

10

15

20

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.095 0.1 0.105 0.11

z

0 2 4 6 8 100

5

10

15

20

25

30

35

40

rp / Mpc

Σ 10 /

Mpc

-2


117

16 17 18 19

1

1.5

2

g

(u -

g)

16 17 18

1

1.5

2

2.5

3

3.5

4

r

(u -

r)

15 16 17 18

1

2

3

4

i

(u -

i)

15 16 17 181

2

3

4

z′

(u -

z′)

16 17 18

0.2

0.4

0.6

0.8

1

1.2

r

(g -

r)

15 16 17 18

0.5

1

1.5

i

(g -

i)

15 16 17 18

0.5

1

1.5

2

z′

(g -

z′)

15 16 17 18

0.3

0.35

0.4

0.45

0.5

0.55

i

(r -

i)

15 16 17 18

0.4

0.6

0.8

1

z′

(r -

z′)

15 16 17 180

0.1

0.2

0.3

0.4

0.5

z′

(i -

z′)



197.729197.750197.771197.792197.813

39.180

39.201

39.222

39.243

39.264

RA / deg

Dec

/ de

g

196 197 198 199 200

37.5

38

38.5

39

39.5

40

40.5

41

RA / deg

Dec

/ de

g

-2000 -1000 0 1000 20000

5

10

15

20

25

30

35

40

45

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.065 0.07 0.075 0.08

z

0 2 4 6 8 100

10

20

30

40

50

60

rp / Mpc

Σ 10 /

Mpc

-2


119



200.841200.859200.876200.893200.911

11.261

11.279

11.296

11.313

11.331

RA / deg

Dec

/ de

g

200 201 202

10

10.5

11

11.5

12

12.5

13

RA / deg

Dec

/ de

g

-2000 0 20000

10

20

30

40

50

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.08 0.085 0.09 0.095 0.1

z

0 2 4 6 8 100

5

10

15

20

rp / Mpc

Σ 10 /

Mpc

-2


121



203.989204.011204.032204.053204.075

59.168

59.190

59.211

59.232

59.254

RA / deg

Dec

/ de

g

200 202 204 206 208

57.5

58

58.5

59

59.5

60

60.5

61

RA / deg

Dec

/ de

g

-2000 -1000 0 1000 20000

10

20

30

40

50

60

70

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.065 0.07 0.075 0.08

z

0 2 4 6 8 100

10

20

30

40

50

60

70

80

rp / Mpc

Σ 10 /

Mpc

-2


123



205.488205.508205.528205.548205.568

2.193

2.213

2.233

2.253

2.273

RA / deg

Dec

/ de

g

204 205 206 207

0.5

1

1.5

2

2.5

3

3.5

4

RA / deg

Dec

/ de

g

-2000 0 20000

10

20

30

40

50

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.07 0.075 0.08 0.085

z

0 2 4 6 8 100

10

20

30

40

50

rp / Mpc

Σ 10 /

Mpc

-2


125



208.236208.256208.275208.294208.314

5.119

5.139

5.158

5.177

5.197

RA / deg

Dec

/ de

g

207 208 209 210

3.5

4

4.5

5

5.5

6

6.5

7

RA / deg

Dec

/ de

g

-2000 0 20000

10

20

30

40

50

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.07 0.075 0.08 0.085 0.09

z

0 2 4 6 8 100

20

40

60

80

100

rp / Mpc

Σ 10 /

Mpc

-2


127



208.474208.486208.499208.512208.524

14.899

14.911

14.924

14.937

14.949

RA / deg

Dec

/ de

g

207.5 208 208.5 209 209.5

14

14.5

15

15.5

16

RA / deg

Dec

/ de

g

-1000 -500 0 500 10000

2

4

6

8

10

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.124 0.126 0.128 0.13

z

0 2 4 6 8 100

5

10

15

rp / Mpc

Σ 10 /

Mpc

-2


129

17 18 19

1

1.2

1.4

1.6

1.8

2

2.2

g

(u -

g)

16 17 18

1.5

2

2.5

3

3.5

4

r

(u -

r)

15 16 17

2

2.5

3

3.5

4

4.5

i

(u -

i)

15 16 17

2

2.5

3

3.5

4

4.5

5

z′

(u -

z′)

16 17 18

0.6

0.8

1

1.2

r

(g -

r)

15 16 17

0.8

1

1.2

1.4

1.6

i

(g -

i)

15 16 17

1

1.2

1.4

1.6

1.8

2

2.2

z′

(g -

z′)

15 16 17

0.3

0.35

0.4

0.45

0.5

0.55

i

(r -

i)

15 16 17

0.5

0.6

0.7

0.8

0.9

1

z′

(r -

z′)

15 16 170.15

0.2

0.25

0.3

0.35

0.4

0.45

z′

(i -

z′)



209.754209.778209.802209.826209.850

27.930

27.954

27.978

28.002

28.026

RA / deg

Dec

/ de

g

208 209 210 211 212

26

26.5

27

27.5

28

28.5

29

29.5

30

RA / deg

Dec

/ de

g

-1000 0 10000

5

10

15

20

25

30

35

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.058 0.06 0.062 0.064 0.066 0.068

z

0 2 4 6 8 100

5

10

15

20

25

rp / Mpc

Σ 10 /

Mpc

-2


131



213.398213.415213.432213.449213.466

43.627

43.644

43.661

43.678

43.695

RA / deg

Dec

/ de

g

212 213 214 21542

42.5

43

43.5

44

44.5

45

RA / deg

Dec

/ de

g

-4000 -2000 0 2000 40000

5

10

15

20

25

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.08 0.085 0.09 0.095 0.1 0.105

z

0 2 4 6 8 100

5

10

15

20

25

rp / Mpc

Σ 10 /

Mpc

-2


133

16 17 18 19

1

1.5

2

g

(u -

g)

15 16 17 18

1

1.5

2

2.5

3

3.5

r

(u -

r)

15 16 17

1

1.5

2

2.5

3

3.5

4

i

(u -

i)

15 16 17

1

2

3

4

z′

(u -

z′)

15 16 17 18

0

0.5

1

r

(g -

r)

15 16 17

0.5

1

1.5

i

(g -

i)

15 16 17

0.5

1

1.5

2

z′

(g -

z′)

15 16 17

0.2

0.3

0.4

0.5

i

(r -

i)

15 16 17

0.2

0.4

0.6

0.8

1

z′

(r -

z′)

15 16 17

0

0.1

0.2

0.3

0.4

0.5

z′

(i -

z′)



217.105217.120217.135217.150217.165

56.849

56.864

56.879

56.894

56.909

RA / deg

Dec

/ de

g

215 216 217 218 219

55.5

56

56.5

57

57.5

58

RA / deg

Dec

/ de

g

-2000 -1000 0 1000 20000

5

10

15

20

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.1 0.105 0.11

z

0 2 4 6 8 100

5

10

15

20

rp / Mpc

Σ 10 /

Mpc

-2


135

16 17 18 19

1

1.5

2

2.5

g

(u -

g)

15 16 17 18

1

1.5

2

2.5

3

3.5

r

(u -

r)

14 15 16 17

1.5

2

2.5

3

3.5

4

i

(u -

i)

14 15 16 17

1.5

2

2.5

3

3.5

4

4.5

z′

(u -

z′)

15 16 17 180.2

0.4

0.6

0.8

1

1.2

r

(g -

r)

14 15 16 17

0.6

0.8

1

1.2

1.4

1.6

1.8

i

(g -

i)

14 15 16 170.5

1

1.5

2

z′

(g -

z′)

14 15 16 17

0.3

0.35

0.4

0.45

0.5

0.55

i

(r -

i)

14 15 16 17

0.4

0.6

0.8

1

z′

(r -

z′)

14 15 16 170

0.1

0.2

0.3

0.4

0.5

z′

(i -

z′)



217.732217.749217.765217.781217.798

25.595

25.612

25.628

25.644

25.661

RA / deg

Dec

/ de

g

216 217 218 21924

24.5

25

25.5

26

26.5

27

RA / deg

Dec

/ de

g

-2000 -1000 0 1000 20000

5

10

15

20

25

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.09 0.095 0.1

z

0 2 4 6 8 100

2

4

6

8

10

rp / Mpc

Σ 10 /

Mpc

-2


137

17 18 19

0.5

1

1.5

2

2.5

g

(u -

g)

16 17 18

1

1.5

2

2.5

3

3.5

r

(u -

r)

15 16 17 18

1.5

2

2.5

3

3.5

4

i

(u -

i)

15 16 17 181

2

3

4

z′

(u -

z′)

16 17 18

0.2

0.4

0.6

0.8

1

1.2

r

(g -

r)

15 16 17 18

0.5

1

1.5

i

(g -

i)

15 16 17 18

0.5

1

1.5

2

z′

(g -

z′)

15 16 17 180.25

0.3

0.35

0.4

0.45

0.5

0.55

i

(r -

i)

15 16 17 180.2

0.4

0.6

0.8

1

z′

(r -

z′)

15 16 17 18

-0.1

0

0.1

0.2

0.3

0.4

0.5

z′

(i -

z′)



227.809227.828227.848227.868227.887

6.280

6.299

6.319

6.339

6.358

RA / deg

Dec

/ de

g

226 227 228 229

4.5

5

5.5

6

6.5

7

7.5

8

RA / deg

Dec

/ de

g

-4000 -2000 0 2000 40000

5

10

15

20

25

30

35

40

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.065 0.07 0.075 0.08 0.085 0.09

z

0 2 4 6 8 100

5

10

15

20

25

30

35

40

45

rp / Mpc

Σ 10 /

Mpc

-2


139



235.004235.021235.038235.055235.072

17.844

17.861

17.878

17.895

17.912

RA / deg

Dec

/ de

g

234 235 236

16.5

17

17.5

18

18.5

19

19.5

RA / deg

Dec

/ de

g

-2000 -1000 0 1000 20000

5

10

15

20

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.085 0.09 0.095 0.1

z

0 2 4 6 8 100

5

10

15

20

25

30

35

rp / Mpc

Σ 10 /

Mpc

-2


141

16 17 18 19

1

1.5

2

2.5

g

(u -

g)

15 16 17 18 19

1

1.5

2

2.5

3

3.5

r

(u -

r)

15 16 17 18

1

1.5

2

2.5

3

3.5

4

i

(u -

i)

15 16 17 18

1

2

3

4

5

z′

(u -

z′)

15 16 17 18 19

0.2

0.4

0.6

0.8

1

1.2

r

(g -

r)

15 16 17 18

0.5

1

1.5

i

(g -

i)

15 16 17 18

0.5

1

1.5

2

z′

(g -

z′)

15 16 17 18

0.3

0.4

0.5

0.6

i

(r -

i)

15 16 17 18

0.2

0.4

0.6

0.8

1

1.2

z′

(r -

z′)

15 16 17 18

0.1

0.2

0.3

0.4

0.5

z′

(i -

z′)



234.920234.936234.952234.968234.984

30.684

30.700

30.716

30.732

30.748

RA / deg

Dec

/ de

g

234 235 236

29.5

30

30.5

31

31.5

32

RA / deg

Dec

/ de

g

-2000 -1000 0 1000 20000

5

10

15

20

25

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.09 0.095 0.1 0.105

z

0 2 4 6 8 100

5

10

15

rp / Mpc

Σ 10 /

Mpc

-2


143

16 17 18 19

0.5

1

1.5

2

2.5

g

(u -

g)

15 16 17 180.5

1

1.5

2

2.5

3

3.5

r

(u -

r)

15 16 171

1.5

2

2.5

3

3.5

4

i

(u -

i)

14 15 16 17

1.5

2

2.5

3

3.5

4

4.5

z′

(u -

z′)

15 16 17 18

0.4

0.6

0.8

1

r

(g -

r)

15 16 17

0.6

0.8

1

1.2

1.4

1.6

i

(g -

i)

14 15 16 170.5

1

1.5

2

z′

(g -

z′)

15 16 17

0.3

0.4

0.5

0.6

i

(r -

i)

14 15 16 170.2

0.4

0.6

0.8

1

z′

(r -

z′)

14 15 16 17

0

0.1

0.2

0.3

0.4

0.5

z′

(i -

z′)



236.205236.228236.250236.272236.295

36.021

36.044

36.066

36.088

36.111

RA / deg

Dec

/ de

g

234 235 236 237 238 239

34

34.5

35

35.5

36

36.5

37

37.5

38

RA / deg

Dec

/ de

g

-2000 -1000 0 1000 20000

10

20

30

40

50

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.06 0.065 0.07 0.075

z

0 2 4 6 8 100

10

20

30

40

50

60

70

80

rp / Mpc

Σ 10 /

Mpc

-2


145



239.415239.425239.436239.447239.457

35.476

35.486

35.497

35.508

35.518

RA / deg

Dec

/ de

g

238.5 239 239.5 240 240.534.5

35

35.5

36

36.5

RA / deg

Dec

/ de

g

-2000 0 20000

2

4

6

8

10

12

14

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.15 0.155 0.16 0.165 0.17

z

0 2 4 6 8 100

2

4

6

8

10

rp / Mpc

Σ 10 /

Mpc

-2


147

17.5 18 18.5 19

0.5

1

1.5

2

2.5

g

(u -

g)

16 17 18

1

1.5

2

2.5

3

3.5

4

r

(u -

r)

15.5 16 16.5 17 17.5

1.5

2

2.5

3

3.5

4

4.5

i

(u -

i)

15 16 17

2

3

4

5

z′

(u -

z′)

16 17 18

0.6

0.8

1

1.2

1.4

r

(g -

r)

15.5 16 16.5 17 17.5

1

1.2

1.4

1.6

1.8

2

2.2

i

(g -

i)

15 16 17

1.5

2

2.5

z′

(g -

z′)

15.5 16 16.5 17 17.5

0.35

0.4

0.45

0.5

0.55

0.6

i

(r -

i)

15 16 17

0.5

0.6

0.7

0.8

0.9

1

z′

(r -

z′)

15 16 170.1

0.2

0.3

0.4

0.5

z′

(i -

z′)



240.724240.741240.759240.777240.794

25.369

25.386

25.404

25.422

25.439

RA / deg

Dec

/ de

g

239 240 241 242

24

24.5

25

25.5

26

26.5

27

RA / deg

Dec

/ de

g

-2000 -1000 0 1000 20000

5

10

15

20

25

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.085 0.09 0.095

z

0 2 4 6 8 100

5

10

15

20

rp / Mpc

Σ 10 /

Mpc

-2


149



240.353240.376240.399240.422240.445

53.872

53.895

53.918

53.941

53.964

RA / deg

Dec

/ de

g

238 240 242 244

52

52.5

53

53.5

54

54.5

55

55.5

56

RA / deg

Dec

/ de

g

-1000 -500 0 500 10000

2

4

6

8

10

12

14

16

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.062 0.064 0.066 0.068

z

0 2 4 6 8 100

5

10

15

20

25

30

rp / Mpc

Σ 10 /

Mpc

-2


151



245.096245.112245.128245.144245.160

29.860

29.876

29.892

29.908

29.924

RA / deg

Dec

/ de

g

244 245 246

28.5

29

29.5

30

30.5

31

31.5

RA / deg

Dec

/ de

g

-2000 0 20000

5

10

15

20

25

30

35

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.09 0.095 0.1 0.105

z

0 2 4 6 8 100

5

10

15

20

25

30

rp / Mpc

Σ 10 /

Mpc

-2


153

16 17 18 19

1

1.5

2

2.5

g

(u -

g)

15 16 17 18

1.5

2

2.5

3

3.5

r

(u -

r)

15 16 171.5

2

2.5

3

3.5

4

i

(u -

i)

14 15 16 171.5

2

2.5

3

3.5

4

4.5

z′

(u -

z′)

15 16 17 180.4

0.6

0.8

1

1.2

r

(g -

r)

15 16 170.6

0.8

1

1.2

1.4

1.6

1.8

i

(g -

i)

14 15 16 17

1

1.5

2

z′

(g -

z′)

15 16 17

0.25

0.3

0.35

0.4

0.45

0.5

0.55

i

(r -

i)

14 15 16 17

0.4

0.6

0.8

1

z′

(r -

z′)

14 15 16 17

0.1

0.2

0.3

0.4

0.5

z′

(i -

z′)




155



251.943251.958251.974251.990252.005

29.912

29.927

29.943

29.959

29.974

RA / deg

Dec

/ de

g

251 252 253

28.5

29

29.5

30

30.5

31

RA / deg

Dec

/ de

g

-2000 0 20000

5

10

15

20

25

30

35

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.09 0.095 0.1 0.105 0.11

z

0 2 4 6 8 100

5

10

15

20

rp / Mpc

Σ 10 /

Mpc

-2


157



125.219125.234125.248125.262125.277

7.825

7.840

7.854

7.868

7.883

RA / deg

Dec

/ de

g

124 124.5 125 125.5 126 126.5

6.5

7

7.5

8

8.5

9

RA / deg

Dec

/ de

g

-2000 -1000 0 1000 20000

2

4

6

8

10

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.105 0.11 0.115

z

0 2 4 6 8 100

5

10

15

rp / Mpc

Σ 10 /

Mpc

-2

Figure A.71: RXJ0820.9+0751 - Same as figure A.1 except these diagrams characteriseRXJ0820.9+0751.

159

17 18 19

1

1.5

2

g

(u -

g)

16 17 18

1.5

2

2.5

3

3.5

r

(u -

r)

15 16 17

2

2.5

3

3.5

4

i

(u -

i)

15 16 17

2

2.5

3

3.5

4

z′

(u -

z′)

16 17 180.4

0.6

0.8

1

r

(g -

r)

15 16 17

0.8

1

1.2

1.4

1.6

i

(g -

i)

15 16 17

1

1.5

2

z′

(g -

z′)

15 16 170.3

0.35

0.4

0.45

0.5

0.55

i

(r -

i)

15 16 17

0.4

0.5

0.6

0.7

0.8

0.9

1

z′

(r -

z′)

15 16 17

0.1

0.2

0.3

0.4

0.5

z′

(i -

z′)

Figure A.72: RXJ0820.9+0751 - Same as figure A.2 except these colour-magnitude diagramsare for RXJ0820.9+0751.


150.108150.119150.130150.141150.152

44.132

44.143

44.154

44.165

44.176

RA / deg

Dec

/ de

g

149 149.5 150 150.5 151 151.5

43.5

44

44.5

45

RA / deg

Dec

/ de

g

-2000 -1000 0 1000 20000

1

2

3

4

5

6

7

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.145 0.15 0.155 0.16

z

0 2 4 6 8 100

1

2

3

4

5

rp / Mpc

Σ 10 /

Mpc

-2


161

17.5 18 18.5 19 19.5

1

1.5

2

2.5

g

(u -

g)

16.5 17 17.5 18 18.51.5

2

2.5

3

3.5

r

(u -

r)

16 17 18

2

2.5

3

3.5

4

4.5

i

(u -

i)

16 17 182

2.5

3

3.5

4

4.5

z′

(u -

z′)

16.5 17 17.5 18 18.50.6

0.7

0.8

0.9

1

1.1

1.2

r

(g -

r)

16 17 18

1

1.2

1.4

1.6

1.8

i

(g -

i)

16 17 18

1.2

1.4

1.6

1.8

2

2.2

z′

(g -

z′)

16 17 18

0.35

0.4

0.45

0.5

0.55

i

(r -

i)

16 17 180.5

0.6

0.7

0.8

0.9

1

1.1

z′

(r -

z′)

16 17 18

0.2

0.25

0.3

0.35

0.4

0.45

z′

(i -

z′)



163.407163.428163.449163.470163.491

54.808

54.829

54.850

54.871

54.892

RA / deg

Dec

/ de

g

160 162 164 166

53

53.5

54

54.5

55

55.5

56

56.5

RA / deg

Dec

/ de

g

-2000 -1000 0 1000 20000

5

10

15

20

25

30

35

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.07 0.075 0.08

z

0 2 4 6 8 100

5

10

15

20

25

30

35

40

45

rp / Mpc

Σ 10 /

Mpc

-2


163



215.938215.957215.976215.995216.014

40.223

40.242

40.261

40.280

40.299

RA / deg

Dec

/ de

g

214 215 216 217 218

38.5

39

39.5

40

40.5

41

41.5

42

RA / deg

Dec

/ de

g

-1000 0 10000

2

4

6

8

10

12

14

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.076 0.078 0.08 0.082 0.084 0.086 0.088

z

0 2 4 6 8 100

5

10

15

20

rp / Mpc

Σ 10 /

Mpc

-2


165

16 17 18 19

1

1.5

2

g

(u -

g)

15 16 17 181

1.5

2

2.5

3

r

(u -

r)

15 16 17

1.5

2

2.5

3

3.5

i

(u -

i)

14 15 16 17

1.5

2

2.5

3

3.5

4

z′

(u -

z′)

15 16 17 180.2

0.4

0.6

0.8

1

r

(g -

r)

15 16 17

0.6

0.8

1

1.2

1.4

1.6

i

(g -

i)

14 15 16 170.5

1

1.5

2

z′

(g -

z′)

15 16 17

0.25

0.3

0.35

0.4

0.45

0.5

0.55

i

(r -

i)

14 15 16 17

0.2

0.4

0.6

0.8

1

z′

(r -

z′)

14 15 16 17

0

0.1

0.2

0.3

0.4

0.5

z′

(i -

z′)



220.541220.557220.573220.589220.605

22.269

22.285

22.301

22.317

22.333

RA / deg

Dec

/ de

g

219 220 221 222

21

21.5

22

22.5

23

23.5

RA / deg

Dec

/ de

g

-1000 0 10000

2

4

6

8

10

12

14

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.09 0.095 0.1

z

0 2 4 6 8 100

2

4

6

8

10

rp / Mpc

Σ 10 /

Mpc

-2


167

17 18 19

1

1.2

1.4

1.6

1.8

2

2.2

g

(u -

g)

16 17 18

1.5

2

2.5

3

r

(u -

r)

15 16 17 18

2

2.5

3

3.5

i

(u -

i)

15 16 172

2.5

3

3.5

4

z′

(u -

z′)

16 17 180.4

0.6

0.8

1

1.2

r

(g -

r)

15 16 17 180.8

1

1.2

1.4

1.6

1.8

i

(g -

i)

15 16 171

1.2

1.4

1.6

1.8

2

2.2

z′

(g -

z′)

15 16 17 18

0.3

0.35

0.4

0.45

0.5

0.55

i

(r -

i)

15 16 17

0.5

0.6

0.7

0.8

0.9

1

z′

(r -

z′)

15 16 17

0.15

0.2

0.25

0.3

0.35

0.4

0.45

z′

(i -

z′)



253.144253.155253.166253.177253.188

40.171

40.182

40.193

40.204

40.215

RA / deg

Dec

/ de

g

252 252.5 253 253.5 254 254.5

39.5

40

40.5

41

RA / deg

Dec

/ de

g

-2000 0 20000

2

4

6

8

10

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.14 0.145 0.15 0.155

z

0 2 4 6 8 100

1

2

3

4

5

rp / Mpc

Σ 10 /

Mpc

-2


169

17 18 19

1

1.5

2

2.5

g

(u -

g)

16 17 18

1.5

2

2.5

3

3.5

r

(u -

r)

16 17 18

2

2.5

3

3.5

4

i

(u -

i)

15 16 17

2

2.5

3

3.5

4

4.5

z′

(u -

z′)

16 17 18

0.6

0.8

1

1.2

r

(g -

r)

16 17 180.8

1

1.2

1.4

1.6

1.8

i

(g -

i)

15 16 17

1

1.2

1.4

1.6

1.8

2

2.2

z′

(g -

z′)

16 17 18

0.35

0.4

0.45

0.5

0.55

i

(r -

i)

15 16 17

0.5

0.6

0.7

0.8

0.9

1

1.1

z′

(r -

z′)

15 16 17

0.15

0.2

0.25

0.3

0.35

0.4

0.45

z′

(i -

z′)



119.888119.904119.919119.934119.950

53.968

53.984

53.999

54.014

54.030

RA / deg

Dec

/ de

g

118 119 120 121 12252.5

53

53.5

54

54.5

55

55.5

RA / deg

Dec

/ de

g

-1000 0 10000

2

4

6

8

10

12

14

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.098 0.1 0.102 0.104 0.106 0.108

z

0 2 4 6 8 100

2

4

6

8

10

rp / Mpc

Σ 10 /

Mpc

-2

Figure A.83: ZwCl 1478 - Same as figure A.1 except these diagrams characterise ZwCl 1478.

171

17 18 191

1.5

2

2.5

g

(u -

g)

16 17 18

1.5

2

2.5

3

3.5

4

r

(u -

r)

15.5 16 16.5 17 17.5

2

2.5

3

3.5

4

4.5

i

(u -

i)

15 16 17

2

2.5

3

3.5

4

4.5

5

z′

(u -

z′)

16 17 18

0.6

0.8

1

1.2

r

(g -

r)

15.5 16 16.5 17 17.5

0.8

1

1.2

1.4

1.6

1.8

2

i

(g -

i)

15 16 17

1

1.5

2

2.5

z′

(g -

z′)

15.5 16 16.5 17 17.5

0.35

0.4

0.45

0.5

i

(r -

i)

15 16 170.5

0.6

0.7

0.8

0.9

1

z′

(r -

z′)

15 16 17

0.15

0.2

0.25

0.3

0.35

0.4

0.45

z′

(i -

z′)

Figure A.84: ZwCl 1478 - Same as figure A.2 except these colour-magnitude diagrams are forZwCl 1478.


182.531182.551182.571182.591182.611

5.352

5.372

5.392

5.412

5.432

RA / deg

Dec

/ de

g

181 182 183 1843.5

4

4.5

5

5.5

6

6.5

7

RA / deg

Dec

/ de

g

-1000 0 10000

5

10

15

20

25

30

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.072 0.074 0.076 0.078 0.08 0.082

z

0 2 4 6 8 100

5

10

15

20

25

30

35

40

45

rp / Mpc

Σ 10 /

Mpc

-2


173



215.359215.380215.401215.422215.443

49.502

49.523

49.544

49.565

49.586

RA / deg

Dec

/ de

g

213 214 215 216 217 21847.5

48

48.5

49

49.5

50

50.5

51

51.5

RA / deg

Dec

/ de

g

-1000 0 10000

2

4

6

8

10

12

14

16

18

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.068 0.07 0.072 0.074 0.076

z

0 2 4 6 8 100

10

20

30

40

50

60

70

80

rp / Mpc

Σ 10 /

Mpc

-2


175



259.520259.534259.548259.562259.576

56.643

56.657

56.671

56.685

56.699

RA / deg

Dec

/ de

g

257 258 259 260 261 262

55.5

56

56.5

57

57.5

58

RA / deg

Dec

/ de

g

-2000 0 20000

2

4

6

8

10

12

14

16

18

c(z-zc) / km s-1

Num

ber

of g

alax

ies

0.105 0.11 0.115 0.12

z

0 2 4 6 8 100

2

4

6

8

10

rp / Mpc

Σ 10 /

Mpc

-2


177

17 18 19

1

1.5

2

2.5

g

(u -

g)

16 17 18

1.5

2

2.5

3

3.5

r

(u -

r)

15 16 17

2

2.5

3

3.5

4

i

(u -

i)

15 16 17

2

2.5

3

3.5

4

4.5

z′

(u -

z′)

16 17 18

0.4

0.6

0.8

1

r

(g -

r)

15 16 170.8

1

1.2

1.4

1.6

i

(g -

i)

15 16 170.8

1

1.2

1.4

1.6

1.8

2

z′

(g -

z′)

15 16 17

0.35

0.4

0.45

0.5

0.55

i

(r -

i)

15 16 17

0.5

0.6

0.7

0.8

0.9

1

1.1

z′

(r -

z′)

15 16 17

0.1

0.2

0.3

0.4

z′

(i -

z′)



BDependence of the Colour-Magnitude Relationon Cluster Global Properties: Supplementary

Figures

179

180Dependence of the Colour-Magnitude Relation on Cluster Global

Properties: Supplementary Figures

0 0.05 0.1 0.15 0.2

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

Redshift, z

d(u

- g)

/ dg

0 0.05 0.1 0.15 0.2-0.4

-0.3

-0.2

-0.1

0

Redshift, zd(

u -

r) /

dr

0 0.05 0.1 0.15 0.2

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

Redshift, z

d(u

- i)

/ di

0 0.05 0.1 0.15 0.2

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

Redshift, z

d(u

- z′

) / d

z′

0 0.05 0.1 0.15 0.2

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

Redshift, z

d(g

- r)

/ dr

0 0.05 0.1 0.15 0.2

-0.15

-0.1

-0.05

0

0.05

Redshift, z

d(g

- i)

/ di

Figure B.1: Evolution of the slope of the CMR with redshift.

181

0 0.05 0.1 0.15 0.2

-0.15

-0.1

-0.05

0

0.05

0.1

Redshift, z

d(g

- z′

) / d

z′

0 0.05 0.1 0.15 0.2

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

Redshift, zd(

r -

i) / d

i

0 0.05 0.1 0.15 0.2

-0.15

-0.1

-0.05

0

Redshift, z

d(r

- z′

) / d

z′

0 0.05 0.1 0.15 0.2

-0.03

-0.02

-0.01

0

0.01

Redshift, z

d(i -

z′)

/ dz′

Figure B.2: Evolution of the slope of the CMR with redshift – continued.



0.7 1 2 3 4

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

LX / 1044 erg s-1

d(u

- g)

/ dg

0.7 1 2 3 4-0.4

-0.3

-0.2

-0.1

0

LX / 1044 erg s-1

d(u

- r)

/ dr

0.7 1 2 3 4

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

LX / 1044 erg s-1

d(u

- i)

/ di

0.7 1 2 3 4

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

LX / 1044 erg s-1

d(u

- z′

) / d

z′

0.7 1 2 3 4

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

LX / 1044 erg s-1

d(g

- r)

/ dr

0.7 1 2 3 4

-0.15

-0.1

-0.05

0

0.05

LX / 1044 erg s-1

d(g

- i)

/ di

Figure B.3: Mass dependence of the slope of the CMR with X-ray luminosity.

183

0.7 1 2 3 4

-0.15

-0.1

-0.05

0

0.05

0.1

LX / 1044 erg s-1

d(g

- z′

) / d

z′

0.7 1 2 3 4

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

LX / 1044 erg s-1

d(r

- i)

/ di

0.7 1 2 3 4

-0.15

-0.1

-0.05

0

LX / 1044 erg s-1

d(r

- z′

) / d

z′

0.7 1 2 3 4

-0.03

-0.02

-0.01

0

0.01

LX / 1044 erg s-1

d(i -

z′)

/ dz′

Figure B.4: Mass dependence of the slope of the CMR with X-ray luminosity – continued.



0 200 400 600 800 1000 1200

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

σz / km s-1

d(u

- g)

/ dg

0 200 400 600 800 1000 1200-0.4

-0.3

-0.2

-0.1

0

σz / km s-1

d(u

- r)

/ dr

0 200 400 600 800 1000 1200

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

σz / km s-1

d(u

- i)

/ di

0 200 400 600 800 1000 1200

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

σz / km s-1

d(u

- z′

) / d

z′

0 200 400 600 800 1000 1200

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

σz / km s-1

d(g

- r)

/ dr

0 200 400 600 800 1000 1200

-0.15

-0.1

-0.05

0

0.05

σz / km s-1

d(g

- i)

/ di

Figure B.5: Mass dependence of the slope of the CMR with velocity dispersion.

185

0 200 400 600 800 1000 1200

-0.15

-0.1

-0.05

0

0.05

0.1

σz / km s-1

d(g

- z′

) / d

z′

0 200 400 600 800 1000 1200

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

σz / km s-1

d(r

- i)

/ di

0 200 400 600 800 1000 1200

-0.15

-0.1

-0.05

0

σz / km s-1

d(r

- z′

) / d

z′

0 200 400 600 800 1000 1200

-0.03

-0.02

-0.01

0

0.01

σz / km s-1

d(i -

z′)

/ dz′

Figure B.6: Mass dependence of the slope of the CMR with velocity dispersion – continued.



0.2 0.4 0.6 0.8

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

Concentration

d(u

- g)

/ dg

0.2 0.4 0.6 0.8-0.4

-0.3

-0.2

-0.1

0

Concentrationd(

u -

r) /

dr

0.2 0.4 0.6 0.8

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

Concentration

d(u

- i)

/ di

0.2 0.4 0.6 0.8

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

Concentration

d(u

- z′

) / d

z′

0.2 0.4 0.6 0.8

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

Concentration

d(g

- r)

/ dr

0.2 0.4 0.6 0.8

-0.15

-0.1

-0.05

0

0.05

Concentration

d(g

- i)

/ di

Figure B.7: Morphology dependence of the slope of the CMR with concentration index.

187

0.2 0.4 0.6 0.8

-0.15

-0.1

-0.05

0

0.05

0.1

Concentration

d(g

- z′

) / d

z′

0.2 0.4 0.6 0.8

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

Concentrationd(

r -

i) / d

i

0.2 0.4 0.6 0.8

-0.15

-0.1

-0.05

0

Concentration

d(r

- z′

) / d

z′

0.2 0.4 0.6 0.8

-0.03

-0.02

-0.01

0

0.01

Concentration

d(i -

z′)

/ dz′

Figure B.8: Morphology dependence of the slope of the CMR with concentration index –continued.



I I-II II II-III III

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

Bautz-Morgan type

d(u

- g)

/ dg

I I-II II II-III III-0.4

-0.3

-0.2

-0.1

0

Bautz-Morgan typed(

u -

r) /

dr


-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

Bautz-Morgan type

d(u

- i)

/ di


-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

Bautz-Morgan type

d(u

- z′

) / d

z′


-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

Bautz-Morgan type

d(g

- r)

/ dr


-0.15

-0.1

-0.05

0

0.05

Bautz-Morgan type

d(g

- i)

/ di

Figure B.9: Morphology dependence of the slope of the CMR with Bautz-Morgan type.

189


-0.15

-0.1

-0.05

0

0.05

0.1

Bautz-Morgan type

d(g

- z′

) / d

z′


-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

Bautz-Morgan typed(

r -

i) / d

i


-0.15

-0.1

-0.05

0

Bautz-Morgan type

d(r

- z′

) / d

z′


-0.03

-0.02

-0.01

0

0.01

Bautz-Morgan type

d(i -

z′)

/ dz′

Figure B.10: Morphology dependence of the average slope of the CMR with Bautz-Morgantype – continued.



0 0.05 0.1 0.15 0.2

-2

0

2

4

6

Redshift, z

(u -

g)

Mg*

0 0.05 0.1 0.15 0.2

-1

0

1

2

3

4

5

6

7

Redshift, z(u

- r

) M

r*

0 0.05 0.1 0.15 0.2

1

2

3

4

5

6

Redshift, z

(u -

i) M

i*

0 0.05 0.1 0.15 0.2

0

1

2

3

4

5

6

7

8

Redshift, z

(u -

z′)

Mz′*

0 0.05 0.1 0.15 0.2

-0.5

0

0.5

1

1.5

2

2.5

Redshift, z

(g -

r)

Mr*

0 0.05 0.1 0.15 0.2

0.5

1

1.5

2

2.5

Redshift, z

(g -

i) M

i*

Figure B.11: Evolution of the colour of the CMR at M∗ with redshift.

191

0 0.05 0.1 0.15 0.2-1

0

1

2

3

4

5

Redshift, z

(g -

z′)

Mz′*

0 0.05 0.1 0.15 0.2

-0.5

0

0.5

1

1.5

Redshift, z(r

- i)

Mi*

0 0.05 0.1 0.15 0.2

-1

-0.5

0

0.5

1

1.5

2

2.5

Redshift, z

(r -

z′)

Mz′*

0 0.05 0.1 0.15 0.2

0

0.2

0.4

0.6

0.8

Redshift, z

(i -

z′)

Mz′*

Figure B.12: Evolution of the colour of the CMR at M∗ with redshift – continued.



0.7 1 2 3 4

-2

0

2

4

6

LX / 1044 erg s-1

(u -

g)

Mg*

0.7 1 2 3 4

-1

0

1

2

3

4

5

6

7

LX / 1044 erg s-1

(u -

r)

Mr*

0.7 1 2 3 4

1

2

3

4

5

6

LX / 1044 erg s-1

(u -

i) M

i*

0.7 1 2 3 4

0

1

2

3

4

5

6

7

8

LX / 1044 erg s-1

(u -

z′)

Mz′*

0.7 1 2 3 4

-0.5

0

0.5

1

1.5

2

2.5

LX / 1044 erg s-1

(g -

r)

Mr*

0.7 1 2 3 4

0.5

1

1.5

2

2.5

LX / 1044 erg s-1

(g -

i) M

i*

Figure B.13: Mass dependence of the colour of the CMR at M∗ with X-ray luminosity.

193

0.7 1 2 3 4-1

0

1

2

3

4

5

LX / 1044 erg s-1

(g -

z′)

Mz′*

0.7 1 2 3 4

-0.5

0

0.5

1

1.5

LX / 1044 erg s-1

(r -

i) M

i*

0.7 1 2 3 4

-1

-0.5

0

0.5

1

1.5

2

2.5

LX / 1044 erg s-1

(r -

z′)

Mz′*

0.7 1 2 3 4

0

0.2

0.4

0.6

0.8

LX / 1044 erg s-1

(i -

z′)

Mz′*

Figure B.14: Mass dependence of the colour of the CMR at M∗ with X-ray luminosity –continued.



200 400 600 800 1000 1200

-2

0

2

4

6

σz / km s-1

(u -

g)

Mg*

200 400 600 800 1000 1200

-1

0

1

2

3

4

5

6

7

σz / km s-1

(u -

r)

Mr*

200 400 600 800 1000 1200

1

2

3

4

5

6

σz / km s-1

(u -

i) M

i*

200 400 600 800 1000 1200

0

1

2

3

4

5

6

7

8

σz / km s-1

(u -

z′)

Mz′*

200 400 600 800 1000 1200

-0.5

0

0.5

1

1.5

2

2.5

σz / km s-1

(g -

r)

Mr*

200 400 600 800 1000 1200

0.5

1

1.5

2

2.5

σz / km s-1

(g -

i) M

i*

Figure B.15: Mass dependence of the colour of the CMR at M∗ with velocity dispersion.

195

200 400 600 800 1000 1200-1

0

1

2

3

4

5

σz / km s-1

(g -

z′)

Mz′*

200 400 600 800 1000 1200

-0.5

0

0.5

1

1.5

σz / km s-1

(r -

i) M

i*

200 400 600 800 1000 1200

-1

-0.5

0

0.5

1

1.5

2

2.5

σz / km s-1

(r -

z′)

Mz′*

200 400 600 800 1000 1200

0

0.2

0.4

0.6

0.8

σz / km s-1

(i -

z′)

Mz′*

Figure B.16: Mass dependence of the colour of the CMR at M∗ with velocity dispersion –continued.



0.2 0.4 0.6 0.8

-2

0

2

4

6

Concentration

(u -

g)

Mg*

0.2 0.4 0.6 0.8

-1

0

1

2

3

4

5

6

7

Concentration(u

- r

) M

r*

0.2 0.4 0.6 0.8

1

2

3

4

5

6

Concentration

(u -

i) M

i*

0.2 0.4 0.6 0.8

0

1

2

3

4

5

6

7

8

Concentration

(u -

z′)

Mz′*

0.2 0.4 0.6 0.8

-0.5

0

0.5

1

1.5

2

2.5

Concentration

(g -

r)

Mr*

0.2 0.4 0.6 0.8

0.5

1

1.5

2

2.5

Concentration

(g -

i) M

i*

Figure B.17: Morphology dependence of the colour of the CMR at M∗ with concentrationindex.

197

0.2 0.4 0.6 0.8-1

0

1

2

3

4

5

Concentration

(g -

z′)

Mz′*

0.2 0.4 0.6 0.8

-0.5

0

0.5

1

1.5

Concentration(r

- i)

Mi*

0.2 0.4 0.6 0.8

-1

-0.5

0

0.5

1

1.5

2

2.5

Concentration

(r -

z′)

Mz′*

0.2 0.4 0.6 0.8

0

0.2

0.4

0.6

0.8

Concentration

(i -

z′)

Mz′*

Figure B.18: Morphology dependence of the colour of the CMR at M∗ with concentrationindex – continued.




-2

0

2

4

6

Bautz-Morgan type

(u -

g)

Mg*


-1

0

1

2

3

4

5

6

7

Bautz-Morgan type(u

- r

) M

r*


1

2

3

4

5

6

Bautz-Morgan type

(u -

i) M

i*


0

1

2

3

4

5

6

7

8

Bautz-Morgan type

(u -

z′)

Mz′*


-0.5

0

0.5

1

1.5

2

2.5

Bautz-Morgan type

(g -

r)

Mr*


0.5

1

1.5

2

2.5

Bautz-Morgan type

(g -

i) M

i*

Figure B.19: Morphology dependence of the average colour of the CMR at M∗ with Bautz-Morgan type.

199

I I-II II II-III III-1

0

1

2

3

4

5

Bautz-Morgan type

(g -

z′)

Mz′*


-0.5

0

0.5

1

1.5

Bautz-Morgan type(r

- i)

Mi*


-1

-0.5

0

0.5

1

1.5

2

2.5

Bautz-Morgan type

(r -

z′)

Mz′*


0

0.2

0.4

0.6

0.8

Bautz-Morgan type

(i -

z′)

Mz′*

Figure B.20: Morphology dependence of the average colour of the CMR at M∗ with Bautz-Morgan type – continued.



CComposite Cluster: Supplementary Figures

201

202 Composite Cluster: Supplementary Figures

Figure C.1: Composite cluster colour-magnitude diagrams.

203

Figure C.2: Composite cluster colour-magnitude diagrams – continued.


0 1 2 3 4 5-0.05

0

0.05

0.1

0.15

rp / Mpc

σ (u

- g

)′

0 1 2 3 4 5

1.84

1.86

1.88

1.9

1.92

1.94

1.96

1.98

2

rp / Mpc

Pea

k (u

- g

)′

Figure C.3: Modal colour and width of CMR versus projected radius in (u-g)′ colour.

205

0 1 2 3 4 5

0

0.05

0.1

0.15

0.2

0.25

0.3

rp / Mpc

σ (u

- r

)′

0 1 2 3 4 5

2.8

2.85

2.9

2.95

rp / Mpc

Pea

k (u

- r

)′

Figure C.4: Modal colour and width of CMR versus projected radius in (u-r)′ colour.


0 1 2 3 4 5

0

0.05

0.1

0.15

0.2

0.25

0.3

rp / Mpc

σ (u

- i)

′

0 1 2 3 4 5

3.2

3.25

3.3

3.35

3.4

rp / Mpc

Pea

k (u

- i)

′

Figure C.5: Modal colour and width of CMR versus projected radius in (u-i)′ colour.

207

0 1 2 3 4 5

0

0.05

0.1

0.15

0.2

0.25

0.3

rp / Mpc

σ (u

- z

′)′

0 1 2 3 4 5

3.55

3.6

3.65

3.7

3.75

3.8

rp / Mpc

Pea

k (u

- z

′)′

Figure C.6: Modal colour and width of CMR versus projected radius in (u-z′)′ colour.


0 1 2 3 4 5

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

rp / Mpc

σ (g

- r

)′

0 1 2 3 4 5

0.94

0.96

0.98

1

1.02

1.04

rp / Mpc

Pea

k (g

- r

)′

Figure C.7: Modal colour and width of CMR versus projected radius in (g-r)′ colour.

209

0 1 2 3 4 5

0

0.05

0.1

0.15

rp / Mpc

σ (g

- z

′)′

0 1 2 3 4 5

1.68

1.7

1.72

1.74

1.76

1.78

1.8

1.82

rp / Mpc

Pea

k (g

- z

′)′

Figure C.8: Modal colour and width of CMR versus projected radius in (g-z′)′ colour.


0 1 2 3 4 5

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

rp / Mpc

σ (r

- i)

′

0 1 2 3 4 5

0.425

0.43

0.435

0.44

0.445

0.45

0.455

rp / Mpc

Pea

k (r

- i)

′

Figure C.9: Modal colour and width of CMR versus projected radius in (r-i)′ colour.

211

0 1 2 3 4 5

0

0.02

0.04

0.06

0.08

0.1

rp / Mpc

σ (r

- z

′)′

0 1 2 3 4 5

0.76

0.77

0.78

0.79

0.8

0.81

0.82

0.83

rp / Mpc

Pea

k (r

- z

′)′

Figure C.10: Modal colour and width of CMR versus projected radius in (r-z′)′ colour.


0 1 2 3 4 5-0.02

0

0.02

0.04

0.06

rp / Mpc

σ (i

- z′

)′

0 1 2 3 4 5

0.33

0.335

0.34

0.345

0.35

0.355

0.36

0.365

rp / Mpc

Pea

k (i

- z′

)′

Figure C.11: Modal colour and width of CMR versus projected radius in (i-z′)′ colour.

213

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

0

0.05

0.1

0.15

0.2

log (rp / Mpc)

σ (u

- g

)′

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

1.86

1.88

1.9

1.92

1.94

1.96

1.98

log (rp / Mpc)

Pea

k (u

- g

)′

Figure C.12: Modal colour and width of CMR versus log projected radius in (u-g)′ colour.


-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

0

0.05

0.1

0.15

0.2

0.25

log (rp / Mpc)

σ (u

- r

)′

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

2.82

2.84

2.86

2.88

2.9

2.92

2.94

2.96

log (rp / Mpc)

Pea

k (u

- r

)′

Figure C.13: Modal colour and width of CMR versus log projected radius in (u-r)′ colour.

215

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

0

0.05

0.1

0.15

0.2

0.25

log (rp / Mpc)

σ (u

- i)

′

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

3.26

3.28

3.3

3.32

3.34

3.36

3.38

3.4

3.42

3.44

log (rp / Mpc)

Pea

k (u

- i)

′

Figure C.14: Modal colour and width of CMR versus log projected radius in (u-i)′ colour.


-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

-0.05

0

0.05

0.1

0.15

0.2

0.25

log (rp / Mpc)

σ (u

- z

′)′

-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

3.6

3.62

3.64

3.66

3.68

3.7

3.72

3.74

3.76

log (rp / Mpc)

Pea

k (u

- z

′)′

Figure C.15: Modal colour and width of CMR versus log projected radius in (u-z′)′ colour.

217

-1 -0.5 0 0.5 1

0.02

0.03

0.04

0.05

0.06

0.07

0.08

log (rp / Mpc)

σ (g

- r

)′

-1 -0.5 0 0.5 1

0.96

0.97

0.98

0.99

1

1.01

log (rp / Mpc)

Pea

k (g

- r

)′

Figure C.16: Modal colour and width of CMR versus log projected radius in (g-r)′ colour.


-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

0.02

0.04

0.06

0.08

0.1

0.12

log (rp / Mpc)

σ (g

- z

′)′

-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

1.72

1.73

1.74

1.75

1.76

1.77

1.78

1.79

log (rp / Mpc)

Pea

k (g

- z

′)′

Figure C.17: Modal colour and width of CMR versus log projected radius in (g-z′)′ colour.

219

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

0.02

0.03

0.04

0.05

log (rp / Mpc)

σ (r

- i)

′

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

0.435

0.44

0.445

0.45

0.455

0.46

log (rp / Mpc)

Pea

k (r

- i)

′

Figure C.18: Modal colour and width of CMR versus log projected radius in (r-i)′ colour.


-1 -0.5 0 0.5 1

0.04

0.06

0.08

0.1

0.12

log (rp / Mpc)

σ (r

- z

′)′

-1 -0.5 0 0.5 10.76

0.77

0.78

0.79

0.8

0.81

0.82

log (rp / Mpc)

Pea

k (r

- z

′)′

Figure C.19: Modal colour and width of CMR versus log projected radius in (r-z′)′ colour.

221

-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 10.015

0.02

0.025

0.03

0.035

0.04

0.045

log (rp / Mpc)

σ (i

- z′

)′

-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

0.335

0.34

0.345

0.35

0.355

0.36

log (rp / Mpc)

Pea

k (i

- z′

)′

Figure C.20: Modal colour and width of CMR versus log projected radius in (i-z′)′ colour.


-0.500.511.52

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

log (Σ / Mpc-2)

σ (u

- g

)′

-0.500.511.52

1.86

1.87

1.88

1.89

1.9

1.91

1.92

1.93

1.94

1.95

1.96

log (Σ / Mpc-2)

Pea

k (u

- g

)′

Figure C.21: Modal colour and width of CMR versus log local galaxy density in (u-g)′ colour.

223

-0.500.511.5

0

0.05

0.1

0.15

0.2

0.25

log (Σ / Mpc-2)

σ (u

- r

)′

-0.500.511.5

2.82

2.83

2.84

2.85

2.86

2.87

2.88

2.89

2.9

2.91

log (Σ / Mpc-2)

Pea

k (u

- r

)′

Figure C.22: Modal colour and width of CMR versus log local galaxy density in (u-r)′ colour.


-0.500.511.52

0.05

0.1

0.15

0.2

0.25

log (Σ / Mpc-2)

σ (u

- i)

′

-0.500.511.52

3.26

3.28

3.3

3.32

3.34

3.36

3.38

3.4

3.42

log (Σ / Mpc-2)

Pea

k (u

- i)

′

Figure C.23: Modal colour and width of CMR versus log local galaxy density in (u-i)′ colour.

225

-0.500.511.52

0

0.05

0.1

0.15

0.2

0.25

0.3

log (Σ / Mpc-2)

σ (u

- z

′)′

-0.500.511.52

3.6

3.62

3.64

3.66

3.68

3.7

3.72

3.74

3.76

3.78

log (Σ / Mpc-2)

Pea

k (u

- z

′)′

Figure C.24: Modal colour and width of CMR versus log local galaxy density in (u-z′)′ colour.


-1-0.500.511.52

0.03

0.04

0.05

0.06

0.07

0.08

log (Σ / Mpc-2)

σ (g

- r

)′

-1-0.500.511.52

0.95

0.955

0.96

0.965

0.97

0.975

0.98

0.985

0.99

log (Σ / Mpc-2)

Pea

k (g

- r

)′

Figure C.25: Modal colour and width of CMR versus log local galaxy density in (g-r)′ colour.

227

-1-0.500.511.52

0.06

0.08

0.1

0.12

0.14

log (Σ / Mpc-2)

σ (g

- z

′)′

-1-0.500.511.52

1.7

1.71

1.72

1.73

1.74

1.75

1.76

1.77

1.78

1.79

1.8

log (Σ / Mpc-2)

Pea

k (g

- z

′)′

Figure C.26: Modal colour and width of CMR versus log local galaxy density in (g-z′)′ colour.


-1-0.500.511.52

0.02

0.025

0.03

0.035

0.04

0.045

0.05

log (Σ / Mpc-2)

σ (r

- i)

′

-1-0.500.511.520.425

0.43

0.435

0.44

0.445

0.45

0.455

log (Σ / Mpc-2)

Pea

k (r

- i)

′

Figure C.27: Modal colour and width of CMR versus log local galaxy density in (r-i)′ colour.

229

-1-0.500.511.52

0.04

0.05

0.06

0.07

0.08

log (Σ / Mpc-2)

σ (r

- z

′)′

-1-0.500.511.52

0.765

0.77

0.775

0.78

0.785

0.79

0.795

0.8

0.805

log (Σ / Mpc-2)

Pea

k (r

- z

′)′

Figure C.28: Modal colour and width of CMR versus log local galaxy density in (r-z′)′ colour.


-1-0.500.511.52

0.02

0.025

0.03

0.035

0.04

0.045

0.05

log (Σ / Mpc-2)

σ (i

- z′

)′

-1-0.500.511.52

0.33

0.335

0.34

0.345

0.35

0.355

log (Σ / Mpc-2)

Pea

k (i

- z′

)′

Figure C.29: Modal colour and width of CMR versus log local galaxy density in (i-z′)′ colour.

DSQL Queries

SQL is an acronym for Structured Query Language. It is the language used to query theSDSS database. In this appendix we present and discuss the most important queries we usedto obtain the data used in this thesis.

D.1 The Galaxy Catalogue

D.1.1 Identification, Positional and Photometric Data

After importing the entire Ebeling et al. catalogue as a table called Ebeling into the myDBenvironment in SDSS, we executed the following queries to generate the galaxy catalogue.This first query creates an empty table into which we dumped the identification, positionaland photometric data of our galaxies.

CREATE TABLE Galaxies (clustID int, objID bigint, specObjID bigint,

specObjType int, ra float, ra_err float, dec float, dec_err float, redshift

float, redshift_err float,u float, u_err float, g float, g_err float, g_ext

float, r float, r_err float, r_ext float, i float, i_err float, i_ext float,

z float, z_err float, z_ext float kcorr_u float, kcorr_g float, kcorr_r float,

kcorr_i float, kcorr_z float)

The next three queries find all the galaxies within 10 Mpc radius apertures around thecluster centers. The galaxies are found using the spGetNeighboursRadius database programwhich reads cluster details from the #upload table and dumps the results in the #tmp table.The third query locates all the galaxies within a 10 Mpc line-of-sight redshift from the clustercenter and dumps their identification, positional and photometric data into the Galaxies

table. The column Mpc in the Ebeling table is the pre-calculated 1 Mpc angular scale factorin units of arcmin at the clustercentric redshift.

231

232 SQL Queries

CREATE TABLE #upload (up_ra float, up_dec float, up_rad float, up_id int)

INSERT INTO #upload

SELECT ra as up_ra, dec as up_dec, 10*Mpc as up_rad, clustID as up_id

FROM myDB.Ebeling

WHERE (z between 0 and 0.2) and (Lx between 0.7 and 4) and (ra between

75 and 285)

CREATE TABLE #tmp (clustID int, objID bigint)

INSERT INTO #tmp

EXEC spGetNeighborsRadius

INSERT INTO myDB.Galaxies

SELECT E.clustID, PO.objID, S.specObjID, S.objType, PO.ra, PO.raErr, PO.dec,

PO.decErr, S.z, S.zErr, PO.u+PO.extinction_u, PO.err_u, PO.g+PO.extinction_g,

PO.err_g, PO.r+PO.extinction_r, PO.err_r, PO.i+PO.extinction_i, PO.err_i,

PO.z+PO.extinction_z, PO.err_z, PZ.kcorr_u, PZ.kcorr_g, PZ.kcorr_r, PZ.kcorr_i,

PZ.kcorr_z

FROM myDB.Ebeling E, PhotoObj PO, PhotoZ PZ, SpecObj S, #tmp T

WHERE (T.clustID = E.clustID) and (T.objID = PO.objID) and (T.objID = PZ.objID)

and (PO.objID = PZ.objID) and (T.objID = S.bestObjID) and (PO.specObjID =

S.specObjID) and (PO.type = 3) and (S.z between E.z-3*E.sigma_z and

E.z+3*E.sigma_z)

ORDER BY clustID, objID

Note how we have summed the magnitudes and extinction terms together in the lastquery. All magnitudes are henceforth corrected for dust extinction. In the WHERE clause,we have specified that galaxies must be within 3σz/c of the of the clustercentric redshift.This can be easily modified to find galaxies within any arbitrary redshift range if one doesnot know the velocity dispersion of the cluster. After analysing the results of the abovequery, we found that a few of the clusters still did not satisfy all of our selection criteria (e.g.overlapping clusters or “clusters” with fewer than 20 members). To exclude the unwantedgalaxies we performed the following query:

INSERT INTO myDB.NewGalaxies

SELECT *

FROM Galaxies

WHERE (clustID != 70) and (clustID != 101) and (clustID != 171)

ORDER BY clustID, objID

D.1.2 Spectroscopic Data

After creating the Galaxies table, we use the specObjID field to find spectroscopic data forthe galaxies in the Galaxies table. First we need to create an empty table into which wecan dump all our spectroscopic data.

CREATE TABLE SpecLines (specObjID bigint, lineID int, ew float, ew_err float)

D.2 Other Queries 233

The following query dumps spectroscopic data into the SpecLines table. This table islinked to the Galaxies table by the specObjID field.

INSERT myDB.SpecLines

SELECT DISTINCT G.specObjID, S.lineID, S.ew, S.ewErr

FROM myDB.Galaxies G, SpecLine S

WHERE (G.specObjID=S.specObjID) and (S.lineID=3727 or S.lineID=3730 or

S.lineID=3971 or S.lineID=4103 or S.lineID=4342 or S.lineID=4863 or

S.lineID=4933 or S.lineID=4960 or S.lineID=5008 or S.lineID=6565)

INSERT myDB.SpecLines

SELECT DISTINCT G.specObjID, 4000, S.ew, S.ewErr

FROM myDB.Galaxies G, SpecLineIndex S

WHERE (G.specObjID=S.specObjID) and (S.name=’4000Abreak’)

D.2 Other Queries

D.2.1 The Cluster Catalogue

This following query generates the cluster catalogue. The cluster catalogue is simply a subsetof the Ebeling table, hence the cluster catalogue is created by finding the overlap of theclusters in the Galaxies and Ebeling tables.

SELECT A.*

FROM Ebeling as A, (SELECT DISTINCT E.clustID FROM Ebeling as E,

Galaxies as G WHERE E.clustID = G.clustID) as B

WHERE A.clustID = B.clustID

ORDER BY A.clustID

D.2.2 Number of Galaxies in Each Cluster

To count the number of galaxies in each cluster we used the following query. The results areordered by count, with the clusters having the most members listed at the top.

SELECT clustID, count(objID) as N

FROM Galaxies

GROUP BY clustID

ORDER BY N desc

D.2.3 Overlapping Clusters

To find the overlapping clusters we used the following set of queries. In the first query wecount the number of clusters to which each galaxy belongs. We use the results of the firstquery to get a list of all the galaxies which are members of more than one cluster. We usethe results of the second query to count the number of galaxies in each cluster which belong

234 SQL Queries

to more than one cluster. As soon as the overlapping clusters were identified, they weremanually removed from the Galaxies table.

CREATE TABLE #tmp1 (objID bigint, N int)

INSERT INTO #tmp1

SELECT distinct objID, count(clustID) as N

FROM Galaxies

GROUP BY objID

ORDER BY N desc

CREATE TABLE #tmp2 (objID bigint, clustID int)

INSERT INTO #tmp2

SELECT G.objID, G.clustID

FROM Galaxies G, #tmp1 T

WHERE T.objID = G.objID AND T.N > 1

CREATE TABLE Overlap (clustID int, overlap int)

INSERT INTO Overlap

SELECT distinct clustID, count(objID) as overlap

FROM #tmp2

GROUP BY clustID

ORDER BY overlap desc, clustID

Date post:	17-Aug-2015
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