Durham E-Theses Large scale structure in the Durham/UKST galaxy Redshift survey Ratclie, Andrew How to cite: Ratclie, Andrew (1996) Large scale structure in the Durham/UKST galaxy Redshift survey, Durham theses, Durham University. Available at Durham E-Theses Online: http://etheses.dur.ac.uk/5345/ Use policy The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that: • a full bibliographic reference is made to the original source • a link is made to the metadata record in Durham E-Theses • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders. Please consult the full Durham E-Theses policy for further details. Academic Support Oce, Durham University, University Oce, Old Elvet, Durham DH1 3HP e-mail: [email protected] Tel: +44 0191 334 6107 http://etheses.dur.ac.uk 2 Large Scale Structure in the .3urham/UKST Galaxy Redshift Survey Andrew Ratcliffe A thesis submitted to the University of Durham in accordance with the regulations for admittance to the Degree of Doctor of Philosophy. The copyright of this thesis rests with the author. No quotation from it should be published without his prior written consent and information derived from it should be acknowledged. Department of Physics University of Durham March 1996 3 I OCT 1996 Abstract The initial results from the Durham/UKST Galaxy Redshift Survey are pre• sented here. Using this redshift survey the luminosity, clustering and dynamical properties of galaxies in the Universe are investigated. The 3-D distribution of galaxies in the Durham/UKST survey appears "cellular" on 50-100/i~^ Mpc scales (where h is Hubble's constant in units of 100 kms"^ Mpc~^) and is clearly more complex than a simple 1-D periodic pattern. The optical galaxy luminosity function of the Durham/UKST survey is estimated and can be fit by a Schechter function. Comparison with other determinations of the luminosity function shows good agreement, favouring a flat faint end slope to Mb J ~ -14. The redshift space 2-point correlation function clustering statistic is estimated from the Durham/UKST survey. Comparison with previous estimates from other redshift surveys again shows good agreement and the Durham/UKST survey gives a detection of large scale power above and beyond that of the standard cold dark mat• ter cosmological model on 10-40/i~^Mpc scales. The projected correlation function is also estimated from the Durham/UKST survey and is compared with models for the real space 2-point correlation function. To estimate this real space correlation function directly, a new application of the Richardson-Lucy inversion technique is developed, tested and then apphed to the Durham/UKST survey. The effects of redshift space distortions on the 2-point correlation function are investigated and modelled in the non-linear and linear regimes. The 1-D pairwise velocity dispersion of galaxies is measured to be 416 ± 36 kms~' which, while being consistent with the canonical value of ~ 350 kms~\ is sHghtly smaller than recently measured values. However, this value is inconsistent with the ~ 1000 kms~' value as measured in the standard cold dark matter cosmological model at a high level of significance. The ratio of the mean mass density of the Universe, Q, and the linear bias factor, b (relating the galaxy and light distributions), is then calculated to be ^0.6/5 ^ 0.45 ± 0.38. This favours either an open (fi < 1) and unbiased (6 = 1) Universe or a flat (0 = 1) and biased {b ~ 2) Universe. Preface The work described in this thesis was undertaken between 1992 and 1995 whilst the author was a research student under the supervision of Dr. T. Shanks in the Depart• ment of Physics at the University of Durham. This work has not been submitted for any other degree at the University of Durham or at any other University. All of the observations presented in chapter 2 and appendix A were undertaken in collaboration with Dr. A. Broadbent, Dr. T.Shanks, (Durham University), Dr. Q.A. Parker (AAO) and Dr. C.A. Collins (Liverpool-John-Moores University). Other collaborators in this project were Dr. R. Fong (Durham University), Dr. F.G. Watson (AAO) and Dr. A.P. Oates (RGO). However, the vast majority of the analysis presented in chapters 3, 4, 5 and 6 was the author's own work. A number of the results presented here have appeared in the following papers : RatclifFe, A., Shanks, T., Broadbent, A., Parker, Q.A., Watson, F.G., Oates, A.P. & Collins, C.A., (1996), submitted to Mon. Not. R. astr. Soc. This thesis is dedicated to the memory of my Mother. It's always tougher to win when everyone expects you to. Dave Johnson You can remember me any way you want to. I don't really care, to be honest. Jimmy Connors Contents Abstract Preface 1 Introduction 6 1.1 The Standard Cosmology 6 1.2 Motivation 6 1.3 Scientific Aims 9 2 The Durham/UKST Galaxy Redshift Survey - Construction of the Data Set 10 2.1 Introduction 10 2.2 The Parent 2-D Galaxy Sample 10 2.3 The Zero-Point Photometry Correction 11 2.4 The Observational Procedures 15 2.5 The Redshift Data Reduction Techniques 15 2.6 The Redshift Data 19 2.6.1 The Durham/UKST Galaxy Redshift Catalogue 19 2.6.2 Accuracy of the Measured Redshifts 19 2.7 Field Completeness 21 2.8 Pictures of the Survey 21 2.9 The Number-Distance Histogram 22 1 2.10 Conclusions 28 3 The Optical Galaxy Luminosity Function 29 3.1 Introduction 29 3.2 Estimating the Luminosity Function 30 3.2.1 Review of the Methods 30 3.2.2 Review of the Error Analysis 33 3.2.3 Review of the Normalisation 35 3.3 Results from the Durham/IIKST Galaxy Redshift Survey 36 3.3.1 The (TT—) Test 36 \ V max / 3.3.2 The Parametric Shape 37 3.3.3 The Non-parametric Shape 39 3.3.4 The Normalisation 42 3.4 Determining the Radial Density 43 3.4.1 Review of the Methods and Error Analysis 43 3.4.2 Results from the Durham/UKST Galaxy Redshift Survey 44 3.5 Comparison with Other Surveys and Discussion 47 3.6 Conclusions 50 4 Optimal Estimation of the 2-Point Correlation Function from a Magnitude Limited Survey 51 4.1 Introduction 51 4.2 Review of the Methods of Estimating the 2-Point Correlation Function 52 4.3 The N-Body Simulations 54 4.3.1 Technical Details of the Simulations 54 4.3.2 Pictures of the Simulations 54 4.4 The Mock Catalogues 55 4.4.1 Construction of the Mock Catalogues 55 4.4.2 Pictures of the Mock Catalogues 61 4.5 The 2-Point Correlation Function 66 4.5.1 The N-Body 2-Point Correlation Functions 66 4.5.2 The Mock Catalogue 2-Point Correlation Functions 67 4.5.3 The Theoretical Error on the 2-Point Correlation Function 87 4.5.4 The Integral Constraint on the 2-Point Correlation Function . 88 4.5.5 The Optimal Estimate of the 2-Point Correlation Function and General Discussion of the Estimates 90 4.6 Conclusions 92 5 Galaxy Clustering via the 2-Point Correlation Function 93 5.1 Introduction 93 5.2 The Redshift Space Correlation Function 93 5.2.1 Method of Calculation 94 5.2.2 Results from the Durham/UKST Galaxy Redshift Survey 94 5.2.3 Comparison with other Redshift Surveys 97 5.2.4 Comparison with the Simulations 101 5.2.5 Checking for Systematic Errors 101 5.3 The Projected Correlation Function 104 5.3.1 Modelling the Projected Correlation Function 105 5.3.2 Method of Calculation 105 5.3.3 Tests of the Method 105 5.3.4 Results from the Durham/UKST Galaxy Redshift Survey 107 5.3.5 Comparison with other Redshift Surveys Ill 5.4 Inversion to find the Real Space Correlation function 113 5.4.1 Direct Abel Inversion of the Integral Equation 113 5.4.2 Inversion by Richardson-Lucy Iteration 114 5.4.3 Testing the Methods of Inversion - Fake Data 115 5.4.4 Testing the Methods of Inversion - SCDM Mock Catalogues 121 5.4.5 Applying the Methods of Inversion to the Durham/UKST Survey 121 5.5 Discussion • 128 5.6 Conclusions 130 6 Redshift Space Distortions via the 2-Point Correlation Function 131 6.1 Introduction 131 6.2 Method of Calculation 132 6.3 Results from the Durham/UKST Galaxy Redshift Survey 132 6.4 Comparison with the CDM Simulations 136 6.4.1 The N-Body Simulations 136 6.4.2 The Mock Catalogues 139 6.5 Non-linear Effects - Small Scales 139 6.5.1 Modelling the Pairwise Velocity Dispersion 139 6.5.2 Testing the Method with the CDM Simulations 145 6.5.3 Results from the Durham/UKST Galaxy Redshift Survey 156 6.5.4 Comparison with other Data Sets and the Simulations .... 163 6.6 Linear Effects - Large Scales 164 4 6.6.1 Modelling the Redshift Space Correlation Function with Lin• ear Theory 164 6.6.2 Testing the Method with the CDM Simulations 166 6.6.3 Results from the Durham/UKST Galaxy Redshift Survey 171 6.6.4 Comparison with other Optical Estimates of ^ 177 6.7 Conclusions 178 7 Conclusions 179 7.1 The Future of Galaxy Redshift Surveys 179 7.1.1 The Durham/UKST Survey and FLAIR 179 7.1.2 The Next Generation of Surveys 180 7.2 Summary of Results 181 Bibliography 184 A The Durham/UKST Galaxy Redshift Catalogue 188 B Completeness of the Durham/UKST Galaxy Redshift Catalogue 218 Acknowledgements Chapter 1 Introduction 1.1 The Standard Cosmology The standard cosmological model ("The Hot Big Bang") assumes that the observable Universe and its properties are spatially homogeneous and isotropic on sufficiently large scales.