Statistics of the Galaxy Distribution / Edition 1 available in Hardcover, Paperback
Statistics of the Galaxy Distribution / Edition 1
- ISBN-10:
- 0367396505
- ISBN-13:
- 9780367396503
- Pub. Date:
- 10/29/2019
- Publisher:
- Taylor & Francis
- ISBN-10:
- 0367396505
- ISBN-13:
- 9780367396503
- Pub. Date:
- 10/29/2019
- Publisher:
- Taylor & Francis
Statistics of the Galaxy Distribution / Edition 1
Buy New
$82.99-
PICK UP IN STORE
Your local store may have stock of this item.
Available within 2 business hours
Overview
Statistics of the Galaxy Distribution describes both the available observational data on the distribution of galaxies and the applications of spatial statistics in cosmology. It gives a detailed derivation of the statistical methods used to study the galaxy distribution and the cosmological physics needed to formulate the statistical models. Because the prevalent approach in cosmological statistics has been frequentist, the authors focus on the most widely used of these methods, but they also explore Bayesian techniques that have become popular in large-scale structure studies.
Describing the most popular methods, their latest applications, and the necessary mathematical and astrophysical background, this groundbreaking book presents the state of the art in the statistical description of the large-scale structure of the Universe.
Cosmology's well-defined and growing data sets represent an important challenge for the statistical analysis, and therefore for the statistics community. Statistics of the Galaxy Distribution presents a unique opportunity for researchers in both fields to strengthen the connection between them and, using a common language, explore the statistical description of the universe.
Product Details
| ISBN-13: | 9780367396503 |
|---|---|
| Publisher: | Taylor & Francis |
| Publication date: | 10/29/2019 |
| Pages: | 452 |
| Product dimensions: | 6.12(w) x 9.19(h) x (d) |
About the Author
Table of Contents
Preface
Acknowledgments
1 The clumpy universe 1
1.1 Galaxies 1
1.1.1 The Milky Way Galaxy 1
1.1.2 Morphological classification and properties 3
1.1.3 Brightness and magnitude systems 6
1.1.4 Distance estimators 7
1.2 Mapping the universe 12
1.2.1 Redshift surveys 14
1.2.2 Peculiar motions 15
1.3 Selection effects and biases 17
1.3.1 Galaxy obscuration 17
1.3.2 Flux limit, luminosity function, and selection function 17
1.3.3 Segregation 22
1.3.4 Cosmic variance 23
1.3.5 Malmquist bias 23
1.3.6 K-correction 25
1.3.7 Velocity corrections 25
1.4 Current and future galaxy catalogs 26
1.4.1 The galaxy distribution in projection 26
1.4.2 The three-dimensional galaxy distribution 28
1.5 The observed structures: clusters, filaments, walls, and voids 34
1.5.1 Groups and clusters of galaxies 34
1.5.2 Catalogs of clusters of galaxies 37
1.5.3 Superclusters: filaments and walls of galaxies 39
1.5.4 Voids 39
1.5.5 The texture of the galaxy distribution 40
2 The standard model of the universe 43
2.1 Introduction 43
2.2 The Friedmann-Robertson-Walker universe 43
2.2.1 Comoving and physical distances and volumes 44
2.2.2 Bubble's law and redshift 48
2.2.3 The Friedmann equations 50
2.2.4 Cosmological time 52
2.2.5 The light cone equation 53
2.2.6 Observational distances 55
2.3 Basic observational data 57
2.3.1 Qlber's paradox and the microwave background 59
2.3.2 Isotropy of the matter distribution 60
2.3.3 Homogeneity of the matter distribution 62
2.3.4 Light element abundances 65
2.3.5 The cosmological parameters 67
3 Cosmological point processes 71
3.1 Introduction 71
3.2 Point processes 72
3.2.1 Intensity functions 73
3.2.2 The binomial random field 73
3.2.3 Poisson processes 74
3.3 The relation between discrete and continuous distributions 75
3.3.1 Estimators of the density field: intensity functions 77
3.4 The two-point correlation function 79
3.4.1 Measuring the two-point galaxy correlation function 81
3.4.2 The angular two-point correlation function 97
3.4.3 The correlation integral 98
3.5 N-point correlation functions 101
3.5.1 Hierarchical models for higher-order correlations 103
3.6 Moments and counts in cells 104
3.7 The void probability function 107
3.8 Nearest neighbor distances 108
3.9 Galaxy distribution as a marked point field 110
3.9.1 The normalized mark correlation function 112
4 Fractal properties of the galaxy distribution 115
4.1 Introduction 115
4.2 Fractal models for the universe 116
4.2.1 Rayleigh-Lévy dust 116
4.2.2 Soneira and Peebles fractal model 118
4.3 Tests on projected data 120
4.4 Fractal dimensions 122
4.4.1 Hausdorff dimension 122
4.4.2 Box-counting dimension 124
4.4.3 Correlation dimension 125
4.4.4 Correlation length and fractal behavior 128
4.4.5 Estimators, edge effects, and possible homogenization 131
4.4.6 Mass-radius dimension 133
4.5 Multifractal measures 134
4.6 Multiscaling 138
4.7 Lacunarity 142
5 Statistical and geometrical models 145
5.1 Introduction 145
5.2 The Neyman-Scott process and related models 146
5.2.1 Cox fields 146
5.2.2 Neyman-Scott fields 150
5.3 The Voronoi model 153
5.3.1 Simulating galaxy surveys 156
5.3.2 Spatial interpolation through Voronoi/Delaunay tessellations 159
5.4 Statistical models for the counts in cells 160
5.4.1 The lognormal model 160
5.4.2 The Saslaw distribution function 161
6 Formation of structure 165
6.1 Introduction 165
6.2 Dynamics of structure 165
6.3 The linear approximation 168
6.3.1 Density evolution 168
6.3.2 Velocity evolution 170
6.3.3 Dimensionless growth rate 172
6.3.4 The Zeldovich approximation 173
6.4 Exact solutions 175
6.4.1 Plane-parallel collapse 175
6.4.2 Spherical collapse 177
6.5 Numerical experiments 182
6.5.1 Dynamics of dark matter 182
6.5.2 Gas and galaxies 184
7 Random fields in cosmology 187
7.1 Introduction 187
7.2 Random fields 187
7.2.1 Spatial correlations 188
7.2.2 Fourier representation 191
7.2.3 Power spectrum 192
7.3 Gaussian random fields 194
7.3.1 Filtered fields 195
7.3.2 Spectra of cosmological Gaussian random fields 197
7.4 Realizations of random fields 203
7.4.1 Fourier method 204
7.4.2 Noise convolution 208
7.4.3 Erratic realizations 208
7.5 Non-Gaussian fields 209
7.6 Statistics of peaks in Gaussian random fields 211
7.6.1 Number density of peaks 211
7.6.2 Structure of peaks in Gaussian random fields 216
7.6.3 Clustering of peaks 217
7.6.4 High-peak asymptotics 219
7.6.5 Peak-background split 220
7.6.6 Peak theory and cluster correlations 222
7.6.7 Peak-patch theory 226
7.7 Press-Schechter method 227
7.8 Halo model of galaxy clustering 232
7.9 Stochastic and nonlinear biasing 237
8 Fourier analysis of clustering 241
8.1 Introduction 241
8.2 Estimation of power spectra 241
8.2.1 Direct methods 242
8.2.2 Selection of weights 245
8.2.3 Integral constraint 249
8.2.4 Bayesian and maximum likelihood methods 253
8.2.5 Karhunen-Loèwe transform 257
8.2.6 Signal-to-noise eigenmodes 258
8.2.7 Quadratic compression 263
8.2.8 Pixelized integral constraint 265
8.3 Redshift distortions 266
8.3.1 General case 267
8.3.2 Far-field approximation 269
8.4 Velocity distortions in power spectrum 272
8.4.1 Fourier-Bessel expansion 273
8.4.2 Modeling the correlation function 275
8.5 Methods for estimating power spectra 277
8.6 Bispectrum 280
8.6.1 Models of the bispectrum 281
8.6.2 Estimation of the bispectrum 283
8.7 Low-dimensional samples 285
8.7.1 Limber's equation 286
8.7.2 Evolution of correlations 288
8.7.3 Power spectra 290
8.7.4 Lucy deconvolution 293
8.7.5 Wide-angle surveys 293
8.7.6 Pencil-beams and slices 295
9 Cosmography 299
9.1 Introduction 299
9.2 Potent method 300
9.3 Wiener filtering 304
9.3.1 Filtering in spherical basis 306
9.3.2 Density interpolation 307
9.3.3 Wiener reconstruction 309
9.3.4 Maps 311
9.3.5 Velocity reconstruction 314
9.4 Constrained fields 319
9.4.1 Constrained realizations for models 321
9.5 Time machines 324
9.6 Gravitational lensing 329
9.6.1 Physics of gravitational lensing 329
9.6.2 Weak leasing 332
9.6.3 Cosmic shear 334
10 Structure statistics 339
10.1 Introduction 339
10.2 Topological description 340
10.2.1 The theory of topological analysis: the genus 340
10.2.2 Estimation of the topology, technicalities 343
10.2.3 Topological measurements: observations 345
10.3 Structure functions 346
10.3.1 Three-dimensional shape statistics 346
10.3.2 Minkowski functionals 348
10.4 Cluster and percolation analysis 351
10.5 Minimal spanning trees 356
10.6 Wavelets 358
10.6.1 Wavelet theory 358
10.6.2 Wavelets and multifractals 360
10.7 Cluster-finding algorithms 362
10.7.1 MST 364
10.7.2 Modified friends-of-friends 364
10.7.3 Wavelets 367
10.8 Void statistics 368
10.9 Checking for periodicity 371
Appendix A Coordinate transformations 377
A.1 Introduction 377
A.2 The equatorial system 377
A.3 Galactic coordinates 378
A.3.1 The supergalactic coordinates 378
A.4 Coordinate transformations 379
A.5 Sky projections 380
Appendix B Some basic concepts in statistics 385
B.1 Introduction 385
B.2 General definitions 385
B.3 Estimation 386
B.4 Properties of estimators 387
B.5 Confidence intervals and tests 391
B.5.1 Probability 391
B.5.2 Bayesian methods 391
B.5.3 Confidence intervals 392
B.5.4 Testing hypotheses 394
References 397
Web site references 423
Index 425