Published in 1995 Physics Reports, Vol. 261, Issues 5-6, pp. 271-431

Abstract. We review the quantitative science that can be and has been done with redshift and peculiar velocity surveys of galaxies in the nearby universe. After a brief background setting the cosmological context for this work, the first part of this review focuses on redshift surveys. The practical issues of how redshift surveys are carried out, and how one turns a distribution of galaxies into a smoothed density field, are discussed. Then follows a description of major redshift surveys that have been done, and the local cosmography out to 8,000 km s^{- 1} that they have mapped. We then discuss in some detail the various quantitative cosmological tests that can be carried out with redshift data. The second half of this review concentrates on peculiar velocity studies, beginning with a thorough review of existing techniques. After discussing the various biases which plague peculiar velocity work, we survey quantitative analyses done with peculiar velocity surveys alone, and finally with the combination of data from both redshift and peculiar velocity surveys. The data presented rule out the standard Cold Dark Matter model, although several variants of Cold Dark Matter with more power on large scales fare better. All the data are consistent with the hypothesis that the initial density field had a Gaussian distribution, although one cannot rule out broad classes of non-Gaussian models. Comparison of the peculiar velocity and density fields constrains the Cosmological Density Parameter. The results here are consistent with a flat universe with mild biasing of the galaxies relative to dark matter, although open universe models are by no means ruled out.

Table of Contents

INTRODUCTION

THEORETICAL BACKGROUND

The Big Bang Model and its Parameters

The Gravitational Instability Paradigm

Power Spectra, Initial Conditions, and Dark Matter

The Correlation Function

The Relation Between the Mass and Galaxy Density Fields

Outstanding Questions

REDSHIFT SURVEYS: SETTING THE QUANTITATIVE GROUNDWORK

The Variety of Redshift Surveys

History of Redshift Surveys

The Measurement of Galaxy Redshifts

Determination of the Luminosity and Selection Functions

Luminosity Functions: Scientific Results

Testing the Hubble Law with Redshift Surveys

The Smoothed Density Field

Filling in the Galactic Plane

REDSHIFT SURVEYS: A COSMOGRAPHICAL TOUR

REDSHIFT SURVEYS: GALAXY CLUSTERING

The Two-Point Correlation Function

Distortions in the Clustering Statistics

Redshift Space Distortions

Non-linear Effects

The Power Spectrum

Higher-Order Statistics

The Density Distribution Function and Counts in Cells

Topology and Related Issues

The Dipole

Spherical Harmonics

Recovering the Real Space Density Field

Clustering of Different Types of Galaxies

PECULIAR VELOCITY FIELDS: TECHNIQUES OF MEASUREMENT AND ANALYSIS

Galaxian Distance Indicator Relations

The Tully-Fisher Relation for Spiral Galaxies

The Faber-Jackson and D_n- Relations for Elliptical Galaxies

Universality of the Distance Indicator Relations

Beyond TF and D_n-: A Look to the Future?

Surface Brightness Fluctuations

BCG L- relation

Possible Methods of Future Peculiar Velocity Work

Statistical Bias and Methods of Peculiar Velocity Analysis

Selection vs. Malmquist Bias - Method I vs. Method II

Bias in a Cluster Sample

Bias in a Field Sample

"Inverse" Distance Indicator Relations

The "Method Matrix" of Peculiar Velocity Analysis

Quantifying Statistical Bias

Forward DIs: Selection Bias

Forward DIs: Malmquist Bias

Distance-Dependent Selection Functions: The "Gould Effect"

Inverse DIs: Selection Bias

Inverse DIs: Malmquist Bias

The Method of Landy and Szalay

STATISTICAL MEASURES OF THE VELOCITY FIELD

A History of Observations of Large-Scale Flow

Early Work

1986-1990: The "Great Attractor"

1990-1994: Very Large-Scale Streaming?

The Lauer-Postman Result

Bulk Flows: A Summary

Homogeneous Peculiar Velocity Catalogs

Velocity Correlation Function

The Cosmic Mach Number

Reconstructing the Three-Dimensional Velocity Field

The Initial Density Distribution Function

Higher-Order Moments of the Velocity Field

Voids in the Reconstructed Density Field

Other Approaches to Reconstructing the Velocity Field

COMPARING THE DENSITY AND VELOCITY FIELDS

Comparison via the Velocity Field

Cluster Infall Models

Unparameterized Velocity Field Models

Method II⁺

Comparison via the Density Field

DISCUSSION

The Initial Power Spectrum

The Distribution Function of the Initial Fluctuations

The Gravitational Instability Paradigm

The Value of ₀

The Relative Distribution of Galaxies and Mass

Is the Big Bang Model Right?

The Future

REFERENCES

For a postscript version of the article, click here.