The density and p eculiar velocity elds of nearby galaxies Michael A Strauss School of Natural Sciences Institute for Advanced Study Princeton New Jersey and Jerey A Willick Observatories of the Carnegie Institute of Washington Santa Barbara Street Pasadena California Abstract We review the quantitative science that can b e and has b een done with redshift and p eculiar velocity surveys of galaxies in the nearby universe After a brief background setting the cosmological context for this work the rst part of this review fo cuses on redshift surveys The practical issues of how redshift surveys are carried out and how one turns a distribution of galaxies into a smo othed density eld are discussed Then follows a description of ma jor redshift surveys that have b een done and the lo cal cosmography out to km s that they have mapp ed We then discuss in some detail the various quantitative cosmological tests that can b e carried out with redshift data The second half of this review concentrates on p eculiar velocity studies b eginning with a thorough review of existing techniques After discussing the various biases which plague p eculiar velocity work we survey quantitative analyses done with p eculiar velocity surveys alone and nally with the combination of data from b oth redshift and p eculiar velocity surveys The data presented rule out the standard Cold Dark Matter mo del although several variants of Cold Dark Matter with more p ower on large scales fare b etter All the data are consistent with the hypothesis that the initial density eld had a Gaussian distribution although one cannot rule out broad classes of nonGaussian mo dels Comparison of the p eculiar velocity and density elds constrains the Cosmological Density Parameter The results here are consistent with a at universe with mild biasing of the galaxies relative to dark matter although op en universe mo dels are by no means ruled out astro-ph/9502079 16 Feb 95 Preprint submitted to Elsevier Science February Contents Introduction Theoretical Background The Big Bang Mo del and its Parameters The Gravitational Instability Paradigm Power Sp ectra Initial Conditions and Dark Matter 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 Scientic Results Testing the Hubble Law with Redshift Surveys The Smo othed Density Field Filling in the Galactic Plane Redshift Surveys A Cosmographical Tour Redshift Surveys Galaxy Clustering The TwoPoint Correlation Function Distortions in the Clustering Statistics The Power Sp ectrum HigherOrder Statistics The Density Distribution Function and Counts in Cells Topology and Related Issues The Dip ole Spherical Harmonics Recovering the Real Space Density Field Clustering of Dierent Types of Galaxies Peculiar Velocity Fields Techniques of Measurement and Analysis Galaxian Distance Indicator Relations Universality of the Distance Indicator Relations Beyond TF and D A Lo ok to the Future n Statistical Bias and Metho ds of Peculiar Velocity Analysis Quantifying Statistical Bias Statistical Measures of the Velocity Field A History of Observations of LargeScale Flow Homogeneous Peculiar Velocity Catalogs Velocity Correlation Function The Cosmic Mach Number Reconstructing the ThreeDimensional Velocity Field Comparing the Density and Velocity Fields Comparison via the Velocity Field Comparison via the Density Field Discussion The Initial Power Sp ectrum The Distribution Function of the Initial Fluctuations The Gravitational Instability Paradigm The Value of The Relative Distribution of Galaxies and Mass Is the Big Bang Mo del Right The Future Acknowledgement References Introduction The last two decades have seen a tremendous growth in our awareness of the richness of the structure of the Universe on scales of galaxies and larger Technical advances in sp ectrographs and detectors in b oth the visible and radio wavebands have allowed redshifts of large numbers of galaxies to b e measured eciently giving us the opp ortunity to map their distribution for the rst time We are in the midst of a golden age of exploration The redshift surveys of the last fteen years have discovered the existence of sup erclusters great voids and coherent structures stretching across the entire volume covered by the surveys But it is not just geography or cosmography as it is called in the astronomical context that has b een done hidden in the statistics of the galaxy distribution is much imp ortant information ab out the structure of the Universe on large scales Thus we can deduce much ab out the early history of the universe and its global structure from careful quantitative analyses of redshift surveys this will b e the central theme of this review The Hubble Law states that at distances much less than the Hubble radius the expansion of the universe causes the recession velocity of a galaxy cz to b e prop ortional to its distance r cz H r where H is the Hubble Constant whose value remains uncertain by a factor of two in astronomers units it is often written as H h km s Mp c the quantity h parameterizing our ignorance of its value Mp c stands for megaparsecs the common unit of distance for much extragalactic work Mp c cm Thus in physicists units H h sec or H h yr In practice we will rarely b e troubled by the uncertain value of h in this review b ecause we will measure distances in units of km s wherein H The observational evidence for the linearity of Eq is reviewed in Peebles and Lauer Postman cf x b elow At the low redshifts discussed in the ma jority of this review relativistic eects are for the most part unimp ortant and the Hubble law is an excellent approximation However galaxies have motions ab ove and b eyond their Hubble velocities deviations from the isotropic expansion that holds only in the theoretical idealization of a p erfectly homogeneous universe Thus Eq is mo died to cz H r r v r v where r is the unit vector towards the galaxy in question vr is the peculiar velocity at p osition r and v is the p eculiar velocity of the observer The development over the past fteen years of redshiftindep endent metho ds of measuring distances have allowed the measurement of the p eculiar velocity eld vr As we will see in detail observations of the p eculiar velocity eld are of great imp ortance it is their study which o ccupies the second half of this review In particular under the hypothesis that structure formed by the gravitational growth of small p erturbations on an initially uniform background there is a direct relation b etween the density and velocity elds which we will exploit to great advantage to put constraints on cosmological mo dels Thus the main emphasis in this review will b e on quantitative constraints that can b e placed on cosmological mo dels from redshift and p eculiar velocity surveys of the lo cal Universe By lo cal we mean at distances small compared with the horizon distance or equivalently at lo okback times small relative to the age of the universe or redshifts small compared to the sp eed of light That is for most of this review we will not b e concerned ab out the general relativistic generalization of Eq and can work in the Newtonian limit almost exclusively Another denition of the lo cal universe is that within which evolutionary eects in the galaxy prop erties can b e assumed to b e negligible In practice we will restrict ourselves to recession velocities b elow km s z There are a number of ma jor reviews and b o oks that are relevant as background material for this review The reader is assumed to b e familiar with the basics of Big Bang cosmology as reviewed in Peebles and Padmanabhan Somewhat more advanced material can b e found in White Efstathiou and Suto Older texts that also discuss this material include Peebles Efstathiou Silk Peebles and Weinberg A useful p o cket summary of the eld is found in Scott et al We will many times skirt the issues of astroparticle physics in the cosmological context Kolb Turner is an excellent overview of the eld Redshift surveys are discussed in Geller Huchra and Giovanelli Haynes and p eculiar velocity surveys are reviewed in Burstein and Dekel The sub ject can also b e followed in the pro ceedings of many conferences among them Br uck Coyne Longair Kolb et al Madore Tully Burbidge Hewitt Kormendy Knapp Audouze Pellatan Szalay Rubin Coyne van den Bergh Pritchet Latham da Costa Chincarini et al and Bouchet LachiezeRey We stress observational asp ects of largescale structure studies in this review Not all asp ects of the eld can b e covered In particular we only touch up on observations of the highredshift universe either in galaxies Spinrad Kron or in background radiation Partridge We fo cus exclusively on galaxies as prob es of largescale structure and do not discuss the distribution of clusters of galaxies eg Bahcall See the review of Efstathiou for a more unied treatment of the largescale distribution of galaxies and clusters We also do not review evidence for dark matter on Galactic scales Faber Gallagher Trimble Binney Tremaine or mo dels for galaxy formation eg White Finally although p eculiar velocities are a ma jor fo cus of this