Abstract:
This contribution is the affirmative side of a debate held with Dr. L. Pietronero at Princeton in June, 1996. I present the observational evidence that the fractal behavior which characterizes the small scale galaxy distribution does not continue to arbitarily large scale, but has a well defined cutoff with an outer length scale of order 30h$^{-1}$ Mpc. For example, plots of the IRAS 1.2 Jy survey exhibit a very clear approach to homogeneity on large scale, in complete contradiction to the endless fractal model.

Abstract:
We present a new method for recovering the underlying velocity field from an observed distribution of galaxies in redshift space. The method is based on a kinematic Zel'dovich relation between the velocity and density fields in redshift space. This relation is expressed in a differential equation slightly modified from the usual Poisson equation, and which depends non-trivially on $\beta \equiv \Omega^{0.6}/b$. The linear equation can be readily solved by standard techniques of separation of variables by means of spherical harmonics. One can also include a term describing the ``rocket effect" discussed by Kaiser (1987). From this redshift space information alone, one can generate a prediction of the peculiar velocity field for each harmonic ($l,m$) as a function of distance. We note that for the quadrupole and higher order moments, the equation is a boundary value problem with solutions dependent on both the interior and exterior mass distribution. However, for a shell at distance $r$, the dipole, as well as the monopole, of the velocity field in the Local Group frame is fully determined by the interior mass distribution. This implies that the shear of the measured velocity field, when fit to a dipole distortion, should be aligned and consistent with the gravity field inferred from the well determined local galaxy distribution. As a preliminary application we compute the velocity dipole of distant shells as predicted from the 1.2Jy IRAS survey compared to the measured velocity dipole on shells, as inferred from a recent POTENT analysis. The coherence between the two fields is good, yielding a best estimate of $\beta= 0.6 \pm 0.2$.

Abstract:
Recent progress in the measurement of relative distances to galaxies has been quite substantial, and catalogs of 3000 galaxies with distances are soon to become available. The peculiar {\it velocity} field (deviations from Hubble flow) derivable from these catalogs, when compared to the peculiar {\it gravity} field derived from all sky redshift surveys of galaxies such as the 1.2Jy IRAS survey, leads to a unique and extremely powerful test of the density parameter $\beta \equiv \Omega^{0.6}/b_I$, where $b_I$ is the possible linear bias of the IRAS selected galaxies relative to the mass fluctuations. We review the status of these large scale flow measurements and present a new methodology to describe the two fields by means of an expansion in a set of orthogonalized functions describing a general potential flow to any chosen resolution. The parameters of the flow can be estimated by minimization of the $\chi^2$ describing the scatter of observed versus predicted linewidths from an inverse Tully-Fisher relation. By this method one can intercompare the gravity and velocity fields coefficient by coefficient, deriving a precise fit for the density parameter and an assessment of the degree of coherence between the fields. The present situation is transitory-- different analyses of the same data are not yielding consistent results. Until this embarassment is untangled, estimates of $\beta$ should be taken with a large grain of salt.

Abstract:
SHORTENED ABSTRACT: We present numerical investigations designed to critically test models of the origin of the Magellanic Stream. The most developed model is the tidal model which fails to reproduce several of its characteristic properties. We suggest an alternative model for the origin of the Stream which can explain all of its observed features and dynamics, as well as provide a strong constraint on the distribution of gas within the halo of the Milky Way. We propose that the Stream consists of material which was ram-pressure stripped from the Magellanic System during its last passage through an extended ionized disk of the Galaxy. This collision took place some 500 million years ago at a galacto-centric distance of about 65 kpc, and swept $\sim 20$\% of the least bound HI into the Stream. The gas with the lowest column density lost the most orbital angular momentum, and is presently at the tip of the Stream, having fallen to a distance of $\sim 20$ kpc from the Milky Way attaining a negative velocity of 200 \kms. To prevent the stripped material from leading the Magellanic Clouds and attaining too large an infall velocity, we postulate the existence of an extended dilute halo of diffuse ionized gas surrounding the Milky Way. If the halo gas is at the virial temperature of the potential well of the Milky Way, its thermal emission would contribute $\sim$ 40\% of the observed diffuse background radiation in the 0.5-1.0 keV (M) band, consistent with recent ROSAT measurements as well as pulsar dispersion measures. Ram pressure stripping

Abstract:
We present a method for deriving a smoothed estimate of the peculiar velocity field of a set of galaxies with measured circular velocities $\eta\equiv {\rm log} \Delta v$ and apparent magnitudes $m$. The method is based on minimizing the scatter of a linear inverse Tully-Fisher relation $\eta= \eta(M)$ where the absolute magnitude of each galaxy is inferred from its redshift $z$, corrected by a peculiar velocity field, $M \propto m - 5\log(z-u)$. We describe the radial peculiar velocity field $u({\bf z})$ in terms of a set of orthogonal functions which can be derived from any convenient basis set; as an example we take them to be linear combinations of low order spherical harmonic and spherical Bessel functions. The model parameters are then found by maximizing the likelihood function for measuring a set of observed $\eta$. The predicted peculiar velocities are free of Malmquist bias in the absence of multi-streaming, provided no selection criteria are imposed on the measurement of circular velocities. This procedure can be considered as a generalized smoothing algorithm of the peculiar velocity field, and is particularly useful for comparison to the smoothed gravity field derived from full-sky galaxy redshift catalogs such as the IRAS surveys. We demonstrate the technique using a catalog of ``galaxies" derived from an N-body simulation. Increasing the resolution of the velocity smoothing beyond a certain level degrades the correlation of fitted velocities against the velocities calculated from linear theory methods, which have finite resolution,

Abstract:
Since the late 1970's, redshift surveys have been vital for progress in understanding large-scale structure in the Universe. The original CfA redshift survey collected spectra of 20-30 galaxies per clear night on a 1.5 meter telescope; over a two year period the project added ~2000 new redshifts to the literature. Subsequent low-z redshift surveys have been up to an order of magnitude larger, and ongoing surveys will yield a similar improvement over the generation preceding them. Full sky redshift surveys have a special role to play as predictors of cosmological flows, and deep pencil beam surveys have provided fundamental constraints on the evolution of properties of galaxies. With the 2DF redshift survey and the SDSS survey, our knowledge of the statistical clustering of low-redshift galaxies will achieve unprecedented precision. Measurements of clustering in the distant Universe are more limited at present, but will become much better in this decade as the VLT/VIRMOS and Keck/DEIMOS projects produce results. As in so many other fields, progress in large scale structure studies, both observational and theoretical, has been made possible by improvements in technologies, especially computing. This review briefly highlights twenty years of progress in this evolving discipline and describes a few novel cosmological tests that will be attempted with the Keck/DEIMOS survey.

Abstract:
We derive estimates for the cosmological bulk flow from the SFI++ Tully-Fisher (TF) catalog. For a sphere of radius $40 \hmpc$ centered on the MW, we derive a bulk flow of $333 \pm 38\kms $ towards Galactic $ (l,b)=(276^\circ,14^\circ)$ within a $3^\circ$ $1\sigma$ error. Within a $ 100\hmpc$ we get $ 257\pm 44\kms$ towards $(l,b)=(279^\circ, 10^\circ)$ within a $6^\circ$ error. These directions are at a $40^\circ$ with the Supergalactic plane, close to the apex of the motion of the Local Group of galaxies after the Virgocentric infall correction. Our findings are consistent with the $\Lambda$CDM model with the latest WMAP best fit cosmological parameters. But the bulk flow allows independent constraints. For WMAP inferred Hubble parameter $h=0.71$ and baryonic mean density parameter $\Omega_b=0.0449$, the constraint from the bulk flow on the matter density $\Omega_m$, the normalization of the density fluctuations, $\sigma_8$, and the growth index, $\gamma$, can be expressed as $\sigma_8\Omega_m^{\gamma-0.55}(\Omega_m/0.266)^{0.28}=0.86\pm 0.11$ (for $\Omega_m\approx 0.266$). Fixing $\sigma_8=0.8$ and $\Omega_m=0.266$ as favored by WMAP, we get $\gamma=0.495\pm 0.096$. The constraint derived here rules out popular DGP models at more than the 99% confidence level. Our results are based on a method termed \ace\ (All Space Constrained Estimate) which reconstructs the bulk flow from an all space three dimensional peculiar velocity field constrained to match the TF measurements. At large distances \ace\ generates a robust bulk flow from the SFI++ that is insensitive to the assumed prior. For comparison, a standard straightforward maximum likelihood estimate leads to very similar results.

Abstract:
A second generation spectrograph for the Keck telescope is under construction at the Lick Observatory shops and will be delivered to Hawaii in 1999. Starting in the Fall of 1999, we shall begin the second phase of the DEEP project: a dense redshift survey of galaxies at Z=1. With each pointing of DEIMOS we shall obtain simultaneous short slit spectra of 70-100 galaxies with $m_I(AB) < 23.0$ in a field of 15' by 2'. Four regions of the sky will be studied in detail, with dense sampling in a region of 120'x15' in each region, plus outrigger fields. The galaxies for spectroscopic analysis will be selected by flux limit and by photometric redshift estimate $Z_{photo}>0.7$. The goal is to obtain high quality spectra of perhaps 30,000 galaxies over the course of 2-3 years. We here review the status of DEIMOS and the science objectives of the survey.

Abstract:
We describe a new statistic for measuring the small-scale velocity dispersion of galaxies directly from redshift surveys. This statistic is based on the object-weighted statistic proposed by Davis, Miller, & White (1997). Compared with the traditional pair-weighted velocity dispersion, our statistic is less sensitive to the presence or absence of rare, rich clusters of galaxies. This measure of the thermal energy of the galaxy distribution is ideally suited for use with a filtered version of the cosmic energy equation. We discuss the application of the statistic to the Las Campanas Redshift Survey. The low observed dispersion strongly favors cosmological models with low matter density, Omega_m ~ 0.2.

Abstract:
The classical dN/dz test allows the determination of fundamental cosmological parameters from the evolution of the cosmic volume element. This test is applied by measuring the redshift distribution of a tracer whose evolution in number density is known. In the past, ordinary galaxies have been used as such a tracer; however, in the absence of a complete theory of galaxy formation, that method is fraught with difficulties. In this paper, we propose studying instead the evolution of the apparent abundance of dark matter halos as a function of their circular velocity, observable via the linewidths or rotation speeds of visible galaxies. Upcoming redshift surveys will allow the linewidth distribution of galaxies to be determined at both z~1 and the present day. In the course of studying this test, we have devised a rapid, improved semi-analytic method for calculating the circular velocity distribution of dark halos based upon the analytic mass function of Sheth et al. (1999) and the formation time distribution of Lacey & Cole (1993). We find that if selection effects are well-controlled and minimal external constraints are applied, the planned DEEP Redshift Survey should allow the measurement of the cosmic equation-of-state parameter w to 10% (as little as 3% if Omega_m has been well-determined from other observations). This type of test has the potential also to provide a constraint on any evolution of w such as that predicted by ``tracker'' models.