Search

We obtain constraints on cosmological parameters from the spherically averaged redshift-space correlation function of the CMASS Data Release 9 (DR9) sample of the Baryonic Oscillation Spectroscopic Survey (BOSS). We combine this information with additional data from recent CMB, SN and BAO measurements. Our results show no significant evidence of deviations from the standard flat-Lambda CDM model, whose basic parameters can be specified by Omega_m = 0.285 +- 0.009, 100 Omega_b = 4.59 +- 0.09, n_s = 0.96 +- 0.009, H_0 = 69.4 +- 0.8 km/s/Mpc and sigma_8 = 0.80 +- 0.02. The CMB+CMASS combination sets tight constraints on the curvature of the Universe, with Omega_k = -0.0043 +- 0.0049, and the tensor-to-scalar amplitude ratio, for which we find r < 0.16 at the 95 per cent confidence level (CL). These data show a clear signature of a deviation from scale-invariance also in the presence of tensor modes, with n_s

We measure the 3D genus topology of large scale structure using Luminous Red Galaxies (LRGs) in the Sloan Digital Sky Survey and find it consistent with the Gaussian random phase initial conditions expected from the simplest scenarios of inflation. This studies 3D topology on the largest scales ever obtained. The topology is sponge-like. We measure topology in two volume-limited samples: a dense shallow sample studied with smoothing length of 21h^{-1}Mpc, and a sparse deep sample studied with a smoothing length of 34h^{-1}Mpc. The amplitude of the genus curve is measured with 4% uncertainty. Small distortions in the genus curve expected from non-linear biasing and gravitational effects are well explained (to about 1-\sigma accuracy) by N-body simulations using a subhalo-finding technique to locate LRGs. This suggests the formation of LRGs is a clean problem that can be modeled well without any free fitting parameters. This bodes well for using LRGs to measure the characteristic scales such as the baryon oscillation scale in future deep redshift surveys.

We measure the three-dimensional topology of large-scale structure in the Sloan Digital Sky Survey (SDSS). This allows the genus statistic to be measured with unprecedented statistical accuracy. The sample size is now sufficiently large to allow the topology to be an important tool for testing galaxy formation models. For comparison, we make mock SDSS samples using several state-of-the-art N-body simulations: the Millennium run of Springel et al. (2005)(10 billion particles), Kim & Park (2006) CDM models (1.1 billion particles), and Cen & Ostriker (2006) hydrodynamic code models (8.6 billion cell hydro mesh). Each of these simulations uses a different method for modeling galaxy formation. The SDSS data show a genus curve that is broadly characteristic of that produced by Gaussian random phase initial conditions. Thus the data strongly support the standard model of inflation where Gaussian random phase initial conditions are produced by random quantum fluctuations in the early universe. But on top of this general shape there are measurable differences produced by non-linear gravitational effects (cf. Matsubara 1994), and biasing connected with galaxy formation. The N-body simulations have been tuned to reproduce the power spectrum and multiplicity function but not topology, so topology is an acid test for these models. The data show a ``meatball'' shift (only partly due to the Sloan Great Wall of Galaxies; this shift also appears in a sub-sample not containing the Wall) which differs at the 2.5��level from the results of the Millennium run and the Kim & Park dark halo models, even including the effects of cosmic variance., 13 Apj pages, 7 figures High-resolution stereo graphic available at http://www.astro.princeton.edu/~dclayh/stereo50.eps

We have produced a new conformal map of the universe illustrating recent discoveries, ranging from Kuiper belt objects in the Solar system, to the galaxies and quasars from the Sloan Digital Sky Survey. This map projection, based on the logarithm map of the complex plane, preserves shapes locally, and yet is able to display the entire range of astronomical scales from the Earth's neighborhood to the cosmic microwave background. The conformal nature of the projection, preserving shapes locally, may be of particular use for analyzing large scale structure. Prominent in the map is a Sloan Great Wall of galaxies 1.37 billion light years long, 80% longer than the Great Wall discovered by Geller and Huchra and therefore the largest observed structure in the universe., Comment: Figure 8, and additional material accessible on the web at: http://www.astro.princeton.edu/~mjuric/universe/

We present the first analysis of three-dimensional genus statistics for the SDSS EDR galaxy sample. Due to the complicated survey volume and the selection function, analytic predictions of the genus statistics for this sample are not feasible, therefore we construct extensive mock catalogs from N-body simulations in order to compare the observed data with model predictions. This comparison allows us to evaluate the effects of a variety of observational systematics on the estimated genus for the SDSS sample, including the shape of the survey volume, the redshift distortion effect, and the radial selection function due to the magnitude limit. The observed genus for the SDSS EDR galaxy sample is consistent with that predicted by simulations of a $\Lambda$-dominated spatially-flat cold dark matter model. Standard ($\Omega_0=1$) cold dark matter model predictions do not match the observations. We discuss how future SDSS galaxy samples will yield improved estimates of the genus., Comment: 20 pages, 10 figures, accepted for publication in PASJ (Vol.54, No.5, 2002)

We study the topology of the publicly available data released by the 2dFGRS. The 2dFGRS data contains over 100,000 galaxy redshifts with a magnitude limit of b_J=19.45 and is the largest such survey to date. The data lie over a wide range of right ascension (75 degree strips) but only within a narrow range of declination (10 degree and 15 degree strips). This allows measurements of the two-dimensional genus to be made. The NGP displays a slight meatball shift topology, whereas the SGP displays a bubble like topology. The current SGP data also have a slightly higher genus amplitude. In both cases, a slight excess of overdense regions are found over underdense regions. We assess the significance of these features using mock catalogs drawn from the Virgo Consortium's Hubble Volume LCDM z=0 simulation. We find that differences between the NGP and SGP genus curves are only significant at the 1 sigma level. The average genus curve of the 2dFGRS agrees well with that extracted from the LCDM mock catalogs. We compare the amplitude of the 2dFGRS genus curve to the amplitude of a Gaussian random field with the same power spectrum as the 2dFGRS and find, contradictory to results for the 3D genus of other samples, that the amplitude of the GRF genus curve is slightly lower than that of the 2dFGRS. This could be due to a a feature in the current data set or the 2D genus may not be as sensitive as the 3D genus to non-linear clustering due to the averaging over the thickness of the slice in 2D. (Abridged)

We study the Physically Self Bound Cold Dark Matter Halo distribution which we associate with the massive galaxies within the Horizon Run 3 to estimate the accuracy in determination of the cosmological distance scale measured by the topology analysis. We apply the routine "Contour 3D" to 108 Mock Survey of $\pi$ steradians out to redshift z = 0.6, which effectively correspond to the SDSS-III BOSS survey, and compare the topology with that of a Gaussian Random Phase Field. We find that given three separate smoothing lengths $\lambda =$ 15, 21, and 34 $h^{-1}{\rm Mpc}$, the least $\chi^2$ fit genus per unit volume g yields a 1.7 % fractional uncertainty in smoothing length and angular diameter distance to $z = 0.6$. This is an improvement upon former calibrations of and presents a competitive error estimate with next BAO scale techniques. We also present three dimensional graphics of the Horizon Run 3 spherical mock survey to show a wealth of large-scale structures of the universe that are predicted in surveys like BOSS., Comment: 6 pages, 5 figures, submitted to ApJ

Making only the assumption that you are a random intelligent observer, limits for the total longevity of our species of 0.2 million to 8 million years can be derived at the 95% confidence level. Further consideration indicates that we are unlikely to colonize the Galaxy, and that we are likely to have a higher population than the median for intelligent species.

We measure the topology of the main galaxy distribution using the Seventh Data Release of the Sloan Digital Sky Survey, examining the dependence of galaxy clustering topology on galaxy properties. The observational results are used to test galaxy formation models. A volume-limited sample defined by $M_r, Comment: 24 pages, 19 figures, 10 tables, submitted to ApJS. Version with full resolution images is available at http://astro.kias.re.kr/~cbp/doc/dr7Topo.pdf

We present the power spectrum of the reconstructed halo density field derived from a sample of Luminous Red Galaxies (LRGs) from the Sloan Digital Sky Survey Seventh Data Release (DR7). The halo power spectrum has a direct connection to the underlying dark matter power for k, Comment: 26 pages, 19 figures, submitted to MNRAS. The power spectrum and a module to calculate the likelihoods is publicly available at http://lambda.gsfc.nasa.gov/toolbox/lrgdr/ . v2 fixes abstract formatting issue

It is shown that slice or pencil-beam redshift surveys of galaxies can be simulated in a box with nonequal sides. This method saves a lot of computer time and memory while providing essentially the same results as from whole-cube simulations. A 2457.6/h Mpc-long rod (out to a redshift z = 0.58 in two opposite directions) is simulated using the standard biased cold dark matter model as an example to mimic the recent deep pencil-beam surveys by Broadhurst et al. (1990). The structures (spikes) seen in these simulated samples occur when the narrow pencil-beam pierces walls, filaments, and clusters appearing randomly along the line-of-sight. A statistical test for goodness of fit to a periodic lattice has been applied to the observations and the simulations. It is found that the statistical significance level (P = 15.4 percent) is not strong enough to reject the null hypothesis that the observations and the simulations were drawn at random from the same set.

In support of the new Sloan III survey, which will measure the baryon oscillation scale using the luminous red galaxies (LRGs), we have run the largest N-body simulation to date using $4120^3 = 69.9$ billion particles, and covering a volume of $(6.592 h^{-1} {\rm Gpc})^3$. This is over 2000 times the volume of the Millennium Run, and corner-to-corner stretches all the way to the horizon of the visible universe. LRG galaxies are selected by finding the most massive gravitationally bound, cold dark matter subhalos, not subject to tidal disruption, a technique that correctly reproduces the 3D topology of the LRG galaxies in the Sloan Survey.We have measured the covariance function, power spectrum, and the 3D topology of the LRG galaxy distribution in our simulation and made 32 mock surveys along the past lightcone to simulate the Sloan III survey. Our large N-body simulation is used to accurately measure the non-linear systematic effects such as gravitational evolution, redshift space distortion, past light cone space gradient, and galaxy biasing, and to calibrate the baryon oscillation scale and the genus topology. For example, we predict from our mock surveys that the baryon acoustic oscillation peak scale can be measured with the cosmic variance-dominated uncertainty of about 5% when the SDSS-III sample is divided into three equal volume shells, or about 2.6% when a thicker shell with $0.4, Comment: 12 pages, 18 figures, and 2 tables, submitted to ApJ. Some figures are changed and appedixes are added

We present a unified picture on the evolution of galaxy luminosity and morphology. Galaxy morphology is found to depend critically on the local environment set up by the nearest neighbor galaxy in addition to luminosity and the large scale density. When a galaxy is located farther than the virial radius from its closest neighbor, the probability for the galaxy to have an early morphological type is an increasing function only of luminosity and the local density due to the nearest neighbor ($\rho_n$). The tide produced by the nearest neighbor is thought to be responsible for the morphology transformation toward the early type at these separations. When the separation is less than the virial radius, i.e. when $\rho_n > \rho_{\rm virial}$, its morphology depends also on the neighbor's morphology and the large-scale background density over a few Mpc scales ($\rho_{20}$) in addition to luminosity and $\rho_n$. The early type probability keeps increasing as $\rho_n$ increases if its neighbor is an early type. But the probability decreases as $\rho_n$ increases when the neighbor is a late type. The cold gas streaming from the late type neighbor can be the reason for the morphology transformation toward late type. The overall early-type fraction increases as $\rho_{20}$ increases when $\rho_n > \rho_{\rm virial}$. This can be attributed to the hot halo gas of the neighbor which is confined by the pressure of the ambient medium held by the background mass. We have also found that galaxy luminosity depends on $\rho_n$, and that the isolated bright galaxies are more likely to be recent merger products. We propose a scenario that a series of morphology and luminosity transformation occur through distant interactions and mergers, which results in the morphology--luminosity--local density relation., Comment: 14 pages, 7 figures, for higher resolution figures download PDF file at http://astro.kias.re.kr/docs/trans.pdf ; references added and typos in section 3.2 corrected; Final version accepted for publication in ApJ

We identify galaxy groups and clusters in volume-limited samples of the SDSS redshift survey, using a redshift-space friends-of-friends algorithm. We optimize the friends-of-friends linking lengths to recover galaxy systems that occupy the same dark matter halos, using a set of mock catalogs created by populating halos of N-body simulations with galaxies. Extensive tests with these mock catalogs show that no combination of perpendicular and line-of-sight linking lengths is able to yield groups and clusters that simultaneously recover the true halo multiplicity function, projected size distribution, and velocity dispersion. We adopt a linking length combination that yields, for galaxy groups with ten or more members: a group multiplicity function that is unbiased with respect to the true halo multiplicity function; an unbiased median relation between the multiplicities of groups and their associated halos; a spurious group fraction of less than ~1%; a halo completeness of more than ~97%; the correct projected size distribution as a function of multiplicity; and a velocity dispersion distribution that is ~20% too low at all multiplicities. These results hold over a range of mock catalogs that use different input recipes of populating halos with galaxies. We apply our group-finding algorithm to the SDSS data and obtain three group and cluster catalogs for three volume-limited samples that cover 3495.1 square degrees on the sky. We correct for incompleteness caused by fiber collisions and survey edges, and obtain measurements of the group multiplicity function, with errors calculated from realistic mock catalogs. These multiplicity function measurements provide a key constraint on the relation between galaxy populations and dark matter halos., 26 emulateapj pages including 19 figures. Replaced with final ApJ version

We investigate the dependence of physical properties of galaxies brighter than M_r=-18.0 in the SDSS on environment, as measured by local density using an adaptive smoothing kernel. We find that variations of galaxy properties with environment are almost entirely due to the dependence of morphology and luminosity on environment. Because galaxy properties depend not only on luminosity but also on morphology, it is clear that galaxy properties cannot be determined solely by dark halo mass. When morphology and luminosity are fixed, other physical properties, such as color, color-gradient, concentration, size, velocity dispersion, and star formation rate, are nearly independent of local density. The only feature is the sharp decrease of late type fraction above the critical luminosity of about M_r=-21.3 in the morphology versus luminosity relation. Weak residual dependences on environment include that of the color of late-types (bluer at lower density) and of the L-sigma relation of early-types (larger dispersion at higher density for bright galaxies). The early-type fraction is a monotonically increasing function of local density and luminosity. The morphology-density- luminosity relation should be a key constraint on galaxy formation models. We demonstrate that the dependence on environment of the morphology of galaxie originates from variations in density on effective Gaussian smoothing scales much smaller than 12 h^{-1}Mpc. We find that galaxy morphology varies both with density measured on an effective Gaussian smoothing scale of 4.7 h^{-1} Mpc and on distance to the nearest bright galaxy (particularly, for about 0.2 h^{-1}Mpc). We propose a mechanism that the morphology of galaxies in galaxy systems is transformed by the tidal force., Comment: typos corrected, matched to the published version

We measure the topology of volume-limited galaxy samples selected from a parent sample of 314,050 galaxies in the Sloan Digital Sky Survey(SDSS), which is now complete enough to describe the fully three-dimensional topology and its dependence on galaxy properties. We compare the observed genus statistic G\nu_f) to predictions for a Gaussian random field and to the genus measured for mock surveys constructed from new large-volume simulations of the LambdaCDM cosmology. In this analysis we carefully examine the dependence of the observed genus statistic on the Gaussian smoothing scale R_G from 3.5 to 11 h^-1Mpc and on the luminosity of galaxies over the range -22.50, Comment: Accepted for publication in ApJ, 19 pages, 10 figures, 2 tables and most of the figures are downgraded to fit in the astroph requirements

We present a first morphometric investigation of a preliminary sample from the SDSS of 154287 galaxies with apparent magnitude 14.5, Comment: 35 pages, 13 figures, accepted for publication in PASJ. For preprint with higher-resolution PS files, see http://www.a.phys.nagoya-u.ac.jp/~hikage/MFs/mf_sdss.ps.gz

We present the topology of a volume-limited sample of 11,884 galaxies, selected from an apparent-magnitude limited sample of over 100,000 galaxies observed as part of the Sloan Digital Sky Survey (SDSS). The data currently cover three main regions on the sky: one in the Galactic north and one in the south, both at zero degrees declination, and one area in the north at higher declination. Each of these areas covers a wide range of survey longitude but a narrow range of survey latitude, allowing the two dimensional genus to be measured. The genus curves of the SDSS sub-samples are similar, after appropriately normalizing these measurements for the different areas. We sum the genus curves from the three areas to obtain the total genus curve of the SDSS. The total curve has a shape similar to the genus curve derived from mock catalogs drawn from the Hubble Volume Lambda CDM simulation and is similar to that of a Gaussian random field. Likewise, comparison with the genus of the 2dFGRS, after normalization for the difference in area, reveals remarkable similarity in the topology of these samples. We test for the effects of galaxy type segregation by splitting the SDSS data into thirds, based on the u^*- r^* colors of the galaxies, and measure the genus of the reddest and bluest sub-samples. This red/blue split in u^*- r^* is essentially a split by morphology (Strateva et al. 2001). We find that the genus curve for the reddest galaxies exhibits a ``meatball'' shift of the topology -- reflecting the concentration of red galaxies in high density regions -- compared to the bluest galaxies and the full sample, in agreement with predictions from simulations., Comment: ApJ Accepted with very minor revisions

We study the three-dimensional genus topology of large-scale structure using the northern region of the CMASS Data Release 10 (DR10) sample of the SDSS-III Baryon Oscillation Spectroscopic Survey. We select galaxies with redshift 0.452 1011.56 M ☉. We study the topology at two smoothing lengths: R G = 21 h –1 Mpc and R G = 34 h –1 Mpc. The genus topology studied at the R G = 21 h –1 Mpc scale results in the highest genus amplitude observed to date. The CMASS sample yields a genus curve that is characteristic of one produced by Gaussian random phase initial conditions. The data thus support the standard model of inflation where random quantum fluctuations in the early universe produced Gaussian random phase initial conditions. Modest deviations in the observed genus from random phase are as expected from shot noise effects and the nonlinear evolution of structure. We suggest the use of a fitting formula motivated by perturbation theory to characterize the shift and asymmetries in the observed genus curve with a single parameter. We construct 54 mock SDSS CMASS surveys along the past light cone from the Horizon Run 3 (HR3) N-body simulations, where gravitationally bound dark matter subhalos are identified as the sites of galaxy formation. We study the genus topology of the HR3 mock surveys with the same geometry and sampling density as the observational sample and find the observed genus topology to be consistent with ΛCDM as simulated by the HR3 mock samples. We conclude that the topology of the large-scale structure in the SDSS CMASS sample is consistent with cosmological models having primordial Gaussian density fluctuations growing in accordance with general relativity to form galaxies in massive dark matter halos.

We measure the topology (genus curve) of the galaxy distribution in a mock redshift catalog designed to resemble the upcoming Sloan Digital Sky Survey (SDSS). The catalog, drawn from a large N-body simulation of a Lambda-CDM cos- mological model, mimics the anticipated spectroscopic selection procedures of the SDSS in some detail. Sky maps, redshift slices, and 3-D contour maps of the mock survey reveal a rich and complex structure, including networks of voids and superclusters that resemble the patterns seen in the CfA redshift survey and the Las Campanas Redshift Survey (LCRS). The 3-D genus curve can be measured from the simulated catalog with superb precision; this curve has the general shape predicted for Gaussian, random phase initial conditions, but the error bars are small enough to demonstrate with high significance the subtle departures from this shape caused by non-linear gravitational evolution. These distortions have the form predicted by Matsubara's (1994) perturbative anal- ysis, but they are much smaller in amplitude. We also measure the 3-D genus curve of the radial peculiar velocity field measured by applying distance- indicator relations (with realistic errors) to the mock catalog. This genus curve is consistent with the Gaussian random phase prediction, though it is of relatively low precision because of the large smoothing length required to overcome noise in the measured velocity field. Finally, we measure the 2-D topology in redshift slices, similar to early slices from the SDSS and to slices already observed in the LCRS. The genus curves of these slices are consistent with the observed genus curves of the LCRS, providing further evidence in favor of the inflationary CDM model with Omega_M~0.4. The catalog is publicly available at http://www.astronomy.ohio-state.edu/~dhw/sdss.html., Comment: ASTeX 4.0 Preprint Style, 5 GIF figures (Figs 1, 2, 3a, 3b, 6; see http://cfa-www.harvard.edu/~wcolley/SDSS_Top/ for PostScript versions), 7 PostScript figures. Figure 5 and Table 1 have minor corrections since publication

The Sloan Digital Sky Survey (SDSS) has been in operation since 2000 April. This paper presents the tenth public data release (DR10) from its current incarnation, SDSS-III. This data release includes the first spectroscopic data from the Apache Point Observatory Galaxy Evolution Experiment (APOGEE), along with spectroscopic data from the Baryon Oscillation Spectroscopic Survey (BOSS) taken through 2012 July. The APOGEE instrument is a near-infrared R~22,500 300-fiber spectrograph covering 1.514--1.696 microns. The APOGEE survey is studying the chemical abundances and radial velocities of roughly 100,000 red giant star candidates in the bulge, bar, disk, and halo of the Milky Way. DR10 includes 178,397 spectra of 57,454 stars, each typically observed three or more times, from APOGEE. Derived quantities from these spectra (radial velocities, effective temperatures, surface gravities, and metallicities) are also included.DR10 also roughly doubles the number of BOSS spectra over those included in the ninth data release. DR10 includes a total of 1,507,954 BOSS spectra, comprising 927,844 galaxy spectra; 182,009 quasar spectra; and 159,327 stellar spectra, selected over 6373.2 square degrees., 15 figures; 1 table. Accepted to ApJS. DR10 is available at http://www.sdss3.org/dr10 v3 fixed 3 diacritic markings in the arXiv HTML listing of the author names

In a flat, k=0 cosmology with galaxies that approximate singular isothermal spheres, gravitational lens image separations should be uncorrelated with source redshift. But in an open k=-1 cosmology such gravitational lens image separations become smaller with increasing source redshift. The observed separations do become smaller with increasing source redshift but the effect is even stronger than that expected in an Omega=0 cosmology. The observations are thus not compatible with the "standard" gravitational lensing statistics model in a flat universe. We try various open and flat cosmologies, galaxy mass profiles, galaxy merging and evolution models, and lensing aided by clusters to explain the correlation. We find the data is not compatible with any of these possibilities within the 95% confidence limit, leaving us with a puzzle. If we regard the observed result as a statistical fluke, it is worth noting that we are about twice as likely to observe it in an open universe (with 0 -2.0., Comment: 21 pages, 4 figures, AASTeX4

Large galaxy redshift surveys have long been used to constrain cosmological models and structure formation scenarios. In particular, the largest structures discovered observationally are thought to carry critical information on the amplitude of large-scale density fluctuations or homogeneity of the universe, and have often challenged the standard cosmological framework. The Sloan Great Wall (SGW) recently found in the Sloan Digital Sky Survey (SDSS) region casts doubt on the concordance cosmological model with a cosmological constant (i.e. the flat LCDM model). Here we show that the existence of the SGW is perfectly consistent with the LCDM model, a result that only our very large cosmological N-body simulation (the Horizon Run 2, HR2) could supply. In addition, we report on the discovery of a void complex in the SDSS much larger than the SGW, and show that such size of the largest void is also predicted in the LCDM paradigm. Our results demonstrate that an initially homogeneous isotropic universe with primordial Gaussian random phase density fluctuations growing in accordance with the General Relativity, can explain the richness and size of the observed large-scale structures in the SDSS. Using the HR2 simulation we predict that a future galaxy redshift survey about four times deeper or with 3 magnitude fainter limit than the SDSS should reveal a largest structure of bright galaxies about twice as big as the SGW., 6 pages, 4 figures, Accepted to ApJL

Can clusters of galaxies be used to trace the large-scale peculiar velocity field of the universe? We answer this question by using large-scale cosmological simulations to compare the motions of rich clusters of galaxies with the motion of the underlying matter distribution. Three models are investigated: Omega = 1 and Omega = 0.3 cold dark matter (CDM), and Omega = 0.3 primeval baryonic isocurvature (PBI) models, all normalized to the Cosmic Background Explorer (COBE) background fluctuations. We compare the cluster and mass distribution of peculiar velocities, bulk motions, velocity dispersions, and Mach numbers as a function of scale for R greater than or = 50/h Mpc. We also present the large-scale velocity and potential maps of clusters and of the matter. We find that clusters of galaxies trace well the large-scale velocity field and can serve as an efficient tool to constrain cosmological models. The recently reported bulk motion of clusters 689 +/- 178 km/s on approximately 150/h Mpc scale (Lauer & Postman 1994) is larger than expected in any of the models studied (less than or = 190 +/- 78 km/s).

This paper proposes a number of methods for recovering the true, real-space large-scale density distributions from redshift data sets. On the largest scales, the effects of peculiar velocities is to compress the galaxy clustering along the line of sight and consequently the density gradient in the radial direction is enhanced in comparison with the density gradient perpendicular to the line of sight. We calculate the relation between the density gradients in real and redshift space in the linear regime and show that it is a simple function of the density parameter, Omega. By considering the anisotropy of density gradients in redshift space it is possible, in principle, to obtain information about the value of Omega. Using N-body simulations we examine different methods for correcting the effects of large-scale velocities to obtain the true density distributions. We derive the peculiar velocity field from the redshift data and iterate to place each galaxy at a distance consistent with its measured redshift and its derived velocity. Linear theory, as well as second-order solutions for the peculiar velocity field are tested. The density distributions in low-density regions predicted by both linear theory and second-order theory are similar, and in good agreement with the true density field in the simulation. The use of the second-order corrections improves the prediction of the density field in high-density regions.

We study the topology of large-scale structure in the Center for Astrophysics Redshift Survey, which now includes approximately 12,000 galaxies with limiting magnitude m(sub B) is less than or equal to 15.5. The dense sampling and large volume of this survey allow us to compute the topology on smoothing scales from 6 to 20/h Mpc; we thus examine the topology of structure in both 'nonlinear' and 'linear' regimes. On smoothing scales less than or equal to 10/h Mpc this sample has 3 times the number of resolution elements of samples examined in previous studies. Isodensity surface of the smoothed galaxy density field demonstrate that coherent high-density structures and large voids dominate the galaxy distribution. We compute the genus-threshold density relation for isodensity surfaces of the CfA survey. To quantify phase correlation in these data, we compare the CfA genus with the genus of realizations of Gaussian random fields with the power spectrum measured for the CfA survey. On scales less than or equal to 10/h Mpc the observed genus amplitude is smaller than random phase (96% confidence level). This decrement reflects the degree of phase coherence in the observed galaxy distribution. In other words the genus amplitude on these scales is not good measure of the power spectrum slope. On scales greater than 10/h Mpc, where the galaxy distribution is rougly in the 'linear' regime, the genus ampitude is consistent with the random phase amplitude. The shape of the genus curve reflects the strong coherence in the observed structure; the observed genus curve appears broader than random phase (94% confidence level for smoothing scales less than or equal to 10/h Mpc) because the topolgoy is spongelike over a very large range of density threshold. This departre from random phase consistent with a distribution like a filamentary net of 'walls with holes.' On smoothing scales approaching approximately 20/h Mpc the shape of the CfA genus curve is consistent with random phase. There is very weak evidence for a shift of the genus toward a 'bubble-like' topology. To test cosmological models, we compute the genus for mock CfA surveys drawn from large (L greater than or approximately 400/h Mpc) N-body simulations of three variants of the cold dark matter (CDM) cosmogony. The genus amplitude of the 'standard' CDM model (omega h = 0.5, b = 1.5) differs from the observations (96% confidence level) on smoothing scales is less than or approximately 10/h Mpc. An open CDM model (omega h = 0.2) and a CDM model with nonzero cosmological constant (omega h = 0.24, lambda (sub 0) = 0.6) are consistent with the observed genus amplitude over the full range of smoothing scales. All of these models fail (97% confidence level) to match the broadness of the observed genus curve on smoothing scales is less than or equal to 10/h Mpc.

Results are reported from a statistical analysis of published observational data on a sample of 860 northern dwarf and low-surface-brightness (D/LSB) galaxies with delta = 0 deg or greater and b between -40 and 40 deg, selected from the Uppsala General Catalogue of Galaxies (Nilson et al., 1973). The results are presented in extensive redshift/space maps, histograms, graphs and tables and characterized in detail. It is shown that the distribution of D/LSB galaxies closely resembles that of bright galaxies, apparently ruling out biased-star-formation models predicting a uniform distribution of D/LSBs. Although bright galaxies outside clusters are somewhat more clustered than the H I-rich D/LSBs, the latters' pairwise peculiar velocity (460 + or - 50 km/sec) is similar to that of the former.

I would like to report on some work that Ed Turner and I have done on groups of galaxies and how groups may be used to obtain useful cosmological information. Of course the classic study of groups of galaxies was done by de Vaucouleurs (1975) who made a catalogue of groups and loose associations of galaxies in the local supercluster. Partly to obtain a larger sample of groups with uniform and well defined statistical properties and partly to obtain a sample of denser groups suitable for virial analysis, Ed Turner and I decided to make a new catalogue of groups of galaxies based on picking the groups as surface density enhancements in the Zwicky catalogue (Turner and Gott 1976) (TGI).

We have recently completed a series of N-body simulations of galaxy clustering in an expanding universe (Aarseth, Gott and Turner 1977). The initial conditions and our results concerning galaxy clustering will be summarized by Sverre Aarseth at this meeting. In this paper I would like to tell about the implications of these models for the value of Ω = 8πGρ0/3H 0 2 (where ρ0 is the present mean density of the universe and H0 = 50 tan s-1 Mpc-1 is Hubble’s constant). In the standard Friedmann models with Λ = 0, Ω > 1 implies that the universe will eventually recollapse while Ω < 1 implies the expansion will continue forever. As discussed in Gott, Gunn, Schramm, and Tinsley (1974), there are a number of theoretical arguments to suggest that even the unseen matter in the universe is clustered the way the galaxies are so that virial mass determinations from groups and clusters and statistical virial theorem methods can provide good estimates of the mean mass density in the universe. We can utilize our N-body simulations to check the accuracy of these techniques.

Axisymmetric systems, having differing amounts of initial angular momentum and containing 2000 stars (mass points) each, are allowed to collapse under their own gravitational attraction. Collapse and violent relaxation are found to lead to the formation of equilibrium structures after only a few free-fall times. The systems contain a sufficient number of mass points so as to be effectively collisionless and the equilibrium structures are consistent with accurate satisfaction of the stationary collisionless Boltzmann equation. Rotating equilibrium models produced in this way resemble elliptical galaxies, with elliptical isophotes. With cosmologically reasonable amounts of initial angular momentum, E0 to E4.5 galaxies can be produced. The equilibrium models show rotation curves in general agreement with that expected from violent relaxation theory. In particular the models show a central region with solid-body rotation. Further out, the systems become differentially rotating. When infall effects are included one can produce models with extended envelopes in good agreement with observed elliptical galaxies. It is suggested that the crucial factor in determining whether an elliptical or a spiral galaxy is formed is whether or not star formation is complete by the time the proto-galaxy reaches its point of maximum collapse.

Photometric monitoring of the gravitational lens system 0957+561A,B in the g and r bands with the Apache Point Observatory (APO) 3.5 m telescope during 1996 shows a sharp g band event in the trailing (B) image light curve at the precise time predicted from the observation of an event during 1995 in the leading (A) image with a delay of 415 days. This success confirms the "short delay," and the lack of any feature at a delay near 540 days rejects the "long delay" for this system, resolving a long-standing controversy. A series of statistical analyses of our light curve data yield a best fit delay of 417 +/- 3 days (95% confidence interval). Recent improvements in the modeling of the lens system (consisting of a galaxy and cluster) allow us to derive a value of the global (at z = 0.36) value of Hubble's constant H_0 using Refsdal's method, a simple and direct distance determination based on securely understood physics and geometry. The result is H_0 = 63 +/- 12 km/s/Mpc (for Omega = 1) where this 95% confidence interval is dominated by remaining lens model uncertainties., Comment: accepted by ApJ, AASTeX 4.0 preprint, 4 PostScript figures

Gravitational lensing by galaxies in a wide variety of cosmological models is considered. For closed models, the lensing depends on the parameter beta(crit). If beta(crit) is greater than zero, a normal lensing case can be obtained with two bright images separated by an angle twice beta(crit) and a third, arbitrarily dim image between them coincident with the position of the lensing galaxy nucleus. As the QSO approaches the antipodal redshift, which can occur in models with large values of the cosmological constant, the cross sections for lensing blow up. An overfocused case where beta(crit) is less than zero can be obtained for a QSO beyond the antipodal redshift. In this case, when a lensing event occurs, only one arbitrarily dim image coincident with the position of the lensing galaxy nucleus is seen. If galaxy rotation curves are always flat or slowly rising, the overfocused case always produces one image.

A quantitative measure of the topology of large-scale structure: the genus of density contours in a smoothed density distribution, is described and applied. For random phase (Gaussian) density fields, the mean genus per unit volume exhibits a universal dependence on threshold density, with a normalizing factor that can be calculated from the power spectrum. If large-scale structure formed from the gravitational instability of small-amplitude density fluctuations, the topology observed today on suitable scales should follow the topology in the initial conditions. The technique is illustrated by applying it to simulations of galaxy clustering in a flat universe dominated by cold dark matter. The technique is also applied to a volume-limited sample of the CfA redshift survey and to a model in which galaxies reside on the surfaces of polyhedral 'bubbles'. The topology of the evolved mass distribution and 'biased' galaxy distribution in the cold dark matter models closely matches the topology of the density fluctuations in the initial conditions. The topology of the observational sample is consistent with the random phase, cold dark matter model.