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The Sloan Digital Sky Survey (SDSS) surveyed 14,555 square degrees, and delivered over a trillion pixels of imaging data. We present a study of galaxy clustering using 900,000 luminous galaxies with photometric redshifts, spanning between $z=0.45$ and $z=0.65$, constructed from the SDSS using methods described in Ross et al. (2011). This data-set spans 11,000 square degrees and probes a volume of $3h^{-3} \rm{Gpc}^3$, making it the largest volume ever used for galaxy clustering measurements. We present a novel treatment of the observational systematics and its applications to the clustering signals from the data set. In this paper, we measure the angular clustering using an optimal quadratic estimator at 4 redshift slices with an accuracy of ~15% with bin size of delta_l = 10 on scales of the Baryon Acoustic Oscillations (BAO) (at l~40-400). We derive cosmological constraints using the full-shape of the power-spectra. For a flat Lambda CDM model, when combined with Cosmic Microwave Background Wilkinson Microwave Anisotropy Probe 7 (WMAP7) and H_0 constraints from 600 Cepheids observed by HST, we find \Omega_\Lambda = 0.73 +/- 0.019 and H_0 to be 70.5 +/- 1.6 km/s/Mpc. For an open Lambda CDM model, when combined with WMAP7 + HST, we find $\Omega_K = 0.0035 +/- 0.0054, improved over WMAP7+HST alone by 40%. For a wCDM model, when combined with WMAP7+HST+SN, we find w = -1.071 +/- 0.078, and H_0 to be 71.3 +/- 1.7 km/s/Mpc, which is competitive with the latest large scale structure constraints from large spectroscopic surveys such as SDSS Data Release 7 (DR7) (Reid et al. 2010, Percival et al. 2010, Montesano et al. 2011) and WiggleZ (Blake et al. 2011). The SDSS-III Data Release 8 (SDSS-III DR8) Angular Clustering Data allows a wide range of investigations into the cosmological model, cosmic expansion (via BAO), Gaussianity of initial conditions and neutrino masses. (abridged), Comment: Two other companion papers on arxiv today: Seo et al. (2012) and de Putter et al. (2012)

The power spectrum from the Southern Sky Redshift Survey and the CfA samples are measured in order to explore the amplitude of fluctuation in the galaxy density. At lambda of less than or equal to 30/h Mpc the observed power spectrum is quite consistent with the standard CDM model. At larger scales the data indicate an excess of power over the standard CDM model. The observed power spectrum from these optical galaxy samples is in good agreement with that drawn from the sparsely sampled IRAS galaxies. The shape of the power spectrum is also studied by examining the relation between the genus per unit volume and the smoothing length. It is found that, over Gaussian smoothing scales from 6 to 14/h Mpc, the power spectrum has a slope of about -1. The topology of the galaxy density field is studied by measuring the shift of the genus curve from the Gaussian case. Over all smoothing scales studied, the observed genus curves are consistent with a random phase distribution of the galaxy density field, as predicted by the inflationary scenarios.

Results of an investigation of the topology of large-scale structure in two observed slices of the universe are presented. Both slices pass through the Coma cluster and their depths are 100 and 230/h Mpc. The present topology study shows that the largest void in the CfA slice is divided into two smaller voids by a statistically significant line of galaxies. The topology of toy models like the white noise and bubble models is shown to be inconsistent with that of the observed slices. A large N-body simulation was made of the biased cloud dark matter model and the slices are simulated by matching them in selection functions and boundary conditions. The genus curves for these simulated slices are spongelike and have a small shift in the direction of a meatball topology like those of observed slices.

A 2D algorithm is applied to observed sky maps and numerical simulations. It is found that when topology is studied on smoothing scales larger than the correlation length, the topology is approximately in agreement with the random phase formula for the 2D genus-threshold density relation, G2(nu) varies as nu(e) exp-nu-squared/2. Some samples show small 'meatball shifts' similar to those seen in corresponding 3D observational samples and similar to those produced by biasing in cold dark matter simulations. The observational results are thus consistent with the standard model in which the structure in the universe today has grown from small fluctuations caused by random quantum noise in the early universe.

Results are reported of a 3D study tracing the three-point correlation function of Abell clusters and of a comparison of this with the biased cold dark matter (CDM) simulations of Park (1990). For the observations, the maximum likelihood fits are Z11 = 0.85 and Q111 = 0.1, in excellent agreement with the result of the 2D study of Toth et al. (1989). For Park's simulation, maximum likelihood fits of Q11 = 0.9 and Q111 = 0.0 are found, which is in excellent agreement with the observational result. It is concluded that the standard biased CDM gravitational instability model reproduces the observed form of the three-point correlation functions for Abell clusters remarkably well. The number of triples as a function of the sides of triangles for Abell clusters, and the number of triples as a function of the sides of triangles for clusters in Park's simulation are illustrated on graphs.

The nonlinear effects of statistical biasing and gravitational evolution on the genus are studied. The biased galaxy subset is picked for the first time by actually identifying galaxy-sized peaks above a fixed threshold in the initial conditions, and their subsequent evolution is followed. It is found that in the standard cold dark matter (CDM) model the statistical biasing in the locations of galaxies produces asymmetry in the genus curve and coupling with gravitational evolution gives rise to a shift in the genus curve to the left in moderately nonlinear regimes. Gravitational evolution alone reduces the amplitude of the genus curve due to strong phase correlations in the density field and also produces asymmetry in the curve. Results on the genus of the mass density field for both CDM and hot dark matter models are consistent with previous work by Melott, Weinberg, and Gott (1987).

Hawking1,2 has shown that event horizons produce thermal radiation. I propose here a new cosmological model which has an early event horizon and in which the observed3 cosmic microwave background radiation is Hawking radiation. The model starts with de Sitter space—a space-time of constant curvature which is a solution to Einstein's vacuum field equations with a positive cosmological constant. Associated with an event E in de Sitter space there is a quantum barrier penetration tunnelling which leads to an open, negatively curved (k = −1) cosmology. This has an early exponential expansion phase but turns into a standard big-bang solution at late times. The geometry and quantum mechanical treatment within the future light cone of E are similar to that found in the Brout, Englert and Spindel (BES) theory4,5. This model has the following advantages: (1) It has no singularities. (2) The observed isotropy of the cosmic microwave background is explained because the different regions we observe have all been in causal contact. (3) The temperature at early epochs (T0 ∼ 1019 Ge V) is high enough to allow grand unified theories (GUTs) to produce the observed baryon excess from an initial thermal distribution through CP violations6,7. (4) T0 is correct to make the BES scenario work. (5) The early exponential expansion phase can naturally account for the observed large number n0 ∼ 1088 of particles within a volume a3 (where a is the radius of curvature) and the Guth8 flatness problem. (6) It predicts that our Universe is an open k = −1, Ω

A Schwarzschild-like metric is presented for the region around a singularity associated with a spacelike world-line (tachyon singularity). Kruskal-type extensions of the metric are provided. The form of the metric suggests a qualitative explanation of tachyon motion (v>c) that does not involve transport of energy or information at speeds greater than the velocity of light. The extended metrics show both normal and time-reversed gravitational Cerenkov cones of high space curvature. The solutions correspond to half-advanced, half-retarded fields in accord with the Wheeler-Feynman absorber theory.

Galactic evolution is reviewed. Topics covered include: observations of galaxies; formation of galaxies from small inhomogenieties in the early universe; the collapse picture of galaxy formation; dissipation models for ellipticals; dissipationless collapse models for elliptical galaxies; and other models; (GHT)

We describe and apply a quantitative measure of the topology of large scale structure: the genus of density contours in a smoothed density distribution. 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. The topology of the observational sample is consistent with the random phase, cold dark matter model.

A newly discovered lens candidate, QSO 1146 + 111B,C, is discussed which appears to consist of two images of equal brightness of a quasar at redshift 1.01 separated by 2.6 arcmin. If this is produced by a cosmic string, its mass per unit length is about 4.0 x 10 to the 23rd g/cm or more. This value is large enough to be interesting for string-assisted galaxy formation and near the upper limits implied by the isotropy of the cosmic microwave background and constraints on gravitational radiation.

A recently developed algorithm for quantitatively measuring the topology of large-scale structures in the universe was applied to a number of important observational data sets. The data sets included an Abell (1958) cluster sample out to Vmax = 22,600 km/sec, the Giovanelli and Haynes (1985) sample out to Vmax = 11,800 km/sec, the CfA sample out to Vmax = 5000 km/sec, the Thuan and Schneider (1988) dwarf sample out to Vmax = 3000 km/sec, and the Tully (1987) sample out to Vmax = 3000 km/sec. It was found that, when the topology is studied on smoothing scales significantly larger than the correlation length (i.e., smoothing length, lambda, not below 1200 km/sec), the topology is spongelike and is consistent with the standard model in which the structure seen today has grown from small fluctuations caused by random noise in the early universe. When the topology is studied on the scale of lambda of about 600 km/sec, a small shift is observed in the genus curve in the direction of a 'meatball' topology.

The angular momentum of galaxies in the Local Group is analyzed in terms of the tidal interaction picture. The protogalaxies are originally frozen in the Hubble for at recombination and possess a quadrupole moment of order unity. They gain angular momentum by tidally interacting with their neighbors. We show that there are a number of geometrical constraints on the orientations of binary galaxies like the Galaxy and M31, if the spins of the two galaxies are produced by mutual tidal interactions. Two solutions satisfying all the observational constraints for the Galaxy--M31 system are possible if it is considered as an isolated system: (1) The original position of M31 was l/sup II/=152/sup 0/, b/sup II/=0; the orbits of the two galaxies are nearly radial (any orbital angular momentum must be supplied by external galaxies), and M/Lapprox.100 for the Local Group. (2) There was a large motion of the line of sight between the two galaxies, the original position of M31 was l/sup II/=332/sup 0/, b/sup II/=0, and M/Lapprox.240 for the Local Group. No external torques are needed. The observed velocity of the Sun relative to the center of mass of the Local Group slightly favors Solution 1 over Solution 2.We showmore » that the effect of external galaxies in the Maffei, Sculptor, M81, and N5128 groups is likely to be nonnegligible. The most likely solution is probably one in which a significant fraction of the Galaxy's angular momentum was produced by M31 (which explains the fact that they lie nearly in each other's planes), with the remaining small fraction produced by more distant galaxies.« less

It has been suggested recently that the topology of a distribution of galaxies can be characterized by the mean Gaussian curvature per unit volume of surfaces of constant density. An expression is derived which relates the mean curvature of isodensity surfaces to the power spectrum of density fluctuations in the linear regime of Gaussian fluctuations with random phases. The result may be compared to real galaxy catalogs if the galaxy density is smoothed over scales larger than a correlation length. The implications of the result for understanding the large-scale structure of the universe are discussed.

We describe and apply a quantitative measure of the topology of large scale structure: the genus of density contours in a smoothed density distribution. 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. The topology of the observational sample is consistent with the random phase, cold dark matter model.

The key factor distinguishing an elliptical from a spiral galaxy is proposed to be the amount of gas left over at the point of maximum collapse of the protogalaxy. The gas left depends on the ratio of the star formation time scale tau/sub s/ to the collapse time of the protogalaxy tau/sub c/. Observed properties of ellipticals imply that they formed out of relatively larger density perturbations at recombination, giving them a relatively small tau/sub s//tau/sub c/ (if a rho/sup 2/ star formation law is adopted); and thus they are expected to essentially complete their star formation by the time of maximum collapse. Observations of spiral galaxies and our Galaxy imply that they formed out of less dense density perturbations giving them a larger tau/sub s//tau/sub c/. In the latter, star formation is not nearly completed by the time of maximum collapse. A detailed numerical model including both stars and gas was used to follow the collapse of a spiral galaxy. The gas and stars collapse together until they hit the plane, whereupon the gas forms a disk and the stars relax to form a spheroidal halo. The competing effects of dissipation and turbulent viscosity are analyzed using a modelmore » of cloud formation in the early protogalaxy. The gas disk does not hit the plane at its equilibrium position, and both radial and nonaxisymmetric oscillations of the disk are expected before equilibrium is reached. ''Zeroth'' order Maclaurin spheroid models for equilibrium spiral and elliptical galaxies are presented, which relate many useful galactic parameters to the original size and angular momentum. Monte Carlo calculations suggest that the tidal interaction picture of Peebles is capable of explaining the angular momentum of our Galaxy and the observed distribution of ellipticities in elliptical galaxies. This also explains why ellipticals are found preferentially in large clusters: because protogalaxies arising from larger initial density fluctuations cluster more easily. (AIP)« less

In a recent series of papers, an algorithm was developed for quantitatively measuring the topology of the large-scale structure of the universe and this algorithm was applied to numerical models and to three-dimensional observational data sets. In this paper, it is shown that topological information can be derived from a two-dimensional cross section of a density field, and analytic expressions are given for a Gaussian random field. The application of a two-dimensional numerical algorithm for measuring topology to cross sections of three-dimensional models is demonstrated.

Simple collapse and violent relaxation models produce sharply cut off envelopes with ϱ(r) ∝ r–4, whereas actual elliptical galaxies have more extended envelopes approximately given by ϱ(r) ∝ r–3 as implied by Hubble's Law. Numerical models are presented, showing that when cosmological infall effects are included, galaxies are produced with more extended envelopes having a ϱ(r) ∝ r–2.8 dependence in excellent agreement with Hubble's Law. We have also computed a realistic rotating model of an E5 galaxy which includes infall effects and where the angular momentum of the galaxy is gained through tidal interactions with neighboring protogalaxies. The envelope displays a Hubble dependence but at great distances shows a cutoff due to the tidal effects. The model is compared to the E5 galaxy NGC 4697 and provides an outstandingly good fit to the observations. Except for simple scaling, this excellent fit is produced without the use of any free fitting parameters.

N-body simulations are used to model galaxy clustering in an expanding universe. The starting point of an N-body simulation corresponds to the epoch of protogalaxy formation when the protogalaxies become density enhancements of order unity and begin to behave like point masses. This typically occurs at a redshift of 10--30. As the models expand, the galaxies cluster; the result is remarkably similar to the observed clustering. In addition to having reasonable covariance functions the models show large empty regions containing no bright galaxies similar to those observed by Gregory and Thompson. By comparing the amplitudes of the covariance functions in the models with the observed value, we estimate the redshift of protogalaxy formation and therefore the typical galaxy collapse time T/sub c/. For H/sub 0/=50 km s/sup -1/ Mpc/sup -1/, T/sub c/approx. =2 x 10/sup 9/ yr for ..cap omega..=1, and T/sub c/approx. =3 x 10/sup 9/ yr for ..cap omega..=0.1, each estimate being uncertain by a factor of about 2.

Paczynski1 and Turner et al.2 have suggested that the extraordinary double quasar 1146 + 111B,C found by Hazard et al.3 is a possible gravitational lens. The hypothetic lensing object is unknown. If the lensing object is a cluster of galaxies4 or a cosmic string5,6, it may cause observable effects in the cosmic background radiation. At millimetre wavelengths, a cluster would be expected to cause a reduction in the temperature of the background in the vicinity of the cluster as the result of the Zeldovich–Sunyaev effect. The area of sky on one side of a cosmic string would have a different radiation temperature from that on the other side. If either of these expected signatures were seen in the cosmic background, it would be strong evidence in favour of that hypothesis. We have searched for microwave background inhomogeneities near 1146 + 111B,C. An east–west strip of sky, 16 arc min long and centred on the point between the quasars, was observed with a beam of diameter 105 arc s at 3 mm wavelength. Our observations show only noise with an r.m.s. noise level of 0.0010 K. These observations set limits on the properties of the lensing object if it is a cosmic string or a cluster of galaxies, and we do not confirm either hypothesis.

The Shane-Wirtanen galaxy count catalog gives the strong visual impression of large-scale linear or filamentary features in the galaxy distribution. Computer simulations of hierarchical galaxy clustering constructed to have two-, three-, and four-point autocorrelation functions like those observed do not have such an appearance. A simple and well-defined algorithm which maps and quantifies filamentary structure is developed. It appears to be successful in identifying those (and only those) filaments which the eye picks out in the Shane-Wirtanen catalog and thus provides an objective tool for studying these structures. A catalog and map of the most prominent Shane-Wirtanen filaments is given. Application of the algorithm to a computer simulation of hierarchical galaxy clustering reveals a set of visually less conspicuous filaments with statistical properties strikingly similar to those of the Shane-Wirtanen filaments in many respects. Long (> or approx. =10/sup 0/) filaments do occur significantly more frequently in the data than in the simulations and the real filaments do occur at slightly higher relative contrast than the simulation filaments. These facts may explain their greater visual impact. It is not yet clear whether the Shane-Wirtanen filaments can be understood in terms of simple hierarchical galaxy clustering models.

The covariance functions of N=1000--4000 body simulations of galaxy clustering, started with a variety of initial conditions, are power laws in the nonlinear regime with slopes ..gamma.. centered on 1.9 and a range of +- 0.15. These results are in agreement with the observed power-law form which has ..gamma..=1.8. This result strongly supports the gravitational instability picture in which galaxies form first and then cluster via mutual gravitational interactions. Our models show strong evidence of two-body relaxation on small scales. In models with two mass groups, the galaxies with twice the mass have covariance functions with approximately twice the amplitude. This effect can be understood in terms of cosmological infall, as can the covariance functions of binary galaxies, early-type galaxies, and clusters. Similar infall arguments may explain the form of the three- and four-point correlation functions. The slope of the covariance function appears to depend both on ..cap omega.. and n (the index of the initial density fluctuation spectrum). Models with (..cap omega..=1, n=-1) and (..cap omega..=0.1, n=0) appear to be ruled out at the 2 sigma level. Models with (..cap omega..=1, n=0) and (..cap omega..=0.1, n=-1) have covariance functions which are indistinguishable from one another and consistent with themore » observations. Thus it appears that the value of ..cap omega.. cannot be determined solely from the observed covariance function, contrary to some earlier suggestions.« less

The tidal interaction picture is applied to elliptical and spiral galaxies. It gives the correct amount of angular momentum for our Galaxy. Monte Carlo calculations are used to predict the distribution of total angular momenta for galaxies of a given mass (or luminosity). The observational data are in good agreement with the predicted individual distribution shapes and also with systematic properties with mass. The data are consistent with a dissipationless collapse for elliptical galaxies. The tidal theory predicts a distribution of relative sizes for elliptical galaxies at a given absolute magnitude in agreement with Fish's observations, but for spiral galaxies predicts too many high-surface-brightness small-scale-length disks. For tidal interactions to produce the correct amount of angular momentum, most of the mass in the universe must be contributed by galaxies and their halos and not by some smooth diffuse component.

Exact interior and exterior solutions to Einstein's field equations are derived for vacuum strings. The exterior solution for a uniform density vacuum string corresponds to a conical space while the interior solution is that of a spherical cap. For Mu equals 0-1/4 the external metric is ds-squared = -dt-squared + dr-squared + (1-4 Mu)-squared r-squared dphi-squared + dz-squared, where Mu is the mass per unit length in the string in Planck masses per Planck length. A maximum mass per unit length for a string is 6.73 x 10 to the 27th g/cm. It is shown that strings cause temperature fluctuations in the cosmic microwave background and produce equal brightness double QSO images separated by up to several minutes of arc. Formulae for lensing probabilities, image splittings, and time delays are derived for strings in a realistic cosmological setting. String searches using ST, the VLA, and the COBE satellite are discussed.

An analytical calculation is presented which determines the probability that the light from a distant quasar can be lensed by objects in a different redshift range. Three types of information are used to make the calculation: (1) the physical properties of the intervening scattering lenses; (2) the intrinsic properties of the quasars and (3) the selection procedures by which the quasar samples are acquired. A series of differential equations is given in which the probability is derived, and a number of recommendations are offered with respect to VLA and Space Telescope observations of quasars lensed in this way.

Two of the previously presented N-body simulations of galaxy clustering are analyzed in terms of the detailed dynamical and morphological properties of their binaries, groups, and clusters. The analysis is closely analogous to the studies of groups among bright Zwicky catalog galaxies by Turner and Gott. The simulated groups, particularly those in the ..cap omega../sub 0/=0.1 and n= -1 model, resemble the observed groups. The models provide complete (position, velocity, mass) information on group and field ''galaxies'' identified using the Turner and Gott surface density enhancement procedure. These data are used to assess the validity of the membership assignments, the influence of non-Hubble motions on descriptions of the clustering, the accuracy and stability of various M/L estimators, the significance of field galaxies, and the statistical properties of binary systems.