Correlations in the Spatial Power Spectrum Inferred from Angular Clustering: Methods and Application to APM

We reconsider the inference of spatial power spectra from angular clustering data and show how to include correlations in both the angular correlation function and the spatial power spectrum. Inclusion of the full covariance matrices loosens the constraints on large-scale structure inferred from the APM survey by over a factor of two. We present a new inversion technique based on singular value decomposition that allows one to propagate the covariance matrix on the angular correlation function through to that of the spatial power spectrum and to reconstruct smooth power spectra without underestimating the errors. Within a parameter space of the CDM shape Gamma and the amplitude sigma_8, we find that the angular correlations in the APM survey constrain Gamma to be 0.19-0.37 at 68% confidence when fit to scales larger than k=0.2h Mpc^-1. A downturn in power at k<0.04h Mpc^-1 is significant at only 1-sigma. These results are optimistic as we include only Gaussian statistical errors and neglect any boundary effects.Comment: 37 pages, LaTex, 9 figures. Submitted to Ap

Gravity's smoking gun?

We present a new constraint on the biased galaxy formation picture. Gravitational instability theory predicts that the two-point mass density correlation function, \xi(r), has an inflection point at the separation r=r_0, corresponding to the boundary between the linear and nonlinear regime of clustering, \xi = 1. We show how this feature can be used to constrain the square of the biasing parameter, b^2 = \xi_g / \xi on scales r = r_0, where \xi_g is the galaxy-galaxy correlation function, allowed to differ from \xi. We apply our method to real data: the \xi_g(r), estimated from the APM galaxy survey. Our results suggest that the APM galaxies trace the mass at separations r > 5 Mpc/h, where h is the Hubble constant in units of 100 km/s Mpc. The present results agree with earlier studies, based on comparing higher order correlations in the APM with weakly non-linear perturbation theory. Both approaches constrain the "b" factor to be within 20% of unity. If the existence of the feature we identified in the APM \xi_g(r) -- the inflection point near \xi_g = 1 -- is confirmed by more accurate surveys, we may have discovered gravity's smoking gun: the long awaited ``shoulder'' in \xi, predicted by Gott and Rees 25 years ago.Comment: 4 pages, 2 figures, minor changes and references added, matches version published in ApJ letter

Assumptions of the primordial spectrum and cosmological parameter estimation

The observables of the perturbed universe, CMB anisotropy and large structures, depend on a set of cosmological parameters, as well as, the assumed nature of primordial perturbations. In particular, the shape of the primordial power spectrum (PPS) is, at best, a well motivated assumption. It is known that the assumed functional form of the PPS in cosmological parameter estimation can affect the best fit parameters and their relative confidence limits. In this paper, we demonstrate that a specific assumed form actually drives the best fit parameters into distinct basins of likelihood in the space of cosmological parameters where the likelihood resists improvement via modifications to the PPS. The regions where considerably better likelihoods are obtained allowing free form PPS lie outside these basins. In the absence of a preferred model of inflation, this raises a concern that current cosmological parameters estimates are strongly prejudiced by the assumed form of PPS. Our results strongly motivate approaches toward simultaneous estimation of the cosmological parameters and the shape of the primordial spectrum from upcoming cosmological data. It is equally important for theorists to keep an open mind towards early universe scenarios that produce features in the PPS.Comment: 11 pages, 2 figures, discussions extended, main results unchanged, matches published versio

Cosmic Variance In the Transparency of the Intergalactic Medium After Reionization

Following the completion of cosmic reionization, the mean-free-path of ionizing photons was set by a population of Ly-limit absorbers. As the mean-free-path steadily grew, the intensity of the ionizing background also grew, thus lowering the residual neutral fraction of hydrogen in ionization equilibrium throughout the diffuse intergalactic medium (IGM). Ly-alpha photons provide a sensitive probe for tracing the distribution of this residual hydrogen at the end of reionization. Here we calculate the cosmic variance among different lines-of-sight in the distribution of the mean Ly-alpha optical depths. We find fractional variations in the effective post-reionization optical depth that are of order unity on a scale of ~100 co-moving Mpc, in agreement with observations towards high-redshift quasars. Significant contributions to these variations are provided by the cosmic variance in the density contrast on the scale of the mean-free-path for ionizing photons, and by fluctuations in the ionizing background induced by delayed or enhanced structure formation. Cosmic variance results in a highly asymmetric distribution of transmission through the IGM, with fractional fluctuations in Ly-alpha transmission that ar larger than in Ly-beta transmission.Comment: 7 pages 3 figures. Replaced with version accepted for publication in Ap

The Angular Power Spectrum of EDSGC Galaxies

We determine the angular power spectrum, C_l, of the Edinburgh/Durham Southern Galaxy Catalog (EDSGC) and use this statistic to constrain cosmological parameters. Our methods for determining C_l, and the parameters that affect it are based on those developed for the analysis of cosmic microwave background maps. We expect them to be useful for future surveys. Assuming flat cold dark matter models with a cosmological constant (constrained by COBE/DMR and local cluster abundances), and a scale--independent bias, b, we find good fits to the EDSGC angular power spectrum with 1.11 < b < 2.35 and 0.2 < Omega_m < 0.55 at 95% confidence. These results are not significantly affected by the ``integral constraint'' or extinction by interstellar dust, but may be by our assumption of Gaussianity.Comment: 11 pages, 9 figures, version to appear in Ap

Large Scale Fluctuations in the X-Ray Background

We present an attempt to measure the large angular scale fluctuations in the X-Ray Background (XRB) from the HEAO1-A2 data, expressed in terms of spherical harmonics. We model the harmonic coefficients assuming a power spectrum and an epoch-dependent bias parameter, and using a phenomenological scenario describing the evolution of the X-ray sources. From the few low-order multipoles detected above shot noise, we estimate the power-spectrum normalization on scales intermediate between those explored by local galaxy redshift surveys (~ 100 Mpc) and by the COBE Microwave Background measurements (~ 1000 Mpc). We find that the HEAO1 harmonics are consistent with present epoch rms fluctuations of the X-ray sources bx(0)sigma8 ~ 1-2 in 8 Mpc spheres. Therefore the observed fluctuations in the XRB are roughly as expected from interpolating between the local galaxy surveys and the COBE CMB experiment. We predict that an X-ray all-sky surface brightness survey resolving sources a factor of 10 fainter than HEAO1, may reveal fluctuations to significantly larger angular scales and therefore more strongly constrain the large scale structure of the Universe on scales of hundreds of Mpcs.Comment: 14 pages, 3 Postscript figures, uses aaspp4.sty and psfig. Revised following referee's report. Accepted for publication in Ap

A Comparison of Semi-Analytic and Smoothed Particle Hydrodynamics Galaxy Formation

We compare the statistical properties of galaxies found in two different models of hierarchical galaxy formation: the semi-analytic model of Cole et al. and the smoothed particle hydrodynamics (SPH) simulations of Pearce et al. Using a `stripped-down' version of the semi-analytic model which mimics the resolution of the SPH simulations and excludes physical processes not included in them, we find that the two models produce an ensemble of galaxies with remarkably similar properties, although there are some differences in the gas cooling rates and in the number of galaxies that populate halos of different mass. The full semi-analytic model, which has effectively no resolution limit and includes a treatment of star formation and supernovae feedback, produces somewhat different (but readily understandable) results. Agreement is particularly good for the present-day global fractions of hot gas, cold dense (i.e. galactic) gas and uncollapsed gas, for which the SPH and stripped-down semi-analytic calculations differ by at most 25%. In the most massive halos, the stripped-down semi-analytic model predicts, on the whole, up to 50% less gas in galaxies than is seen in the SPH simulations. The two techniques apportion this cold gas somewhat differently amongst galaxies in a given halo. This difference can be tracked down to the greater cooling rate in massive halos in the SPH simulation compared to the semi-analytic model. (abridged)Comment: 19 pages, 13 figures, to appear in MNRAS. Significantly extended to explore galaxy progenitor distributions and behaviour of models at high redshift

Stochastic Biasing and Weakly Non-linear Evolution of Power Spectrum

Distribution of galaxies may be a biased tracer of the dark matter distribution and the relation between the galaxies and the total mass may be stochastic, non-linear and time-dependent. Since many observations of galaxy clustering will be done at high redshift, the time evolution of non-linear stochastic biasing would play a crucial role for the data analysis of the future sky surveys. In this paper, we develop the weakly non-linear analysis and attempt to clarify the non-linear feature of the stochastic biasing. We compute the one-loop correction of the power spectrum for the total mass, the galaxies and their cross correlation. Assuming the local functional form for the initial galaxy distribution, we investigate the time evolution of the biasing parameter and the correlation coefficient. On large scales, we first find that the time evolution of the biasing parameter could deviate from the linear prediction in presence of the initial skewness. However, the deviation can be reduced when the initial stochasticity exists. Next, we focus on the quasi-linear scales, where the non-linear growth of the total mass becomes important. It is recognized that the scale-dependence of the biasing dynamically appears and the initial stochasticity could affect the time evolution of the scale-dependence. The result is compared with the recent N-body simulation that the scale-dependence of the halo biasing can appear on relatively large scales and the biasing parameter takes the lower value on smaller scales. Qualitatively, our weakly non-linear results can explain this trend if the halo-mass biasing relation has the large scatter at high redshift.Comment: 29pages, 7 postscript figures, submitted to Ap