[en] Baryon acoustic oscillations (BAO) are a powerful probe of the expansion history of the universe, which can tell us about the nature of dark energy. In order to accurately characterize the dark energy equation of state using BAO, we must understand the effects of both nonlinearities and redshift space distortions on the location and shape of the acoustic peak. In a previous paper, we introduced a novel approach to second order perturbation theory in configuration space using the Zel'dovich approximation, and presented a simple result for the first nonlinear term of the correlation function. In this paper, we extend this approach to redshift space. We show how to perform the computation and present the analytic result for the first nonlinear term in the correlation function. Finally, we validate our result through comparison with numerical simulations

[en] Baryon acoustic oscillations are an excellent technique to constrain the properties of dark energy in the universe. In order to accurately characterize the dark energy equation of state, we must understand the effects of both the nonlinearities and redshift space distortions on the location and shape of the acoustic peak. In this paper, we consider these effects using the Zel'dovich approximation and a novel approach to second-order perturbation theory. The second-order term of the Zel'dovich power spectrum is built from convolutions of the linear power spectrum with polynomial kernels in Fourier space, suggesting that the corresponding term of the Zel'dovich correlation function can be written as a sum of quadratic products of a broader class of correlation functions, expressed through simple spherical Bessel transforms of the linear power spectrum. We show how to systematically perform such a computation. We explicitly prove that our result is the Fourier transform of the Zel'dovich power spectrum and compare our expressions to numerical simulations. Finally, we highlight the advantages of writing the nonlinear expansion in configuration space, as this calculation is easily extended to redshift space, and the higher-order terms are mathematically simpler than their Fourier counterparts.

[en] We investigate the quality of associations of astronomical sources from multi-wavelength observations using simulated detections that are realistic in terms of their astrometric accuracy, small-scale clustering properties and selection functions. We present a general method to build such mock catalogs for studying associations, and compare the statistics of cross-identifications based on angular separation and Bayesian probability criteria. In particular, we focus on the highly relevant problem of cross-correlating the ultraviolet Galaxy Evolution Explorer (GALEX) and optical Sloan Digital Sky Survey (SDSS) surveys. Using refined simulations of the relevant catalogs, we find that the probability thresholds yield lower contamination of false associations, and are more efficient than angular separation. Our study presents a set of recommended criteria to construct reliable cross-match catalogs between SDSS and GALEX with minimal artifacts.

[en] We present the ORIGAMI method of identifying structures, particularly halos, in cosmological N-body simulations. Structure formation can be thought of as the folding of an initially flat three-dimensional manifold in six-dimensional phase space. ORIGAMI finds the outer folds that delineate these structures. Halo particles are identified as those that have undergone shell-crossing along three orthogonal axes, providing a dynamical definition of halo regions that is independent of density. ORIGAMI also identifies other morphological structures: particles that have undergone shell-crossing along 2, 1, or 0 orthogonal axes correspond to filaments, walls, and voids, respectively. We compare this method to a standard friends-of-friends halo-finding algorithm and find that ORIGAMI halos are somewhat larger, more diffuse, and less spherical, though the global properties of ORIGAMI halos are in good agreement with other modern halo-finding algorithms.

[en] We investigate the use of a logarithmic density variable in estimating the Lagrangian displacement field motivated by the success of a logarithmic transformation in restoring information to the matter power spectrum. The logarithmic relation is an extension of the linear relation, motivated by the continuity equation, in which the density field is assumed to be proportional to the divergence of the displacement field; we compare the linear and logarithmic relations by measuring both of these fields directly in a cosmological N-body simulation. The relative success of the logarithmic and linear relations depends on the scale at which the density field is smoothed. Thus we explore several ways of measuring the density field, including Cloud-In-Cell smoothing, adaptive smoothing, and the (scale-independent) Delaunay tessellation, and we use both a Fourier-space and a geometrical tessellation approach to measuring the divergence. We find that the relation between the divergence of the displacement field and the density is significantly tighter and straighter with a logarithmic density variable, especially at low redshifts and for very small (∼2 h^–1 Mpc) smoothing scales. We find that the grid-based methods are more reliable than the tessellation-based method of calculating both the density and the divergence fields, though in both cases the logarithmic relation works better in the appropriate regime, which corresponds to nonlinear scales for the grid-based methods and low densities for the tessellation-based method.

[en] We show that redshift-space distortions of galaxy correlations have a strong effect on correlation functions with distinct, localized features, like the signature of the baryon acoustic oscillations (BAO). Near the line of sight, the features become sharper as a result of redshift-space distortions. We demonstrate this effect by measuring the correlation function in Gaussian simulations and the Millennium simulation. We also analyze the SDSS DR7 main-galaxy sample, splitting the sample into slices 2.⁰5 on the sky in various rotations. Measuring two-dimensional correlation functions in each slice, we do see a sharp bump along the line of sight. Using Mexican-hat wavelets, we localize it to (110 ± 10) h^-1 Mpc. Averaging only along the line of sight, we estimate its significance at a particular wavelet scale and location at 2.2σ. In a flat angular weighting in the (π, r_p ) coordinate system, the noise level is suppressed, pushing the bump's significance to 4σ. We estimate that there is about a 0.2% chance of getting such a signal anywhere in the vicinity of the BAO scale from a power spectrum lacking a BAO feature. However, these estimates of the significances make some use of idealized Gaussian simulations, and thus are likely a bit optimistic.

[en] We present a method to extract the redshift-space distortion β parameter in configuration space with a minimal set of cosmological assumptions. We show that a novel combination of the observed monopole and quadrupole correlation functions can remove efficiently the impact of mild nonlinearities and redshift errors. The method offers a series of convenient properties: it does not depend on the theoretical linear correlation function, the mean galaxy density is irrelevant, only convolutions are used, and there is no explicit dependence on linear bias. Analyses based on dark matter N-body simulations and Fisher matrix demonstrate that errors of a few percent on β are possible with a full-sky, 1 (h ^–1 Gpc)³ survey centered at a redshift of unity and with negligible shot noise. We also find a baryonic feature in the normalized quadrupole in configuration space that should complicate the extraction of the growth parameter from the linear theory asymptote, but that does not have a major impact on our method.

[en] We present the SpineWeb framework for the topological analysis of the Cosmic Web and the identification of its walls, filaments, and cluster nodes. Based on the watershed segmentation of the cosmic density field, the SpineWeb method invokes the local adjacency properties of the boundaries between the watershed basins to trace the critical points in the density field and the separatrices defined by them. The separatrices are classified into walls and the spine, the network of filaments and nodes in the matter distribution. Testing the method with a heuristic Voronoi model yields outstanding results. Following the discussion of the test results, we apply the SpineWeb method to a set of cosmological N-body simulations. The latter illustrates the potential for studying the structure and dynamics of the Cosmic Web.

[en] We find that nonlinearities in the dark matter power spectrum are dramatically smaller if the density field first undergoes a logarithmic mapping. In the Millennium simulation, this procedure gives a power spectrum with a shape hardly departing from the linear power spectrum for k ∼< 1 h Mpc^-1 at all redshifts. Also, this procedure unveils pristine Fisher information on a range of scales reaching a factor of 2-3 smaller than in the standard power spectrum, yielding 10 times more cumulative signal to noise at z = 0.

[en] We find that, even in the presence of discreteness noise, a Gaussianizing transform (producing a more Gaussian one-point distribution) reduces nonlinearities in the power spectra of cosmological matter and galaxy density fields, in many cases drastically. Although Gaussianization does increase the effective shot noise, it also increases the power spectrum's fidelity to the linear power spectrum on scales where the shot noise is negligible. Gaussianizing also increases the Fisher information in the power spectrum in all cases and resolutions, although the gains are smaller in redshift space than in real space. We also find that the gain in cumulative Fisher information from Gaussianizing peaks at a particular grid resolution depends on the sampling level.