Power spectrum for the small-scale Universe

The first objects to arise in a cold dark matter universe present a daunting challenge for models of structure formation. In the ultra small-scale limit, CDM structures form nearly simultaneously across a wide range of scales. Hierarchical clustering no longer provides a guiding principle for theoretical analyses and the computation time required to carry out credible simulations becomes prohibitively high. To gain insight into this problem, we perform high-resolution (N=720^3 - 1584^3) simulations of an Einstein-de Sitter cosmology where the initial power spectrum is P(k) propto k^n, with -2.5 < n < -1. Self-similar scaling is established for n=-1 and n=-2 more convincingly than in previous, lower-resolution simulations and for the first time, self-similar scaling is established for an n=-2.25 simulation. However, finite box-size effects induce departures from self-similar scaling in our n=-2.5 simulation. We compare our results with the predictions for the power spectrum from (one-loop) perturbation theory and demonstrate that the renormalization group approach suggested by McDonald improves perturbation theory's ability to predict the power spectrum in the quasilinear regime. In the nonlinear regime, our power spectra differ significantly from the widely used fitting formulae of Peacock & Dodds and Smith et al. and a new fitting formula is presented. Implications of our results for the stable clustering hypothesis vs. halo model debate are discussed. Our power spectra are inconsistent with predictions of the stable clustering hypothesis in the high-k limit and lend credence to the halo model. Nevertheless, the fitting formula advocated in this paper is purely empirical and not derived from a specific formulation of the halo model.Comment: 30 pages including 10 figures; accepted for publication in MNRA

A New Statistic for Analyzing Baryon Acoustic Oscillations

We introduce a new statistic omega_l for measuring and analyzing large-scale structure and particularly the baryon acoustic oscillations. omega_l is a band-filtered, configuration space statistic that is easily implemented and has advantages over the traditional power spectrum and correlation function estimators. Unlike these estimators, omega_l can localize most of the acoustic information into a single dip at the acoustic scale while also avoiding sensitivity to the poorly constrained large scale power (i.e., the integral constraint) through the use of a localized and compensated filter. It is also sensitive to anisotropic clustering through pair counting and does not require any binning. We measure the shift in the acoustic peak due to nonlinear effects using the monopole omega_0 derived from subsampled dark matter catalogues as well as from mock galaxy catalogues created via halo occupation distribution (HOD) modeling. All of these are drawn from 44 realizations of 1024^3 particle dark matter simulations in a 1h^{-1}Gpc box at z=1. We compare these shifts with those obtained from the power spectrum and conclude that the results agree. This indicates that any distance measurements obtained from omega_0 and P(k) will be consistent with each other. We also show that it is possible to extract the same amount of acoustic information using either omega_0 or P(k) from equal volume surveys.Comment: 12 pages, 7 figures. ApJ accepted. Edit: Now updated with final accepted versio

Taking advantage of photometric galaxy catalogues to determine the halo occupation distribution

Context. Halo occupation distribution (HOD) is a powerful statistic that allows the study of several aspects of the matter distribution in the Universe, such as evaluating semi-analytic models of galaxy formation or imposing constraints on cosmological models. Consequently, it is important to have a reliable method for estimating this statistic, taking full advantage of the available information on current and future galaxy surveys. Aims. The main goal of this project is to combine photometric and spectroscopic information using a discount method of background galaxies in order to extend the range of absolute magnitudes and to increase the upper limit of masses in which the HOD is estimated. We also evaluate the proposed method and apply it to estimating the HOD on the Sloan Digital Sky Survey Data Release 7 (SDSS DR7) galaxy survey. Methods. We propose the background subtraction technique to mel information provided by spectroscopic galaxy groups and photometric survey of galaxies. To evaluate the feasibility of the method, we implement the proposed technique on a mock catalogue built from a semi-analytic model of galaxy formation. Furthermore, we apply the method to the SDSS DR7 using a galaxy group catalogue taken from spectroscopic version and the corresponding photometric galaxy survey. Results. We demonstrated the validity of the method using the mock catalogue. We applied this technique to obtain the SDSS DR7 HOD in absolute magnitudes ranging from M = −21.5 to M = −16.0 and masses up to ≃1015 M⊙ throughout this range. On the brighter extreme, we found that our results are in excellent agreement with those obtained in previous works