A New Statistic for Analyzing Baryon Acoustic Oscillations

Abstract

We introduce a new statistic ω ℓ (r s ) for measuring and analyzing large-scale structure and particularly the baryon acoustic oscillations. ω ℓ (r s ) 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, ω ℓ (r s ) 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 of data. We measure the shift in the acoustic peak due to nonlinear effects using the monopole ω 0 (r s ) 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. We therefore expect that distance measurements obtained from ω 0 (r s ) and P (k) will be consistent with each other. We also show that it is possible to extract the same amount of acoustic information by fitting over a finite range using either ω 0 (r s ) or P (k) derived from equal volume surveys. Subject headings: distance scale -cosmological parameters -large-scale structure of universecosmology: theory

Observational probes of cosmic acceleration

“…A value α = 1 indicates that the acoustic scale of the linear-theory model is incorrect or that the distance scale assumed in measuring the galaxy clustering was wrong. Simple alterations of this prescription can be made for fitting the correlation function or mixed-space ω or wavelet statistics (Xu et al, 2010;Arnalte-Mur et al, 2012). This appproach thus allows one to fit for the scale of a standard ruler without having to recompute a full predicted power spectrum at every point in parameter space.…”

Quantifying the colour-dependent stochasticity of large-scale structure

“…However, while correlation functions provide a useful measurement of the stochasticity parameter, it is possible to extend this analysis by using a statistic that is both more computationally efficient and less susceptible to poorly constrained or measured fluctuations from both small and large scales. Such a statistic is provided by Xu et al (2010), who define an ω statistic whose monopole term is:…”

“…where W is a smooth, compensated filter, chosen by Xu et al (2010) (see also Padmanabhan et al 2007) to be:…”

“…Now, following Xu et al (2010), if we define a simple pair-count estimator of the correlation function as:…”

“…The key to discerning the presence of stochasticity, then, is the measurement of the correlation coefficient. We use pair counting to calculate both the traditional correlation function statistics as well as the more recent ω statistic of Xu et al (2010) using the BOSS CMASS sample of galaxies from SDSS-III DR12; we then calculate a correlation coefficient for each statistic. Our focus is on intermediate scales, roughly 20 r 100 h −1 Mpc, which can be compared to the results of previous analyses at smaller scales using similar statistical methods (e.g., Zehavi et al 2005).…”