Markov-chain reconstruction of the 2dF Galaxy Redshift Survey real-space power spectrum

Abstract

The real-space power spectrum of L* galaxies measured from the 2dF Galaxy Redshift Survey (2dFGRS) is presented. Markov-Chain Monte-Carlo (MCMC) sampling was used to fit radial and angular modes resulting from a Spherical Harmonics decomposition of the 2dFGRS overdensity field (described in Percival et al. 2004) with 16 real-space power spectrum values and linear redshift-space distortion parameter β(L*,0). The recovered marginalised band-powers are compared to previous estimates of galaxy power spectra. Additionally, we provide a simple model for the 17 dimensional likelihood hyper-surface in order to allow the likelihood to be quickly estimated given a set of model band-powers and β(L*,0). The likelihood surface is not well approximated by a multi-variate Gaussian distribution with model-independent covariances. Instead, a model is presented in which the distribution of each band-power has a Gaussian distribution in a combination of the band-power and its logarithm. The relative contribution of each component was determined by fitting the MCMC output. Using these distributions, we demonstrate how the likelihood of a given cosmological model can be quickly and accurately estimated, and use a simple set of models to compare estimated likelihoods with likelihoods calculated using the full Spherical Harmonics procedure. All of the data are made publically available (from http://www.roe.ac.uk/~wjp/, enabling the Spherical Harmonics decomposition of the 2dFGRS of Percival et al. (2004) to be easily used as a cosmological constraint.