Galaxy 2-Point Covariance Matrix Estimation for Next Generation Surveys

Abstract

We perform a detailed analysis of the covariance matrix of the spherically averaged galaxy power spectrum and present a new, practical method for estimating this within an arbitrary survey without the need for running mock galaxy simulations that cover the full survey volume. The method uses theoretical arguments to modify the covariance matrix measured from a set of small-volume cubic galaxy simulations, which are computationally cheap to produce compared to larger simulations and match the measured small-scale galaxy clustering more accurately than is possible using theoretical modelling. We include prescriptions to analytically account for the window function of the survey, which convolves the measured covariance matrix in a non-trivial way. We also present a new method to include the effects of supersample covariance and modes outside the small simulation volume which requires no additional simulations and still allows us to scale the covariance matrix. As validation, we compare the covariance matrix estimated using our new method to that from a brute force calculation using 500 simulations originally created for analysis of the Sloan Digital Sky Survey Main Galaxy Sample (SDSS-MGS). We find excellent agreement on all scales of interest for large scale structure analysis, including those dominated by the effects of the survey window, and on scales where theoretical models of the clustering normally break-down, but the new method produces a covariance matrix with significantly better signal-to-noise. Although only formally correct in real-space, we also discuss how our method can be extended to incorporate the effects of Redshift Space Distortions.