Reconstructing Nonlinear Stochastic Bias from Velocity Space Distortions

Abstract

We propose a strategy to measure the dark matter power spectrum using minimal assumptions about the galaxy distribution and the galaxy-dark matter cross-correlations. We argue that on large scales the central limit theorem generically assures Gaussianity of each smoothed density field, but not coherence. Asymptotically, the only surviving parameters on a given scale are galaxy variance σ, bias b = Ω0.6/β, and the galaxy-dark matter cross-correlation coefficient r. These can all be determined by measuring the quadrupole and hexadecapole velocity distortions in the power spectrum. Measuring them simultaneously may restore consistency between all β-determinations independent of galaxy type. The leading deviations from Gaussianity are conveniently parameterized by an Edgeworth expansion. In the mildly nonlinear regime, two additional parameters describe the full picture: the skewness parameter s and nonlinear bias b2. They can both be determined from the measured skewness combined with second-order perturbation theory or from an N-body simulation. By measuring the redshift distortion of the skewness, one can measure the density parameter Ω with minimal assumptions about the galaxy formation process. This formalism also provides a convenient parameterization to quantify statistical galaxy formation properties.