Reconstructing Nonlinear Stochastic Bias from Velocity Space Distortions

We propose a strategy to measure the dark matter power spectrum using minimalassumptions about the galaxy distribution and the galaxy-dark mattercross-correlations. We argue that on large scales the central limit theoremgenerically assures Gaussianity of each smoothed density field, but notcoherence. Asymptotically, the only surviving parameters on a given scale aregalaxy variance $\sigma$, bias $b=\Omega^{.6}/\beta$ and the galaxy-dark mattercorrelation coefficient $r$. These can all be determined by measuring thequadrupole and octupole velocity distortions in the power spectrum. Measuringthem simultaneously may restore consistency between all $\beta$ determinationsindependent of galaxy type. The leading deviations from Gaussianity are conveniently parameterized by anEdgeworth expansion. In the mildly non-linear regime, two additional parametersdescribe the full picture: the skewness parameter $s$ and non-linear bias$b_2$. They can both be determined from the measured skewness combined withsecond order perturbation theory or from an N-body simulation. By measuring theredshift distortion of the skewness, one can measure the density parameter$\Omega$ with minimal assumptions about the galaxy formation process. Thisformalism also provides a convenient parametrization to quantify statisticalgalaxy formation properties.Comment: 15 pages incl 2 figures, submitted to Ap