Evolution of the probability distribution function of galaxies in redshift space

We present a new analytic calculation for the redshift-space evolution of the one-point galaxy probability distribution function (PDF). The non-linear evolution of the matter density field is treated by second-order Eulerian perturbation theory and transformed to the galaxy density field via a second-order local biasing scheme. We then transform the galaxy density field to redshift space, again to second order. Our method uses an exact statistical treatment based on the Chapman–Kolmogorov equation to propagate the probability distribution of the initial mass field to the final redshifted galaxy density field. The moment generating function of the PDF is derived and used to find a new, closed-form expression for the skewness of the redshifted galaxy distribution. The formalism is shown to be general enough to allow a non-deterministic (or stochastic) biasing prescription. We demonstrate the dependence of the redshift-space PDF on cosmological and biasing parameters. Our results are compared with existing models for the PDF in redshift space and with the results of biased N-body simulations. We find that our PDF accurately models the redshift-space evolution and the non-linear biasing.