Generating Log-normal Mock Catalog of Galaxies in Redshift Space
  We present a public code to generate a mock galaxy catalog in redshift space
assuming a log-normal probability density function (PDF) of galaxy and matter
density fields. We draw galaxies by Poisson-sampling the log-normal field, and
calculate the velocity field from the linearised continuity equation of matter
fields, assuming zero vorticity. This procedure yields a PDF of the pairwise
velocity fields that is qualitatively similar to that of N-body simulations. We
check fidelity of the catalog, showing that the measured two-point correlation
function and power spectrum in real space agree with the input precisely. We
find that a linear bias relation in the power spectrum does not guarantee a
linear bias relation in the density contrasts, leading to a cross-correlation
coefficient of matter and galaxies deviating from unity on small scales. We
also find that linearising the Jacobian of the real-to-redshift space mapping
provides a poor model for the two-point statistics in redshift space. That is,
non-linear redshift-space distortion is dominated by non-linearity in the
Jacobian. The power spectrum in redshift space shows a damping on small scales
that is qualitatively similar to that of the well-known Fingers-of-God (FoG)
effect due to random velocities, except that the log-normal mock does not
include random velocities. This damping is a consequence of non-linearity in
the Jacobian, and thus attributing the damping of the power spectrum solely to
FoG, as commonly done in the literature, is misleading.
