Distribution function approach to redshift space distortions, Part III:
  halos and galaxies
  It was recently shown that the power spectrum in redshift space can be
written as a sum of cross-power spectra between number weighted velocity
moments. We investigate the properties of these power spectra for simulated
galaxies and dark matter halos and compare them to the dark matter power
spectra, generalizing the concept of the bias. Because all of the quantities
are number weighted this approach is well defined even for sparse systems such
as massive halos, in contrasts to the previous approaches to RSD where velocity
correlations have been explored. We find that the number density weighting
leads to a strong scale dependence of the bias terms for momentum density
auto-correlation and cross-correlation with density. This trend becomes more
significant for the more biased halos and leads to an enhancement of RSD power
relative to the linear theory. Fingers-of-god effects, which in this formalism
come from the correlations of the higher order moments beyond the momentum
density, lead to smoothing of the power spectrum and can reduce this
enhancement of power, but are relatively small for halos with no small-scale
velocity dispersion. In comparison, for a more realistic galaxy sample with
satellites the velocity dispersion generated by satellite motions inside the
halos leads to a larger power suppression on small scales, but this depends on
the satellite fraction. We investigate several statistics such as the
two-dimensional power spectrum, its multipole moments, its powers of mu^2, and
configuration space statistics. Overall we find that the nonlinear effects in
realistic galaxy samples such as luminous red galaxies affect the redshift
space clustering on very large scales: for example, the quadrupole moment is
affected by 10% for k<0.1h/mpc, which means that these effects need to be
understood if we want to extract cosmological information from the redshift
space distortions.
