## Abstract

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, of which the lowest are density and momentum density. We investigate numerically 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 in density-density power spectra. Because all of the quantities are number weighted this approach is well defined even for sparse systems such as massive halos. This contrasts to the previous approaches to RSD where velocity correlations have been explored, but velocity field is a poorly defined concept for sparse systems. 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 from the scale dependent bias, but are relatively small for halos with no small scale velocity dispersion. In comparison, for a more realistic galaxy sample with satellites the small scale 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 and on the details of how the satellites are distributed inside the halo. We investigate several statistics such as the two-dimensional power spectrum P(k,μ), where μ is the angle between the Fourier mode and line of sight, its multipole moments, its powers of μ2, 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 < 0.1hMpc-1, which means that these effects need to be understood if we want to extract cosmological information from the redshift space distortions.