Understanding redshift space distortions in density-weighted peculiar
  velocity
  Observations of the kinetic Sunyaev-Zel'dovich (kSZ) effect measure the
density-weighted velocity field, a potentially powerful cosmological probe.
This paper presents an analytical method to predict the power spectrum and
two-point correlation function of the density-weighted velocity in redshift
space, the direct observables in kSZ surveys. We show a simple relation between
the density power spectrum and the density-weighted velocity power spectrum
that holds for both dark matter and halos. Using this relation, we can then
extend familiar perturbation expansion techniques to the kSZ power spectrum.
One of the most important features of density-weighted velocity statistics in
redshift space is the change in sign of the cross-correlation between the
density and density-weighted velocity at mildly small scales due to nonlinear
redshift space distortions. Our model can explain this characteristic feature
without any free parameters. As a result, our results can precisely predict the
non-linear behavior of the density-weighted velocity field in redshift space up
to $\sim30\ h^{-1} {\rm Mpc}$ for dark matter particles at the redshifts of
$z=0.0$, $0.5$, and $1.0$.
