Exploring the Redshift-Space Peculiar Velocity Field and its Power
  Spectrum
  Redshift-space distortions (RSD) generically affect any spatially-dependent
observable that is mapped using redshift information. The effect on the
observed clustering of galaxies is the primary example of this. This paper is
devoted to another example: the effect of RSD on the apparent peculiar motions
of tracers as inferred from their positions in redshift space (i.e. the
observed distance). Our theoretical study is motivated by practical
considerations, mainly, the direct estimation of the velocity power spectrum,
which is preferably carried out using the tracer's redshift-space position (so
as to avoid uncertainties in distance measurements). We formulate the
redshift-space velocity field and show that RSD enters as a higher-order
effect. Physically, this effect may be interpreted as a dissipative correction
to the usual perfect-fluid description of dark matter. We show that the effect
on the power spectrum is a damping on relatively large, quasilinear scales
($k>0.01\,h\,{\rm Mpc}^{-1}$), as was observed, though unexplained, in $N$-body
simulations elsewhere. This paper presents two power spectrum models for the
peculiar velocity field in redshift space, both of which can be considered
velocity analogues of existing clustering models. In particular, we show that
the "Finger-of-God" effect, while also present in the velocity field, cannot be
entirely blamed for the observed damping in simulations. Our work provides some
of the missing modelling ingredients required for a density--velocity
multi-tracer analysis, which has been proposed for upcoming redshift surveys.
