Exploring the redshift-space peculiar velocity field and its power spectrum

Abstract

Redshift-space distortions (RSD) generically affect any spatially-dependent observable that is mappedusing redshift information. The effect on the observed clustering of galaxies is the primary example ofthis. This paper is devoted to another example: the effect of RSD on the apparent peculiar motions oftracers as inferred from their positions in redshift space (i.e. the observed distance). Our theoreticalstudy is motivated by practical considerations, mainly, the direct estimation of the velocity powerspectrum, which is preferably carried out using the tracer's redshift-space position (so as to avoiduncertainties 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-fluiddescription of dark matter. We show that the effect on the power spectrum is a damping on relativelylarge, quasilinear scales (k≳0.01 h-1), as was observed, though unexplained, inN-body simulations elsewhere. This paper presents two power spectrum models for the peculiarvelocity field in redshift space, both of which can be considered velocity analogues of existingclustering models. In particular, we show that the “Finger-of-God” effect, while also present in thevelocity field, cannot be entirely blamed for the observed damping in simulations. Our work providessome of the missing modelling ingredients required for a density-velocity multi-tracer analysis,which has been proposed for upcoming redshift surveys.