Exploring the Redshift-Space Peculiar Velocity Field and its Power Spectrum

Abstract

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 ($k>0.01h{\mathrm{Mpc}}^{-1}$), 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.

31+12 pages, 8 figures, 1 table; corresponds to version published in JCAP

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• Growth-rate measurement with type-Ia supernovae using ZTF survey simulations
• The 6x2pt method: supernova velocities meet multiple tracers
• The lure of sirens: joint distance and velocity measurements with third generation detectors
• The Instantaneous Redshift Difference of Gravitationally Lensed Images: Theory and Observational Prospects
• Generalized framework for likelihood-based field-level inference of growth rate from velocity and density fields
• Anchors no more: Using peculiar velocities to constrain $H_0$ and the primordial Universe without calibrators
• Gravitational redshift from large-scale structure: nonlinearities, antisymmetries, and the dipole