Fingers-of-God effect of infalling satellite galaxies

Non-linear redshift-space distortion known as the Fingers-of-God (FoG) effect is a major systematic uncertainty in redshift-space distortion studies conducted to test gravity models. The FoG effect has been usually attributed to the random motion of galaxies inside their clusters. When the internal galaxy motion is not well virialized, however, the coherent infalling motion towards the cluster centre generates the FoG effect. Here, we derive an analytical model of the satellite velocity distribution due to the infall motion combined with the random motion. We show that the velocity distribution becomes far from Maxwellian when the infalling motion is dominant. We use simulated subhalo catalogues to find that the contribution of infall motion is important to massive subhaloes and that the velocity distribution has a top-hat like shape as expected from our analytic model. We also study the FoG effect due to infall motion on the redshift-space power spectrum. Using simulated mock samples of luminous red galaxies constructed from haloes and massive subhaloes in N-body simulations, we show that the redshift-space power spectra can differ from expectations when the infall motion is ignored.