On the halo velocity bias

TL;DR

This paper investigates the discrepancy between the observed non-decaying halo velocity bias and the predictions of the standard fluid approximation, proposing modifications based on phase space conservation laws and peak constraints.

Contribution

It introduces a revised formalism for halo velocity bias that incorporates peak constraints, aligning theoretical predictions with recent simulation results.

Findings

Halo velocity bias does not decay to unity as previously thought.

Standard fluid models need modification to include peak constraints.

Proper treatment of phase space conservation explains the persistent bias.

Abstract

It has been recently shown that any halo velocity bias present in the initial conditions does not decay to unity, in agreement with predictions from peak theory. However, this is at odds with the standard formalism based on the coupled fluids approximation for the coevolution of dark matter and halos. Starting from conservation laws in phase space, we discuss why the fluid momentum conservation equation for the biased tracers needs to be modified in accordance with the change advocated in Baldauf, Desjacques & Seljak (2014). Our findings indicate that a correct description of the halo properties should properly take into account peak constraints when starting from the Vlasov-Boltzmann equation.