Impact of a Warm Dark Matter late-time velocity dispersion on large-scale structures

TL;DR

This study examines the influence of late-time velocity dispersion in Warm Dark Matter on large-scale cosmic structures, finding negligible effects on the power spectrum but significant impacts on small-scale density distributions.

Contribution

It introduces an effective hydrodynamical approach to model WDM velocity dispersion and analyzes its effects on structure formation using analytical methods.

Findings

Negligible impact on the power spectrum and halo mass function.

Significant effect on the density contrast PDF at small scales.

Simulations should start at redshift z ≥ 100 to accurately capture clustering.

Abstract

We investigate whether the late-time (at $z\leq 100$) velocity dispersion expected in Warm Dark Matter scenarios could have some effect on the cosmic web (i.e., outside of virialized halos). We consider effective hydrodynamical equations, with a pressurelike term that agrees at the linear level with the analysis of the Vlasov equation. Then, using analytical methods, based on perturbative expansions and the spherical dynamics, we investigate the impact of this term for a 1 keV dark matter particle. We find that the late-time velocity dispersion has a negligible effect on the power spectrum on perturbative scales and on the halo mass function. However, it has a significant impact on the probability distribution function of the density contrast at $z \sim 3$ on scales smaller than $0.1 h^{-1}$Mpc, which correspond to Lyman-$\alpha$ clouds. Finally, we note that numerical simulations should start at $z_i\geq 100$ rather than $z_i \leq 50$ to avoid underestimating gravitational clustering at low redshifts.