The Effect of Thermal Velocities on Structure Formation in N-body Simulations of Warm Dark Matter

Matteo Leo, Carlton M. Baugh, Baojiu Li, Silvia Pascoli

Published 2017-06-23Version 1

We investigate the role of thermal velocities in N-body simulations of structure formation in warm dark matter models. Starting from the commonly used approach of adding thermal velocities, randomly selected from a Fermi-Dirac distribution, to the gravitationally-induced (peculiar) velocities of the simulation particles, we compare the matter and velocity power spectra measured from CDM and WDM simulations with and without thermal velocities. This prescription for adding thermal velocities results in deviations in the velocity field in the initial conditions away from the linear theory predictions, which affects the evolution of structure at later times. We show that this is entirely due to numerical noise. For a warm candidate with mass $3.3$ keV, the matter and velocity power spectra measured from simulations with thermal velocities starting at $z=199$ deviate from the linear prediction at $k \gtrsim10$ $h/$Mpc, with an enhancement of the matter power spectrum $\sim \mathcal{O}(10)$ and of the velocity power spectrum $\sim \mathcal{O}(10^2)$ at wavenumbers $k \sim 64$ $h/$Mpc with respect to the case without thermal velocities. At late times, these effects tend to be less pronounced. Indeed, at $z=0$ the deviations do not exceed $6\%$ (in the velocity spectrum) and $1\%$ (in the matter spectrum) for scales $10 <k< 64$ $h/$Mpc. Increasing the resolution of the N-body simulations shifts these deviations to higher wavenumbers. The noise introduces more spurious structures in WDM simulations with thermal velocities and modifies the radial density profiles of dark matter haloes. We find that spurious haloes start to appear in simulations which include thermal velocities at a mass that is $\sim$3 times larger than in simulations without thermal velocities.