Clustering properties of a sterile neutrino dark matter candidate

TL;DR

This paper investigates the clustering behavior of sterile neutrino dark matter produced via scalar decay, revealing enhanced small-scale power spectrum features that could address existing observational tensions.

Contribution

It provides a detailed analysis of sterile neutrino clustering, including the transfer function and power spectrum, highlighting the impact of out-of-equilibrium production on structure formation.

Findings

Enhanced power spectrum at small scales compared to thermal relics.

Suppression scale of the power spectrum around 488 kpc.

Memory effects in gravitational clustering influence small-scale structure.

Abstract

The clustering properties of sterile neutrinos are studied within an extension of the minimal standard model, where these are produced via the decay of a gauge singlet scalar. The distribution function after decoupling is strongly out of equilibrium. (DM) abundance and phase space density constraints from (dSphs) constrain the mass in the $\mathrm{keV}$ range consistent with a gauge singlet with mass and vacuum expectation value $\sim 100,\mathrm{GeV}$ decoupling at this temperature. The (DM) transfer function and power spectrum are obtained from the solution of the non-relativistic Boltzmann-Vlasov equation in the matter dominated era. The small momentum enhancement of the distribution function leads to long range memory of gravitational clustering and a \emph{substantial enhancement of the power spectrum at small scales compared to a thermal relic or sterile neutrino produced via non-resonant mixing with active neutrinos}. The scale of suppression of the power spectrum for such sterile neutrino with $m\sim \mathrm{keV}$ is $\lambda \sim 488 ,\mathrm{kpc}$. At large scales $T(k)\sim 1-C, k^2/k^2_{fs}(t_{eq}) +...$ with $C \sim \mathrm{O}(1)$. At small scales $65 \mathrm{kpc} \lesssim \lambda \lesssim 500 \mathrm{kpc}$ corrections to the fluid description and memory of gravitational clustering become important, and we find $T(k) \simeq 1.902 e^{-k/k_{fs}(t_{eq})}$, where $k_{fs}(t_{eq}) \sim 0.013/\mathrm{kpc}$ is the free streaming wavevector at matter-radiation equality. The enhancement of power at small scales may provide a possible relief to the tension between the constraints from X-ray and Lyman-$\alpha$ forest data.