Clustering properties of a sterile neutrino dark matter candidate

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.