Clustering properties of a sterile neutrino dark matter candidate
Abstract
Description
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 $λ\sim 488 ,\mathrm{kpc}$. At large scales $T(k)\sim 1-C, k^2/k^2_{fs}(t_{eq}) +...$ with $C \sim \mathrm{O}(1)$. At small scales $65 \mathrm{kpc} \lesssim λ\lesssim 500 \mathrm{kpc}$ 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-$α$ forest data.
matches version to appear in PRD
matches version to appear in PRD