Clustering properties of a sterile neutrino dark matter candidate

The clustering properties of sterile neutrinos are studied within a simple extension of the minimal standard model, where these neutrinos are produced via the decay of a gauge singlet scalar. The distribution function after decoupling is strongly out of equilibrium and features an enhancement at small comoving momentum ∝1/√p. Dark matter abundance and phase space density constraints from dwarf spheroidal galaxies constrain the mass in the keV range consistent with a Yukawa coupling to a gauge singlet with mass and vacuum expectation value in the range ~100 GeV and a decoupling temperature of this order. The dark matter transfer function and power spectrum are obtained from the solution of the nonrelativistic Boltzmann-Vlasov equation in the matter dominated era. The small momentum enhancement of the nonequilibrium distribution function leads to long range memory of gravitational clustering and a substantial enhancement of the power spectrum at small scales as compared to a thermal relic or sterile neutrino produced via nonresonant mixing with active neutrinos. The scale of suppression of the power spectrum for a sterile neutrino with m~keV produced by scalar decay that decouples at ~100 GeV is λ~488 kpc. At large scales T(k)~1-Ck²/kfs²(teq)+⋯ with C~O(1). At small scales 65 kpcλ500 kpc corrections to the fluid description and memory of gravitational clustering become important, and we find T(k)1.902e^-k/kfs(teq), where kfs(teq)~0.013/kpc is the free-streaming wave vector at matter-radiation equality. The enhancement of power at small scales may provide possible relief to the tension between the constraints from x-ray and Lyman-α forest data.