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 proportional to 1/. 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 similar to 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 similar to keV produced by scalar decay that decouples at similar to 100 GeV is lambda similar to 488 kpc. At large scales T(k)similar to 1-Ck(2)/k(fs)(2)(t(eq))+center dot with C similar to O(1). At small scales 65 kpc less than or similar to lambda less than or similar to 500 kpc corrections to the fluid description and memory of gravitational clustering become important, and we find T(k)similar or equal to 1.902e(fs)(-k/k)(t(eq)), where k(fs)(t(eq))similar to 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-alpha forest data.