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 produced by scalar decay that decouples at 100 GeV is 488 kpc. At large scales T (k) 1-Ck^2/k₅ₒ^2 (t₄ₐ) + with C (1). At small scales 65 kpc500 kpc corrections to the fluid description and memory of gravitational clustering become important, and we find T (k) 1. 902e^-k/{k₅ₒ (t₄ₐ) }, where k₅ₒ (t₄ₐ) 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- forest data.