Clustering properties of a sterile neutrino dark matter candidate

TL;DR

The paper investigates keV-scale sterile neutrinos produced by the decay of a gauge-singlet scalar as a warm dark matter candidate. By solving a quantum kinetic equation, it shows the post-decoupling distribution is strongly out of equilibrium, with f_0(y) ∝ y^{−1/2} at small momentum, yielding colder relics than DW scenarios. Employing a non-relativistic Boltzmann–Vlasov framework with a memory kernel, it derives a transfer function that enhances small-scale power relative to thermal relics or DW-produced sterile neutrinos, and identifies a small-scale suppression characterized by k_fs(t_eq) ≈ 0.013 /kpc (λ_fs(t_eq) ≈ 488 kpc). The results suggest this non-thermal production channel can alleviate some small-scale tensions while remaining consistent with DM abundance and dSph phase-space constraints, though further work with baryons and nonlinear simulations is needed. Future directions include combining scalar-decay production with DW mixing and performing full Boltzmann/N-body analyses to assess dSph cores and Lyman-α/X-ray constraints more precisely.

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 $λ\sim 488 ,\mathrm{kpc}$. 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.

Figures (9)

• Figure 1: Left panel: $dn(y;\tau)/d\tau \Lambda$ for $y=0.2,0.5,1$. Right panel $n(y;\tau)/\Lambda$ for the same values of $y$ .
• Figure 2: The distribution function $f_0(y)=n(y;\infty)$.
• Figure 3: The free streaming solution $I[z]$ eqn. (\ref{['Inho']}) and $z^\frac{5}{2}I[z]$ vs. $z=\alpha u$.
• Figure 4: The free streaming solution $I[z]$ for the non-equilibrium distribution (\ref{['f0']}) eqn. (\ref{['Inho']}) (solid line) and for the generalized distribution function eqn. (\ref{['fdw']}) (dashed line) vs. $z=\alpha u$.
• Figure 5: The kernel $\Pi[z]$ vs. $z=\alpha\,(u-u')$ .