Production and Evolution of Perturbations of Sterile Neutrino Dark Matter

TL;DR

The paper assesses sterile neutrinos as dark matter by calculating their nonthermal production in the early universe and tracing the resulting linear perturbations. It treats production with a density-matrix–Boltzmann framework, including the quark-hadron transition, finite-temperature effects, and plasma heating, yielding a nonthermal momentum spectrum. It then propagates these distributions through linear growth with CAMB to obtain present-day matter power spectra and a calibrated transfer function T_s(k) with a compact fit. The results show significant deviations from previous, thermally- or mono-energetic assumptions, refine the allowed mass range, and provide a practical tool for connecting sterile neutrino DM to small-scale structure and observational limits such as the Lyman-alpha forest and X-ray constraints.

Abstract

Sterile neutrinos, fermions with no standard model couplings [SU(2) singlets], are predicted by most extensions of the standard model, and may be the dark matter. I describe the nonthermal production and linear perturbation evolution in the early universe of this dark matter candidate. I calculate production of sterile neutrino dark matter including effects of Friedmann dynamics dictated by the quark-hadron transition and particle population, the alteration of finite temperature effective mass of active neutrinos due to the presence of thermal leptons, and heating of the coupled species due to the disappearance of degrees of freedom in the plasma. These effects leave the sterile neutrinos with a non-trivial momentum distribution. I also calculate the evolution of sterile neutrino density perturbations in the early universe through the linear regime and provide a fitting function form for the transfer function describing the suppression of small scale fluctuations for this warm dark matter candidate. The results presented here differ quantitatively from previous work due to the inclusion here of the relevant physical effects during the production epoch.

Figures (4)

• Figure 1: The resulting relative distribution coming from the production epoch for sterile neutrino dark matter relative to the active neutrinos, $\rho(\epsilon) = f_s(\epsilon)/f_\alpha(\epsilon)$, ($\epsilon \equiv p/T$) over a mass range $0.3 < m_s < 140{\rm\ keV}$, for fifty cases, and increasing $m_s$ having decreasing distribution amplitudes. All cases have $\Omega_{\rm DM} = 0.26$. The upper thick (red) line is for the case of $m_s = 1.7\rm\ keV$ and lower thick (blue) line is for the case $m_s = 8.2\rm\ keV$.
• Figure 2: Contours of predicted critical density $\Omega_{\rm DM} =0.26$ from the direct numerical calculation in this work (solid red), the fit provided here (dot-dashed purple), the results of Ref. Abazajian:2001nj which used a different quark-hadron transition and particle population model (dashed blue), and that of Ref. Dolgov:2000ew (dotted black) for the inaccurate but common choice of $g_*^\prime = 10.75$ (more realistic choices of $g_*^\prime$ make the predicted abundance more inaccurate). Also shown are the upper flux constraint from X-ray observations of the Virgo cluster Abazajian:2001vt, the constraint from the diffuse X-ray background Boyarsky:2005us, the lower mass constraint from the CMB, SDSS galaxy clustering and Lyman-$\alpha$ forest, and the possible constraint from also including the high-resolution (HR) Lyman-$\alpha$ forest AbazajianLower05.
• Figure 3: Shown are the resulting linear matter power spectra for nonthermal sterile neutrinos in the mass range $0.3 < m_s < 140{\rm\ keV}$ (gray/cyan). The thick (red) low-$k$ suppression case is for the lower-mass limit inferred from the Lyman-$\alpha$ forest ($m_s > 1.7\rm\ keV$) , and the thick (blue) high-$k$ suppression case is for the upper-mass limit from X-ray observations of the Virgo cluster ($m_s < 8.2\rm\ keV$). The CDM case is the dashed (black) line. Measures of large-scale structure in the linear regime are in the region of $0.01 h{\rm\ Mpc}^{-1}<k<0.2 h{\rm\ Mpc}^{-1}$ for galaxy surveys, while neutral gas clustering observed in the Ly-$\alpha$ forest may extend observations of linear structure to $0.1 h{\rm\ Mpc}^{-1}<k<3 h{\rm\ Mpc^{-1}}$.
• Figure 4: Shown here are the relative sterile neutrino transfer function $T_s(k)$ to CDM for the same large scale amplitude of perturbations, for the cases of $m_s = 0.5, 1.7, 8.2\rm\ keV$ with increasing wave number $k$ suppression scale, respectively. The solid (black) lines are from the full numerical calculation, the dashed (red) lines are fitting form in Eq. (\ref{['transfer_sterile_fit']}), and the dotted (blue) lines are the results of Ref. Viel:2005qj.