A lower bound on the mass of Dark Matter particles

Abstract

We discuss the bounds on the mass of Dark Matter (DM) particles, coming from the analysis of DM phase-space distribution in dwarf spheroidal galaxies (dSphs). After reviewing the existing approaches, we choose two methods to derive such a bound. The first one depends on the information about the current phase space distribution of DM particles only, while the second one uses both the initial and final distributions. We discuss the recent data on dSphs as well as astronomical uncertainties in relevant parameters. As an application, we present lower bounds on the mass of DM particles, coming from various dSphs, using both methods. The model-independent bound holds for any type of fermionic DM. Stronger, model-dependent bounds are quoted for several DM models (thermal relics, non-resonantly and resonantly produced sterile neutrinos, etc.). The latter bounds rely on the assumption that baryonic feedback cannot significantly increase the maximum of a distribution function of DM particles. For the scenario in which all the DM is made of sterile neutrinos produced via non-resonant mixing with the active neutrinos (NRP) this gives m_nrp > 1.7 keV. Combining these results in their most conservative form with the X-ray bounds of DM decay lines, we conclude that the NRP scenario remains allowed in a very narrow parameter window only. This conclusion is independent of the results of the Lyman-alpha analysis. The DM model in which sterile neutrinos are resonantly produced in the presence of lepton asymmetry remains viable. Within the minimal neutrino extension of the Standard Model (the nuMSM), both mass and the mixing angle of the DM sterile neutrino are bounded from above and below, which suggests the possibility for its experimental search.

Figures (4)

• Figure 1: Comparison of velocity profiles assumed in Tremaine:79 (red solid line) and in this work (black dashed line).
• Figure 2: Restrictions on parameters of sterile neutrino (mass and mixing $\sin^2(2\theta)$ between sterile and active neutrinos) from X-rays (Boyarsky:06cBoyarsky:06dBoyarsky:06fBoyarsky:07aBoyarsky:07b) and phase-space density considerations (this work). Our analysis excludes the region to the left of the vertical line (\ref{['eq:29']}) (purple shaded region). Two dashed-dotted vertical lines mark the systematic uncertainties of this bound. The dotted line on the left marks the bound (\ref{['eq:28']}) based on the Pauli exclusion principle. The double-dotted dark orange line marks the bound (\ref{['eq:30']}). The black dashed-dotted line is the NRP production curve (i.e. pairs of $m_{\textsc{nrp}}$ and $\theta$ that lead to the correct DM abundance) Asaka:06c. The gray region marked "NRP production" accounts for possible uncertainties in the abundance computations (see Asaka:06bAsaka:06c for details).
• Figure 3: Restrictions on resonantly produced sterile neutrinos. Primordial $f_{max}$ is computed numerically based on the spectra from Laine:08aShaposhnikov:08a. Different colors parametrize different lepton asymmetries for a given mass (see definition of lepton asymmetry in Laine:08aShaposhnikov:08a). Grey shaded region is bounded by the maximal and minimal values of $\bar{F}$ for Leo IV (from Table \ref{['tab:gilmore']}, column 5). Horizontal dotted lines represent central value for $\bar{F}$ (lower) and $F_{\textsc{tg}}$ (upper) for Leo IV. The DM spectrum is ruled out if the point falls into the shaded region (below the dotted line).
• Figure 4: Allowed window of parameters for sterile neutrinos produced via resonant oscillations (white unshaded strip between two black lines). Two bounding black lines are obtained for non-resonant (upper line, lepton asymmetry $=0$) and resonant production with the maximal lepton asymmetry, attainable in the $\nu$MSM Laine:08aShaposhnikov:08a (lower line). The colored regions in the upper right corner represent X-ray bounds Boyarsky:06cBoyarsky:06dBoyarsky:07aBoyarsky:07b. Region below $1\:\mathrm{keV}$ is ruled out from the PSD arguments (this work).