Particle Models and the Small-Scale Structure of Dark Matter

TL;DR

This work connects WIMP microphysics to the small-scale structure of dark matter by precisely determining the kinetic decoupling temperature $T_{\rm kd}$ and translating it into a cutoff mass $M_{\rm cut}$ for protohalos. By solving the full Boltzmann equation and evaluating non-relativistic scattering with time-dependent degrees of freedom, it clarifies the relative roles of free streaming and acoustic damping in suppressing the matter power spectrum, showing a broad $M_{\rm cut}$ range that depends on the DM candidate. A comprehensive scan of MSSM/mSUGRA parameter space yields $M_{\rm cut}$ from $10^{-11} M_\odot$ to $\sim 10^{-4} M_\odot$, with typical deviations from earlier estimates by up to ~10^3 for individual models. The results have important implications for the formation of the first protohalos and for indirect detection strategies targeting dark matter substructure, and the methodology is implemented in DarkSUSY for broader use.

Abstract

The kinetic decoupling of weakly interacting massive particles (WIMPs) in the early universe sets a scale that can directly be translated into a small-scale cutoff in the spectrum of matter density fluctuations. The formalism presented here allows a precise description of the decoupling process and thus the determination of this scale to a high accuracy from the details of the underlying WIMP microphysics. With decoupling temperatures of several MeV to a few GeV, the smallest protohalos to be formed range between 10^{-11} and almost 10^{-3} solar masses -- a somewhat smaller range than what was found earlier using order-of-magnitude estimates for the decoupling temperature; for a given WIMP model, the actual cutoff mass is typically about a factor of 10 greater than derived in that way, though in some cases the difference may be as large as a factor of several 100. Observational consequences and prospects to probe this small-scale cutoff, which would provide a fascinating new window into the particle nature of dark matter, are discussed

Figures (4)

• Figure 1: The left panel shows the phaseplot and solution for the WIMP temperature evolution, for $m_\chi\sim100\,$GeV and $\overline{\left|\mathcal{M}\right|}^2\sim g_Y^4(m_\chi/\omega)^2$, expressed in the dimensionless variables introduced in Eqs. (\ref{['xdef']}, \ref{['ydef']}). At $T\lesssim T_{\rm kd}$, any departure from thermal equilibrium ($T_\chi=T$) is restored almost immediately (except for a short period around the QCD phase transition); for $T\gtrsim T_{\rm kd}$, the WIMPs decouple from the thermal bath and cool down with the Hubble expansion as $T_\chi\propto a^{-2}$. In the right panel, the effective number of relativistic degrees of freedom is plotted as a function of the temperature, implementing the results of Hindmarsh:2005ix for the evolution of this quantity during the QCD phase transition; for reference, the decoupling of muons and electrons is also indicated.
• Figure 2: The range of decoupling temperatures for neutralino DM. For models that fall inside or above the gray band marking the QCD phase transition, the actual value of $T_{\rm kd}$ will be slightly smaller than indicated. See text for further details.
• Figure 3: The left panel shows the exponential cutoff scales associated to the main damping mechanisms of the matter power spectrum after kinetic decoupling, viz. free streaming and the effect of acoustic oscillations, respectively; for models above (below) the dashed line, the former (latter) mechanism thus provides a stronger suppression of the power spectrum. In the right panel, the cutoff mass resulting from the dominating of these two independent effects is plotted against the neutralino mass, indicating the typical size of the smallest protohalos to be formed.
• Figure 4: The kinetic decoupling temperature and the corresponding cutoff scale for the lightest Kaluza-Klein particle in universal extra dimensions. For high Higgs masses, $m_h\gtrsim150\,$GeV, the grey region corresponding to the relic density constraint given in Eq.(\ref{['wmap']}) shifts upwards, allowing an LKP mass up to around $1\,$TeV Kakizaki:2006dz.