Damping scales of neutralino cold dark matter

TL;DR

This work analyzes the small-scale damping of neutralino CDM by identifying two damping channels: collisional damping during kinetic decoupling at $T_{\rm kd}$ and post-decoupling free streaming after last scattering. By formulating CDM as an imperfect fluid and developing a kinetic theory with a relaxation-time collision operator, the authors compute transport coefficients, showing bulk viscosity is significant while heat conduction is negligible. They derive a damping mass scale $M_d \sim 10^{-9}M_\odot$ from collisional damping and a free-streaming mass scale $M_{fs} \sim 10^{-7}M_\odot$, producing a sharp exponential cut-off in the neutralino CDM power spectrum. These results imply a well-defined minimum mass for the first CDM objects and have potential implications for substructure in halos and cosmic voids, with future work to present the corresponding transfer functions and power spectra.

Abstract

The lightest supersymmetric particle, most likely the neutralino, might account for a large fraction of dark matter in the Universe. We show that the primordial spectrum of density fluctuations in neutralino cold dark matter (CDM) has a sharp cut-off due to two damping mechanisms: collisional damping during the kinetic decoupling of the neutralinos at about 30 MeV (for typical neutralino and sfermion masses) and free streaming after last scattering of neutralinos. The last scattering temperature is lower than the kinetic decoupling temperature by one order of magnitude. The cut-off in the primordial spectrum defines a minimal mass for CDM objects in hierarchical structure formation. For typical neutralino and sfermion masses the first gravitationally bound neutralino clouds have to have masses above 10^(-7) solar masses.

Figures (5)

• Figure 1: The chemical decoupling as a function of the sfermion mass $M_{\tilde{F}}$ for three values of the neutralino mass $M_{\tilde{\chi}} = 50, 100, 150$ GeV (increasing from bottom to top).
• Figure 2: The relic abundance of neutralinos expressed by $\omega_{\tilde{\chi}} = \Omega_{\tilde{\chi}} h^2$ as a function of the neutralino mass $M_{\tilde{\chi}}$ for different values of the sfermion mass $M_{\tilde{F}} = 150, 200, 250, 300, 400$ GeV. The sfermion mass increases from the bottom to the top. The dark shaded region is excluded by the conservative assumptions: $\Omega \leq 1$ and $h < 0.8$. The light shaded region indicates typical values of $\omega$ in a $\Lambda$CDM model.
• Figure 3: The temperature of kinetic decoupling of neutralinos from radiation as a function of the sfermion mass for $M_{\tilde{\chi}} = 50, 100, 200$ GeV (bottom to top).
• Figure 4: The damping scale $M_{\rm d}$ in solar masses as a function of the neutralino mass $M_{\tilde{\chi}}$ for different values of the slepton Mass $M_{\tilde{L}}=150, 200, 300, 400$ GeV. The slepton mass increases from the bottom to the top.
• Figure 5: The free streaming mass $M_{\rm fs}$ at matter-radiation equality in solar masses as a function of the neutralino mass $M_{\tilde{\chi}}$ for different values of the slepton mass $M_{\tilde{L}}=150, 200, 300, 400$ GeV. The slepton mass increases from the bottom to the top.