Dark Radiation Alleviates Problems with Dark Matter Halos

We show that a scalar and a fermion charged under a global $U(1)$ symmetry can not only explain the existence and abundance of dark matter (DM) and dark radiation (DR), but can also imbue DM with improved scattering properties at galactic scales, while remaining consistent with all other observations. Delayed DM-DR kinetic decoupling eases the missing satellites problem, while scalar-mediated self-interactions of DM ease the cusp versus core and too big to fail problems. In this scenario, DM is expected to be pseudo-Dirac and have a mass $100\mathrm{keV}\lesssim m_{\chi }\lesssim 10\mathrm{GeV}$. The predicted DR may be measurable using the primordial elemental abundances from big bang nucleosynthesis, and using the cosmic microwave background.

Figure 1

DM-DR scattering via $u$, $s$, and $t$ channels.

Figure 2

Solution of all small-scale problems of DM. For a DM mass $m_{\chi }$, the coupling ${\alpha }_{\text{d}}$ (top $x$ axis) is determined by the relic density. Small-scale problems are solved within the band. Three thin solid lines in the band correspond to $⟨{\sigma }_T⟩/m_{\chi }\sim 0.1$, 1, $10{\mathrm{cm}}^2/\mathrm{g}$, respectively (top down), at $v_{\text{rel}}\sim 10\mathrm{km}/\mathrm{s}$, addressing the cusp versus core and too big to fail problems. The color gradient inside shows the common logarithm of $\delta \equiv \mathrm{\Delta }{m}_{\chi }/m_{\chi }$, which leads to $T_{\text{kd}}=0.5\mathrm{keV}$ and solves the missing satellites problem. The hatched region at the bottom shows the constraint from galaxy clusters, $⟨{\sigma }_T⟩/m_{\chi }\lesssim 1{\mathrm{cm}}^2/\mathrm{g}$ at $v_{\text{rel}}\sim 10^3\mathrm{km}/\mathrm{s}$, while the dashed line indicates the largest $m_{\rho }$ for which the scalar potential for $\varphi$ is perturbative.

Figure 3

$\mathrm{\Delta }{N}_{\nu }$ generated by dark radiation, depending on the DM mass $m_{\chi }$ and the temperature $T_{\star }$ at which the dark and visible sectors decoupled. The white area denotes $\mathrm{\Delta }{N}_{\nu }\ge 1$.