Resonant Dark Forces and Small-Scale Structure

A dark force can impact the cosmological history of dark matter (DM), both explaining observed cores in dwarf galaxies and setting the DM relic density through annihilation to dark force bosons. For GeV–TeV DM mass, DM self-scattering in dwarf galaxy halos exhibits quantum mechanical resonances, analogous to a Sommerfeld enhancement for annihilation. We show that a simple model of DM with a dark force can accommodate all astrophysical bounds on self-interactions in halos and explain the observed relic density, through a single coupling constant.

Figure 1

Velocity-dependence of ${\sigma }_T$ for sample parameters within different regimes. Blue line shows Born formula (a1), in agreement with numerical results (blue dots), for $m_X=4\mathrm{GeV}$, $m_{\varphi }=7.2\mathrm{MeV}$, ${\alpha }_X=1.8\times {10}^{-4}$. Green line shows classical formula (a2), in agreement with numerical results (stars), for $m_X=2\mathrm{TeV}$, $m_{\varphi }=1\mathrm{MeV}$, ${\alpha }_X=0.05$. Red lines show ${\sigma }_T$ in the resonant regime for $m_X=100\mathrm{GeV}$, ${\alpha }_X=3.4\times {10}^{-3}$, illustrating $s$-wave resonance (solid, $m_{\varphi }=205\mathrm{MeV}$), $p$-wave resonance (dot-dashed, $m_{\varphi }=20\mathrm{MeV}$), and $s$-wave antiresonance (dashed, $m_{\varphi }=77\mathrm{MeV}$).

Figure 2

Symmetric (left) and asymmetric (right) DM parameter space in $m_X\mathrm{\text{−}}{m}_{\varphi }$ plane. Blue shaded regions show where DM self-scattering solves dwarf-scale structure anomalies, whereas red (green) lines show bounds from Milky Way (cluster) scales. Numerical values indicate $⟨{\sigma }_T⟩/m_X$ in ${\mathrm{cm}}^2/\mathrm{g}$ on dwarf (“dw”), Milky Way (“MW”), and cluster (“cl”) scales. For symmetric DM, ${\alpha }_X$ is fixed to obtain the observed relic density; for asymmetric DM, ${\alpha }_X={10}^{-2}$ is fixed to deplete $X$, $\overline{X}$ density for $m_X\lesssim 300\mathrm{GeV}$ (dotted line). Dashed lines show extrapolation using analytic formulas, whereas the “$x$” marks indicate the parameter points utilized in Fig. 1.