Self-Interaction of Super-Resonant Dark Matter

TL;DR

This work tackles small-scale tensions in ΛCDM by proposing super-resonant dark matter (SRDM), where a narrow resonance and Sommerfeld enhancements jointly amplify both DM self-interactions and annihilation. The authors derive cross sections and implement coupled Boltzmann equations (cBEs) to account for early kinetic decoupling, enabling accurate relic density calculations that align with Planck data. A minimal SRDM model with χ, V, and A mediators yields a velocity-dependent self-interaction cross section that matches dwarf- and cluster-scale observations for DM masses in the 70–250 GeV range, with a best-fit around m_χ ≈ 110 GeV and v_res ≈ 1950 km/s. The study demonstrates that SRDM can reconcile small-scale structure problems without spoiling large-scale ΛCDM predictions, while highlighting that TeV-scale DM would require additional mechanisms to achieve the necessary  self-interactions.

Abstract

The $Λ$CDM model, while successful on large cosmological scales, faces challenges on small scales. A promising solution posits that dark matter (DM) exhibits strong self-interaction, enhanced through the narrow resonance or Sommerfeld effects. We demonstrate that the ``super-resonance" phenomenon, combining these effects, significantly amplifies the DM self-scattering cross section, enabling strong self-interactions for DM candidates in the $\mathcal{O}(100)$ GeV mass range. This mechanism also enhances the DM annihilation cross section, causing early kinetic decoupling that renders the standard Boltzmann equation inadequate. By implementing coupled Boltzmann equations, we achieve precise calculations of the relic density for super-resonant DM, aligning with observational constraints.

Figures (3)

• Figure 1: Thermal evolution of the $Y$ (left vertical axis of left panel), $\langle \sigma v \rangle$ (right vertical axis of left panel), and effective temperature $y$ (right panel) as a function of $x=m_\chi/T$. Blue and gray dotted lines for the evolution of $Y$ and $y$ are obtained with solving the cBEs and the nBE, respectively.
• Figure 2: Upper panels show $\Delta \chi^2$ for two different parameter spaces, while $g_l$ as a color-bar shown in lower panel. Red stars are best-fit point with $\Delta \chi^2 = 0$ (assuming $\chi^2_{\rm anni} = 0$ for upper panels). Blue and red contours represent $2\sigma$ and $3\sigma$ limit with $\Delta \chi^2 < 6$ and $\Delta \chi^2 < 13$, respectively. Inserted texts $m_\chi = 110$ GeV and $v_{res} = 1950$ km/s are best-fit parameters.
• Figure 3: Velocity-averaged self-scattering cross section per unit mass $\langle \sigma_{\text{SI}}v \rangle/m_\chi$ as a function of galactic mean velocity. The purple solid curve is from our SRDM model with best-fit parameters. Gray dashed guidelines denote contours of constant $\langle \sigma_{\text{SI}}v \rangle/m_\chi$ values. Colored data points show converted $\langle \sigma_{\text{SI}}v \rangle/m_\chi$ constraints derived via semi-analytic methods from multi-galactic observations: five red points correspond to dwarf galaxies in the THINGS sample Oh:2010ea, six green points represent galaxy clusters from Newman et al. Newman:2012nwNewman:2012nv, and seven blue points indicate low-surface-brightness (LSB) spiral galaxies in the Kuzio de Naray sample KuziodeNaray:2007qi.