Cores in Dwarf Galaxies from Dark Matter with a Yukawa Potential

We show that cold dark matter particles interacting through a Yukawa potential could naturally explain the recently observed cores in dwarf galaxies without affecting the dynamics of objects with a much larger velocity dispersion, such as clusters of galaxies. The velocity dependence of the associated cross section as well as the possible exothermic nature of the interaction alleviates earlier concerns about strongly interacting dark matter. Dark matter evaporation in low-mass objects might explain the observed deficit of satellite galaxies in the Milky Way halo and have important implications for the first galaxies and reionization.

Figure 1

Dependence of the self-interaction cross section ($\sigma$) on the relative velocity ($v$) for dark matter interacting through a Yukawa potential. The normalizations of $\sigma$ and $v$ are set by free parameters in the underlying Lagrangian (see 29 ), and we show two possible curves peaking at $v_{\sigma }=10\mathrm{km}{\mathrm{s}}^{-1}$ and $v_{\sigma }=100\mathrm{km}{\mathrm{s}}^{-1}$ (blue, solid line and purple, dashed line, respectively).

Figure 2

Astrophysical constraints on the normalization of the self-interaction cross section (${\sigma }_{\max }$) as a function of the velocity at which the peak collision rate is obtained ($v_{\sigma }$) in Fig. 1. The red solid line is normalized to have $⟨\sigma {⟩}_{\max }/m_{\chi }\approx 6\times {10}^{-25}{\mathrm{cm}}^2/\mathrm{GeV}$ at $v_{\mathrm{dwarf}}\approx 10\mathrm{km}{\mathrm{s}}^{-1}$, which should be regarded as the minimum interaction necessary to flatten the cores of dwarf galaxies. Additional lines indicate upper limits on the cross section based on astrophysical considerations: X-ray cluster ellipticity (blue, dashed line), limiting $({\sigma }_{\max }/m_{\chi })\lesssim 4\times {10}^{-26}{\mathrm{cm}}^2/\mathrm{GeV}$ at $v\sim {10}^3\mathrm{km}{\mathrm{s}}^{-1}$; destruction of dwarf subhalos through collisions with high velocity particles from a larger parent halo in which these dwarfs are embedded (green, dotted line), limiting $({\sigma }_{\max }/m_{\chi })\lesssim 5\times {10}^{-25}{\mathrm{cm}}^2/\mathrm{GeV}$ [48] at $v\sim 200\mathrm{km}{\mathrm{s}}^{-1}$; and requiring the number of scatters in dwarfs to be less than $\sim {10}^2$ during the age of the Universe to avoid the gravothermal catastrophe (purple, dash-dotted line). Related limits are summarized in 26.