Constraints on dark matter-neutrino scattering from the Milky-Way satellites and subhalo modeling for dark acoustic oscillations

The elastic scattering between dark matter (DM) and radiation can potentially explain small-scale observations that the cold dark matter faces as a challenge, as damping density fluctuations via dark acoustic oscillations in the early universe erases small-scale structure. We study a semi-analytical subhalo model for interacting dark matter with radiation, based on the extended Press-Schechter formalism and subhalos’ tidal evolution prescription. We also test the elastic scattering between DM and neutrinos using observations of Milky-Way satellites from the Dark Energy Survey and PanSTARRS1. We conservatively impose strong constraints on the DM-neutrino scattering cross section of ${\sigma }_{\mathrm{D}\mathrm{M}\text{-}\nu ,n}\propto E_{\nu }^n$ $(n=0,2,4)$ at $95\mathrm{\%}$ confidence level (CL), ${\sigma }_{\mathrm{D}\mathrm{M}\text{-}\nu ,0}<{10}^{-32}\mathrm{c}{\mathrm{m}}^2(m_{\mathrm{D}\mathrm{M}}\mathrm{/}\mathrm{G}\mathrm{e}\mathrm{V})$, ${\sigma }_{\mathrm{D}\mathrm{M}\text{-}\nu ,2}<{10}^{-43}\mathrm{c}{\mathrm{m}}^2(m_{\mathrm{D}\mathrm{M}}\mathrm{/}\mathrm{G}\mathrm{e}\mathrm{V})(E_{\nu }\mathrm{/}{E}_{\nu }^0{)}^2$ and ${\sigma }_{\mathrm{D}\mathrm{M}\text{-}\nu ,4}<{10}^{-54}\mathrm{c}{\mathrm{m}}^2(m_{\mathrm{D}\mathrm{M}}\mathrm{/}\mathrm{G}\mathrm{e}\mathrm{V})(E_{\nu }\mathrm{/}{E}_{\nu }^0{)}^4$, where $E_{\nu }$ is the neutrino energy and $E_{\nu }^0$ is the average momentum of relic cosmic neutrinos today, $E_{\nu }^0\simeq 6.1\mathrm{K}$. By imposing a satellite forming condition, we obtain the strongest upper bounds on the DM-neutrino cross section at $95\mathrm{\%}$ CL, ${\sigma }_{\mathrm{D}\mathrm{M}\text{-}\nu ,0}<4\times {10}^{-34}\mathrm{c}{\mathrm{m}}^2(m_{\mathrm{D}\mathrm{M}}\mathrm{/}\mathrm{G}\mathrm{e}\mathrm{V})$, ${\sigma }_{\mathrm{D}\mathrm{M}\text{-}\nu ,2}<{10}^{-46}\mathrm{c}{\mathrm{m}}^2(m_{\mathrm{D}\mathrm{M}}\mathrm{/}\mathrm{G}\mathrm{e}\mathrm{V})(E_{\nu }\mathrm{/}{E}_{\nu }^0{)}^2$ and ${\sigma }_{\mathrm{D}\mathrm{M}\text{-}\nu ,4}<7\times {10}^{-59}\mathrm{c}{\mathrm{m}}^2(m_{\mathrm{D}\mathrm{M}}\mathrm{/}\mathrm{G}\mathrm{e}\mathrm{V})(E_{\nu }\mathrm{/}{E}_{\nu }^0{)}^4$.