XENON1T excess in local $Z_2$ DM models with light dark sector

Recently XENON1T Collaboration announced that they observed some excess in the electron recoil energy around a 2-3 keV. We show that this excess can be interpreted as exothermic scattering of excited dark matter (XDM), $XDM + e_{atomic} \rightarrow DM + e_{free}$ on atomic electron through dark photon exchange. We consider DM models with local dark $U(1)$ gauge symmetry that is spontaneously broken into its $Z_2$ subgroup by Krauss-Wilczek mechanism. In order to explain the XENON1T excess with the correct DM thermal relic density within freeze-out scenario, all the particles in the dark sector should be light enough, namely $\sim O(100)$ MeV for scalar DM and $\sim O(1-10)$ MeV for fermion DM cases. And even lighter dark Higgs $\phi$ plays an important role in the DM relic density calculation: $X X^\dagger \rightarrow Z' \phi$ for scalar DM ($X$) and $\chi \bar{\chi} \rightarrow \phi \phi$for fermion DM ($\chi$) assuming $m_{Z'} > m_\chi$. Both of them are in the $p$-wave annihilation, and one can easily evade stringent bounds from Planck data on CMB on the $s$-wave annihilations, assuming other dangerous $s$-wave annihilations are kinematically forbidden.