Constraining annihilating dark matter by x-ray data

In the past decade, gamma-ray observations and radio observations put strong constraints on the parameters of dark matter annihilation. In this article, we suggest another robust way to constrain the parameters of dark matter annihilation. We expect that the electrons and positrons produced from dark matter annihilation would scatter with the cosmic microwave background photons and boost the photon energy to $\sim$ keV order. Based on the x-ray data from the Draco dwarf galaxy, the new constraints for some of the annihilation channels are generally tighter than the constraints obtained from 6 years of Fermi Large Area Telescope (Fermi-LAT) gamma-ray observations of the Milky Way dwarf spheroidal satellite galaxies. The lower limits of dark matter mass annihilating via $e^+e^-$, $\mu^+\mu^-$, $\tau^+\tau^-$, $gg$, $u\bar{u}$ and $b\bar{b}$ channels are 40 GeV, 28 GeV, 30 GeV, 57 GeV, 58 GeV and 66 GeV respectively with the canonical thermal relic cross section. This method is particularly useful to constrain dark matter annihilating via $e^+e^-$, $\mu^+\mu^-$, $gg$, $u\bar{u}$ and $b\bar{b}$ channels.