In the past few years, some studies claimed that annihilating dark matter with mass $sim 10-100$ GeV can explain the GeV gamma-ray excess in our Galaxy. However, recent analyses of the Fermi-LAT and radio observational data rule out the possibility of the thermal relic annihilating dark matter with mass $m le 100$ GeV for some popular annihilation channels. By using the new observed radio data of the Andromeda galaxy, we rule out the existence of $sim 100-300$ GeV thermal relic annihilating dark matter for ten annihilation channels. The lower limits of annihilating dark matter mass are improved to larger than 330 GeV for the most conservative case, which is a few times larger than the current best constraints. Moreover, these limits strongly disfavor the benchmark model of weakly interacting massive particle (WIMP) produced through the thermal freeze-out mechanism.
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