Some recent studies have examined the gamma-ray flux profile of our Galaxy to determine the signal of dark matter annihilation. However, the results are controversial and no confirmation is obtained. In this article, we study the radio flux density profile of the M31 galaxy and show that it could manifest a possible signal of dark matter annihilation. By comparing the likelihoods between the archival observed radio flux density profile data and the predicted radio flux density profile contributed by dark matter and stellar emission, we can constrain the relevant dark matter parameters. Specifically, for the thermal annihilation cross section via the $bbar{b}$ channel, the best-fit value of dark matter mass is $sim 30$ GeV, which is consistent with the results of many recent studies. We expect that this method would become another useful way to constrain dark matter, which is complementary to the traditional radio analyses and the other indirect detections.
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