Strong Limits on Dark Matter Annihilation from the Event Horizon Telescope Observations of M87$^\star$

The fast developments of radio astronomy open a new window to explore the properties of Dark Matter (DM). The recent direct imaging of the supermassive black hole (SMBH) at the center of M87 radio galaxy by the Event Horizon Telescope (EHT) collaboration is expected to be very useful to search for possible new physics. In this work, we illustrate that such results can be used to detect the possible synchrotron radiation signature produced by DM annihilation from the innermost region of the SMBH. Assuming the existence of a spiky DM density profile, we obtain the flux density due to DM annihilation induced electrons and positrons, and derive new limits on the DM annihilation cross section via the comparison with the EHT integral flux density at 230 GHz. Our results show that the parameter space can be probed by the EHT observations is largely complementary to other experiments. For DM with typical mass regions of being weakly interacting massive particles, the annihilation cross section several orders of magnitude below the thermal production level can be excluded by the EHT observations under the density spike assumption. Future EHT observations may further improve the sensitivity on the DM searches, and may also provide a unique opportunity to test the interplay between DM and the SMBH.