Ruling out thermal dark matter with a black hole induced spiky profile in the M87 galaxy

Using the spectral energy distribution of M87, a nearby radio galaxy in the Virgo cluster, and assuming a supermassive black hole induced spike in the dark matter halo profile, we exclude any dark matter candidate with a velocity-independent (s-wave) annihilation cross-section of the order of sigma v ~ 10^{-26} cm^3/s and a mass up to O(100) TeV. These limits supersede all previous constraints on thermal, s-wave, annihilating dark matter candidates by orders of magnitude, and rule out the entire canonical mass range. We remark in addition that, under the assumption of a spike, dark matter particles with a mass of a few TeV and an annihilation cross-section of ~ 10^{-27} cm^3/s could explain the TeV gamma-ray emission observed in M87. A central dark matter spike is plausibly present around the supermassive black hole at the center of M87, for various, although not all, formation scenarios, and would have profound implications for our understanding of the dark matter microphysics.