  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.
