Résumé
We demonstrate the unprecedented capabilities of the Event Horizon Telescope (EHT) to image the innermost dark matter profile in the vicinity of the supermassive black hole at the center of the M87 radio galaxy. We present the first model of the synchrotron emission induced by dark matter annihilations from a spiky profile in the close vicinity of a supermassive black hole, accounting for strong gravitational lensing effects. Our results show that the EHT should readily resolve dark matter spikes if present. Moreover, the photon ring surrounding the silhouette of the black hole is clearly visible in the spike emission, which introduces observable small-scale structure into the signal. We find that the dark matter-induced emission provides an adequate fit to the existing EHT data, implying that in addition to the jet, a dark matter spike may account for a sizable portion of the millimeter emission from the innermost (sub-parsec) region of M87. Regardless, our results show that the EHT can probe very weakly annihilating dark matter. Current EHT observations already constrain very small cross-sections, typically down to a few 10^{-31} cm^3/s for a 10 GeV candidate, close to characteristic values for p-wave-suppressed annihilation. Future EHT observations will further improve constraints on the DM scenario.