Dark matter (DM) is the most abundant material in the Universe, but has so far been detected only via its gravitational effects. Several theories suggest that pairs of DM particles can annihilate into a flash of light at gamma-ray wavelengths. While gamma-ray emission has been observed from environments where DM is expected to accumulate, such as the centre of our Galaxy, other high energy sources can create a contaminating astrophysical gamma-ray background, thus making DM detection difficult. In principle, dwarf galaxies around the Milky Way are a better place to look -- they contain a greater fraction of DM with no astrophysical gamma-ray background -- but they are too distant for gamma-rays to have been seen. A range of observational evidence suggests that Omega Centauri (omega Cen or NGC 5139), usually classified as the Milky Ways largest globular cluster, is really the core of a captured and stripped dwarf galaxy. Importantly, Omega Cen is ten times closer to us than known dwarfs. Here we show that not only does Omega Cen contain DM with density as high as compact dwarf galaxies, but also that it emits gamma-rays with an energy spectrum matching that expected from the annihilation of DM particles with mass 31$pm$4 GeV (68% confidence limit). No astrophysical sources have been found that would otherwise explain Omega Cens gamma-ray emission, despite deep multi-wavelength searches. We anticipate our results to be the starting point for even deeper radio observations of Omega Cen. If multi-wavelength searches continue to find no astrophysical explanations, this pristine, nearby clump of DM will become the best place to study DM interactions through forces other than gravity.
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