  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 Way's
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 Cen's 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.
