Radio and gamma-ray constraints on dark matter annihilation in the Galactic center

We determine upper limits on the dark matter (DM) self-annihilation cross section for scenarios in which annihilation leads to the production of electron--positron pairs. In the Galactic centre (GC), relativistic electrons and positrons produce a radio flux via synchroton emission, and a gamma ray flux via bremsstrahlung and inverse Compton scattering. On the basis of archival, interferometric and single-dish radio data, we have determined the radio spectrum of an elliptical region around the Galactic centre of extent 3 degrees semi-major axis (along the Galactic plane) and 1 degree semi-minor axis and a second, rectangular region, also centered on the GC, of extent 1.6 degrees x 0.6 degrees. The radio spectra of both regions are non-thermal over the range of frequencies for which we have data: 74 MHz -- 10 GHz. We also consider gamma-ray data covering the same region from the EGRET instrument (about GeV) and from HESS (around TeV). We show how the combination of these data can be used to place robust constraints on DM annihilation scenarios, in a way which is relatively insensitive to assumptions about the magnetic field amplitude in this region. Our results are approximately an order of magnitude more constraining than existing Galactic centre radio and gamma ray limits. For a DM mass of m_\chi =10 GeV, and an NFW profile, we find that the velocity-averaged cross-section must be less than a few times 10^-25 cm^3 s^-1.