  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.

High Energy Physics - Phenomenology;Astrophysics of Galaxies