  We used radio observations of the neighbour galaxy M31 in order to put
constraints on dark matter particle mass and annihilation cross section. Dark
matter annihilation in M31 halo produces highly energetic leptons, which emit
synchrotron radiation on radio frequencies in the galactic magnetic field. We
predicted expected radio fluxes for the two annihilation channels: \chi\chi ->
bb* and \chi\chi -> \tau^+\tau^-. We then compared them with available data on
the central radio emission of M31 as observed by four radio surveys: VLSS (74
MHz), WENSS (325 MHz), NVSS (1400 MHz) and GB6 (4850 MHz). Assuming a standard
NFW dark matter density profile and a conservative magnetic field distribution
inside the Andromeda galaxy, we find that the thermal relic annihilation cross
section <\sigma v> = 3*10^{-26} cm^3/s or higher are only allowed for WIMP
masses greater than 100 GeV and 55 GeV for annihilation into bb* and
\tau^+\tau^- respectively. Taking into account potential uncertainties in the
distributions of DM density and magnetic field, the mentioned WIMP limiting
masses can be as low as 23 GeV for both channels, and as high as 280 and 130
GeV for annihilation into bb* and \tau^+\tau^- respectively. These mass values
exceed the best up-to-day known constraints from Fermi gamma observations: 40
GeV and 19 GeV respectively [A.Geringer-Sameth and S.M.Koushiappas, Phys. Rev.
Lett. 107, 241303 (2011)]. Precise measurements of the magnetic field in the
relevant region and better reconstruction of the DM density profile of M31 will
be able to reduce the uncertainties of our exclusion limits.
