  The annihilations of neutralino dark matter (or other dark matter candidate)
generate, among other Standard Model states, electrons and positrons. These
particles emit synchrotron photons as a result of their interaction with the
Galactic Magnetic Field. In this letter, we use the measurements of the WMAP
satellite to constrain the intensity of this synchrotron emission and, in turn,
the annihilation cross section of the lightest neutralino. We find this
constraint to be more stringent than that provided by any other current
indirect detection channel. In particular, the neutralino annihilation cross
section must be less than ~ 3 x 10^-26 cm^3/s (1 x 10^25 cm^3/s) for 100 GeV
(500 GeV) neutralinos distributed with an NFW halo profile. For the
conservative case of an entirely flat dark matter distribution within the inner
8 kiloparsecs of the Milky Way, the constraint is approximately a factor of 30
less stringent. Even in this conservative case, synchrotron measurements
strongly constrain, for example, the possibility of wino or higgsino neutralino
dark matter produced non-thermally in the early universe.
