  The possibility of explaining the positron and electron excess recently found
by the PAMELA and ATIC collaborations in terms of dark matter (DM) annihilation
has attracted considerable attention. Models surviving bounds from, e.g,
antiproton production generally fall into two classes, where either DM
annihilates directly with a large branching fraction into light leptons, or, as
in the recent models of Arkani-Hamed et al., and of Nomura and Thaler, the
annihilation gives low-mass (pseudo)scalars or vectors $\phi$ which then decay
into $\mu^+\mu^-$ or $e^+e^-$. While the constraints on the first kind of
models have recently been treated by several authors, we study here
specifically models of the second type which rely on an efficient Sommerfeld
enhancement in order to obtain the necessary boost in the annihilation cross
section. We compute the photon flux generated by QED radiative corrections to
the decay of $\phi$ and show that this indeed gives a rather spectacular broad
peak in $E^2d\sigma/dE$, that for these extreme values of the cross section
violate gamma-ray observations of the Galactic center for DM density profiles
steeper than that of Navarro, Frenk and White. The most stringent constraint
comes from the comparison of the predicted synchrotron radiation in the central
part of the Galaxy with radio observations of Sgr A*. For the most commonly
adopted DM profiles, the models that provide a good fit to the PAMELA and ATIC
data are ruled out, unless there are physical processes that boost the local
anti-matter fluxes more than one order of magnitude, while not affecting the
gamma-ray or radio fluxes.
