  An analysis of the Fermi gamma ray space telescope data has recently revealed
a resolved gamma-ray feature close to the galactic center which is consistent
with monochromatic photons at an energy of about 130 GeV. If interpreted in
terms of dark matter (DM) annihilating into \gamma\gamma (\gamma Z, \gamma h),
this would correspond to a DM particle mass of roughly 130 GeV (145 GeV, 155
GeV). The rate for these loop-suppressed processes, however, is larger than
typically expected for thermally produced DM. Correspondingly, one would
generically expect even larger tree level production rates of standard model
fermions or gauge bosons. Here, we quantify this expectation in a rather
model-independent way by relating the tree level and loop amplitudes with the
help of the optical theorem. As an application, we consider bounds from
continuum gamma rays, radio and antiproton data on the tree level amplitudes
and translate them into constraints on the loop amplitudes. We find that,
independently of the DM production mechanism, any DM model aiming at explaining
the line signal in terms of charged standard model particles running in the
loop is in rather strong tension with at least one of these constraints, with
the exception of loops dominated by top quarks. We stress that attempts to
explain the 130 GeV feature with internal bremsstrahlung do not suffer from
such difficulties.
