  Tentative evidence for excess GeV-scale gamma rays from the galactic center
has been corroborated by several groups, including the Fermi collaboration, on
whose data the observation is based. Dark matter annihilation into standard
model particles has been shown to give a good fit to the signal for a variety
of final state particles, but generic models are inconsistent with constraints
from direct detection. Models where the dark matter annihilates to mediators
that subsequently decay are less constrained. We perform global fits of such
models to recent data, allowing branching fractions to all possible fermionic
final states to vary. The best fit models, including constraints from the
AMS-02 experiment (and also antiproton ratio), require branching primarily to
muons, with a $\sim 10-20\%$ admixture of $b$ quarks, and no other species.
This suggests models in which there are two scalar mediators that mix with the
Higgs, and have masses consistent with such a decay pattern. The scalar that
decays to $\mu^+\mu^-$ must therefore be lighter than $2m_\tau \cong 3.6$ GeV.
Such a small mass can cause Sommerfeld enhancement, which is useful to explain
why the best-fit annihilation cross section is larger than the value needed for
a thermal relic density. For light mediator masses $\sim (0.2-2)$ GeV, it can
also naturally lead to elastic DM self-interactions at the right level for
addressing discrepancies in small structure formation as predicted by
collisionless cold dark matter.
