  Indirect detection is one of the most powerful methods to search for
annihilating dark matter. In this work, we investigate the impact of
non-perturbative effects in the indirect detection of dark matter. For this
purpose we utilize a minimal model consisting of a fermionic dark matter
candidate in the TeV mass range that interacts via scalar- and pseudo-scalar
interactions with a massive scalar mediator mixing with the Higgs. The scalar
interaction induces an attractive Yukawa potential between dark matter
particles, such that annihilations are Sommerfeld enhanced, and bound states
can form. These non-perturbative effects are systematically dealt with
(potential) non-relativistic effective field theories and we derive the
relevant cross sections for dark matter. We discuss their impact on the relic
density and indirect detection. Annihilations in dwarf galaxies and the
Galactic Center require special care and we derive generalized $J$-factors for
these objects that account for the non-trivial velocity dependence of the cross
sections in our model. We use limits on the gamma-ray flux based on Fermi-LAT
observations and limits on the rate of exotic energy injection from Planck to
derive bounds on the parameter space of the model. Finally, we estimate the
impact that future limits from the Cherenkov Telescope Array are expected to
have on the model.
