Celestial-Body Focused Dark Matter Annihilation Throughout the Galaxy
  Indirect detection experiments typically measure the flux of annihilating
dark matter (DM) particles propagating freely through galactic halos. We
consider a new scenario where celestial bodies "focus" DM annihilation events,
increasing the efficiency of halo annihilation. In this setup, DM is first
captured by celestial bodies, such as neutron stars or brown dwarfs, and then
annihilates within them. If DM annihilates to sufficiently long-lived
particles, they can escape and subsequently decay into detectable radiation.
This produces a distinctive annihilation morphology, which scales as the
product of the DM and celestial body densities, rather than as DM density
squared. We show that this signal can dominate over the halo annihilation rate
in $\gamma$-ray observations in both the Milky Way Galactic center and globular
clusters. We use \textit{Fermi} and H.E.S.S. data to constrain the DM-nucleon
scattering cross section, setting powerful new limits down to
$\sim10^{-39}~$cm$^2$ for sub-GeV DM using brown dwarfs, which is up to nine
orders of magnitude stronger than existing limits. We demonstrate that neutron
stars can set limits for TeV-scale DM down to about $10^{-47}~$cm$^2$.
