Gamma Rays from Dark Matter Annihilations Strongly Constrain the Substructure in Halos

To fit recent data, $e^{\pm }$ from dark matter (DM) needs a boosted annihilation rate. This may imply an observable level of gamma rays from nearby galaxy clusters for the Fermi satellite. Using EGRET data, we limit the minimum mass of DM substructures to be about $5\times {10}^3$ times larger than for cold DM, meaning a cutoff similar to, e.g., warm DM. We numerically simulate clusters to reliably model the background. If we assume no anomalous boost factor, we find comparable levels of gamma-ray emission from DM and cosmic ray interactions, giving a chance with future data to characterize the DM.