We present a new formalism designed to discover dark matter annihilation occurring in the Milky Way’s dwarf galaxies. The statistical framework extracts all available information in the data by simultaneously combining observations of all the dwarf galaxies and incorporating the impact of particle physics properties, the distribution of dark matter in the dwarfs, and the detector response. The method performs maximally powerful frequentist searches and produces confidence limits on particle physics parameters. Probability distributions of test statistics under various hypotheses are constructed exactly, without relying on large sample approximations. The derived limits have proper coverage by construction and claims of detection are not biased by imperfect background modeling. We implement this formalism using data from the Fermi Gamma-ray Space Telescope to search for an annihilation signal in the complete sample of Milky Way dwarfs whose dark matter distributions can be reliably determined. We find that the observed data are consistent with background for each of the dwarf galaxies individually as well as in a joint analysis. The strongest constraints are at small dark matter particle masses. Taking the median of the systematic uncertainty in dwarf density profiles, the cross section upper limits are below the pure $s$-wave weak scale relic abundance value ($2.2\times 10^{-26}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$) for dark matter masses below 26 GeV (for annihilation into $b\overline{b}$), 29 GeV (${\tau }^{+}{\tau }^{-}$), 35 GeV ($u\overline{u},d\overline{d},s\overline{s},c\overline{c}$, and $gg$), 6 GeV ($e^{+}{e}^{-}$), and 114 GeV ($\gamma \gamma$). For dark matter particle masses less than 1 TeV, these represent the strongest limits obtained to date using dwarf galaxies.

• Received 16 October 2014

DOI:https://doi.org/10.1103/PhysRevD.91.083535