Systematic Uncertainties and Their Impact on Gamma-Ray Searches for Dark Matter in Dwarf Galaxies
Gamma-ray observations of Milky Way dwarf galaxies provide some of the strongest constraints on dark matter annihilation and are approaching the sensitivity required to test dark matter interpretations of the Galactic Center Gamma-Ray Excess. The results, however, depend critically on the inferred dark matter distributions in these systems, conventionally described by their $J$-factors and spatial profiles. We review several sources of systematic uncertainty in dwarf galaxy $J$-factor determinations, including stellar membership, unresolved binaries, departures from equilibrium and spherical symmetry, and assumptions regarding the stellar and dark matter density profiles. Most $J$-factor determinations reported in the literature neglect several of these uncertainties, and the resulting measurements are often more dispersed than their quoted uncertainties would suggest. This indicates uncertainties of order $Δ\log_{10}J\sim0.5$ or larger may be warranted for many of these systems. Using an ensemble of simulated Fermi-LAT observations of a stacked sample of 27 dwarf galaxies, we quantify how these unmodeled uncertainties affect the resulting constraints on the dark matter annihilation cross section. We find that adding an uncertainty of $Δ\log_{10}J\sim 0.5$ or 1.0 in quadrature weakens the median upper limits of a stacked analysis by factors of 1.4 or 3.2, respectively. Furthermore, underestimating these uncertainties can cause such analyses to exclude the true annihilation cross section more frequently than the nominal confidence level would imply. Such undercoverage is especially pronounced in stacked analyses and persists even when the adopted and true $J$-factor uncertainties agree. Mismodeling spatially extended halos as point sources, as is sometimes done, further strengthens the resulting limits and increases the probability that true signals will be incorrectly excluded.