The expected gamma-ray flux coming from dark matter annihilation in dwarf spheroidal (dSph) galaxies depends on the so-called `J-factor, the integral of the squared dark matter density along the line-of-sight. We examine the degree to which estimates of J are sensitive to contamination (by foreground Milky Way stars and stellar streams) of the stellar-kinematic samples that are used to infer dark matter densities in `ultrafaint dSphs. Applying standard kinematic analyses to hundreds of mock data sets that include varying levels of contamination, we find that mis-classified contaminants can cause J-factors to be overestimated by orders of magnitude. Stellar-kinematic data sets for which we obtain such biased estimates tend 1) to include relatively large fractions of stars with ambiguous membership status, and 2) to give estimates for J that are sensitive to specific choices about how to weight and/or to exclude stars with ambiguous status. Comparing publicly-available stellar-kinematic samples for the nearby dSphs Reticulum~II and Segue~I, we find that only the latter displays both of these characteristics. Estimates of Segue~Is J-factor should therefore be regarded with a larger degree of caution when planning and interpreting gamma-ray observations. Moreover, robust interpretations regarding dark matter annihilation in dSph galaxies in general will require explicit examination of how interlopers might affect the inferred dark matter density profile.
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