Abstract : The Milky Way's dwarf spheroidal (dSph) galaxies are among the best targets for the indirect detection of dark matter (DM) with γ-rays. The expected gamma-ray flux depends on the so-called 'J-factor', the integral of the squared DM density along the line-of-sight. Using a large number of simulated dSphs, we have defined an optimized Jeans analysis setup for the reconstruction of the DM density with stellar-kinematic data. Employing this setup, we provide here estimates of astrophysical J-factors for twenty-two Galactic dSphs, including the newly discovered Reticulum II. We finally identify several criteria that may indicate a contamination of a kinematic dataset by interlopers, leading to unreliable J-factors. We find that the kinematic sample of Segue I, one of the closest dSph, might be affected by this issue.
