Dwarf spheroidal galaxies are among the most promising targets for indirect dark matter (DM) searches in γ-rays. The γ-ray flux from DM annihilation in a dwarf spheroidal galaxy is proportional to the J-factor of the source. The J-factor of a dwarf spheroidal galaxy is the line-of-sight integral of the DM mass density squared times σannv rel /(σannv rel )0, where σannv rel is the DM annihilation cross-section times relative velocity v rel = |v rel |, angle brackets denote average over v rel , and (σannv rel )0 is the v rel -independent part of σannv rel . If σannv rel is constant in v rel , J-factors only depend on the DM space distribution in the source. However, if σannv rel varies with v rel , as in the presence of DM self-interactions, J-factors also depend on the DM velocity distribution, and on the strength and range of the DM self-interaction. Models for self-interacting DM are increasingly important in the study of the small scale clustering of DM, and are compatible with current astronomical and cosmological observations. Here we derive the J-factor of 20 dwarf spheroidal galaxies from stellar kinematic data under the assumption of Yukawa DM self-interactions. J-factors are derived through a profile Likelihood approach, assuming either NFW or cored DM profiles. We also compare our results with J-factors derived assuming the same velocity for all DM particles in the target galaxy. We find that this common approximation overestimates the J-factors by up to one order of magnitude. J-factors for a sample of DM particle masses and self-interaction coupling constants, as well as for NFW and cored density profiles, are provided electronically, ready to be used in other projects.
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