J -factors for self-interacting dark matter in 20 dwarf spheroidal galaxies

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 σannvrel (σannvrel)0, where σannvrel is the DM annihilation cross-section times relative velocity vrel=|vrel|, angle brackets denote average over vrel, and (σannvrel)0 is the vrel-independent part of σannvrel. If σannvrel is constant in vrel, J-factors only depend on the DM space distribution in the source. However, if σannvrel varies with vrel, 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 Navarro-Frenk-White (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 1 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.