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 gamma rays. The gamma-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 / (0), where sigma(ann)v(rel) is the DM annihilation cross-section times relative velocity v(rel) = vertical bar v(rel)vertical bar angle brackets denote average over v(rel), and (sigma(ann)v(rel)) is the v(rel)-independent part of sigma(ann)v(rel). If sigma(ann)v(rel) is constant in v(rel), J-factors only depend on the DM space distribution in the source. However, if sigma(ann)v(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 NavarroFrenk-White (NEW) 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 Mactors 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 he used in other projects.