Title: <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>J</mml:mi></mml:math>-factors for self-interacting dark matter in 20 dwarf spheroidal galaxies
Abstract: Dwarf spheroidal galaxies are among the most promising targets for indirect dark matter (DM) searches in $\ensuremath{\gamma}$ rays. The $\ensuremath{\gamma}$-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 $⟨{\ensuremath{\sigma}}_{\mathrm{ann}}{v}_{\mathrm{rel}}⟩/({\ensuremath{\sigma}}_{\mathrm{ann}}{v}_{\mathrm{rel}}{)}_{0}$, where ${\ensuremath{\sigma}}_{\mathrm{ann}}{v}_{\mathrm{rel}}$ is the DM annihilation cross-section times relative velocity ${v}_{\mathrm{rel}}=|{\mathbit{v}}_{\mathrm{rel}}|$, angle brackets denote average over ${\mathbit{v}}_{\mathrm{rel}}$, and $({\ensuremath{\sigma}}_{\mathrm{ann}}{v}_{\mathrm{rel}}{)}_{0}$ is the ${v}_{\mathrm{rel}}$-independent part of ${\ensuremath{\sigma}}_{\mathrm{ann}}{v}_{\mathrm{rel}}$. If ${\ensuremath{\sigma}}_{\mathrm{ann}}{v}_{\mathrm{rel}}$ is constant in ${v}_{\mathrm{rel}}$, $J$-factors only depend on the DM space distribution in the source. However, if ${\ensuremath{\sigma}}_{\mathrm{ann}}{v}_{\mathrm{rel}}$ varies with ${v}_{\mathrm{rel}}$, 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 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.