$J$-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 $\gamma$-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 $⟨{\sigma }_{\mathrm{ann}}{v}_{\mathrm{rel}}⟩/({\sigma }_{\mathrm{ann}}{v}_{\mathrm{rel}}{)}_0$, where ${\sigma }_{\mathrm{ann}}{v}_{\mathrm{rel}}$ is the DM annihilation cross-section times relative velocity $v_{\mathrm{rel}}=|{\mathbf{v}}_{\mathrm{rel}}|$, angle brackets denote average over ${\mathbf{v}}_{\mathrm{rel}}$, and $({\sigma }_{\mathrm{ann}}{v}_{\mathrm{rel}}{)}_0$ is the $v_{\mathrm{rel}}$-independent part of ${\sigma }_{\mathrm{ann}}{v}_{\mathrm{rel}}$. If ${\sigma }_{\mathrm{ann}}{v}_{\mathrm{rel}}$ is constant in $v_{\mathrm{rel}}$, $J$-factors only depend on the DM space distribution in the source. However, if ${\sigma }_{\mathrm{ann}}{v}_{\mathrm{rel}}$ 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 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, self-interaction coupling constants and density profiles are provided electronically, ready to be used in other projects.

10 pages, 3 figures and 2 tables

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