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.

The present paper describes a quasi‐experimental research presenting a workplace training program aimed at helping managers to be more supportive of their employees' autonomy. Drawing on self‐determination theory, we built a pre/post questionnaire design measuring perceived autonomy support, need satisfaction, need frustration, autonomous motivation, controlled motivation, work engagement and job burnout. Seven managers were trained according to the autonomy support training program. We assessed 39 of their employees before and after the intervention. Moreover, 133 employees whose managers were not included in the training program constituted the control group. Regarding the experimental group, the results showed significant statistical differences regarding perceived autonomy support from managers, autonomous motivation, need satisfaction, work engagement and job burnout. No significant effects regarding perceived autonomy support from coworkers controlled motivation, or need frustration were observed. This study provides added value to the theory of need satisfaction and demonstrates that training managers to be need‐supportive may be effective in improving positive work‐related outcomes and reducing negative outcomes.