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 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.

Effective J -factor of the Galactic Center for velocity-dependent dark matter annihilation

“…Another well-motivated scenario is Sommerfeld-enhanced dark matter annihilation [29], in which case S(v) is large at small v. The effective J-factors for this scenario have been considered previously in the context of dwarf spheroidal galaxies (dSphs) [19][20][21]. Since the dark matter velocity dispersion at the GC is expected to be much larger than in known dSphs, the enhancement is correspondingly larger in dSphs.…”

“…This dependence can lead to a suppression or enhancement of the annihilation rate for low-velocity dark matter. In either case, using the standard J-factor is no longer suitable; instead, it is necessary to calculate an effective J-factor, which incorporates information from the full dark matter velocity distribution [17][18][19][20][21]. Since this velocity distribution has a nontrivial spatial dependence, any velocity dependence of the annihilation cross section leads to a departure from the expected angular distribution of the photon flux arising from dark matter annihilation near the GC.…”

A global analysis of dark matter signals from 27 dwarf spheroidal galaxies using 11 years of Fermi-LAT observations

“…There is an extensive literature on determining J -factors of dSphs [37,40,[48][49][50][51][52][53][54][55][56][57][58][59]. Typically, studies constrain the dark matter distributions within dSphs by using their member stars as tracers of the gravitational poten- 3 6 We use the make3FGLxml.py script by T. Johnson, available at https://fermi.gsfc.nasa.gov/ssc/data/analysis/user/.…”

“…This re-interpretation poses a conceptual difficulty as discussed in Ref. [29,Sec. IX.C] and recent progress has been made in creating a frequentist likelihood function for the spectroscopic observations [56,58,59]. However, at the present time it is not possible to treat the majority of dSphs in the frequentist framework.…”

On velocity-dependent dark matter annihilations in dwarf satellites

“…The fact that accurate predictions for the gamma-ray flux induced by DM annihilations require a careful study of the phase-space distribution f DM ( x, v) -as apposed to results approximating it with velocity moments -was acknowledged only recently, see e.g. [29][30][31], with the notable exception of the pioneering study in ref. [32].…”