Cosmological prior for the $J$-factor estimation of dwarf spheroidal galaxies

Dark matter halos of dwarf spheroidal galaxies (dSphs) play important roles in dark matter detection. Generally we estimate the halo profile using a kinematical equation of dSphs but the halo profile has a large uncertainty because we have only a limited number of kinematical dataset. In this paper, we utilize cosmological models of dark matter subhalos to obtain better constraints on halo profile of dSphs. The constraints are realized as two cosmological priors: satellite prior, based on a semi-analytic model of the accretion history of subhalos and their tidal stripping effect, and stellar-to-halo mass relation prior, which estimates halo mass of a galaxy from its stellar mass using empirical correlations. In addition, we adopt a radial dependent likelihood function by considering velocity dispersion profile, which allows us to mitigate the parameter degeneracy in the previous analysis using a radial independent likelihood function with averaged dispersion. Using these priors, we estimate the squared dark matter density integrated over the region-of-interest (so-called $J$-factor) of 8 classical and 27 ultra-faint dSphs. Our method significantly decreases the uncertainty of $J$-factors (upto about $20\%$) compared to the previous radial independent analysis. We confirm the model dependence of $J$-factor estimates by evaluating Bayes factors of different model setups and find that the estimates are still stable even when assuming different cosmological models.