  We study observable signals from dark matter that self-annihilates via the
Sommerfeld effect in dwarf spheroidal galaxies (dSphs). Since the effect of the
Sommerfeld enhancement depends on the velocity of dark matter, it is crucial to
determine the profile of dSphs to compute the J-factor, i.e., the line-of-sight
integral of density squared. In our study we use the prior distributions of the
parameters for satellite density profiles in order to determine the J-factor,
making most out of the recent developments in the N-body simulations and
semi-analytical modeling for the structure formation. As concrete models, we
analyze fermionic dark matter that annihilates via a light scalar and Wino dark
matter in supersymmetric models. We find that, with the more realistic prior
distributions that we adopt in this study, the J-factor of the most promising
dSphs is decreased by a factor of a few, compared with earlier estimates based
on non-informative priors. Nevertheless, the Cherenkov Telescope Array should
be able to detect the thermal Wino dark matter by pointing it toward best
classical or ultrafaint dSphs for 500 hours.
