  We present an analysis of the Dark S3 model in the heavy DM mass region, this
model features an S3 symmetric extension of the scalar sector of the SM
including a scalar $SU(2)$ doublet dark matter candidate. We use publicly
available tools to compute, in addition to conventional physical constraints on
the parameter space of the model, the Sommerfeld enhancement factors for the
present day annihilation cross section and the likelihood profile for a
simulation of an observation run by the Cherenkov Telescope Array of the Coma
Berenices dwarf galaxy. Our results disfavour masses above $\sim$5 TeV mainly
because of overproduction of dark matter not consistent with the relic
abundance observations; we also find a moderately large region with masses in
between 1.2 and 4.9 TeV which predict the correct value of the DM relic and in
addition have a light scalar with the characteristics of the SM Higgs boson
(i.e. within the decoupling limit akin to the THDM). Comparison of our results
with model independent exclusion curves from HESS and other CTA simulations
show that these limits fall short only an order of magnitude in the value of
the annihilation cross section in order to exclude the best fit point of the
model.
