  We study the structure of compact objects that contain non-self annihilating,
self-interacting dark matter admixed with ordinary matter made of neutron star
and white dwarf materials. We extend the previous work Phys. Rev. D 92 123002
(2015) on these dark compact objects by analyzing the effect of weak and
strongly interacting dark matter with particle masses in the range of 1-500
GeV, so as to set some constraints in the strength of the interaction and the
mass of the dark matter particle. We find that the total mass of the compact
objects increases with decreasing dark matter particle mass. In the strong
interacting case and for dark matter particle masses in the range 1-10 GeV, the
total mass of the compact objects largely exceeds the $2M_\odot$ constraint for
neutron star masses and the nominal $1M_\odot$for white dwarfs, while for
larger dark matter particle masses or in the weakly interacting case the
compact objects show masses in agreement or smaller than these constraints,
thus hinting at the exclusion of strongly self-interacting dark matter of
masses 1-10 GeV in the interior of these compact objects. Moreover, we observe
that the smaller the dark matter particle mass, the larger the quantity of dark
matter captured is, putting constraints on the dark matter mass trapped in the
compact objects so as to fullfill $\simeq 2M_\odot$ observations. Finally, the
inhomogeneity of distribution of dark matter in the Galaxy implies a mass
dependence of compact objects from the environment which can be used to put
constraints on the characteristics of the Galaxy halo DM profile and on
particle mass. In view of the these results, we discuss the formation of the
dark compact objects in an homogeneous and non-homogeneous dark matter
environment.
