  We present a model of compact stars with a dark matter core. The hadronic
equation of state is based on the parity doublet model and does not present a
phase transition to quark matter. Instead, a strong first-order phase
transition to dark matter described by a constant speed of sound model leads to
the scenario of compact star mass twins. Compact star structural properties
which obey state-of-the-art measurements and constraints are presented.
