Exotic Cores with and without Dark-Matter Admixtures in Compact Stars

We parameterize the core of compact spherical star configurations
by a mass ($m_x$) and a radius ($r_x$)
and study the resulting admissible areas in the total-mass -- total-radius plane.
The employed fiducial equation-of-state models of the corona at radii $r \ge r_x$ and
pressures $p \le p_x = p(r = r_x)$ are that (i) of constant sound velocity and (ii)
a proxy of DY$\Delta$ DD-ME2 provided by Buchdahl's exactly solvable ansatz.
The core ($r < r_x$) may contain any type of material,
e.g.\ Standard-Model matter with unspecified equation of state or/and
an unspecified Dark-Matter admixture.
Employing a toy model for the cool equation of state with first-order phase transition
we discuss also the mass-radius relation of compact stars with an admixture of Dark Matter
in a Mirror-World scenario.