  The properties of compact stars and in particular the existence of twin star
solutions are investigated within an effective model that is constrained by
lattice QCD thermodynamics. The model is modified at large baryon densities to
incorporate a large variety of scenarios of first order phase transitions to a
phase of deconfined quarks. This is achieved by matching two different variants
of the bag model equation of state, in order to estimate the role of the Bag
model parameters on the appearance of a second family of neutron stars. The
produced sequences of neutron stars are compared with modern constrains on
stellar masses, radii, and tidal deformability from astrophysical observations
and gravitational wave analyses. It is found that most of the possible
scenarios disfavor a strong phase transition to quark matter and do not support
the conjecture of a second family of neutron stars.
