  We report on a three--month research project for undergraduate students about
the mass-radius relation of compact stars. The equation of state used is
constrained at low densities by well-established equations of state of the
nuclear phase (the solid crust) and then extended to higher densities with a
phenomenological, parametric approach. A first order phase transition from
hadronic matter to a phase of higher density, assumed to be quark matter is
studied in addition. The mass-radius relation is obtained by solving
numerically the Tolman-Oppenheimer-Volkoff equation. We derive some conditions
for the existence of a third family of compact stars on the form of the
equation of state and its different global properties.
