The appearance of quark phases in the dense interior of neutron stars
provides one possibility to soften the equation of state (EOS) of neutron star
matter at high densities. This softening leads to more compact equilibrium
configurations of neutron stars compared to pure hadronic stars of the same
mass. We investigate the question to which amount the compactness of a neutron
star can be attributed to the presence of a quark phase. For this purpose we
employ several hadronic EOS in the framework of the relativistic mean-field
(RMF) model and an extended MIT bag model to describe the quark phase. We find
that - almost independent of the model parameters - the radius of a pure
hadronic neutron star gets typically reduced by 20-30% if a pure quark phase in
the center of the star does exist. For some EOS we furthermore find the
possibility of a "third family" of compact stars which may exist besides the
two known families of white dwarfs and neutron stars. We show how an
experimental proof of the existence of a third family by mass and radius
measurements may provide a unique signature for a phase transition inside
neutron stars.Comment: 37 pages, 18 eps-figures included, LaTe
