The detection of gravitational waves from binary neutron star mergers has opened the possibility to constrain the equation of state (EoS) and probing for a phase transition of high-density QCD matter. The measurement of GW170817 points to a soft equation of state that feature more compact neutron stars. We find that a first order phase transition from hadronic matter to quark matter can generate neutron stars compact enough to be compatible with the GW170817 measurement, even for comparatively hard hadronic EOSs.  For GW190814 an unidentified compact obejct with a mass of 2.5 M⊙ was observed.  We investigate the implications of that object being a 2.5 M⊙ neutron star in regard to the possibility of a strong phase transition.  We use EOSs of varying stiffness provided by a parameterizable relativistic mean field model transitioning in a first order phase transition to quark matter with a constant speed of sound.  We find a strong connection between the discontinuity in energy density and the maximal mass generated by the EOS.  We demonstrate, that high maximal masses cannot be realized for large discontinuities in energy density, which are necessary for visible mass gaps in the mass radius relation, i.e. twin stars, especially for soft EOSs.  As a result we conclude that twin stars and maximal masses of Mmax > 2.2 M⊙ are mutually exclusive.

 

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