Supermassive neutron stars rule out twin stars

We investigate the implications of a hypothetical 2.5 M_⊙ neutron star in regard to the possibility of a first order phase transition to quark matter. We use equations of state (EoS) of varying stiffness provided by a parametrizable relativistic mean field model transitioning to a constant speed of sound EoS. We find a strong connection between the discontinuity in energy density and the maximal neutron star mass. We demonstrate, that high maximal masses cannot be realized for large discontinuities. As a result visible mass gaps, i.e., twin stars, and masses of M_max≳2.2 M_⊙ are mutually exclusive.