Supermassive neutron stars rule out twin stars

We investigate the implications of a hypothetical $2.5\,\mathrm{M_\odot}$ neutron star in regard to the possibility of a strong phase transition to quark matter. We use equations of state (EoS) of varying stiffness provided by a parameterizable relativistic mean filed 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 twin stars, especially for soft EoSs. As a result twin stars and maximal masses of $M_{max}\gtrsim2.2\,M_\odot$ are mutually exclusive.