Twin Stars and the Stiffness of the Nuclear Equation of State: Ruling Out Strong Phase Transitions below 1.7 n(0) with the New NICER Radius Measurements

We explore the connection between the stiffness of a hadronic equation of state (EoS) with a sharp phase transition to quark matter to its tidal deformability. For this we employ a hadronic relativistic mean field model with a parameterized effective nucleon mass to vary the stiffness in conjunction with a constant speed of sound EoS for quark matter. We compute multiple scenarios with phase transitions according to the four possible cases of a hybrid star EoS with a stable second branch. We demonstrate how the effective nucleon mass can be constrained by using gravitational-wave data. We find that certain values of the effective nucleon mass are incompatible with GW170817 and a phase transition simultaneously. By using the recent NICER measurements of J0030+0451 we constrain our results further and find that strong phase transitions with a visible jump in the mass-radius relation are ruled out at 1 sigma at densities below 1.7 times saturation density.