Indication of Sharp and Strong Phase-Transitions from NICER Observations

We present a new method that quantitatively identifies the occurrence probability of equations of state (EoS) beyond "standard" EoS models that disfavor sharp and strong phase-transitions, based on neutron star mass and radius observations. The radii of two neutron stars with different masses are naturally correlated, in part because both of them are sensitive to the symmetry energy of the EoS. We show the radii of two neutron stars observed by NICER (PSR J0740+6620 and PSR 0030+0451) are correlated if these two neutron stars are built upon EoSs with no sharp and strong first-order phase transitions. We further show that the linear correlation of the neutron star radii can be significantly weakened, when strong and sharp first-order phase transitions occur. We propose a new quantity, DL, which measures the extent to which the linear correlation of the radii of two neutron stars is weakened. Our method gives a 48% identification probability (with a 5% false alarm rate) that the NICER observations indicate the necessity for a sharp and strong phase transition. Future observations can confirm or rule out this identification. Our method is generalizable to any pair of neutron star masses and can be employed with other sets of observations in the future.