Indication of Sharp and Strong Phase-Transitions from NICER Observations

In this letter, we present a new, weakly model-dependent, test for ``standard" equations of state (EoS) models that disfavor sharp and strong phase-transitions, by using neutron star mass and radius observations. 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 standard EoS models. The radii of neutron stars with different masses are sensitive to the pressures at different densities, and the pressures at different densities are strongly correlated in standard EoS models. We further show that the correlation of the neutron star radii can be significantly weakened, when additional degrees of freedom concerning the first-order phase transitions are added into the EoSs. We propose a new quantity, ${D}_{\mathrm{L}}$, 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) of finding beyond standard EoS models in NICER observations. Future observations with higher measurement accuracy 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.