Confronting new NICER mass-radius measurements with phase transition in dense matter and twin compact stars

The (re)analysis of data on the X-ray emitting pulsars PSR J0030+0451 and J0740+6620, as well as new results on PSR J0437-4715 and J1231-1411, are confronted with the predictions of the equation of state (EoS) models allowing for strong first-order phase transition for the mass-radius ($M$-$R$) diagram. We use models that are based on a covariant density functional (CDF) EoS for nucleonic matter at low densities and a quark matter EoS, parameterized by the speed of sound, at higher densities. To account for the variations in the ellipses for PSR J0030+0451 obtained from different analyses, we examined three scenarios to assess their consistency with our models, focusing particularly on the potential formation of twin stars. We found that in two scenarios, where the ellipses for PSR J0030+0451 and J0437-4715 with masses close to the canonical mass $\sim 1.4\,M_{\odot}$ are significantly separated, our models allow for the presence of twin stars as a natural explanation for potential differences in the radii of these stars.