On the moment of inertia of PSR J0737-3039 A from LIGO/Virgo and NICER

We perform a Bayesian analysis of neutrons star moment of inertia by utilizing the available gravitational-wave data from LIGO/Virgo (GW170817 and GW190425) and mass-radius measurements from the Neutron Star Interior Composition Explorer (PSR J0030+0415 and PSR J0740+6620), incorporating the possible phase transition in the pulsar inner core. We find that the moment of inertia of pulsar A in the double pulsar binary J0737-3039 is $\sim1.30\times10^{45}\,{\rm g\,cm^2}$, which only slightly depends on the employed hadronic equation of states. We also demonstrate how a moment of inertia measurement would improve our knowledge of the equation of state and the mass-radius relation for neutron stars and discuss whether a quark deconfinement phase transition is supported by the available data and forthcoming data that could be consistent with this hypothesis. We find that if pulsar A is a quark star, that its moment of inertia is a large value of $\sim1.55\times10^{45}\,{\rm g\,cm^2}$ suggesting the possibility of distinguishing it from (hybrid-)neutron stars with measurements of PSR J0737-3039A moment of inertia. We finally demonstrate the moment-of-inertia-compactness universal relations and provide analytical fits for both (hybrid-)neutron star and quark star results based on our analysis.