Bayesian analysis of the properties of hybrid stars with the Nambu-Jona-Lasinio model

The possible presence of deconfined matter in the cores of massive neutron stars is the subject of a large debate. In this context, it is important to set limits on the size and characteristics of a hypothetical quark core compatible with the present astrophysical constraints. To this aim, we present a Bayesian analysis of the properties of nonrotating hybrid stars at equilibrium with quark matter cores, as described by the SU(3) Nambu-Jona-Lasinio (NJL) model. The hadronic phase is described by a unified metamodeling approach, with a prior parameter space covering the present uncertainties on nuclear matter properties with nucleonic degrees of freedom. The parameter space of the NJL model includes vector-isoscalar and vector-isovector couplings and, additionally, an effective bag constant for the quark pressure is introduced as a free parameter. The phase transition is assumed to be first order with charge neutral phases, following the Maxwell construction. Our Bayesian framework includes filters on the experimental and theoretical low-density nuclear physics knowledge (atomic masses, ab initio calculations of the EoS) and high density constraints from astrophysical observations (maximum mass of J0348 + 0432, binary tidal deformability of the GW170817 event). We find that microscopic vector interactions play an important role in quark matter in order to stiffen the equation of state sufficiently to reach high star masses, in agreement with previous studies. Even within a very large prior for both the hadronic phase and the quark phase and the important freedom brought by the effective bag constant, our posterior quark cores tend to be relatively small and only appear in very heavy stars (M greater than or similar to 2M(circle dot)). Coincidentally, the inclusion of the nucleon-quark transition (deconfinement transition) only weakly affects the radii of compact stars, foreshadowing a very low observability of a possible phase transition using x-ray radii measurements.