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The recent NICER measurement of the radius of the neutron star PSR J0740+6620, and the inferred small variation of radii from 1.4 to 2.1M_⊙, reveal key features of the equation of state of neutron star matter. The pressure rises rapidly in the regime of baryon densityn∼ 2–4 times nuclear saturation density,n₀—the region where we expect hadronic matter to be undergoing transformation into quark matter—and the pressure in the nuclear regime is greater than predicted by microscopic many-body variational calculations of nuclear matter. To incorporate these insights into the microscopic physics from the nuclear to the quark matter regimes, we construct an equation of state, QHC21, within the framework of quark–hadron crossover. We include nuclear matter results primarily based on the state-of-the-art chiral effective field theory, but also note results of using nuclear matter variational calculations based on empirical nuclear forces. We employ explicit nuclear degrees of freedom only up ton∼ 1.5n₀, in order to explore the possibility of further physical degrees of freedom than nucleonic here. The resulting QHC21, which has a peak in sound velocity in ∼2–4n₀, is stiffer than the earlier QHC19 below 2n₀, predicting larger radii in substantial agreement with the NICER data.

 

Neutron stars were first posited in the early thirties and discovered as pulsars in late sixties; however, only recently are we beginning to understand the matter they contain. This talk describes the continuing development of a consistent picture of the liquid interiors of neutron stars, driven by four advances: observations of heavy neutron stars with masses in the range of two solar masses; inferences of masses and radii simultaneously for an increasing number of neutron stars in low mass X-ray binaries, and ongoing determinations via the NICER observatory; the observation of the binary neutron star merger, GW170817, through gravitational waves as well as across the electromagnetic spectrum; and an emerging understanding in QCD of how nuclear matter can turn into deconfined quark matter in the interior. We describe the modern quark-hadron crossover equation of state, QHC18 and now QHC19, and the corresponding neutron stars, which agree well with current observations. 

We present a much improved equation of state for neutron star matter, QHC19, with a smooth crossover from the hadronic regime at lower densities to the quark regime at higher densities. We now use the Togashi et al.equation of state, a generalization of the Akmal–Pandharipande–Ravenhall equation of state of uniform nuclear matter, in the entire hadronic regime; the Togashi equation of state consistently describes nonuniform as well as uniform matter, and matter at beta equilibrium without the need for an interpolation between pure neutron and symmetric nuclear matter. We describe the quark matter regime at higher densities with the Nambu–Jona–Lasinio model, now identifying tight constraints on the phenomenological universal vector repulsion between quarks and the pairing interaction between quarks arising from the requirements of thermodynamic stability and causal propagation of sound. The resultant neutron star properties agree very well with the inferences of the LIGO/Virgo collaboration, from GW170817, of the pressure versus baryon density, neutron star radii, and tidal deformabilities. The maximum neutron star mass allowed by QHC19 is 2.35 solar masses, consistent with all neutron star mass determinations.