Dense matter equation of state and neutron star properties from nuclear theory and experiment

The equation of state of dense matter determines the structure of neutron stars, their typical radii, and maximum masses. Recent improvements in theoretical modeling of nuclear forces from the low-energy effective field theory of QCD has led to tighter constraints on the equation of state of neutron-rich matter at and somewhat above the densities of atomic nuclei, while the equation of state and composition of matter at high densities remains largely uncertain and open to a multitude of theoretical speculations. In the present work we review the latest advances in microscopic modeling of the nuclear equation of state and demonstrate how to consistently include also empirical nuclear data into a Bayesian posterior probability distribution for the model parameters. Derived bulk neutron star properties such as radii, moments of inertia, and tidal deformabilities are computed, and we discuss as well the limitations of our modeling.Comment: 9 pages, 5 figures. To appear in the AIP Proceedings of the Xiamen-CUSTIPEN Workshop on the EOS of Dense Neutron-Rich Matter in the Era of Gravitational Wave Astronomy, Jan. 3-7, Xiamen, Chin

Proton pairing in neutron stars from chiral effective field theory

We study the ${}^{1}S_0$ proton pairing gap in beta-equilibrated neutron star matter within the framework of chiral effective field theory. We focus on the role of three-body forces, which strongly modify the effective proton-proton spin-singlet interaction in dense matter. We find that three-body forces generically reduce both the size of the pairing gap and the maximum density at which proton pairing may occur. The pairing gap is computed within BCS theory, and model uncertainties are estimated by varying the nuclear potential and the choice of single-particle spectrum in the gap equation. We find that a second-order perturbative treatment of the single-particle spectrum suppresses the proton ${}^{1}S_0$ pairing gap relative to the use of a free spectrum. We estimate the critical temperature for the onset of proton superconductivity to be $T_c = (3.7 - 6.0)\times 10^{9}$ K, which is consistent with previous theoretical results in the literature and marginally within the range deduced from a recent Bayesian analysis of neutron star cooling observations.Comment: 8 pages, 9 figure

Hans Bethe: The Nuclear Many Body Problem

We discuss the work of Hans Bethe and others in formulating a theoretical foundation for the nuclear shell model. Written for a general audience, this article describes the evolution from Brueckner's reaction matrix theory to the Moszkowski-Scott separation method and ultimately to the Reference Spectrum method of Bethe, Brandow, and Petschek. We also discuss connections with the recently developed low momentum nucleon-nucleon interactions.Comment: 25 pages, 15 figures, In "Hans Bethe and His Physics" (World Scientific, Singapore, 2006

Divergence of the isospin-asymmetry expansion of the nuclear equation of state in many-body perturbation theory

The isospin-asymmetry dependence of the nuclear matter equation of state obtained from microscopic chiral two- and three-body interactions in second-order many-body perturbation theory is examined in detail. The quadratic, quartic and sextic coefficients in the Maclaurin expansion of the free energy per particle of infinite homogeneous nuclear matter with respect to the isospin asymmetry are extracted numerically using finite differences, and the resulting polynomial isospin-asymmetry parametrizations are compared to the full isospin-asymmetry dependence of the free energy. It is found that in the low-temperature and high-density regime where the radius of convergence of the expansion is generically zero, the inclusion of higher-order terms beyond the leading quadratic approximation leads overall to a significantly poorer description of the isospin-asymmetry dependence. In contrast, at high temperatures and densities well below nuclear saturation density, the interaction contributions to the higher-order coefficients are negligible and the deviations from the quadratic approximation are predominantly from the noninteracting term in the many-body perturbation series. Furthermore, we extract the leading logarithmic term in the isospin-asymmetry expansion of the equation of state at zero temperature from the analysis of linear combinations of finite differences. It is shown that the logarithmic term leads to a considerably improved description of the isospin-asymmetry dependence at zero temperature.Comment: 14 pages, 9 figures, 2 tables, some minor changes, references updated, matches published versio