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Register a new userMicroscopic Theory of the Nuclear Equation of State and Neutron Star Structure
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The Bethe-Brueckner-Goldstone many-body theory of the Nuclear Equation of State is reviewed in some details. In the theory, one performs an expansion in terms of the Brueckner two-body scattering matrix and an ordering of the corresponding many-body diagrams according to the number of their hole-lines. Recent results are reported, both for symmetric and for pure neutron matter, based on realistic two-nucleon interactions. It is shown that there is strong evidence of convergence in the expansion. Once three-body forces are introduced, the phenomenological saturation point is reproduced and the theory is applied to the study of neutron star properties. One finds that in the interior of neutron stars the onset of hyperons strongly softens the Nuclear Equation of State. As a consequence, the maximum mass of neutron stars turns out to be at the lower limit of the present phenomenological observation.
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We review the current status and recent progress of microscopic many-body approaches and phenomenological models, which are employed to construct the equation of state of neutron stars. The equation of state is relevant for the description of their structure and dynamical properties, and it rules also the dynamics of core-collapse supernovae and binary neutron star mergers. We describe neutron star matter assuming that the main degrees of freedom are nucleons and hyperons, disregarding the appearance of quark matter. We compare the theoretical predictions of the different equation-of-state models with the currently available data coming from both terrestrial laboratory experiments and recent astrophysical observations. We also analyse the importance of the nuclear strong interaction and equation of state for the cooling properties of neutron stars. We discuss the main open challenges in the description of the equation of state, mainly focusing on the limits of the different many-body techniques, the so-called hyperon puzzle, and the dependence of the direct URCA processes on the equation of state.
Neutron star (NS) is a unique astronomical compact object where the four fundamental interactions have been revealed from the observation and studied in different ways. While the macroscopic properties of NS like mass and radius can be determined within the General Relativity using a realistic equation of state (EOS) of NS matter, such an EOS is usually generated by a nuclear structure model like, e.g., the nuclear mean-field approach to asymmetric nuclear matter. Given the radius of NS extended to above 10 km and its mass up to twice the solar mass, NS is expected to be tidally deformed when it is embedded in a strong tidal field. Such a tidal effect was confirmed unambiguously in the gravitation wave signals detected recently by the LIGO and Virgo laser interferometers from GW170817, the first ever direct observation of a binary NS merger. A nonrelativistic mean-field study is carried out in the present work within the Hartree-Fock formalism to construct the EOS of NS matter, which is then used to determine the tidal deformability, gravitational mass, and radius of NS. The mean-field results are compared with the constraints imposed for these quantities by the global analysis of the observed GW170817 data, and a strong impact by the incompressibility of nuclear matter on the hydrostatic configuration of NS is shown.
We present predictions for neutron star tidal deformabilities obtained from a Bayesian analysis of the nuclear equation of state, assuming a minimal model at high-density that neglects the possibility of phase transitions. The Bayesian posterior probability distribution is constructed from priors obtained from microscopic many-body theory based on realistic two- and three-body nuclear forces, while the likelihood functions incorporate empirical information about the equation of state from nuclear experiments. The neutron star crust equation of state is constructed from the liquid drop model, and the core-crust transition density is found by comparing the energy per baryon in inhomogeneous matter and uniform nuclear matter. From the cold $beta$-equilibrated neutron star equation of state, we then compute neutron star tidal deformabilities as well as the mass-radius relationship. Finally, we investigate correlations between the neutron star tidal deformability and properties of finite nuclei.
Constraints set on key parameters of the nuclear matter equation of state (EoS) by the values of the tidal deformability, inferred from GW170817, are examined by using a diverse set of relativistic and non-relativistic mean field models. These models are consistent with bulk properties of finite nuclei as well as with the observed lower bound on the maximum mass of neutron star $sim 2 ~ {rm M}_odot$. The tidal deformability shows a strong correlation with specific linear combinations of the isoscalar and isovector nuclear matter parameters associated with the EoS. Such correlations suggest that a precise value of the tidal deformability can put tight bounds on several EoS parameters, in particular, on the slope of the incompressibility and the curvature of the symmetry energy. The tidal deformability obtained from the GW170817 and its UV/optical/infrared counterpart sets the radius of a canonical $1.4~ {rm M}_{odot}$ neutron star to be $11.82leqslant R_{1.4}leqslant13.72$ km.
Because of the development of many-body theories of nuclear matter, the long-standing, open problem of the equation of state (EOS) of dense matter may be understood in the near future through the confrontation of theoretical calculations with laboratory measurements of nuclear properties & reactions and increasingly accurate observations in astronomy. In this review, we focus on the following six aspects: 1) providing a survey of the quark mean-field (QMF) model, which consistently describes a nucleon and many-body nucleonic system from a quark potential; 2) applying QMF to both nuclear matter and neutron stars; 3) extending QMF formalism to the description of hypernuclei and hyperon matter, as well as hyperon stars; 4) exploring the hadron-quark phase transition and hybrid stars by combining the QMF model with the quark matter model characterized by the sound speed; 5) constraining interquark interactions through both the gravitational wave signals and electromagnetic signals of binary merger event GW170817; and 6) discussing further opportunities to study dense matter EOS from compact objects, such as neutron star cooling and pulsar glitches.
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