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Register a new userMethodology study of machine learning for the neutron star equation of state
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We discuss a methodology of machine learning to deduce the neutron star equation of state from a set of mass-radius observational data. We propose an efficient procedure to deal with a mapping from finite data points with observational errors onto an equation of state. We generate training data and optimize the neural network. Using independent validation data (mock observational data) we confirm that the equation of state is correctly reconstructed with precision surpassing observational errors. We finally discuss the relation between our method and Bayesian analysis with an emphasis put on generality of our method for underdetermined problems.
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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.
We propose an interpolating equation of state that satisfies phenomenologically established boundary conditions in two extreme regimes at high temperature and low baryon density and at low temperature and high baryon density. We confirm that the hadron resonance gas model with the Carnahan-Starling excluded volume effect can reasonably fit the empirical equation of state at high density up to several times the normal nuclear density. We identify the onsets of strange particles and quantify the strangeness contents in dense matter. We finally discuss the finite temperature effects and estimate the thermal index $Gamma_{rm th}$ as a function of the baryon density, which should be a crucial input for the core-collapse supernova and the binary neutron star merger simulations.
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.
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.
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