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Register a new userBayesian Inference of Dense Matter Equation of State within Relativistic Mean Field Models using Astrophysical Measurements
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We present a Bayesian analysis to constrain the equation of state of dense nucleonic matter by exploiting the available data from symmetric nuclear matter at saturation and from observations of compact X-ray sources and from the gravitational wave event GW170817. For the first time, such analysis is performed by using a class of models, the relativistic mean field models, which allow to consistently construct an equation of state in a wide range of densities, isospin asymmetries and temperatures. The selected class of models contains five nuclear physics empirical parameters at saturation for which we construct the joint posterior distributions. By exploring different types of priors, we find that the equations of state with the largest evidence are the ones featuring a strong reduction of the effective mass of the nucleons in dense matter which can be interpreted as an indication of a phase transition to a chiral symmetry restored phase. Those equations of state in turn predict $R_{1.4} sim 12$ km. Finally, we present a preliminary investigation on the effect of including $Lambda$ hyperons showing that they appear in stars more massive than about $1.6 M_{odot}$ and lead to radii larger than about $R_{1.4} sim 14$ km. Within the model here explored, the formation of such particles provide a poor agreement with the constraints from GW170817.
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The first detection of gravitational waves from the binary neutron star merger event GW170817 has started to provide important new constraints on the nuclear equation of state at high density. The tidal deformability bound of GW170817 combined with the observed two solar mass neutron star poses a serious challenge to theoretical formulations of realistic equations of state. We analyze a fully comprehensive set of relativistic nuclear mean-field theories by confronting them with the observational bounds and the measured neutron-skin thickness. We find that only a few models can withstand these bounds which predict a stiff overall equation of state but with a soft neutron-proton symmetry energy. Two possible indications are proposed: Circumstantial evidence of hadron-quark phase transition inside the star and new parametrizations that are consistent with ground state properties of finite nuclei and observational bounds. Based on extensive analysis of these sets, an upper limit on the radius of a $1.4M_odot$ neutron star of $R_{1.4}lesssim 12.9$ km is deduced.
Using an explicitly isospin-dependent parametric Equation of State (EOS) for the core of neutron stars (NSs) within the Bayesian statistical approach, we infer the EOS parameters of super-dense neutron-rich nuclear matter from three sets of imagined mass-radius correlation data representing typical predictions by various nuclear many-body theories, i.e, the radius stays the same, decreases or increases with increasing NS mass within $pm 15%$ between 1.4 M$_{odot}$ and 2.0 M$_{odot}$. The corresponding average density increases quickly, slowly or slightly decreases as the NS mass increases from 1.4 M$_{odot}$ to 2.0 M$_{odot}$. Using the posterior probability distribution functions (PDFs) of EOS parameters inferred from GW170817 and NICER radius data for canonical NSs as references, we investigate how future radius measurements of massive NS will improve our knowledge about the EOS of super-dense neutron-rich nuclear matter, especially its symmetry energy term, compared to what people have already learned from analyzing the GW170817 and NICER data. While the EOS of symmetric nuclear matter (SNM) inferred from the three data sets are approximately the same, the corresponding high-density symmetry energies at densities above about $2rho_0$ are very different, indicating that the radii of massive NSs carry reliable information about the high-density behavior of nuclear symmetry energy with little influence from the remaining uncertainties of the SNM EOS.
Recent developments in the theory of pure neutron matter and experiments concerning the symmetry energy of nuclear matter, coupled with recent measurements of high-mass neutron stars, now allow for relatively tight constraints on the equation of state of dense matter. We review how these constraints are formulated and describe the implications they have for neutron stars and core-collapse supernovae. We also examine thermal properties of dense matter, which are important for supernovae and neutron star mergers, but which cannot be nearly as well constrained at this time by experiment. In addition, we consider the role of the equation of state in medium-energy heavy-ion collisions.
We construct the equation of state (EOS) of dense matter covering a wide range of temperature, proton fraction, and density for the use of core-collapse supernova simulations. The study is based on the relativistic mean-field (RMF) theory, which can provide an excellent description of nuclear matter and finite nuclei. The Thomas--Fermi approximation in combination with assumed nucleon distribution functions and a free energy minimization is adopted to describe the non-uniform matter, which is composed of a lattice of heavy nuclei. We treat the uniform matter and non-uniform matter consistently using the same RMF theory. We present two sets of EOS tables, namely EOS2 and EOS3. EOS2 is an update of our earlier work published in 1998 (EOS1), where only the nucleon degree of freedom is taken into account. EOS3 includes additional contributions from $Lambda$ hyperons. The effect of $Lambda$ hyperons on the EOS is negligible in the low-temperature and low-density region, whereas it tends to soften the EOS at high density. In comparison with EOS1, EOS2 and EOS3 have an improved design of ranges and grids, which covers the temperature range $T=0.1$--$10^{2.6}$ MeV with the logarithmic grid spacing $Delta log_{10}(T/rm{[MeV]})=0.04$ (92 points including T=0), the proton fraction range $Y_p=0$--0.65 with the linear grid spacing $Delta Y_p = 0.01$ (66 points), and the density range $rho_B=10^{5.1}$--$10^{16},rm{g,cm^{-3}}$ with the logarithmic grid spacing $Delta log_{10}(rho_B/rm{[g,cm^{-3}]}) = 0.1$ (110 points).
Quark matter may appear due to a hadronic-quark transition in the core of a hybrid star. Quarkyonic matter is an approach in which both quarks and nucleons appear as quasi-particles in a crossover transition, and provides an explicit realization of early ideas concerning quark matter (e.g., the MIT bag model). This description has recently been employed by McLerran and Reddy to model chargeless (pure neutron) matter with an approach that has the virtue that the speed of sound rises quickly at a neutron-quark transition so as to satisfy observational constraints on the neutron star maximum mass ($gtrsim2M_odot$) and the radius of a $1.4M_odot$ star ($R_{1.4}lesssim 13.5$ km). Traditional models involving first-order transitions result in softer pressure-energy density relations that have difficulty satisfying these constraints except with very narrow choices of parameters. We propose a variation of quarkyonic matter involving protons and leptons whose energy can be explicitly minimized to achieve both chemical and beta equilibrium, which cannot be done in the chargeless formulation. Quarkyonic stellar models are able to satisfy observed mass and radius constraints with a wide range of model parameters, avoiding the obligatory fine-tuning of conventional hybrid star models, including requiring the transition density to be very close to the nuclear saturation density. Our formulation fits experimental and theoretical properties of the nuclear symmetry energy and pure neutron matter, and contains as few as three free parameters. This makes it an ideal tool for the study of high-density matter that is an efficient alternative to piecewise polytrope or spectral decomposition methods.
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