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Register a new userFrom Microscales to Macroscales in 3D: Selfconsistent Equation of State for Supernova and Neutron Star Models
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First results from a fully self-consistent, temperature-dependent equation of state that spans the whole density range of neutron stars and supernova cores are presented. The equation of state (EoS) is calculated using a mean-field Hartree-Fock method in three dimensions (3D). The nuclear interaction is represented by the phenomenological Skyrme model in this work, but the EoS can be obtained in our framework for any suitable form of the nucleon-nucleon effective interaction. The scheme we employ naturally allows effects such as (i) neutron drip, which results in an external neutron gas, (ii) the variety of exotic nuclear shapes expected for extremely neutron heavy nuclei, and (iii) the subsequent dissolution of these nuclei into nuclear matter. In this way, the equation of state is calculated across phase transitions without recourse to interpolation techniques between density regimes described by different physical models. EoS tables are calculated in the wide range of densities, temperature and proton/neutron ratios on the ORNL NCCS XT3, using up to 2000 processors simultaneously.
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In this work we present a detailed explanation of the construction of an appropriate equation of state (EoS) for nuclear astrophysics. We use a relativistic model in order to obtain an EoS for neutrally charged matter that extends from very low to high densities, from zero temperature to 100 MeV with proton fractions ranging from 0 (no protons) to 0.6 (asymmetric matter with proton excess). For the achievement of complete convergence, the Sommerfeld approximation is used at low temperatures and the Boltzman distribution for relativistic particles is used in the calculation of the electron properties at very low densities. Photons are also incorporated as blackbody radiation. An extension of this EoS is also presented with the inclusion of strangeness by taking into account the sigma minus hyperon only. Strangeness fractions range from 0.02 to 0.3.
We study the effects of very strong magnetic fields on the equation of state (EOS) in multicomponent, interacting matter by developing a covariant description for the inclusion of the anomalous magnetic moments of nucleons. For the description of neutron star matter, we employ a field-theoretical approach which permits the study of several models which differ in their behavior at high density. Effects of Landau quantization in ultra-strong magnetic fields ($B>10^{14}$ Gauss) lead to a reduction in the electron chemical potential and a substantial increase in the proton fraction. We find the generic result for $B>10^{18}$ Gauss that the softening of the EOS caused by Landau quantization is overwhelmed by stiffening due to the incorporation of the anomalous magnetic moments of the nucleons. In addition, the neutrons become completely spin polarized. The inclusion of ultra-strong magnetic fields leads to a dramatic increase in the proton fraction, with consequences for the direct Urca process and neutron star cooling. The magnetization of the matter never appears to become very large, as the value of $|H/B|$ never deviates from unity by more than a few percent. Our findings have implications for the structure of neutron stars in the presence of large frozen-in magnetic fields.
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).
Neutron star matter spans a wide range of densities, from that of nuclei at the surface to exceeding several times normal nuclear matter density in the core. While terrestrial experiments, such as nuclear or heavy-ion collision experiments, provide clues about the behaviour of dense nuclear matter, one must resort to theoretical models of neutron star matter to extrapolate to higher density and finite neutron/proton asymmetry relevant for neutron stars. In this work, we explore the parameter space within the framework of the Relativistic Mean Field model allowed by present uncertainties compatible with state-of-the-art experimental data. We apply a Bayesian scheme to constrain the parameter space using multi-physics constraints at different density regimes: chiral effective field theory, nuclear and heavy-ion collision data as well as multi-messenger astrophysical observations of neutron stars. Using the results of the study, we investigate possible correlations between nuclear and astrophysical observables.
One of the key goals of observing neutron stars is to infer the equation of state (EoS) of the cold, ultradense matter in their interiors. We present here a Bayesian statistical method of inferring the pressures at five fixed densities, from a sample of mock neutron star masses and radii. We show that while five polytropic segments are needed for maximum flexibility in the absence of any prior knowledge of the EoS, regularizers are also necessary to ensure that simple underlying EoS are not over-parametrized. For ideal data with small measurement uncertainties, we show that the pressure at roughly twice the nuclear saturation density, rho_sat, can be inferred to within 0.3 dex for many realizations of potential sources of uncertainties. The pressures of more complicated EoS with significant phase transitions can also be inferred to within ~30%. We also find that marginalizing the multi-dimensional parameter space of pressure to infer a mass-radius relation can lead to biases of nearly 1 km in radius, towards larger radii. Using the full, five-dimensional posterior likelihoods avoids this bias.
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