Kohsuke Sumiyoshi

Relativistic equation of state of nuclear matter for supernova and neutron star

Abstract We construct the equation of state (EOS) of nuclear matter using the relativistic mean field (RMF) theory in the wide density, temperature range with various proton fractions for the use of supernova simulation and the neutron star calculations. We first construct the EOS of homogeneous nuclear matter. We use then the Thomas-Fermi approximation to describe inhomogeneous matter, where heavy nuclei are formed together with free nucleon gas. We discuss the results on free energy, pressure and entropy in the wide range of astrophysical interest. As an example, we apply the resulting EOS on the neutron star properties by using the Oppenheimer-Volkoff equation.We construct the equation of state (EOS) of nuclear matter using the relativistic mean field (RMF) theory in the wide density, temperature range with various proton fractions for the use of supernova simulation and the neutron star calculations. We first construct the EOS of homogeneous nuclear matter. We use then the Thomas-Fermi approximation to describe inhomogeneous matter, where heavy nuclei are formed together with free nucleon gas. We discuss the results on free energy, pressure and entropy in the wide range of astrophysical interest. As an example, we apply the resulting EOS on the neutron star properties by using the Oppenheimer-Volkoff equation.

Relativistic Equation of State of Nuclear Matter for Supernova Explosion

We construct the equation of state (EOS) of nuclear matter at finite temperature and density with various proton fractions within the relativistic mean field (RMF) theory for the use in the supernova simulations. The Thomas-Fermi approximation is adopted to describe the non-uniform matter where we consider nucleus, alpha-particle, proton and neutron in equilibrium. We treat the uniform matter and non-uniform matter consistently using the RMF theory. We tabulate the outcome as the pressure, free energy, entropy etc, with enough mesh points in wide ranges of the temperature, proton fraction, and baryon mass density.

Postbounce Evolution of Core-Collapse Supernovae: Long-Term Effects of the Equation of State

We study the evolution of a supernova core from the beginning of the gravitational collapse of a 15 M☉ star up to 1 s after core bounce. We present results of spherically symmetric simulations of core-collapse supernovae by solving general relativistic ν-radiation hydrodynamics in the implicit time differencing. We aim to explore the evolution of shock waves in the long term and investigate the formation of proto-neutron stars together with supernova neutrino signatures. These studies are done to examine the influence of the equation of state (EOS) on the postbounce evolution of shock waves in the late phase and the resulting thermal evolution of proto-neutron stars. We compare two sets of EOSs, namely, those by Lattimer and Swesty (LS-EOS) and by Shen et al. (SH-EOS). We found that, for both EOSs, the core does not explode and the shock wave stalls similarly in the first 100 ms after bounce. A revival of the shock wave does not occur even after a long period in either case. However, the recession of the shock wave appears different beyond 200 ms after bounce, having different thermal evolution of the central core. A more compact proto-neutron star is found for LS-EOS than SH-EOS with a difference in the central density by a factor of ~2 and a difference of ~10 MeV in the peak temperature. The resulting spectra of supernova neutrinos are different to an extent that may be detectable by terrestrial neutrino detectors.

New Nuclear Reaction Flow during r-Process Nucleosynthesis in Supernovae: Critical Role of Light, Neutron-rich Nuclei

We study the role of light, neutron-rich nuclei during r-process nucleosynthesis in supernovae. Most previous studies of the r-process have concentrated on the reaction flow of heavy, unstable nuclei. Although the nuclear reaction network includes a few thousand heavy nuclei, only limited reaction flow through light nuclei near the stability line has been used in those studies. However, in a viable scenario of the r-process in neutrino-driven winds, the initial condition is a high-entropy hot plasma consisting of neutrons, protons, and electron-positron pairs experiencing an intense flux of neutrinos. In such environments, light nuclei, as well as heavy nuclei, are expected to play important roles in the production of seed nuclei and r-process elements. Thus, we have extended our fully implicit nuclear reaction network so that it includes all nuclei up to the neutron-drip line for Z ≤ 10, in addition to a larger network for Z ≥ 10. In the present nucleosynthesis study, we utilize a wind model of massive Type II supernova explosions to study the effects of this extended network. We find that a new nuclear reaction flow path opens in the very light, neutron-rich region. This new nuclear reaction flow can change the final heavy-element abundances by as much as an order of magnitude.

r-Process in Prompt Supernova Explosions Revisited

We reanalyze r-process nucleosynthesis in the neutron-rich ejecta from a prompt supernova explosion of a low-mass (11 M?) progenitor. Although it has not yet been established that a prompt explosion can occur, it is not yet ruled out as a possibility for low-mass supernova progenitors. Moreover, there is mounting evidence that a new r-process site may be required. Hence, we assume that a prompt explosion can occur and make a study of r-process nucleosynthesis in the supernova ejecta. To achieve a prompt explosion we have performed a general relativistic hydrodynamic simulation of adiabatic collapse and bounce using a relativistic nuclear-matter equation of state. The electron fraction Ye during the collapse was fixed at the initial-model value. The size of the inner collapsing core was then large enough to enable a prompt explosion to occur in the hydrodynamic calculation. Adopting the calculated trajectories of promptly ejected material, we explicitly computed the burst of neutronization due to electron captures on free protons in the photodissociated ejecta after the passage of the shock. The thermal and compositional evolution of the resulting neutron-rich ejecta originating from near the surface of the proto-neutron star was obtained. These were used in nuclear reaction network calculations to evaluate the products of r-process nucleosynthesis. We find that, unlike earlier studies of nucleosynthesis in prompt supernovae, the amount of r-process material ejected per supernova is quite consistent with observed Galactic r-process abundances. Furthermore, the computed r-process abundances are in good agreement with solar abundances of r-process elements for A > 100. This suggests that prompt supernovae are still viable r-process sites. Such events may be responsible for the abundances of the heaviest r-process nuclei.

Neutrino signals from the formation of a black hole: A probe of the equation of state of dense matter.

The gravitational collapse of a nonrotating, black-hole-forming massive star is studied by nu-radiation-hydrodynamical simulations for two different sets of realistic equation of state of dense matter. We show that the event will produce as many neutrinos as the ordinary supernova, but with distinctive characteristics in luminosities and spectra that will be an unmistakable indication of black hole formation. More importantly, the neutrino signals are quite sensitive to the difference of equation of state and can be used as a useful probe into the properties of dense matter. The event will be unique in that they will be shining only by neutrinos (and, possibly, gravitational waves) but not by photons, and hence they should be an important target of neutrino astronomy.

Gravitational radiation from rotational core collapse: Effects of magnetic fields and realistic equations of state

We perform a series of two-dimensional, axisymmetric, magnetohydrodynamic simulations of the rotational collapse of a supernova core. In order to calculate the waveforms of the gravitational wave, we derive the quadrupole formula including the contributions from the electromagnetic fields. Recent stellar evolution calculations imply that the magnetic fields of the toroidal components are much stronger than those of the poloidal ones at the presupernova stage. Thus, we systematically investigate the effects of the toroidal magnetic fields on the amplitudes and waveforms. Furthermore, we employ the two kinds of the realistic equation of states, which are often used in the supernova simulations. Then, we investigate the effects of the equation of states on the gravitational wave signals. With these computations, we find that the peak amplitudes are lowered by an order of 10% for the models with the strongest toroidal magnetic fields. However, the peak amplitudes are mostly within sensitivity range of laser interferometers such as TAMA and the first LIGO for a source at a distance of 10 kpc. Furthermore, we point out that the amplitudes of second peaks are still within the detection limit of the first LIGO for the source, although the characteristics of second peaks are reduced by the magnetic fields. We stress the importance of the detection, since it will give us information about the angular momentum distribution of massive evolved stars. When we compare the gravitational waves from the two realistic equation of states, significant differences are not found, except that the typical frequencies of the gravitational wave become slightly higher for the softer equation of state.

Tables of hyperonic matter equation of state for core-collapse supernovae*

We present sets of equation of state (EOS) of nuclear matter including hyperons using an SUf(3) extended relativistic mean field (RMF) model with a wide coverage of density, temperature and charge fraction for numerical simulations of core-collapse supernovae. Coupling constants of ? and ? hyperons with the ? meson are determined to fit the hyperon potential depths in nuclear matter, U?(?0) +30 MeV and U?(?0) ?15 MeV, which are suggested from recent analyses of hyperon production reactions. At low densities, the EOS of uniform matter is connected with the EOS by Shen et al, in which the formation of finite nuclei is included in the Thomas?Fermi approximation. In the present EOS, the maximum mass of neutron stars decreases from 2.17 M? (Ne?) to 1.63 M? (NYe?) when hyperons are included. In a spherical, adiabatic collapse of a 15 M? star by the hydrodynamics without neutrino transfer, hyperon effects are found to be small, since the temperature and density do not reach the region of hyperon mixture, where the hyperon fraction is above 1 % (T > 40 MeV or ?B > 0.4 fm?3).

Can the equation of state of asymmetric nuclear matter be studied using unstable nuclei

Abstract The paper shows that nuclear radii and neutron skins do directly reflect the saturation density of asymmetric nuclear matter. The proton distributions in a nucleus have been found to be remarkably independent of the equation of state (EOS) of the asymmetric matter. It is the neutron distributions that are dependent on the EOS. Macroscopic model calculations have been performed over the entire range of the nuclear chart based on two popular phenomenological, but distinctively different, EOS: the SIII parameter set for the non-relativistic Skyrme Hartree-Fock theory and the TM1 parameter set in the relativistic mean field theory. The saturation density for a small proton fraction remains almost the same as the normal nuclear matter density for SIII EOS, but it becomes significantly small for the TM1 EOS. The key EOS parameters used to describe the saturation density are the density derivative of the symmetry energy and the incompressibility of symmetric nuclear matter, while the saturation energy is written using the symmetry energy alone as a good approximation. We conclude that a systematic experimental study of heavy unstable nuclei would enable us to determine the EOS of asymmetric nuclear matter at about the normal nuclear matter density with a fixed proton fraction down to about 0.3.

Relativistic mean-field theory with non-linear σ and ω terms for neutron stars and supernovae

Abstract We study the properties of dense matter in neutron stars and supernovae in the relativistic mean-field (RMF) theory with non-linear σ and ω terms. The lagrangian of the RMF theory is motivated by the recent success of the relativistic Brueckner-Hartree-Fock (RBHF) theory. The parameters in the lagrangian are determined by the properties of nuclei including unstable ones and provide the equation of state of nuclear matter similar to the one in the RBHF theory. The proton fraction in neutron-star matter is found to be large enough to allow the direct URCA process for rapid cooling of neutron stars. We calculate nuclear matter having arbitrary proton fractions at finite temperature to provide the equation of state for studies of supernova explosions. The properties of supernova matter containing abundant leptons are studied in detail and the consequences on the gravitational mass of hot neutron stars at the birth era are discussed.