Justification of Power-Law Canonical Distributions Based on Generalized Central Limit Theorem

A self-consistent thermodynamic framework is presented for power-law canonical distributions based on the generalized central limit theorem by extending the discussion given by Khinchin for deriving Gibbsian canonical ensemble theory. The thermodynamic Legendre transform structure is invoked in establishing its connection to nonextensive statistical mechanics.Comment: 8 pages. Some minor corrections are made, with no changes in the conclusion

R-Process Nucleosynthesis In Neutrino-Driven Winds From A Typical Neutron Star With M = 1.4 Msun

We study the effects of the outer boundary conditions in neutrino-driven winds on the r-process nucleosynthesis. We perform numerical simulations of hydrodynamics of neutrino-driven winds and nuclear reaction network calculations of the r-process. As an outer boundary condition of hydrodynamic calculations, we set a pressure upon the outermost layer of the wind, which is approaching toward the shock wall. Varying the boundary pressure, we obtain various asymptotic thermal temperature of expanding material in the neutrino-driven winds for resulting nucleosynthesis. We find that the asymptotic temperature slightly lower than those used in the previous studies of the neutrino-driven winds can lead to a successful r-process abundance pattern, which is in a reasonable agreement with the solar system r-process abundance pattern even for the typical proto-neutron star mass Mns ~ 1.4 Msun. A slightly lower asymptotic temperature reduces the charged particle reaction rates and the resulting amount of seed elements and lead to a high neutron-to-seed ratio for successful r-process. This is a new idea which is different from the previous models of neutrino-driven winds from very massive (Mns ~ 2.0 Msun) and compact (Rns ~ 10 km) neutron star to get a short expansion time and a high entropy for a successful r-process abundance pattern. Although such a large mass is sometimes criticized from observational facts on a neutron star mass, we dissolve this criticism by reconsidering the boundary condition of the wind. We also explore the relation between the boundary condition and neutron star mass, which is related to the progenitor mass, for successful r-process.Comment: 14 pages, 2 figure

An approach toward the successful supernova explosion by physics of unstable nuclei

We study the explosion mechanism of collapse-driven supernovae by numerical simulations with a new nuclear EOS based on unstable nuclei. We report new results of simulations of general relativistic hydrodynamics together with the Boltzmann neutrino-transport in spherical symmetry. We adopt the new data set of relativistic EOS and the conventional set of EOS (Lattimer-Swesty EOS) to examine the influence on dynamics of core-collapse, bounce and shock propagation. We follow the behavior of stalled shock more than 500 ms after the bounce and compare the evolutions of supernova core.Comment: 4 pages, 2 figures, contribution to Nuclei in the Cosmos 8, to appear in Nucl. Phys.

Relativistic Equation of State of Nuclear Matter for Supernova and Neutron Star

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.Comment: 15 pages, LaTeX, 14 ps-figures, accepted for publication in Nucl.Phys.

Relativistic Equation of State for Core-Collapse Supernova Simulations

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).Comment: 43 pages, 10 figure

Variational Calculation for the Equation of State of Nuclear Matter at Finite Temperatures

An equation of state (EOS) for uniform nuclear matter is constructed at zero and finite temperatures with the variational method starting from the realistic nuclear Hamiltonian composed of the Argonne V18 and UIX potentials. The energy is evaluated in the two-body cluster approximation with the three-body-force contribution treated phenomenologically so as to reproduce the empirical saturation conditions. The obtained energies for symmetric nuclear matter and neutron matter at zero temperature are in fair agreement with those by Akmal, Pandharipande and Ravenhall, and the maximum mass of the neutron star is 2.2 Msolar. At finite temperatures, a variational method by Schmidt and Pandharipande is employed to evaluate the free energy, which is used to derive various thermodynamic quantities of nuclear matter necessary for supernova simulations. The result of this variational method at finite temperatures is found to be self-consistent.Comment: Revised Versio