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We describe a numerical method for calculating the (3+1) dimensional general relativistic hydrodynamics of a coalescing neutron-star binary system. The relativistic field equations are solved at each time slice with a spatial 3-metric chosen to be conformally flat. Against this solution to the general relativistic field equations the hydrodynamic variables and gravitational radiation are allowed to respond. The gravitational radiation signal is derived via a multipole expansion of the metric perturbation to the hexadecapole (l = 4) order including both mass and current moments and a correction for the slow motion approximation. Using this expansion, the effect of gravitational radiation on the system evolution can also be recovered by introducing an acceleration term in the matter evolution. In the present work we illustrate the method by applying this model to evaluate various orbits of two neutron stars with a gravitational mass of 1.45 M⊙ near the time of the final merger. We discuss the evidence that, for a realistic neutron star equation of state, general relativistic effects may cause the stars to individually collapse into black holes prior to merging. Also, the strong fields cause the last stable orbit to occur at a larger separation distance and lower frequency than previously estimated.PACS Numbers: 04.20.Jb, 04.30.+x, 47.75+f,, 95.30.Lz, 95.30.Sf 97.60.Jd,

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-mass 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-mass 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 SNeII 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.

We use heavy element nucleosynthesis from supernovae to probe the mixing of v, with v, (or v") possessing cosmologically significant masses (1 to 100 eV). We conclude that the v, (v")-v, vacuum mixing angle must satisfy sin 20 & 10, in order to ensure that r-process heavy elements can be produced in neutrino-heated supernova ejecta. Mixing at a level exceeding this limit precludes r-process nucleosynthesis in this site.

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We present calculations of r-process nucleosynthesis in neutrino-driven winds from the nascent neutron stars of core-collapse supernovae. A full dynamical reaction network for both the α-rich freezeout and the subsequent r-process is employed. The physical properties of the neutrino-heated ejecta are deduced from a general relativistic model in which spherical symmetry and steady flow are assumed. Our results suggest that protoneutron stars with a large compaction ratio provide the most robust physical conditions for the r-process. The third peak of the r-process is well reproduced in the winds from these "compact" proto-neutron stars even for a moderate entropy, ∼ 100 − 200N A k, and a neutrino luminosity as high as ∼ 10 52 ergs s −1 . This is due to the short dynamical timescale of material in the wind. As a result, the overproduction of nuclei with A ∼ < 120 is diminished (although some overproduction of nuclei with A ≈ 90 is still evident). The abundances of the r-process elements per event is significantly higher than in previous studies. The total-integrated nucleosynthesis yields are in good agreement with the solar r-process abundance pattern. Our results have confirmed that the neutrino-driven wind scenario is still a promising site in which to form the solar r-process abundances. However, our best results seem to imply both a rather soft neutron-star equation of state and a massive proto-neutron star which is difficult to achieve with standard corecollapse models. We propose that the most favorable conditions perhaps require that a massive supernova progenitor forms a massive proto-neutron star by accretion after a failed initial neutrino burst.

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