Conservative formulations of general relativistic kinetic theory

Experience with core-collapse supernova simulations shows that accurate accounting of total particle number and 4-momentum can be a challenge for computational radiative transfer. This accurate accounting would be facilitated by the use of particle number and 4-momentum transport equations that allow transparent conversion between volume and surface integrals in both configuration and momentum space. Such conservative formulations of general relativistic kinetic theory in multiple spatial dimensions are presented in this paper, and their relevance to core-collapse supernova simulations is described.Comment: 48 page

A supersymmetric model for triggering Supernova Ia in isolated white dwarfs

We propose a model for supernovae Ia explosions based on a phase transition to a supersymmetric state which becomes the active trigger for the deflagration starting the explosion in an isolated sub-Chandrasekhar white dwarf star. With two free parameters we fit the rate and several properties of type Ia supernovae and address the gap in the supermassive black hole mass distribution. One parameter is a critical density fit to about $3 \cdot 10^7$ g/cc while the other has the units of a space time volume and is found to be of order $0.05\,$ Gyr $R_E^3$ where $R_E$ is the earth radius. The model involves a phase transition to an exact supersymmetry in a small core of a dense star.Comment: 20 pages, 5 figures, expanded version to be published in Physical Review

The consequences of nuclear electron capture in core collapse supernovae

The most important weak nuclear interaction to the dynamics of stellar core collapse is electron capture, primarily on nuclei with masses larger than 60. In prior simulations of core collapse, electron capture on these nuclei has been treated in a highly parameterized fashion, if not ignored. With realistic treatment of electron capture on heavy nuclei come significant changes in the hydrodynamics of core collapse and bounce. We discuss these as well as the ramifications for the post-bounce evolution in core collapse supernovae.Comment: Accepted by PRL, 5 pages, 2 figure

Spin-down of neutron stars by neutrino emission

We study the spin-down of a neutron star during its early stages due to the neutrino emission. The mechanism we consider is the subsequent collisions of the produced neutrinos with the outer shells of the star. We find that this mechanism can indeed slow down the star rotation but only in the first tens of seconds of the core formation, which is when the appropriate conditions of flux and collision rate are met. We find that this mechanism can extract less than 1 % of the star angular momentum, a result which is much less than previously estimated by other authors.Comment: 9 pages, 2 eps figures, RevTeX 4-1. The paper was significantly modified. Now it addresses only the issues of a neutron star spin-down. Version to be published in Phys. Rev.

Pulsar spins from an instability in the accretion shock of supernovae

Rotation-powered radio pulsars are born with inferred initial rotation periods of order 300 ms (some as short as 20 ms) in core-collapse supernovae. In the traditional picture, this fast rotation is the result of conservation of angular momentum during the collapse of a rotating stellar core. This leads to the inevitable conclusion that pulsar spin is directly correlated with the rotation of the progenitor star. So far, however, stellar theory has not been able to explain the distribution of pulsar spins, suggesting that the birth rotation is either too slow or too fast. Here we report a robust instability of the stalled accretion shock in core-collapse supernovae that is able to generate a strong rotational flow in the vicinity of the accreting proto-neutron star. Sufficient angular momentum is deposited on the proto-neutron star to generate a final spin period consistent with observations, even beginning with spherically symmetrical initial conditions. This provides a new mechanism for the generation of neutron star spin and weakens, if not breaks, the assumed correlation between the rotational periods of supernova progenitor cores and pulsar spin.Comment: To be published in Natur

Neutrino - nucleon reaction rates in the supernova core in the relativistic random phase approximation

In view of the application to supernova simulations, we calculate neutrino reaction rates with nucleons via the neutral and charged currents in the supernova core in the relativistic random phase approximation (RPA) and study their effects on the opacity of the supernova core. The formulation is based on the Lagrangian employed in the calculation of nuclear equation of state (EOS) in the relativistic mean field theory (RMF). The nonlinear meson terms are treated appropriately so that the consistency of the density correlation derived in RPA with the thermodynamic derivative obtained from EOS by RMF is satisfied in the static and long wave length limit. We employ pion and rho meson exchange interactions together with the phenomenological Landau-Migdal parameters for the isospin-dependent nuclear interactions. We find that both the charged and neutral current reaction rates are suppressed from the standard Bruenn's approximate formula considerably in the high density regime. In the low density regime, on the other hand, the vector current contribution to the neutrino-nucleon scattering rate is enhanced in the vicinity of the boundary of the liquid-gas phase transition, while the other contributions are moderately suppressed there also. In the high temperature regime or in the regime where electrons have a large chemical potential, the latter of which is important only for the electron capture process and its inverse process, the recoil of nucleons cannot be neglected and further reduces the reaction rates with respect to the standard approximate formula which discards any energy transfer in the processes. These issues could have a great impact on the neutrino heating mechanism of collapse-driven supernovae.Comment: 16pages, 19figures, submitted to PR

A New Algorithm for Supernova Neutrino Transport and Some Applications

We have developed an implicit, multi-group, time-dependent, spherical neutrino transport code based on the Feautrier variables, the tangent-ray method, and accelerated ${\bf \Lambda}$ iteration. The code achieves high angular resolution, is good to O($v/c$), is equivalent to a Boltzmann solver (without gravitational redshifts), and solves the transport equation at all optical depths with precision. In this paper, we present our formulation of the relevant numerics and microphysics and explore protoneutron star atmospheres for snapshot post-bounce models. Our major focus is on spectra, neutrino-matter heating rates, Eddington factors, angular distributions, and phase-space occupancies. In addition, we investigate the influence on neutrino spectra and heating of final-state electron blocking, stimulated absorption, velocity terms in the transport equation, neutrino-nucleon scattering asymmetry, and weak magnetism and recoil effects. Furthermore, we compare the emergent spectra and heating rates obtained using full transport with those obtained using representative flux-limited transport formulations to gauge their accuracy and viability. Finally, we derive useful formulae for the neutrino source strength due to nucleon-nucleon bremsstrahlung and determine bremsstrahlung's influence on the emergent $\nu_{\mu}$ and $\nu_{\tau}$ neutrino spectra.Comment: 58 pages, single-spaced LaTeX, 23 figures, revised title, also available at http://jupiter.as.arizona.edu/~burrows/papers, accepted for publication in the Ap.

Magnetic field generation by the stationary accretion shock instability

By adding a weak magnetic field to a spherically symmetric fluid configuration that caricatures a stalled shock in the post-bounce supernova environment, we explore the capacity of the stationary accretion shock instability (SASI) to generate magnetic fields. The SASI develops upon perturbation of the initial condition, and the ensuing flow generates--{\em in the absence of rotation}--dynamically significant magnetic fields ($\sim 10^{15}$ G) on a time scale that is relevant for the explosion mechanism of core-collapse supernovae. We describe our model, present some recent results, and discuss their potential relevance for supernova models.Comment: 5 pages, 3 figures, submitted to Journal of Physics: Conference Series, SciDAC 200

Modeling core collapse supernovae in 2 and 3 dimensions with spectral neutrino transport

The overwhelming evidence that the core collapse supernova mechanism is inherently multidimensional, the complexity of the physical processes involved, and the increasing evidence from simulations that the explosion is marginal presents great computational challenges for the realistic modeling of this event, particularly in 3 spatial dimensions. We have developed a code which is scalable to computations in 3 dimensions which couples PPM Lagrangian with remap hydrodynamics [1], multigroup, flux-limited diffusion neutrino transport [2], with many improvements), and a nuclear network [3]. The neutrino transport is performed in a ray-by-ray plus approximation wherein all the lateral effects of neutrinos are included (e.g., pressure, velocity corrections, advection) except the transport. A moving radial grid option permits the evolution to be carried out from initial core collapse with only modest demands on the number of radial zones. The inner part of the core is evolved after collapse along with the rest of the core and mantle by subcycling the lateral evolution near the center as demanded by the small Courant times. We present results of 2-D simulations of a symmetric and an asymmetric collapse of both a 15 and an 11 M progenitor. In each of these simulations we have discovered that once the oxygen rich material reaches the shock there is a synergistic interplay between the reduced ram pressure, the energy released by the burning of the shock heated oxygen rich material, and the neutrino energy deposition which leads to a revival of the shock and an explosion.Comment: 10 pages, 3 figure