We present an implicit finite difference representation for general relativistic radiation hydrodynamics in spherical symmetry. Our code, AGILE-BOLTZTRAN, solves the Boltzmann transport equation for the angular and spectral neutrino distribution functions in self-consistent simulations of stellar core collapse and postbounce evolution. It implements a dynamically adaptive grid in comoving coordinates. A comoving frame in the momentum phase space facilitates the evaluation and tabulation of neutrino-matter interaction cross sections but produces a multitude of observer corrections in the transport equation. Most macroscopically interesting physical quantities are defined by expectation values of the distribution function. We optimize the finite differencing of the microscopic transport equation for a consistent evolution of important expectation values. We test our code in simulations launched from progenitor stars with 13 solar masses and 40 solar masses. Half a second after core collapse and bounce, the protoneutron star in the latter case reaches its maximum mass and collapses further to form a black hole. When the hydrostatic gravitational contraction sets in, we find a transient increase in electron flavor neutrino luminosities due to a change in the accretion rate. The -and -neutrino luminosities and rms energies, however, continue to rise because previously shock-heated material with a nondegenerate electron gas starts to replace the cool degenerate material at their production site. We demonstrate this by supplementing the concept of neutrinospheres with a more detailed statistical description of the origin of escaping neutrinos. Adhering to our tradition, we compare the evolution of the 13 M progenitor star to corresponding simulations with the multigroup flux-limited diffusion approximation, based on a recently developed flux limiter. We find similar results in the postbounce phase and validate this MGFLD approach for the spherically symmetric case with standard input physics.

Supernova simulations to date have assumed that during core collapse electron captures occur dominantly on free protons, while captures on heavy nuclei are Pauli-blocked and are ignored. We have calculated rates for electron capture on nuclei with mass numbers A = 65-112 for the temperatures and densities appropriate for core collapse. We find that these rates are large enough so that, in contrast to previous assumptions, electron capture on nuclei dominates over capture on free protons. This leads to significant changes in core collapse simulations. PACS numbers: 26.50.+x, 97.60.Bw, At the end of their lives, stars with masses exceeding roughly 10 M ⊙ reach a moment in their evolution when their iron core provides no further source of nuclear energy generation. At this time, they collapse and, if not too massive, bounce and explode in spectacular events known as type II or Ib/c supernovae. As the density, ρ, of the star's center increases, electrons become more degenerate and their chemical potential µ e grows (µ e ∼ ρ 1/3 ). For sufficiently high values of the chemical potential electrons are captured by nuclei producing neutrinos, which for densities 10 11 g cm −3 , freely escape from the star, removing energy and entropy from the core. Thus the entropy stays low during collapse ensuring that nuclei dominate in the composition over free protons and neutrons. During the presupernova stage, i.e. for core densities 10 10 g cm −3 and proton-to-nucleon ratios Y e 0.42, nuclei with A = 55-65 dominate. The relevant rates for weak-interaction processes (including β ± decay and electron and positron capture) were first estimated by Fuller, Fowler and Newman [1] (for nuclei with A < 60), considering that at such conditions allowed (Fermi and Gamow-Teller) transitions dominate. The rates have been recently improved based on modern data and state-of-the-art many-body models [2], considering nuclei with A = 45-65. (This rate set will be denoted LMP in the following.) Presupernova models utilizing these improved weak rates are presented in [3]. In collapse simulations, i.e. densities 10 10 g cm −3 , a much simpler description of electron capture on nuclei is used. Here the rates are estimated in the spirit of the independent particle model (IPM), assuming pure Gamow-Teller (GT) transitions and considering only single particle states for proton and neutron numbers be- During core collapse, temperatures and densities are high enough to ensure that nuclear statistical equilibrium (NSE) is achieved. This means that for sufficiently low entropies, the matter composition is dominated by the nuclei with the highest binding energy for a given Y e . Electron capture reduces Y e , driving the nuclear composition to more neutron rich and heavier nuclei, including those with N > 40, which dominate the matter composition for densities larger than a few 10 10 g cm −3 . As a consequence of the model applied in previous collapse simulations, electron capture on nuclei ceases at these densities and the capture is entirely due to free proto...