We examine the stability of standing, spherical accretion shocks. Accretion shocks arise in core collapse supernovae (the focus of this paper), star formation, and accreting white dwarfs and neutron stars. We present a simple analytic model and use timedependent hydrodynamics simulations to show that this solution is stable to radial perturbations. In two dimensions we show that small perturbations to a spherical shock front can lead to rapid growth of turbulence behind the shock, driven by the injection of vorticity from the now non-spherical shock. We discuss the ramifications this instability may have for the supernova mechanism.

Massive stars end their lives in explosions with kinetic energies on the order of 10 51 erg. Immediately after the explosion has been launched, a region of low density and high entropy forms behind the ejecta, which is continuously subject to neutrino heating. The neutrinos emitted from the remnant at the center, the protoneutron star (PNS), heat the material above the PNS surface. This heat is partly converted into kinetic energy, and the material accelerates to an outflow that is known as the neutrino-driven wind. For the first time we simulate the collapse, bounce, explosion, and the neutrino-driven wind phases consistently over more than 20 s. Our numerical model is based on spherically symmetric general relativistic radiation hydrodynamics using spectral three-flavor Boltzmann neutrino transport. In simulations where no explosions are obtained naturally, we model neutrino-driven explosions for low-and intermediatemass Fe-core progenitor stars by enhancing the charged current reaction rates. In the case of a special progenitor star, the 8.8 M O-Ne-Mg-core, the explosion in spherical symmetry was obtained without enhanced opacities. The post-explosion evolution is in qualitative agreement with static steady-state and parametrized dynamic models of the neutrino-driven wind. On the other hand, we generally find lower neutrino luminosities and mean neutrino energies, as well as a different evolutionary behavior of the neutrino luminosities and mean neutrino energies. The neutrino-driven wind is proton-rich for more than 10 s and the contraction of the PNS differs from the assumptions made for the conditions at the inner boundary in previous neutrino-driven wind studies. Despite the moderately high entropies of about 100 k B /baryon and the fast expansion timescales, the conditions found in our models are unlikely to favor r-process nucleosynthesis. The simulations are carried out until the neutrino-driven wind settles down to a quasi-stationary state. About 5 s after the bounce, the peak temperature inside the PNS already starts to decrease because of the continued deleptonization. This moment determines the beginning of a cooling phase dominated by the emission of neutrinos. We discuss the physical conditions of the quasi-static PNS evolution and take the effects of deleptonization and mass accretion from early fallback into account.

Accurate neutrino transport has been built into spherically symmetric simulations of stellar core collapse and postbounce evolution. The results of such simulations agree that spherically symmetric models with standard microphysical input fail to explode by the delayed, neutrino-driven mechanism. Independent groups implemented fundamentally different numerical methods to tackle the Boltzmann neutrino transport equation. Here we present a direct and detailed comparison of such neutrino radiation-hydrodynamical simulations for two codes, agile-boltztran of the Oak Ridge-Basel group and vertex of the Garching group. The former solves the Boltzmann equation directly by an implicit, general relativistic discrete angle method on the adaptive grid of a conservative implicit hydrodynamics code with second-order TVD advection. In contrast, the latter couples a variable Eddington factor technique with an explicit, moving-grid, conservative high-order Riemann solver with important relativistic effects treated by an effective gravitational potential. The presented study is meant to test both neutrino radiation-hydrodynamics implementations and to provide a data basis for comparisons and verifications of supernova codes to be developed in the future. Results are discussed for simulations of the core collapse and post-bounce evolution of a 13 M ⊙ star with Newtonian gravity and a 15 M ⊙ star with relativistic gravity.

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.

We explore the implications of the QCD phase transition during the postbounce evolution of corecollapse supernovae. Using the MIT bag model for the description of quark matter and assuming small bag constants, we find that the phase transition occurs during the early postbounce accretion phase. This stage of the evolution can be simulated with general relativistic three-flavor Boltzmann neutrino transport. The phase transition produces a second shock wave that triggers a delayed supernova explosion. If such a phase transition happens in a future galactic supernova, its existence and properties should become observable as a second peak in the neutrino signal that is accompanied by significant changes in the energy of the emitted neutrinos. In contrast to the first neutronization burst, this second neutrino burst is dominated by the emission of anti-neutrinos because the electrondegeneracy is lifted when the second shock passes through the previously neutronized matter. In search of the phase transition from hadronic to deconfined matter, heavy ion experiments at RHIC and at LHC at CERN explore the QCD phase diagram for large temperatures and small baryochemical potentials. For these conditions, which were also present in the early universe, lattice QCD calculations predict a crossover transition between the deconfined chirally symmetric phase and the confined phase with broken chiral symmetry. For high chemical potentials and low temperatures a first order chiral phase transition is expected and will be tested at the FAIR facility at GSI Darmstadt.Due to their large central densities, compact stars can also serve as laboratories for nuclear matter beyond saturation density and may contain quark matter [1]. The formation of quark matter in compact stars is mainly discussed in two scenarios, in protoneutron stars (PNS) after the supernova explosion [2] and in old accreting neutron stars [3,4]. For the first case, deleptonization leads to the loss of lepton pressure and therefore to an increase in the central density so that the phase transition takes place. Possible observables are the emission of gravitational waves [3,4] due to the contraction of the neutron star or delayed γ-ray bursts [5].In this article we want to follow a third and less discussed case. The phase transition from hadronic to quark matter can already occur in the early postbounce phase of a core-collapse supernova [6,7,8,9,10]. This requires a phase transition onset close to saturation density, which can be realized for high temperatures and low proton fractions. For such a scenario Ref. [8] found the formation of a second shock as a direct consequence of the phase transition. However, the lack of neutrino transport in their model allowed them to investigate the dynamics only for a few ms after bounce. Very recently, a quark matter phase transition has been considered with Boltzmann neutrino transport for a 100 M ⊙ progenitor [11]. The appearance of quark matter shortened the time until black hole formation due to the softening of the equation o...

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...

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.

We report on the stellar core collapse, bounce, and postbounce evolution of a 13 M ᭪ star in a self-consistent general relativistic spherically symmetric simulation based on Boltzmann neutrino transport. We conclude that approximations to exact neutrino transport and the omission of general relativistic effects were not alone responsible for the failure of numerous preceding attempts to model supernova explosions in spherical symmetry. Compared to simulations in Newtonian gravity, the general relativistic simulation results in a smaller shock radius. We however argue that the higher neutrino luminosities and rms energies in the general relativistic case could lead to a larger supernova explosion energy.