We investigate in this paper the core-collapse supernova explosion mechanism in both one and two dimensions. With a radiation/hydrodynamic code based upon the PPM algorithm, we verify the usefulness of neutrino-driven overturn ("convection") between the shock and the neutrinosphere in igniting the supernova explosion. The 2-D simulation of the core of a 15M ⊙ star that we present here indicates that the breaking of spherical symmetry may be central to the explosion itself and that a multitude of bent and broken fingers is a common feature of the ejecta. As in one-dimension, the explosion seems to be a mathematically critical phenomenon, evolving from a steady-state to explosion after a critical mass accretion rate through the stalled shock has been reached. In the 2-D simulation we show here, the pre-explosion convective phase lasted ∼30 overturns (∼100 milliseconds) before exploding. The pre-explosion steady-state in 2-D is similar to that achieved in 1-D, but, in 2-D, due to the higher dwell time of matter in the overturning region, the average entropy achieved behind the stalled shock is larger. In addition, the entropy gradient in the convecting region is flatter. These effects, together with the dynamical pressure of the buoyant plumes, serve to increase the steady-state shock radius (R s ) over its value in 1-D by 30%-100%. A large R s enlarges the volume of the gain region, puts shocked matter lower in the gravitational potential well, and lowers the accretion ram pressure at the shock for a givenṀ. The critical condition for explosion is thereby relaxed. Since the "escape" temperature (T esc ) decreases with radius faster than the actual matter temperature (T ) behind the shock, a larger R s puts a larger fraction of the shocked material above its local escape temperature. T > T esc is the condition for a thermally-driven corona to lift off of a star. In one, two, or three dimensions, since supernovae are driven by 100 milliseconds of the explosion, a strong, neutrino-driven wind is blowing outward from the protoneutron star that clears the interior of mass and, while operative, does not allow fallback. At the base of the rising explosion plumes (in the early wind), a few high entropy (∼ 60) clumps are ejected, whose subsequent evolution may prove to be of relevance to the r-process.

New data imply that the average velocity of radio pulsars is large [1].Under the assumption that these data imply that a pulsar is born with an \intrinsic" kick, we i n v estigate whether such kicks can be a consequence of asymmetrical stellar collapse and explosion. We calculate the gravitational wave (GW) signature of such asymmetries due to anisotropic neutrino radiation and mass motions. We predict that any recoils imparted to the neutron star at birth will result in a gravitational wave strain, h T T zz , that does not go to zero with time. Hence, there may be \memory" [2] in the gravitational waveform from a protoneutron star that is correlated with its recoil and neutrino emissions.PACS numbers: 97.60. Bw, 97.60.Gb, 97.60.Jd, 95.30.Lz, 97.10.Wn Typeset using REVT E X 1

This paper describes ZEUS-MP, a multi-physics, massively parallel, message-passing implementation of the ZEUS code. ZEUS-MP differs significantly from the thoroughly documented ZEUS-2D code, the completely undocumented (in peer-reviewed literature) ZEUS-3D code, and a marginally documented "version 1" of ZEUS-MP first distributed publicly in 1999. ZEUS-MP offers an MHD algorithm which is better suited for multidimensional flows than the ZEUS-2D module by virtue of modifications to the Method of Characteristics scheme first suggested by Hawley & Stone (1995). This MHD module is shown to compare quite favorably to the TVD scheme described by Ryu et al. (1998). ZEUS-MP is the first publicly-available ZEUS code to allow the advection of multiple chemical (or nuclear) species. Radiation hydrodynamic simulations are enabled via an implicit flux-limited radiation diffusion (FLD) module. The hydrodynamic, MHD, and FLD modules may be used, singly or in concert, in one, two, or three space dimensions. Additionally, so-called "1.5-D" and "2.5-D" grids, in which the "half-D" denotes a symmetry axis along which a constant but non-zero value of velocity or magnetic field is evolved, are supported. Self gravity may be included either through the assumption of a GM/r potential or a solution of Poisson's equation using one of three linear solver packages (conjugategradient, multigrid, and FFT) provided for that purpose. Point-mass potentials are also supported.Because ZEUS-MP is designed for large simulations on parallel computing platforms, considerable attention is paid to the parallel performance characteristics of each module in the code. Strong-scaling tests involving pure hydrodynamics (with and without self-gravity), MHD, and RHD are performed in which large problems (256 3 zones) are distributed among as many as 1024 processors of an IBM SP3. Parallel efficiency is a strong function of the amount of communication required between processors in a given algorithm, but all modules are shown to scale well on up to 1024 processors for the chosen fixed problem size.

This paper presents a new code for performing multidimensional radiation hydrodynamic (RHD) simulations on parallel computers involving anisotropic radiation fields and nonequilibrium effects. The radiation evolution modules described here encapsulate the physics provided by the serial algorithm of Stone et. al (1992), but add new functionality both with regard to physics and numerics. In detailing our method, we have documented both the analytic and discrete forms of the radiation moment solution and the variable tensor Eddington factor (VTEF) closure term. We have described three different methods for computing a short-characteristic formal solution to the transfer equation, from which our VTEF closure term is derived. Two of these techniques include time dependence, a primary physics enhancement of the method not present in the Stone algorithm. An additional physics modification is the adoption of a matter-radiation coupling scheme which is particularly robust for nonequilibrium problems and which also reduces the operations cost of our radiation moment solution. Two key numerical components of our implementation are highlighted: the biconjugate gradient linear system solver, written for general use on massively parallel computers, and our techniques for parallelizing both the radiation moment solution and the transfer solution. Additionally, we present a suite of test problems with a much broader scope than that covered in the Stone work; new tests include nonequilibrium Marshak waves, two dimensional "shadow" tests showing the one-sided illumination of an opaque cloud, and full RHD+VTEF calculations of radiating shocks. We use the results of these tests to assess the virtues and vices of the method as currently implemented, and we identify a key area in which the method may be improved. We conclude that radiation moment solutions closed with variable tensor Eddington factors show a dramatic qualitative improvement over results obtained with flux-limited diffusion, and further that this approach has a bright future in the context of parallel RHD simulations in astrophysics.Subject headings: hydrodynamics -methods:numerical -methods:parallel -radiative transfer the radiation field within a medium in which both light-crossing timescales and (far longer) thermal timescales are important. The test problem specified for benchmarking a new algorithm was the "tophat" (or "crooked pipe") test, a description of which is given by Gentile (2001). The algorithm desired was one that could capture the aforementioned features of the problem at a fraction of the cost of more elaborate Boltzmann (e.g. S n ) or Monte Carlo methods. We felt that a moment-based approach like that described in Paper III was an ideal candidate for treating the tophat test, and further that the original serial method could be adapted for parallel use.The final product of this project is a new set of numerical routines for performing RHD simulations in a parallel environment. These routines provide all of the abilities advertised for the serial rou...

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. arXiv:0709.0537v1 [astro-ph]

We consider a PDE system comprising compressible hydrodynamics, flux-limited diffusion radiation transport and chemical ionization kinetics in a cosmologicallyexpanding universe. Under an operator-split framework, the cosmological hydrodynamics equations are solved through the Piecewise Parabolic Method, as implemented in the Enzo community hydrodynamics code. The remainder of the model, including radiation transport, chemical ionization kinetics, and gas energy feedback, form a stiff coupled PDE system, which we solve using a fullyimplicit inexact Newton approach, and which forms the crux of this paper. The inner linear Newton systems are solved using a Schur complement formulation, and employ a multigrid-preconditioned conjugate gradient solver for the inner Schur systems. We describe this approach and provide results on a suite of test problems, demonstrating its accuracy, robustness, and scalability to very large problems.

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M uch of the contemporary research in astrophysics necessarily involves the development of models and simulation technology to help us understand the complex phenomena underlying astrophysical events. As with any modeling approach, numerical models and simulation codes developed for astrophysical applications must be thoroughly verified and validated to demonstrate their accuracy and assess their credibility. Although verification and validation (V&V) is maturing as a discipline due to its importance in fields such as computational fluid dynamics (CFD), until recently it has received scant attention in the astrophysical literature.In astrophysics, validation is a challenging problem because many of the conditions of interest can't be reproduced in terrestrial laboratories. In addition, astrophysical settings such as the interiors of stars are not directly observable. Even if this were not a problem, most astrophysical events happen at extreme distances, making observation difficult if not impossible. The complexity of astrophysical events also makes validating an astrophysical simulation code difficult. Astrophysical events typically involve many complex interacting physical processes, all of which must be included in a realistic model. Direct numerical simulations (for example, resolving all of a problem's scales of interest) are often beyond the capabilities of current computers, requiring the development of approximate methods and descriptions of the physical processes on scales smaller than the simulation can track (subgrid models).Validation requires identifying the physical Copublished by the IEEE CS and the AIP Astrophysical simulations model phenomena that can't be fully reproduced terrestrially. Validation then requires carefully devising feasible experiments with the relevant physics. The authors describe validating simulations against experiments that probe fluid instabilities, nuclear burning, and radiation transport, and then discuss insights from-and the limitations of-these tests.