The turbulent Rayleigh-Taylor instability is investigated in the limit of strong mode-coupling using a variety of high-resolution, multimode, three dimensional numerical simulations ͑NS͒. The perturbations are initialized with only short wavelength modes so that the self-similar evolution ͑i.e., bubble diameter D b ϰamplitude h b) occurs solely by the nonlinear coupling ͑merger͒ of saturated modes. After an initial transient, it is found that h b ϳ␣ b Agt 2 , where AϭAtwood number, gϭacceleration, and tϭtime. The NS yield D b ϳh b /3 in agreement with experiment but the simulation value ␣ b ϳ0.025Ϯ0.003 is smaller than the experimental value ␣ b ϳ0.057Ϯ0.008. By analyzing the dominant bubbles, it is found that the small value of ␣ b can be attributed to a density dilution due to fine-scale mixing in our NS without interface reconstruction ͑IR͒ or an equivalent entrainment in our NS with IR. This may be characteristic of the mode coupling limit studied here and the associated ␣ b may represent a lower bound that is insensitive to the initial amplitude. Larger values of ␣ b can be obtained in the presence of additional long wavelength perturbations and this may be more characteristic of experiments. Here, the simulation data are also analyzed in terms of bubble dynamics, energy balance and the density fluctuation spectra.

We present a new mechanism for Type Ia supernova explosions in massive white dwarfs. The proposed scenario follows from relaxing the assumption of symmetry in the model and involves a detonation created in an unconfined environment. The explosion begins with an essentially central ignition of stellar material initiating a deflagration. This deflagration results in the formation of a buoyantly-driven bubble of hot material that reaches the stellar surface at supersonic speeds. The bubble breakout forms a strong pressure wave that laterally accelerates fuel-rich outer stellar layers. This material, confined by gravity to the white dwarf, races along the stellar surface and is focused at the location opposite to the point of the bubble breakout. These streams of nuclear fuel carry enough mass and energy to trigger a detonation just above the stellar surface. The flow conditions at that moment support a detonation that will incinerate the white dwarf and result in an energetic explosion. The stellar expansion following the deflagration redistributes stellar mass in a way that ensures production of intermediate mass and iron group elements consistent with observations. The ejecta will have a strongly layered structure with a mild amount of asymmetry following from the early deflagration phase. This asymmetry, combined with the amount of stellar expansion determined by details of the evolution (principally the energetics of deflagration, timing of detonation, and structure of the progenitor), can be expected to create a family of mildly diverse Type Ia supernova explosions.Comment: 4 pages, 6 figures at reduced resolution, submitted to ApJ Letter

We develop an improved method for tracking the nuclear flame during the deflagration phase of a Type Ia supernova, and apply it to study the variation in outcomes expected from the gravitationally confined detonation (GCD) paradigm. A simplified 3-stage burning model and a non-static ash state are integrated with an artificially thickened advection-diffusion-reaction (ADR) flame front in order to provide an accurate but highly efficient representation of the energy release and electron capture in and after the unresolvable flame. We demonstrate that both our ADR and energy release methods do not generate significant acoustic noise, as has been a problem with previous ADR-based schemes. We proceed to model aspects of the deflagration, particularly the role of buoyancy of the hot ash, and find that our methods are reasonably well-behaved with respect to numerical resolution. We show that if a detonation occurs in material swept up by the material ejected by the first rising bubble but gravitationally confined to the white dwarf (WD) surface (the GCD paradigm), the density structure of the WD at detonation is systematically correlated with the distance of the deflagration ignition point from the center of the star. Coupled to a suitably stochastic ignition process, this correlation may provide a plausible explanation for the variety of nickel masses seen in Type Ia Supernovae.

We investigate neutrino-driven convection in core collapse supernovae and its ramifications for the explosion mechanism. We begin with an "optimistic" postbounce model in two important respects: (1) we begin with a 15 M ⊙ precollapse model, which is representative of the class of stars with compact iron cores; (2) we implement Newtonian gravity. Our precollapse model is evolved through core collapse and bounce in one dimension using multigroup (neutrino-energy-dependent) flux-limited diffusion (MGFLD) neutrino transport and Newtonian Lagrangian hydrodynamics, providing realistic initial conditions for the postbounce convection and evolution.Our two-dimensional simulation began at 12 ms after bounce and proceeded for 500 ms.We couple two-dimensional (PPM) hydrodynamics to precalculated one-dimensional MGFLD neutrino transport. (The neutrino distributions used for matter heating and deleptonization in our 2D run are obtained from an accompanying 1D simulation. The accuracy of this approximation is assessed.) For the moment we sacrifice dimensionality for realism in other aspects of our neutrino transport. MGFLD is an implementation of neutrino transport that simultaneously (a) is multigroup and (b) simulates with sufficient realism the transport of neutrinos in opaque, semitransparent, and transparent regions. Both are crucial to the accurate determination of postshock neutrino heating, which sensitively depends on the luminosities, spectra, and flux factors of the electron neutrinos and antineutrinos emerging from their respective neutrinospheres.By 137 ms after bounce, we see neutrino-driven convection rapidly developing beneath the shock. By 212 ms after bounce, this convection becomes large-scale, characterized by higher-entropy, expanding upflows and denser, lower-entropy, finger-like downflows. The upflows reach the shock and distort it from sphericity. The radial convection velocities at this time become supersonic just below the shock, reaching magnitudes in excess of 10 9 cm/sec. Eventually, however, the shock recedes to smaller radii, and at ∼500 ms after bounce there is no evidence in our simulation of an explosion or of a developing explosion.Our angle-averaged density, entropy, electron fraction, and radial velocity profiles in our below the electron neutrino and antineutrino gain radii, above which the neutrino luminosities are essentially constant (i.e., the neutrino sources are entirely enclosed), in an effort to assess how spherically symmetric our neutrino sources remain during our 2D evolution, and therefore, to assess our use of precalculated 1D MGFLD neutrino distributions in calculating the matter heating and deleptonization. We find no differences below the neutrinosphere radii, and between the neutrinosphere and gain radii, no differences with obvious ramifications for the supernova outcome.We note that the interplay between neutrino transport and convection below the neutrinospheres is a delicate matter, and is discussed at greater length in another paper (Mezzacappa et al. 1997a).However, ...

We present a case study of validating an astrophysical simulation code. Our study focuses on validating FLASH, a parallel, adaptive-mesh hydrodynamics code for studying the compressible, reactive flows found in many astrophysical environments. We describe the astrophysics problems of interest and the challenges associated with simulating these problems. We describe methodology and discuss solutions to difficulties encountered in verification and validation. We describe verification tests regularly administered to the code, present the results of new verification tests, and outline a method for testing general equations of state. We present the results of two validation tests in which we compared simulations to experimental data. The first is of a laser-driven shock propagating through a multi-layer target, a configuration subject to both Rayleigh-Taylor and Richtmyer-Meshkov instabilities. The second test is a classic Rayleigh-Taylor instability, where a heavy fluid is supported against the force of gravity by a light fluid. Our simulations of the multi-layer target experiments showed good agreement with the experimental results, but our simulations of the Rayleigh-Taylor instability did not agree well with the experimental results. We discuss our findings and present results of additional simulations undertaken to further investigate the Rayleigh-Taylor instability.Comment: 76 pages, 26 figures (3 color), Accepted for publication in the ApJ

We report the results of a series of three-dimensional (3D) simulations of the deflagration phase of the gravitationally confined detonation mechanism for Type Ia supernovae. In this mechanism, ignition occurs at one or several off-center points, resulting in a burning bubble of hot ash that rises rapidly, breaks through the surface of the star, and collides at a point opposite the breakout on the stellar surface. We find that detonation conditions are robustly reached in our 3D simulations for a range of initial conditions and resolutions. Detonation conditions are achieved as the result of an inwardly directed jet that is produced by the compression of unburnt surface material when the surface flow collides with itself. A high-velocity outwardly directed jet is also produced. The initial conditions explored in this paper lead to conditions at detonation that can be expected to produce large amounts of 56 Ni and small amounts of intermediate-mass elements. These particular simulations are therefore relevant only to high-luminosity Type Ia supernovae. Recent observations of Type Ia supernovae imply a compositional structure that is qualitatively consistent with that expected from these simulations.

We develop and calibrate a realistic model flame for hydrodynamical simulations of deflagrations in white dwarf (Type Ia) supernovae. Our flame model builds on the advection-diffusion-reaction model of Khokhlov and includes electron screening and Coulomb corrections to the equation of state in a self-consistent way. We calibrate this model flame-its energetics and timescales for energy release and neutronization-with self-heating reaction network calculations that include both these Coulomb effects and up-to-date weak interactions. The burned material evolves post-flame due to both weak interactions and hydrodynamic changes in density and temperature. We develop a scheme to follow the evolution, including neutronization, of the NSE state subsequent to the passage of the flame front. As a result, our model flame is suitable for deflagration simulations over a wide range of initial central densities and can track the temperature and electron fraction of the burned material through the explosion and into the expansion of the ejecta.

We present a theoretical framework for formal study of systematic effects in Supernovae Type Ia (SN Ia) that utilizes two-dimensional simulations to implement a form of the deflagration-detonation transition (DDT) explosion scenario. The framework is developed from a randomized initial condition that leads to a sample of simulated SN Ia whose 56 Ni masses have a similar average and range to those observed, and have many other modestly realistic features such the velocity extent of intermediate mass elements. The intended purpose is to enable statistically well-defined studies of both physical and theoretical parameters of the SN Ia explosion simulation. We present here a thorough description of the outcome of the SN Ia explosions produced by our current simulations.A first application of this framework is utilized to study the dependence of the SN Ia on the 22 Ne content, which is known to be directly influenced by the progenitor stellar population's metallicity. Our study is very specifically tailored to measure how the 22 Ne content influences the competition between the rise of plumes of burned material and the expansion of the star before these plumes reach DDT conditions. This influence arises from the dependence of the energy release, progenitor structure and laminar flame speed on 22 Ne content. For this study, we explore these three effects for a fixed carbon content and DDT density. By setting the density at which nucleosynthesis takes place during the detonation phase of the explosion, the competition between plume rise and stellar expansion controls the amount of material in nuclear statistical equilibrium (NSE) and therefore 56 Ni produced. Of particular interest is how this influence of 22 Ne content compares to the direct modification of the 56 Ni mass via the inherent neutron excess as discussed by Timmes, Brown & Truran (2003). Although the outcome following from any particular ignition condition can change dramatically with 22 Ne content, with a sample of 20 ignition conditions we find that the systematic change in the expansion of the star prior to detonation is not large enough to compete with the dependence discussed by Timmes, . In fact, our results show no statistically significant dependence of the pre-detonation expansion on 22 Ne content, pointing to the morphology of the ignition condition as being the dominant dynamical driver of the 56 Ni yield of the explosion. However, variations in the DDT density, which were specifically excluded here, are also expected to be important and to depend systematically on 22 Ne content.