K. Olson

FLASH: An Adaptive Mesh Hydrodynamics Code for Modeling Astrophysical Thermonuclear Flashes

We report on the completion of the first version of a new-generation simulation code, FLASH. The FLASH code solves the fully compressible, reactive hydrodynamic equations and allows for the use of adaptive mesh refinement. It also contains state-of-the-art modules for the equations of state and thermonuclear reaction networks. The FLASH code was developed to study the problems of nuclear flashes on the surfaces of neutron stars and white dwarfs, as well as in the interior of white dwarfs. We expect, however, that the FLASH code will be useful for solving a wide variety of other problems. This first version of the code has been subjected to a large variety of test cases and is currently being used for production simulations of X-ray bursts, Rayleigh-Taylor and Richtmyer-Meshkov instabilities, and thermonuclear flame fronts. The FLASH code is portable and already runs on a wide variety of massively parallel machines, including some of the largest machines now extant.

On validating an astrophysical simulation code

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 multilayer 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 multilayer 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.

Morphology of Rising Hydrodynamic and Magnetohydrodynamic Bubbles from Numerical Simulations

Recent Chandra and XMM-Newton observations of galaxy cluster cooling flows have revealed X-ray emission voids of up to 30 kpc in size that have been identified with buoyant, magnetized bubbles. Motivated by these observations, we have investigated the behavior of rising bubbles in stratified atmospheres using the FLASH adaptive-mesh simulation code. We present results from two-dimensional simulations with and without the effects of magnetic fields and with varying bubble sizes and background stratifications. We find purely hydrodynamic bubbles to be unstable; a dynamically important magnetic field is required to maintain a bubbles integrity. This suggests that, even absent thermal conduction, for bubbles to be persistent enough to be regularly observed, they must be supported in large part by magnetic fields. Thermal conduction unmitigated by magnetic fields can dissipate the bubbles even faster. We also observe that the bubbles leave a tail as they rise; the structure of these tails can indicate the history of the dynamics of the rising bubble.

Mapping Initial Hydrostatic Models in Godunov Codes

We look in detail at the process of mapping an astrophysical initial model from a stellar evolution code onto the computational grid of an explicit, Godunov-type code while maintaining hydrostatic equilibrium. This mapping process is common in astrophysical simulations, when it is necessary to follow short-timescale dynamics after a period of long-timescale buildup. We look at the effects of spatial resolution, boundary conditions, the treatment of the gravitational source terms in the hydrodynamics solver, and the initialization process itself. We conclude with a summary detailing the mapping process that yields the lowest ambient velocities in the mapped model.

On heavy element enrichment in classical novae

Many classical nova ejecta are enriched in CNO and Ne. Rosner and coworkers recently suggested that the enrichment might originate in the resonant interaction between large-scale shear flows in the accreted H/He envelope and gravity waves at the interface between the envelope and the underlying C/O white dwarf (WD). The shear flow amplifies the waves, which eventually form cusps and break. This wave breaking injects a spray of C/O into the superincumbent H/He. Using two-dimensional simulations, we formulate a quantitative expression for the amount of C/O per unit area that can be entrained, at saturation, into the H/He. The fraction of the envelope that is enriched depends on the horizontal distribution of shear velocity and the density contrast between the C/O WD and the H/He layer but is roughly independent of the vertical shape of the shear profile. Using this parameterization for the mixed mass, we then perform several one-dimensional Lagrangian calculations of an accreting WD envelope and consider two scenarios: that the wave breaking and mixing is driven by the convective flows and that the mixing occurs prior to the onset of convection. In the absence of enrichment prior to ignition, the base of the convective zone, as calculated from mixing-length theory with the Ledoux instability criterion, does not reach the C/O interface. As a result, there is no additional mixing, and the runaway is slow. In contrast, the formation of a mixed layer during the accretion of H/He, prior to ignition, causes a more violent runaway. The envelope can be enriched by 25% of C/O by mass (consistent with that observed in some ejecta) for shear velocities, over the surface, with Mach numbers 0.4.

Helium Detonations on Neutron Stars

We present the results of a numerical study of helium detonations on the surfaces of neutron stars. We describe two-dimensional simulations of the evolution of a detonation as it breaks through the accreted envelope of the neutron star and propagates laterally through the accreted material. The detonation front propagates laterally at nearly the Chapman-Jouguet velocity, v = 1.3 × 109 cm s-1. A series of surface waves propagate across the pool of hot ash behind the detonation front with the same speed, matching the speed expected from shallow water wave theory. The entire envelope oscillates in the gravitational potential well of the neutron star with a period of ~50 μs. The photosphere reaches an estimated height of 10 km above the surface of the neutron star. Our study confirms that such a detonation can insure the spread of burning over the entire neutron star surface on a timescale consistent with burst rise times. We analyze the sensitivity of the results to the spatial resolution and the assumed initial conditions. We conclude by presenting a comparison of this model to type I X-ray bursts.

On the Cellular Structure of Carbon Detonations

We present the results of a numerical study on two-dimensional carbon detonations. For an upstream density of 107 g cm-3 the length-to-width ratio of the detonation cells is about 1.6 and is not strongly dependent on the spatial resolution of the simulation. However, the curvature of the weak incident shocks, strength of the triple points and transverse waves, and sizes of the underreacted and overreacted regions all depend strongly on the spatial resolution of the calculation. These resolution studies help define the minimum resolution required by multidimensional Type Ia supernovae models where the cellular structure of a detonation front is a key feature of the model.

The Response of Model and Astrophysical Thermonuclear Flames to Curvature and Stretch

Critically understanding the standard candle-like behavior of Type Ia supernovae requires understanding their explosion mechanism. One family of models for Type Ia supernovae begins with a deflagration in a carbon-oxygen white dwarf that greatly accelerates through wrinkling and flame instabilities. While the planar speed and behavior of astrophysically relevant flames is increasingly well understood, more complex behavior, such as the flames response to stretch and curvature, has not been extensively explored in the astrophysical literature; this behavior can greatly enhance or suppress instabilities and local flame-wrinkling, which in turn can increase or decrease the bulk burning rate. In this paper, we explore the effects of curvature on both nuclear flames and simpler model flames to understand the effect of curvature on the flame structure and speed.

On the nonlinear evolution of wind-driven gravity waves

We present a study of wind-driven nonlinear interfacial gravity waves using numerical simulations in two dimensions. We consider a case relevant to mixing phenomenon in astrophysical events such as novae in which the density ratio is approximately 1:10. Our physical setup follows the proposed mechanism of Miles [ J. Fluid Mech. 3, 185 (1957) ] for the amplification of such waves. Our results show good agreement with linear predictions for the growth of the waves. We explore how the wind strength affects the wave dynamics and the resulting mixing in the nonlinear stage. We identify two regimes of mixing, namely, the overturning and the cusp-breaking regimes. The former occurs when the wind is strong enough to overcome the gravitational potential barrier and overturn the wave. This result is in agreement with the common notion of turbulent mixing in which density gradients are increased to diffusion scales by the stretching of a series of vortices. In the latter case, mixing is the result of cusp instabilit...

Mixing by Non‐linear Gravity Wave Breaking on a White Dwarf Surface

We present the results of a simulation of a wind‐driven non‐linear gravity wave breaking on the surface of a white dwarf. The “wind” consists of H/He from an accreted envelope, and the simulation demonstrates that this breaking wave mechanism can produce a well‐mixed layer of H/He with C/O from the white dwarf above the surface. Material from this mixed layer may then be transported throughout the accreted envelope by convection, which would enrich the C/O abundance of the envelope as is expected from observations of novae.