(This Research Statement is also available as a PDF)

I'm interested in computational astrophysics broadly - understanding complex astrophysical systems through large-scale parallel multiphysics simulations; carefully examining microphysics both for its own sake and so that it can be included quantitatively in larger-scale models; and developing and analyzing computational techniques for use in astrophysical simulations. I currently study the physics of Type Ia supernovae; bubbles and turbulence in galaxy clusters; turbulence in disks; and efficient and accurate computational techniques for studying these phenomenon. Here I outline my plans for these projects for the next few years.

Why Computational Astrophysics?

Astrophysics is an observational science. As astrophysicists, we generally do not have the option of making direct measurements, or performing experiments on the objects we wish to study. In such a discipline, quantitatively generating and testing models to compare to observations is critical, as such models are often the only window available into the science underlying the objects that define our field.

Astrophysics is also an integrative science, taking knowledge from many other disciplines and applying them to the objects we study. In some phenomenon, one or two pieces of physics dominate and fairly simple models can capture its behavior. But as the field advances - observations become richer in detail and broader in scope, and theoretical understanding improves - interesting astrophysics usually results from the interactions between many different physical mechanisms.

That astrophysics is an observational science makes accurate models crucial; that astrophysics studies objects driven by a wide range of physics makes accurate models very complex. The richness of the interactions involved, however maddening, is essential to the phenomena we'd like to understand. The only way to adequately explore such complex models is often through high-performance computation.

Type Ia Supernovae

Supernova Type Ia scenarios previously considered ‘exotic’ may be required to explain observations; even those scenarios which turn out not to produce Type Ia almost certainly result in observable events. Over the next three years, armed with better understanding of the microphysical inputs, I plan to perform large-scale multi-physics 3d simulations on at least two of these ‘exotic’ scenario. This will both constrain models of Type Ia and investigate possibly interesting new stellar explosions.

Fig 1. Evolution of nuclear flame-turbulence interaction. Note that the flame suppresses small-scale wrinkling at the front, while material behind the front is greatly wrinkled.

Increasing scrutiny shows Type Ia aren't as uniform as previously thought. Cosmological interest requires determining the extent to which these things are truly standard candles, or finding new relations to reduce the scatter in inferred luminosity. This requires better constraining the scenario which leads to explosion, and a more detailed understanding of the ignition and burning that occurs once the process has begun.

More intriguingly, new observations suggest that there may be a ‘prompt’ population of Type Ia. Since this is very difficult to accommodate with the standard model, there is growing interest in what had previously been considered quite exotic models (WD mergers, pulsational detonations, helium detonations on the surface of low-mass CO WD). Indeed, it is well past time for closer re-examination of these possibilities; all have interesting predicted frequencies, and certainly all must have observational consequences, even the ones which do not generate Type Ia.

However, critically examining both the ignition/burning mechanisms and the large scale mechanism simultaneously has been impossible, which has made distinguishing between scenarios difficult. I and others have put much work recently into understanding important microphysical effects which are necessary inputs to large-scale simulations. One example of my own work is the effect of flow on flame speed (Fig. 1). Another is work done this past summer with two undergraduate students measuring ignition limits very accurately. Both of these are important because large scale models cannot possibly resolve both the ignition scenario under consideration and the ignition or burning. Turbulent ignition, in particular, is likely to happen first at extremely small scales. Now that these small scale effects are better understood, they can be used as sub-grid inputs to large scale simulations. I plan to perform these large-scale simulations for at least the following two scenario in the coming three years.

Pulsational Detonations

Fig 2. Results from a simulation of spherically compressed reactive turbulence.

Pure-deflagration models for Type Ia supernovae have yet to produce explosions of the energies seen, and abundances in ejecta seem to be better matched by simulations where a detonation runs through pre-expanded material than by those with a pure deflagration. One scenario I will model is a ‘delayed detonation’ scenario, where an almost-unbound white dwarf re-collapses. Because many deflagration models robustly leave unburned matter in the center of the star, there is fuel available for a central compression-driven ignition. The likelihood and energetics of an ignition for any given compression profile will be enhanced in the presence of turbulent hotspots, which will run away before the ambient material.

The questions I intend to answer through simulations are: Can any reasonable infall from a failed explosion produce a detonation that will then propagate through the star? Can it succeed without hotspots in the center? If not, what sort of hotspots must exist - ie, how intense does the central turbulence have to be for this to be a viable model? And what roles do diffusive and turbulent transport have in preparing the central regions?

Preliminary work on this project has begun; a parameter study of small-scale spherical hotspot compression simulations have been run, as have preliminary two-dimensional simulations of compressed reactive turbulence (eg, Fig~2). The next steps are to perform increasingly large-scale simulations connecting these small scale results to the global problem of a partially burned white dwarf re-collapse.

The first step is to perform one-dimensional simulations of the re-collapse of a realistic burned white dwarf. This allows us to connect to work already done, as well as extend it by including more recent information as to how the initial deflagration phase proceeds. These 1d global simulations then provide the compression time profile for 2d and 3d simulations of compressed reactive turbulence with and without rotation.

These computationally large-scale (but physically small-scale) simulations will then give constraints for the properties of the turbulence and the central region for the collapse to successfully ignite a detonation. Meso-scale simulations then connect the two, determining if these constraints are realizable.

White Dwarf Mergers

Some recent work has gone into examining the merging of white dwarfs as a mechanism for more than a Chandrasekhar mass of carbon and oxygen to ignite. The secondary dwarf is seen to be completely disrupted, and - after some transient mass transfer - form an accretion disk. While a ‘flash’ is seen, no propagating burning occurs in the models to date. But such models could not observe such an event; a typical size for a detonation ignition would be hundreds of metres, while for a flame that might be millimetres.

I propose to perform a series of large-scale white dwarf merger simulations, with an eye to trying to better resolve the initial flash from the transient transfer of material before a steady accretion disk forms. Because resolving the white dwarf structure during the merger is important, these are extremely large simulations; however, the merger itself happens relatively quickly, meaning the total amount of computational resources per simulation is reasonable. At least one of the merger simulations will be computed with both SPH and AMR codes to ensure that different numerical methods do not lead to significantly different effects.

The global merger simulations and the initial mass transfer provide the initial conditions for meso-scale and small-scale simulations examining whether propagating burning can be ignited by the merger. If it is shown that a detonation can be ignited, then the detonation can be mapped into the global simulation to confirm that the detonation can disrupt the system.

Bubbles, Turbulence in Galaxy Clusters

The absence of catastrophic cooling in galaxy clusters has been explained somewhat by recent observations of galaxy clusters, revealing X-ray emission voids of up to 30 kpc in size that have been identified with buoyant, magnetized bubbles. The mechanism by which these outflows heat the cluster medium as a whole remains unclear, but herein lies an opportunity; comparing the results of different heating mechanisms to the observed temperatures allows us to examine the outflow/ICM interactions, and thus to probe the ICM properties.

Fig 3. A bubble self-disrupting in a stratified atmosphere.

Recent \it Chandra and \it 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. These bubbles, presumably inflated by a central AGN, suggest a way of heating the ICM and preventing a cooling catastrophe. However, while the presence of large amounts of hot gas is suggestive, the process by which the bubble gas heats the ICM is unclear. For example, it is unclear what role thermal diffusion plays, as the ICM magnetic field could potentially be very tangled and all but completely suppress conduction of heat. Turbulence or weak shocks could also play a role.

Previous work of mine (eg, Fig 3) suggests that coherent magnetic fields may well play a role in the coherence of the bubbles, but this doesn't answer the question of energy transport. Interestingly, the different mechanisms of heat transfer - thermal conductivity, subsonic turbulence, or nonlinear sound waves or weak shocks - all carry energy at very different characteristic speeds, and so the observed temperature profiles contain clues as to the properties of the transport in the ICM.

I have already performed two dimensional and preliminary three dimensional simulations of the basic physical setup. After improving the time-accuracy of thermal conductivity in the FLASH code, I will conduct a series of simplified-geometry simulations varying the strength of thermal conductivity (from Spitzer values to zero, representing increasing magnetic suppression of diffusion) and the Mach number of the rising bubbles, to try to understand the spatial patterns of heating by the three different mechanisms. Then more realistic initial conditions will be used, taking cluster profiles from cosmological simulations, in an attempt to look for situations where the amplitude of the differences in the pattern may be observable.

Turbulence, Mixing, and Instabilities in Disks

Disks are ubiquitous in astrophysics, but many fundamental questions remain about their behaviour. In both protoplanetary and AGN disks, turbulence, shocks, cooling, and fragmentation play important roles. The details of transport is determined by the turbulence, and the details of heating are determined by the shock physics in the disk. Two projects I plan to begin involve the formation of a turbulent boundary layer at the surface of a disk interacting with a wind; and the interaction of cooling, shock-heating, and accretion in protoplanetary and AGN disks.

Fig 4. A hot supersonic wind mixing with the surface of a disk.

Accretion disks involve rich physics, and are involved in key stages of many astrophysical processes. I am beginning two projects at CITA on disks that will continue over the coming year.

Fragmentation is an important issue in disks, both for angular momentum transport and for planet or star formation. Fragmentation is largely controlled by the balance between shock heating and local cooling process, meaning that getting the cooling rates, shock physics, and dimensionality correct is essential to properly determine limits for the creation of structures.

I am beginning projects with R. Rafikov and C. Matzner (CITA) to perform 3d global simulations of protoplanetary and AGN disks, paying close attention to the cooling physics. I will perform one set of simulations using both a grid code (FLASH) and an SPH code (GADGET-2), to examine carefully the difference in fragmentation - caused both directly and indirectly (through shock physics) - due to different numerical methods. The next step will be to refine the thermal physics and the relation between fragmentation and accretion.

Another project involves wind-disk interactions (eg, Fig 4). If the central object emits a wind, then on the surface of a disk a turbulent boundary layer will be set up, determined by the incoming hot wind and the cooling rate in the disk material. The turbulent boundary layer mediates the ablation of the disk by the wind, and determines the vertical boundary conditions of the disk. I am performing a study of such disk-wind interactions with Chris Thompson (CITA) to understand the interplay of cooling, Kelvin-Helmholtz, and rotation in the formation of the turbulent boundary layer.

Computational Techniques

For both experimentalists and computational scientists, doing new science sometimes means building your own equipment. I have been one of the developers of the FLASH code, a multi-physics, highly parallel, astrophysical fluids code that has won a Gordon Bell prize. But doing the next big experiment always requires adding one more tool. In parallel with computational projects using tools already at my disposal, over the next five years I plan to develop ‘all-speed’ hydrodynamic solvers (already in use in other disciplines) for use in publicly available codes, to make accessible regimes unavailable to the current generation of astrophysical solvers. In testing such a solver, collaboration with experimentalists will be essential, and can generate interesting science in its own right.

Efficient Parallel Computation

Doing large-scale computation, such as the simulations sketched here, often involves parallel computation, which introduces great possibilities but also great complexities. Many of my contributions to the Flash code involved improving the efficiency of the parallel computation.

An important stage in this development is the implementation of efficient elliptic solvers. FLASH, which I intend to use as the framework in which to implement this solver, has a multigrid solver which is widely known to be unnecessarily slow. Over the next months — that is, during my remaining time at CITA — I plan to re-write the multigrid solver to greatly improve its performance. This will improve the performance of the FLASH self-gravity module, but will also be an input into other physics solvers.

Hydrodynamic Solvers

Many astrophysical problems involve long periods of relatively quiet, secular evolution followed by a rapid stage of high-speed evolution. Generally, the current generation of multidimensional general-purpose astrophysical hydrodynamic solvers are quite capable at high-speed flows, but timestep restrictions render low speed evolutionary stages inaccessible. Some of my previous work has modestly extended the range of applicability of these methods by eliminating transients and improving accuracy, but many problems remain inaccessible.

Other disciplines (such as within the combustion research community) have problems with similar natures, and they have developed hydrodynamic solvers capable of dealing with either low-speed flows or even switching smoothly between low- and high-speed flows. In some cases, these methods can be directly used for astrophysical problems; in other cases, fairly significant generalizations must be made because of the highly nonlinear equations of state that occur.

Although there are a variety of methods, they fall largely into two sets of techniques; projection methods and dual-timestepping, representing extending different sorts of techniques into this regime. Projection methods, in particular, use methods similar to those used in other sorts of astrophysical codes, such as for solving for self-gravity, or implicit flux-limited diffusion. It is this class of solvers, then, that I propose to implement and eventually make publicly available.

Validation and Verification

As simulations become more complex, and more important in the understanding of astrophysical phenomenon, it becomes increasingly vital to have a verification and validation strategy for testing a new method. Slowly, more sophisticated approaches are being used in the astrophysical community for verification (ensuring that the model equation are being solved correctly), including the method of manufactured solutions. Validation, however, requires comparison with experimental results.

Low-speed flows in particular lend themselves to comparing simulations with table-top hydrodynamics experiments. For the comparison to be evidence for trusting the astrophysical aspects of the code, the problem being investigated must be a significant part of the target astrophysical problem, but still be simple enough to make a detailed understanding of the results possible. To get experimentalists interested in collaborating, the problem being studied must be interesting in and of itself. These considerations lead naturally to the examination of fluid instabilities, which are important in many astrophysical situations, and generally remain quite poorly understood in the fully nonlinear regime. By pursuing collaborations with experimental groups for investigations of fluid instabilities, one can both test a new solver and do real science with astrophysical application.