DOESciDAC ReviewOffice of Science
FLASH CENTER
Computing the DETONATION of a White Dwarf Star
Stars that explode in the distinctive blasts called Type Ia supernovae are crucial to illuminating the evolution and fate of the Universe. Astrophysicists have struggled for decades to understand the physics of these powerful events. New simulations funded by the DOE’s National Nuclear Security Administration Office of Advanced Simulation and Computation have revealed a surprising mechanism, called gravitationally confined detonation, that may trigger the explosions.
Figure 1. A series of 3D simulations of the successive phases of the gravitationally confined detonation (GCD) explosion mechanism for Type Ia supernovae. The surface of the white dwarf star is shown in blue, and the surface of the burned ash is shown in yellow.
Among the red giants, brown dwarfs, black holes, and other colorful inhabitants of the cosmos, white dwarfs hold a special place. Our Sun will become one of these compact objects when its central furnace of nuclear fusion expires in about 5 billion years. Unable to resist its own gravitational pull, the Sun’s mass will squeeze into a sphere about the size of Earth. This future dwarf star will glow white-hot for billions of years, a pinprick of light still encircled by most of its planets. Ultimately, like a cinder on the hearth, it will fade to blackness.
Not all white dwarfs face such an anonymous fate. Some of them, born as members of binary star systems, steal matter from their nearby companions. This additional gas gradually spirals onto the white dwarfs, making them massive and unstable. At a critical point, the stars detonate in planet-sized thermonuclear bombs. The explosions are visible more than halfway across the Universe as temporary flares of light that rival entire galaxies of stars.
These events—known as Type Ia supernovae—rank among the most valuable probes of how the Universe has grown over time (sidebar “Our Accelerating Universe,” p12). They also have changed the chemical ingredients of our galaxy by seeding space with the building blocks of planets: iron, silicon, and other elements synthesized when the stars blow up. But despite a half-century of theoretical investigation, researchers do not yet know what happens deep inside the dwarfs to make them explode. The physics of the fateful spark remain elusive.
New research by a team at the University of Chicago, funded by the National Nuclear Security Administration (NNSA) Office of Advanced Simulation and Computation (ASC) Academic Strategic Alliance Program, suggests the solution may lie in a surprising place—at the surfaces of the doomed stars. A simulation devised by physicists at the Center for Astrophysical Thermonuclear Flashes (the “Flash Center”) successfully exploded a white dwarf for the first time. The model—run on high-performance computers at LLNL and LBNL—tracked a superheated plume of ash that rose from the star’s interior, erupted through the surface, and enveloped the star (figure 1). When it raced to a collision point on the opposite side of the dwarf, this nuclear storm front packed enough punch to ignite a detonation. The blast wave destroyed the star in a fraction of a second.
The model requires detailed verification and testing, and other models may explain why some Type Ia supernovae do not fit this mold. Still, Flash Center researchers believe they have made a major advance, enabled by what they call “extreme computing” through the DOE’s NNSA ASC Academic Strategic Alliance Program. “This is proof by demonstration of a way that a detonation can happen,” says Dr. Donald Lamb, director of the Flash Center. “The confidence we’re on the right track will increase only with further verification of this model, and by rigorous validation with what astronomers see.”

A 50-Year Puzzle
The brightest minds in astronomy and nuclear physics have been drawn to the challenge of understanding Type Ia supernovae supernovae (figures 2–3). The “Type Ia” designation arose because these supernovae are fundamentally different from the most common stellar explosions, called “Type II” supernovae. A Type II event is the death of a giant star at least seven to eight times as massive as our Sun. The cores of such stars implode catastrophically when they run out of nuclear fuel. This implosion triggers a burst of neutrinos and an outward shock wave, which blows the star apart (“Modeling the First Instants of a Star’s Death,” SciDAC Review, Spring 2006, p26). Left behind is a rapidly rotating neutron star or—for the most massive stars—a black hole. Type II supernovae are rich in hydrogen gas, the main ingredient of the stars’ outermost layers.
Type Ia supernovae rank among the most valuable probes of how the Universe has grown over time. They also have changed the chemical ingredients of our galaxy by seeding space with the building blocks of planets: iron, silicon, and other elements synthesized when the stars blow up.
In contrast, Type Ia supernovae lack a telltale signature of hydrogen. Astronomer Dr. Fred Hoyle of the University of Cambridge and nuclear astrophysicist Dr. Willie Fowler of the California Institute of Technology explained this curiosity in 1960 by hypothesizing that the explosions came not from full-sized stars, but from white dwarfs. These objects contain processed stellar matter, primarily carbon and oxygen, crushed into a “degenerate” state by gravity. A white dwarf can exist in this dense quantum-mechanical equilibrium indefinitely—unless it somehow gains mass.
The tipping point is the “Chandrasekhar mass” of about 1.4 times the mass of our Sun. Beyond that value, the degenerate matter cannot fight the inward force of gravity. Dr. Hoyle and Dr. Fowler claimed that white dwarfs approaching this razor’s edge would shatter in a flash of thermonuclear fusion, creating a rich supply of “iron-group” elements such as chromium, manganese, iron, cobalt, and nickel. Indeed, nuclear astrophysicist Dr. James Truran of the Flash Center has calculated that Type Ia supernovae produce one-half to two-thirds of these key elements in our galaxy, even though they are three to six times rarer than Type II explosions. Type Ia events also forge “intermediate-mass” elements including magnesium, aluminum, silicon, sulfur, and calcium.
But this framework did not address how the explosions might actually begin. The last several decades have seen steady progress but no definitive solution. In 1969, Dr. David Arnett of the California Institute of Technology used a one-dimensional hydrodynamical simulation to calculate the conditions of extreme pressure and temperature under which carbon would detonate at the core of a carbon–oxygen white dwarf. By 1976, another contending model emerged—“deflagration,” in which a subsonic flame burns the stellar material without detonating it. Calculations by Dr. Ken’ichi Nomoto of the University of Tokyo and his colleagues suggested that rapid deflagration—which moves through the star’s interior by thermal conductivity, rather than by a supersonic shock wave—could disrupt the entire star.
Figure 2. A Hubble Space Telescope (HST) optical image of Type Ia supernova 1994D in Galaxy NGC 4526. Figure 3. A Chandra X-ray image of Tycho supernova remnant.
These two scenarios—detonation and deflagration—soon formed the heart of the debate over the nature of Type Ia supernovae. Simulations grew more complex as computing power allowed astrophysicists to model a white dwarf in two dimensions. A hybrid picture emerged from this approach in 1991. Dr. Alexei Khokhlov, then at the Academy of Sciences in Russia and now at the Flash Center, proposed a model in which initial pulses of deflagration near the dwarf’s core led to a sudden detonation. This “delayed detonation” scenario quickly won favor. It seemed to produce an explosion with the right energy, and the mixture of intermediate-mass and iron-group elements looked promising.
The tipping point is the “Chandrasekhar mass” of about 1.4 times the mass of our Sun. Beyond that value, the degenerate matter cannot fight the inward force of gravity.
But the scenario had one vexing problem: no one knew what sparked the detonation. Instead, modelers inserted the detonation into their simulations by hand, then calculated the results. “To this day, we don’t have a clue how the detonation transition might happen,” says Dr. Lamb, who sometimes refers to this as “here, a miracle occurs.”
The particular challenge, Dr. Lamb notes, is the lack of boundaries inside a white dwarf. Laboratory experiments exploring the physics of detonation—in particular, the “match head” that ignites the shock wave—occur in containers that reflect sound waves, amplifying pressures and densities past the necessary threshold. With no such walls in a star, physicists struggled to develop a model that reached the strict conditions needed to set off the apocalyptic shock.

Computation on the Edge
With the relentless progression of Moore’s Law, an answer seemed probable as two-dimensional models matured into three-dimensional simulations. But it still took years to refine the techniques. The latest work by Flash Center researchers using 3D FLASH code simulations run on the unclassified portion of the ASC Purple supercomputer at LLNL and on the Bassi and Seaborg clusters at LBNL, led to the first successful 3D detonation of a simulated Type Ia supernova.
The team built upon its work from 2004, which unveiled a possible detonation mechanism in a 2D cylindrical model. Scaling up to 3D was essential to demonstrate the model’s viability, Dr. Lamb observes, for one main reason: “The behavior of turbulence is totally different in 3D than in 2D.” The effort pushed the Center’s FLASH 3.0 code to its limits (sidebar “The FLASH Code,” p16). The team also drew upon experimental tests of laser-driven turbulence, as well as the most comprehensive simulation of a uniform turbulent fluid ever carried out (section “Verification and Validation,” p16).
The computational cost of each 3D whole-star simulation, from the start of burning near the white dwarf’s core to the star’s complete detonationdetonation (figure 4, p14–15), was about 150,000 CPU-hours. The FLASH code worked seamlessly with the massively parallel processors at LLNL and at LBNL’s National Energy Research Scientific Computing (NERSC) Center, but not without some fast-paced challenges. Team members wore pagers 24 hours a day to respond to error messages and to tweak the FLASH code on the fly. For instance, they adjusted the simulation to focus the highest resolution on the “hot zone” where detonation appeared imminent. “This was the bleeding edge of computation,” says Dr. Cal Jordan of the Flash Center, lead author of a paper on the new simulations (section “Further Reading,” p21). “I’ve really had to up my game to work here.”
The scenario had one vexing problem: no one knew what sparked the detonation.

Figure 4. In these 3D simulations of the successive phases of the GCD explosion mechanism for Type Ia supernovae, the surface of the white dwarf is shown in green and the temperature of the matter in the burned ash and flowing over the surface of the star is shown in various colors, with blue being the coolest and yellow being the hottest. Images on the left-hand page are from the same simulation as those on the right-hand page, but with temperatures colored differently in the visualization. Note the outward- and inward-directed jets that form when the material flowing over the stellar surface collides at the “south pole” of the star.
Verification and Validation
In the early days of détente with the former Soviet Union, President Ronald Reagan coined a memorable motto during tense negotiations of nuclear disarmament treaties: “Trust, but verify.” Code verification and validation is a key component of the ASC Academic Strategic Alliance Program and thus researchers at the Flash Center verify and validate their complex FLASH code by every possible means.
In its verification tests, the team ensures that the code solves the necessary equations correctly. This entails testing the code against sets of equations with analytical solutions, such as the propagation of shock waves. Some complex sets of equations lack exact solutions. In these cases, the team uses carefully validated benchmarks to test the code. “It’s an amazing amount of work to do it right,” says Dr. Nathan Hearn of the Flash Center.
Validation is the deeper, real-world problem: do the equations solve the proper physics for the processes being studied? This is a new pursuit in astrophysics, as the conditions in space are so extreme compared to anything that physicists on Earth can replicate. “It’s a difficult problem,” says Dr. Jordan of the Flash Center. “How do you validate an exploding star? You can’t have a piece of white-dwarf matter in the lab.”
Code verification and validation is a key component of the ASC Academic Strategic Alliance Program and thus researchers at the Flash Center verify and validate their complex FLASH code by every possible means.
One crucial aspect of Type Ia supernovae that physicists wish to mimic in the laboratory is turbulent mixing between layers of matter. The most notable phenomenon to scrutinize is the Rayleigh–Taylor instability, the classic formation of mushroom-shaped whorls at ever-finer scales as two media of different densities forcibly mix together (figure 10, p19). Inside a white dwarf, this highly nonlinear process can determine the amount of nuclear material that burns and the rate at which the flame spreads through the star.
To validate the FLASH code’s treatment of the Rayleigh–Taylor instability, a Flash Center team led by Dr. Alan Calder compared the results of 3D simulations with data from experiments carried out by Dr. Guy Dimonte and his group at LANL as part of a comprehensive study led by Dr. Dimonte.
Figure 7. Comparison of light curves and spectra predicted by 2D simulations of the GCD model of Type Ia supernovae and observations. On the left, a comparison with light curves observed for supernova 2001el. On the right, a comparison with spectra observed for supernova 1994D (figure 2, p13).
More recently, Dr. Hearn and Dr. Tomasz Plewa of the Flash Center teamed with physicists at the University of Michigan, Dr. Paul Drake and Dr. Carolyn Kuranz, to devise an experiment to study the Rayleigh–Taylor instability at the OMEGA laser at the University of Rochester. The laser’s 60 ultraviolet beams bombard a small cylinder just 900 microns (0.9 millimeters) in diameter. The cylinder is packed with a high-density polyimide plastic and a low-density foam, separated by an interface with sinusoidal ripples to seed the growth of instabilities. The laser ablates the polyimide, sending a shock wave through the dense material and across the boundary layer. High-speed radiographs of the mixing region reveal turbulent eddies of polyimide cascading into the foam.
The team studied a weakly compressible homogeneous fluid within a cube containing nearly 8 billion grid points. The simulation tracked the motions of 17 million tracer particles churning through this cube in response to driven turbulence.
By simulating this heat-driven shock with the FLASH code and comparing the results to the images from OMEGA, Dr. Hearn and his colleagues can check the code’s ability to treat Rayleigh–Taylor mixing. Scaling this process to the equation of state of degenerate matter inside a white dwarf is a stiff challenge, Dr. Hearn says. However, the laser experiments give the team a starting point based on demonstrated physics.
Another important mode of validation is to conduct high-resolution simulations of fluid turbulence. To do this, a Flash Center team led by Dr. Robert Fisher worked with the staff at LLNL in December 2005 to use IBM’s BlueGene/L—which has set the world mark for sustained computing power during scientific applications—on one of the largest classical turbulence simulation ever performed (figure 12, p20). The team studied a weakly compressible homogeneous fluid within a cube containing nearly 8 billion grid points. The simulation tracked the motions of 17 million tracer particles churning through this cube in response to driven turbulence.
After about 12 million CPU hours on BlueGene/L—one full week of wall clock time on 65,000 processors—the team was able to understand and quantify the systematic and statistical errors in its turbulence modeling. Notably, the results had such fine detail that the team could discriminate among the predictions of mathematical models of turbulent flow for the first time.
The results are critical to validate the FLASH code’s treatment of turbulence in supernovae, says Flash Center director Dr. Lamb. The work also provides new insights into a physical process that is of interest to the DOE’s Stockpile Stewardship Program. Further, all 22.5 terabytes of data are publicly available to the community on fast mass-storage devices at the University of Chicago’s Computation Institute.

A Surprising Bubble
Dr. Jordan and his colleagues were probing the 3D behavior of a bizarre mechanism dubbed gravitationally confined detonation (GCD). The combustion starts innocently as a small, hot bubble near the center of the white dwarf. Initially this bubble of burning carbon and oxygen remains spherical as it grows. But the hot ashes inside the bubble—primarily nickel, iron, and silicon—are less dense than the surrounding degenerate fuel. Like an air-filled inner tube held under water, the bubble is buoyant and pops up to the surface of the star.
The team’s earlier 2D simulation of this event suggested the smashup was fierce enough to set off a detonation at the collision point. But the resolution provided by the full 3D model was even more interesting.
To get there, the buoyant ashes must fight their way through 2,000 kilometers of dense matter. At the boundaries of this bubble, the nuclear flame quickly grows more complex (sidebar “The Fickle Physics of Nuclear Flames”). At this stage it resembles an ascending cauliflower, which Dr. Lamb compares to a rising blob within a glowing lava lamp from the 1970s. Fluid-dynamics instabilities sculpt the margins of the blob into intricate curlicues, leaving much unburned carbon and oxygen behind. Finally—about one second after it started burning—the bubble bursts through the surface in a geyser of superheated ash.
Then the action really heats up, according to the simulation. Some of the ash escapes into space, but most remains trapped by the white dwarf’s prodigious gravity. It sweeps around the star in all directions, plowing unburned material in front of it. In one second, these hot waves of fuel, driven by the ash clouds, collide at the opposite pole of the star from where the geyser emerged.
The team’s earlier 2D simulation of this event suggested the smashup was fierce enough to set off a detonation at the collision point. But the resolution provided by the full 3D model was even more interesting (figure 9). The colliding material forms two intense jets, one shooting into space and the other ramming into the white dwarf’s surface. At the same time, that pole of the star gets compressed by the onrushing wave of ashes from all sides.
Dr. Jordan recalls watching the data stream in as the FLASH code adapted its resolution to scrutinize this region in detail. “I was really surprised at the strength of the temperature and density spikes” as the jet pounded into the star, he says. Quickly, the spikes surpassed the threshold needed to ignite a detonation—a temperature of about 2 billion degrees Kelvin and densities of more than 10 million grams per cubic centimeter. Once unleashed, the detonation blast wave swept through the white dwarf at 10,000 kilometers per second, destroying the star.
Figure 9. A view through the white dwarf star of the collision region in 3D simulations of the GCD explosion mechanism for Type Ia supernovae. The surface of the white dwarf is shown in green, and the temperature of the matter in the burned ash and flowing over the surface of the star is shown in various colors, with blue being the coolest and yellow being the hottest. Note the very hot region at the “south pole” of the star. This is the place where a supersonic detonation starts that explodes the star.
The outcome of this jet-initiated detonation lines up tantalizingly well with observations by astronomers. For instance, the explosion converts the remaining unburned carbon and oxygen into massive amounts of radioactive nickel-56. As this isotope decays into cobalt-56 and then iron-56, its radiation powers a display of light as bright as some of the most vigorous events seen. The shapes of some Type Ia supernovae appear more ellipsoidal than spherical, as if they were set off at one pole of the star. Furthermore, new infrared observations with the Spitzer Space Telescope suggest that intermediate-mass elements from Type Ia supernovae cascade into space as a jumbled mixed cloud, while the iron-group elements are far more uniform. That jibes with the GCD scenario—an outer layer churned by the eruption of ashes, while the inner core remains largely unscathed until the star blows up.
As computing power grows, Dr. Lamb believes, supernova modeling—and other areas of astrophysical simulation—may become a predictive science.
Unsurprisingly, the model has sparked intense debate within the community. Another leading team of modelers, directed by Dr. Wolfgang Hillebrandt of the Max Planck Institute for Astrophysics in Garching, Germany, put the GCD chain of events to the test in its own 3D simulations. They found the white dwarf did not detonate when the ash flows collided at the surface. The discrepancy appears to arise from the two teams’ different prescriptions for turbulence and the burning rate during deflagration. The German group’s flame spreads about three times faster, burning more fuel and heating up the star more markedly. As a result, the dwarf expands so much that its matter is no longer dense enough to ignite the detonation after the ash bursts through the surface.
Figure 10. A 3D simulation of Rayleigh–Taylor mixing between a heavy fluid and a light fluid.
Instead, Dr. Hillebrandt and his colleagues still advocate the two older scenarios: a pure deflagration that destroys the star, or, for brighter supernovae, a period of deflagration followed by a delayed detonation near the core. Some observational astronomers wryly note that several Type Ia supernova models have come and gone, discarded because of new observations or simulations.

The Case for Predictions
The GCD model may yet fall into the same bin, Dr. Lamb admits. “We certainly don’t consider it to be the final answer, but we see it as very promising,” he says. “It naturally has many of the features seen in the observations, some of which are not reproducible in the other models.”
For now, physicists must continue their efforts to verify that their models of the physical processes in Type Ia supernovae, particularly of turbulent nuclear burning, behave correctly. One test of this is that the outcome should not depend on the spatial resolution of the simulation. “We have worked hard to meet this test,” Dr. Lamb says. “Ours are the only 3D, whole star simulations so far that do.”
Physicists must also continue trying to validate the outcomes of their models by testing simulations of their important physical processes against the results of laboratory experiments and comparing their gross physical features to those detected in real Type Ia supernovae. But Dr. Lamb sees a day in the near future when the converse may be true. As computing power grows, he believes, supernova modeling—and other areas of astrophysical simulation—may become a predictive science. Detailed models on next-generation machines (sidebar “The Need for Petascale Computing”) may shed light on subtle aspects of the explosions that are difficult for telescopes to observe with precision.
Figure 12. A 3D simulation of homogeneous, isotropic, driven turbulence performed on the IBM BlueGene/L supercomputer at LLNL. Shown are a subset of the 17 million tracer particles used to follow the turbulent motions. The colors of the particle indicate their velocities, with higher velocity particles in yellow and lower velocity particles in blue. Also shown in gray are the partial trajectories of three particles, which show the vortices that exist in the flow.
There is one pressing need for such an advance: The DOE and NASA are planning a scientific satellite designed to observe thousands of Type Ia supernovae (sidebar “The Joint Dark Energy Mission”). This mission, likely to cost hundreds of millions of dollars, is regarded as the best hope of unraveling why the expansion of the Universe is accelerating. To achieve that goal, astrophysicists will need to adjust for innate differences among supernovae and standardize their light outputs with better than 1% precision. Current observations have uncertainties of around 15%, so there’s a long way to go.
Models at ever-finer physical scales will help observers whittle down these uncertainties by tracing correlations among Type Ia supernovae depending on their luminosities, their distributions and velocities of elements, and other properties, Dr. Lamb believes. He envisions simulations that will provide observers with “a map of the interior of the star after the explosion.” Armed with predictive models for rafts of supernovae, he says, the teams would be in a better position to optimize their instrument design, their scientific observing strategy, and their data analysis.
The NNSA ASC Academic Strategic Alliance Program has put the Flash Center in a position to contribute such insights, Dr. Lamb says—and to pursue an unexpected twist in the quest to find out how white dwarfs explode. “We’ve turned the whole problem inside out,” he says with a smile. “We’re thinking outside the sphere.”
Contributor:
Robert Irion is the Director of the Science Communication Program, University of California–Santa Cruz
Further Reading:
The DOE NNSA ASC and ASAP Programs: http://www.sandia.gov/NNSA/ASC/

The DOE Office of Science INCITE Program: http://hpc.science.doe.gov/allocations/incite/

The NNSA ASC Academic Strategic Alliance FLASH Center: http://flash.uchicago.edu

B. Frxyell et al. 2000. FLASH: An adaptive mesh hydrodynamics code for modeling astrophysical thermonuclear flashes. Astrophys. J. Suppl., 131: 273-334.

T. Plewa, A. C. Calder, and D. Q. Lamb. 2004. Type Ia supernova explosion: gravitationally confined detonation. Astrophys. J., 612: 37-40.

G. C. Jordan et al. (in press). Three-dimensional simulations of the deflagration phase of the gravitationally confined detonation model of Type Ia supernovae. Astrophys. J. http://arxiv.org/abs/astro-ph/0703573