The National Institute for Computational Sciences

No Glasses Necessary

3-D simulations of core-collapse supernovas point to neutrino-driven mechanism

by Gregory Scott Jones



3-D is all the rage these days. It makes everything seem more realistic, from Hollywood blockbusters to the Super Bowl. It is quickly emerging as an entertainment revolution.

Much like modern moviegoers, computational scientists also crave three-dimensions, not so much for the visual experience but for the accuracy it brings to simulations of various scientific phenomena.

Historically, even the world’s most powerful computers have lacked adequate muscle to accurately simulate numerous natural processes, relegating researchers to the realm of one or two dimensions, where phenomena could be investigated but in many cases at too elementary a level. Today, however, as supercomputers have entered the petascale (or reached peak speeds eclipsing a thousand trillion calculations per second), the third dimension is alive and well, much like the televisions in today’s department stores.

And few people are happier than Adam Burrows, an astrophysicist at Princeton University. Burrows and his team have been using supercomputers such as Kraken, a Cray XT5 capable of 1.17 petaflops (or more than a thousand trillion calculations per second) funded by National Science Foundation and managed by the University of Tennessee’s National Institute for Computational Sciences (NICS), to study the explosions of core-collapse supernovas (CCSNs). Recent simulations by Burrows’ team suggest that perhaps neutrinos, those minute, neutral subatomic particles that seem omnipresent throughout the universe, may play a bigger role than previously thought in these extremely important and mysterious natural cataclysms.

Besides littering the interstellar medium with chemical elements necessary for life, CCSNs are also responsible for producing black holes, neutron stars, pulsars, and possibly gamma-ray bursts. The energy generated by these explosions is a major force behind star formation and galactic evolution. When they explode, CCSNs can be brighter than whole galaxies and their incredible luminosity is being investigated for use as standard candles against which to measure the size and shape of the universe. Understanding these events is “one of the most fundamental unsolved problems in astrophysics,” said Burrows.

With computers like Kraken, however, Burrows and others are getting closer to this understanding, simulating the entire evolution of these giant stellar explosions. While astrophysicists have been simulating these events for some time, it is only with the addition of the third dimension that they are becoming confident that that the truth is truly within reach.

While Burrows and his team would like to simulate the entire series of events in 3D, these calculations are extremely demanding and computationally expensive. Therefore, the team chooses to perform a variety of calculations with varying complexity for different phenomena, from the entire evolution of the explosion to individual phenomena such as the rotation or hydrodynamics of the star.

As the simulations ramp up, from 1D to 2D to 3D, more approximations have to be made to accommodate the limited horsepower that is inevitable even in machines such as Kraken. These approximations can negatively affect a simulation’s results as they compare with observation. In Burrows’ case, however, they are beginning to coincide with observation, precisely the reason the results are so exciting.


Explosions are a good thing

This still renders the early debris field of the explosion of the core of a massive star via a Type II supernova only ~300 milliseconds after the onset of explosion. The outer blue contour traces the shock wave that bounds the exploding ejecta. The inner green and red structures trace the distribution of the entropy of the outgoing matter. Entropy is a measure of heat and its elevation by neutrino heating is necessary for explosion to ensue. The inner sphere with a slightly orange tinge is the residual neutron star to which the supernova explosion and associated processes give birth. The overall spatial scale is ~1000 kilometers.

CCSNs begin as stellar masses eight times the size of our sun, or larger. For context, imagine a radius the length of Jupiter’s orbit, and a dense core roughly the size of the Earth. Like all stars, however, their fusion-driven cores can only burn for so long. Eventually, they will become neutron stars or black holes, but not before spewing every element with a weight up to iron across the interstellar medium, providing the cold, dark universe with the raw materials for life itself.

As the progenitor stars of CCSNs evolve and the lighter elements fuse into heavier elements, the core becomes denser until it becomes iron and eventually hits the Chandrasekhar mass, or the point at which the repulsion of electrons can’t support the core’s mass. Then come the fireworks.

As the star explodes it sends a shockwave outward that eventually stalls due to the debilitating effects of the imploding matter through which it first passes. As the expanding shockwave driving the supernova explosion comes to a halt, matter outside the shockwave boundary enters the interior while there is massive neutrino loss from the core.

In nature, somehow the shock wave rebounds, and that’s where the surety of the simulations runs out. “With the best physics done in spherical symmetry in 1D, we don’t get generic explosions,” said Burrows. “The shock is just stuck there and accretes the outward material of the object and turns into a black hole.” In other words, the star never explodes. It seems, said Burrows, that there is insufficient energy for an explosion, and that’s where the neutrinos come in: it is thought that they might provide the missing energy that produces one of nature’s most important cataclysms. On the upside, the 1D simulations reveal plenty of nonlinear, unstable turbulence and produced the idea that turbulence is indeed important to the final event.

When the same simulations are performed in 2D, however, explosions do occur, though not all the time, and still not with sufficient energy. Furthermore, added Burrows, it seems that the explosions nearly always were the result of a neutrino mechanism and turbulence within the neutrino context, lending credence to the neutrino-driven hypothesis.

But it’s the third dimension that really makes things interesting. Most importantly, the simulations in 3D produce more explosions than both 1D and 2D, a sign that the simulations are moving towards reality. But that’s not all: Burrows’ team also sees pulsar kicks, a phenomenon indicative of an asymmetrical object, a property shared by CCSNs.

Ultimately, said Burrows, the latest 3D simulations reveal that the turbulence behind the shockwave acts differently in 3D than in 2D, a validation of their simulation approach, and that the revival of the shock is likely neutrino-driven.

“Finally, 3D simulations incorporating the core physics of CCSNs seem within computational reach,” said Burrows. “They are progressively more explosive as you add dimensions, which is good . . . we would like to be able to reproduce nature in 3D, but it’s very computationally expensive, and therefore Kraken is very necessary.”

Not to be confused with Fidel

Burrows’ weapons of choice in his quest to unravel one of nature’s greatest events is known as Compressible Astro (CASTRO), a state-of-the-art radiation/hydrodynamics code developed at Lawrence Berkeley National Laboratory with John Bell.

Simulation Movie: This movie depicts the evolution of an iso-entropy contour of hot material that resides just slightly interior to the supernova blast (shock) wave. The clock at the bottom left shows the time relative to the core bounce time, in seconds, all the way to ~500 milliseconds. The rotation seen is merely a consequence of the rotation of the camera and is not the rotation of the object itself. At the latest times, the debris are rendered translucent, revealing the dense neutron star created in the interior.

While Burrows’ current runs on Kraken use only a few thousand cores, when the radiation and hydrodynamics are incorporated into the 3D simulations, CASTRO will easily begin to occupy cores in the tens of thousands. Eventually, said Burrows, it’s realistic to believe that the team could require 150,000 or more cores as they continue to scale up the simulations, which would consume most or all of the world’s most powerful computers.

Burrows’ team has been using the code for approximately three years now, and it has been the platform for the team’s most important discoveries. For instance, it has helped to downplay the role of magnetohydrodynamics, or the dynamics of magnetized fluids, and the rapid rotation of CCSNs in their eventual explosions, culminating in the latest idea of a neutrino-driven mechanism. “The neutrino mechanisms make sense,” said Burrows, “but we need to be able to quantify it.”

This year, the team was awarded 15 million hours on Kraken to continue exploring the mechanisms behind one of nature’s most important events. But, said Burrows, even computers such as Kraken aren’t yet powerful enough to paint the entire picture. “In the next few years, time will tell,” he said. “As long as we get the resources, we’ll be able to explain how these things explode.”

Until then, however, the team will continue their work in three dimensions, which, it turns out, isn’t such a bad place to be, whether you’re at the movies or Princeton.

About NICS: The National Institute for Computational Sciences (NICS) is a joint effort of the University of Tennessee and Oak Ridge National Laboratory that is funded by the National Science Foundation (NSF). Located on the campus of Oak Ridge National Laboratory, NICS is a major partner in NSF’s Extreme Science and Engineering Discovery Environment (XSEDE).