Example of the neutron density distribution in supernova matter forming cylindrical holes, a pasta structure, where the red areas represent the maximum density values and the blue ones the minimum.—Image courtesy Helena Pais

ORNL team analyzes frustrated matter in stellar explosions

The collapsing iron core of a giant star is a violent and confusing scene.

Iron cannot fuel the nuclear fusion that has kept the star going for millions of years, so no energy is available to support the core against its own gravity. This is the event that triggers the star’s death in a stunning explosion.

The collapse is over in a few thousandths of a second. In it, the innermost core, a portion half the mass of our sun, falls at up to 70 percent the speed of light until it becomes so dense that a teaspoon would weigh more than 300 Empire State Buildings.

Then the core bounces—and what a bounce it is. The resulting shock wave takes the star, which may be up to 40 times as massive as the sun, and blows it into space, leaving behind a new-born neutron star or a black hole.

This is a core-collapse supernova, one of the universe’s most impressive calamities, and one of its most valuable. Stars are the universe’s element factories and core-collapse supernovas are the distribution channels. We can thank them for most of the elements in our environment, and in our bodies.

A battle of forces

The supernova not only illustrates all of nature’s forces—from the gravity that extends across the universe to the nuclear force that binds and arranges the smallest building blocks of matter. It also illustrates what happens when these forces battle one another for dominance.

The University of Tennessee-Knoxville’s (UTK’s) Jirina Stone and Helena Pais have adopted the most detailed and accurate model to date of one such battle. Using the lab’s Jaguar supercomputer, they simulated matter at the core’s bounce, when the shock wave starts to develop. The core is formed by a thick soup of neutrons, protons, and electrons, and up to 20 percent of the matter is believed to form into cylinders, sheets, bubbles and other odd forms.

This is nuclear pasta—a form of frustrated matter—a rare ordering found within the supernova and in the neutron star that will be all that remains when it is over. For a split second as the star blows outward there will be a layer of these strange forms in the core about 100 kilometers from the center.

The forces battling for supremacy of nuclear pasta are the Coulomb force and surface tension. Coulomb energy refers to the attraction or repulsion of electrically charged particles (think magnets); in this case it is pushing positively charged protons apart. Surface tension, on the other hand, is the internal pressures that pull liquids into the smallest possible area (think water droplets); in this case it is enticing the neutrons and protons to form coherent structures.

Stone and Pais published their results in the October 12, 2012, issue of Physical Review Letters. The work also plays an important role in Pais’s doctoral thesis from UTK.

“Imagine what happens,” said Stone. “When the neutrons and protons are close enough that the strength of the coulomb force and nuclear forces are comparable, the coulomb force is telling all the nucleons to get apart, while the surface forces are saying, ‘Come on, I want to keep you together.’ Because the Coulomb interaction is just repulsive, but the nuclear interaction is both repulsive and attractive, there is a competition between these controversial effects. One is saying, go apart, and the other is saying, no stay here.”

As a result, this layer of the exploding star is dominated by odd shapes, resembling penne, lasagna, and bowties, as well as spheres and other not-quite-pasta shapes. Below the pasta is a very dense liquid of mainly neutrons. Above it is a particle gas of free neutrons, heavy nuclei and electrons.

30 million processor hours

The team used an approach called Skyrme-Hartree-Fock, with Pais handling the calculations. All told, the project used 30 million processor hours on Jaguar, with each 12-hour run making use of 45,000 processor cores. The adaptation of the original code for use in this mode was provided by Reuben Budiardja of UTK’s National Institute for Computational Sciences, while ORNL’s Eric Lingerfelt helped implement the VisIt visualization package.

“‘Hartree-Fock’ is the mathematical method that makes a description of systems made of many quantum particles possible to the best approximation,” Stone explained, “as exact treatment of such a system is currently beyond reach of the fastest computers in the world. The Skyrme interaction is a prescription of how nucleons talk to each other.”

The model, called “3D-SHF-EOS,” was developed by Will Newton, former graduate student of Stone’s at England’s Oxford University and now an assistant professor at Texas A&M–Commerce. It assumes that all matter under the same temperature and density will behave the same, so it can be described using representative cells.

“What we do in the model is say that the matter in the star can be modeled by a sequence of cubic cells—little cubes—which are connected to each other through something we call ‘periodic boundary conditions,’” Stone explained. “This means you go from one cell to another cell to another cell, and you just reproduce the situation in one cell to the other and so forth.”

Each cell is a tiny cube, 25 quadrillionths of a meter on a side. By modeling a range of these cubes and calculating what happens to the matter under different temperature and density conditions, the project provides all the information needed by a supernova simulation to accurately describe the pasta phase of nuclear matter.

“People before us suspected there was pasta,” Stone said. “People would assume a certain formation, like the sheet or a rod, and they would calculate the distribution in the cell and look at whether the energy of that cell is lower or higher than the energy of the uniform matter (no pasta), which they could also calculate.

“What we do is assume absolutely nothing. We evolve shapes. This is our main contribution, because we evolve these formations without actually any assumptions about what should evolve under what conditions. Moreover, we actually show the onset of the pasta and the dissolution of pasta and can study the conditions at which the pasta appears and disappears.”

The confirmation that nuclear pasta exists in the stellar environment adds to observations of frustrated matter in other areas—such as solid state physics, magnetism and biology—that also exhibit strange orderings of matter under the influence of conflicting forces.

In addition, Stone’s and Pais’s work has at least two purposes beyond the fascination of the pasta itself. First, it is a valuable input into simulations of the exploding star itself. Second, it helps contributes to explanation of the cooling of the neutron star that is left behind.

A matter of neutrinos

Each of these has to do with neutrinos. Neutrinos are tiny, elementary, usually inconsequential particles that normally go on their way without interacting with other matter. They have no electrical charge. Their mass is very small. Billions go through your body each second and do nothing along the way.

In the collapsed core of a supernova, however, neutrinos are a major byproduct of the collapse. They are so numerous and the matter around them so dense that the neutrinos power the explosion that blasts the star into space. Along the way, they cool the remnant neutron star by taking energy away from the collapsed core.

Exactly how the neutrinos do their thing depends on the makeup of the matter they’re blasting through. This is where the model developed by Stone and Pais may be especially valuable.

“Neutrinos play a big role in the core-collapse supernova,” Stone said. “The density at the bounce is such that the neutrinos for some fraction of a millisecond cannot get out. So, in principle, at first the neutrinos are trapped in the matter, but when the bounce releases the matter a little bit, the neutrinos will be able to pass through the core to propagate the shock. They carry a lot of energy.

“At that point it matters what the composition of the star is, because the neutrinos behave differently if they pass through homogeneous matter or if they pass through these complicated structures. And this may affect the shock.”

The output of the project is information that will refine the input conditions for supernova simulations currently used.

“We will give them the numbers which they need,” Stone noted. “Pressure, chemical potentials, all the numbers they need. So this calculation has been done once forever, if you like.”

Related Publication:

Pais, Helena, and Jirina R. Stone. “Exploring the Nuclear Pasta Phase in Core-Collapse Supernova Matter.” Physical Review Letters 109.15 (2012): 151101.