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A moving question

by Barbara Jewett

NCSA and XSEDE aid an Indiana University researcher studying the migration of massive planets in protoplanetary disks. Understanding how planets shift is one of the first steps in the quest to discover other life in the universe.

Looking for planets similar to Earth is “the Holy Grail of planetary and extrasolar planetary studies,” says Indiana University astronomer Scott Michael. That’s why his group’s discoveries concerning the movement of gas giant planets in protoplanetary disks are so significant. Improved understanding of the dynamics of the planets he studies may help others predict stable orbits of terrestrial-type planets.

Extrasolar planets, also called exoplanets, are planets outside of our solar system. Up until about 1995 there had been no exoplanet discoveries. The recent renewed interest in the formation of gas giant planets is due to the fact that over the past 15 years, says Michael, astronomers have discovered more than 500 stellar systems with planets. Some of those systems have multiple planets, raising the number of discovered exoplanets to over 700. Most of those exoplanets are gas giant planets.

Michael studies the migration of massive planets in protoplanetary disks. He first used NCSA’s Cobalt and Ember and now uses the Pittsburgh Supercomputing Center’s Blacklight. A protoplanetary disk is a gaseous nebula around a newly forming star called a protostar, also known as young stellar objects. Protoplanetary disks are flattened nebulae and have a flared disk shape.

“These are observationally confirmed objects; they have been seen. We’re trying to study how a gas giant planet forms in such a nebula,” Michael says. “By understanding whether they form at the location that we observe them or whether they move, we can then start looking into the planetary dynamics of an entire system.”

Which is where the planetary Holy Grail comes in. Planetary astronomers believe that if they can find a planet similar to Earth’s size and composition in orbit at an equivalent distance from a system’s central star as the sun is from the earth, that it might be a habitable planet. Better understanding of planetary dynamics may yield the information they seek.

Planet formation

It’s fairly well understood how terrestrial, rocky-type, planets form. Dust, rocks and boulders are in the nebula, and after the gas has partially dissipated the leftover bits collide, sticking together to build up a rocky planet. Planets like Earth, Mars, Mercury, and Venus. But the gas giant planets—those like Jupiter and Saturn—have a large fraction of their composition made up of hydrogen and helium gas, which astronomers believe must have come from a gaseous nebula.

“The rub in the whole thing is that those planets need to form in the time that the gas is around, before the nebula dissipates. Which is a fairly short timescale when it comes to astronomical time,” says Michael.

Currently there are two theories as to how that can happen, he notes. One is called core accretion, also known as nucleated instability. In this theory a rocky core builds up through particles colliding and sticking together until it reaches a critical mass and starts to accrete the surrounding gas. Eventually it reaches the runaway growth phase where it very rapidly accretes all of the gas surrounding it within its gravitational influence. The result is a gas giant planet.

“There’s a lot of issues with that theory, but one of the bigger ones is it takes quite a long time for that process to occur. And because the nebula doesn’t tend to stay around for a very long time in astronomical timescales, that presents an issue with the timing,” says Michael.

The other theory is called gravitational instability. That’s the theory Michael’s group studies.

If the conditions are right in the protoplanetary disk—a high enough gas density and a low enough temperature—the disk will undergo a condition called gravitational instability. The force of gravity collapses parts of the disk to form very dense structures, perhaps collapsing to form a spherical object that would shrink down until it became a gas giant planet. Michael’s team conducts simulations to look at the physical mechanisms that can affect when the gravitational instability might be active in a disk, how efficient those instabilities might be at actually forming gas giant planets, and under what conditions instability causes gas giant planet formation.

One of the benefits of the gravitational instability theory, says Michael, is that when it forms planets it forms them relatively quickly—within a few thousand to 10,000 years, well within the lifetime of the nebula. To form the gas giant planets in the core accretion model takes millions of years.

Planet migration

Scientists believe that, once formed, a planet in the nebula’s protoplanetary disk will very rapidly move toward the central star, and may even be accreted on to the central star.

“Part of that theory fits nicely, as many of the extrasolar planets first discovered were found very close to their central star,” explains Michael. “So the fact that planets rapidly migrate inward creates the question: What stops the planets from continuing to migrate inward and being accreted on to the central star? What mechanism could be responsible for these ‘hot Jupiters’?”

The team looked at gravitational instabilities as a possible mechanism of altering that pattern of migration and causing planets to stop. In a variety of different simulations some of the planets they put in the protoplanetary disk began to migrate inward very rapidly but then stopped at a certain radius. They were able to correlate the place that they stopped with the gravitational instabilities tapering off as well.

“This would explain why planets halt their inward migration and could explain those gas giant planets found close to the central star,” Michael says.

But the team had another interesting discovery as well. When they put planets into a gravitationally unstable disk, in some cases the planets actually migrated outward. That fits with exoplanet discoveries. As the observational community matured and looked for different techniques to discover exoplanets, says Michael, they began to find gas giant planets at a variety of radii. In fact, he notes, there are planets discovered at very large distances from their central star.

In a typical protplanetary disk, the surface density of the nebula decreases as you go farther and farther away from the star. At very large radii the gas probably isn’t dense enough to form gas giant planets via core accretion, he says. So, his team’s finding that gravitational instability can in fact cause planets to migrate either inward or out away from their central star is significant, as it might help explain the vast range of separations from the central star at which gas giant planets are found. Initial results of Michael’s studies have been published in the Astrophysical Journal Letters.

Simulating the systems

The team does simulations using a code with a fixed cylindrical grid, meaning there are a certain number of grid cells in each of the directions r, Ø and z. The amount of physical time simulated for each time step of the simulation is limited by the cell that has the most rapidly moving gases. When they get to a part of the nebula in the simulation that becomes very dense or very hot, it will have very rapidly moving gas and that causes the time steps to become very short in physical time.

Michael says his team developed a very nice workflow using first NCSA’s now-retired Cobalt, then Ember. Since their code can only run on machines that have shared memory architecture, they moved to PSC’s Blacklight when Ember did not transfer into the XSEDE resource system last year.

“One of the big issues when we first started using the supercomputer was transferring the data from the machine to our resources at Indiana in order to do the analysis. The solution we were able to employ was a piece of technology we came up with at IU called the Data Capacitor on the wide-area network, or DC-WAN,” says Michael.

With the DC-WAN, the team can run the simulation and have the output data directly written at their university. They can even do analysis in real time to see what is going on as the simulation progressed. That workflow works really well, says Michael.

“We ran simulations on Cobalt and Ember using between 64-256 cores, data written directly to DC-WAN here at IU and we did our analysis as soon as it arrived,” says Michael. “Working with the folks at NCSA was wonderful. They were so helpful and willing to work with us on mounting the DC-WAN file system on the machine. It was really a sad day the day they took Ember off of XSEDE as it denied us a really valuable and useful resource.”

But he was able to move the hundreds of thousands of corehours allocated to his project on Ember to the Blacklight machine at Pittsburgh, and his team established a similar workflow there.

“We were lucky that we were able to get almost all of our allocation transferred over to Pittsburgh. But this was a fairly major disruption for us, as it took almost three months to get everything set up on Blacklight so we were back in full production mode,” he notes.

Typically the team will perform between1 to 4 million timesteps over a grid of 16 million computational cells. That will take approximately a month or so of continuous wall time, he says.

“In practice, it takes about two months because you have to checkpoint and restart systems on these big HPC machines. The longest stretch you can usually run is four to five days. So we’ll run for a few days, we’ll checkpoint, then we’ll resubmit the job. We’ll take a look at the results from our analysis on DC-WAN, resubmit the job, wait a few days in the queue due to Blacklight’s demand, then it will run another four to five days. And we just keep on doing that. What we’ve started doing when we want to explore parameter space, say we want to compare the migration rates of planets of different mass, is to run several simulations at the same time. That way we can get three or four simulations done in a two-month time period,” says Michael.

Next phase

Almost all of the team’s studies have been focused on nebulae about the size of our solar system, about 40 AU in radius. The unit AU stands for astronomical unit, defined as the distance between the Earth and sun; the distance from the sun to Pluto is about 40 AU.

There have been observed protoplanetary disks that are 100, 200, even up to 400 AU in extent, says Michael, and members of the team are now beginning to simulate those.

“It turns out that even though there a lower surface density at those larger radii, because it is so much colder being so distant from the central star they actually have a much higher likelihood of becoming gravitationally unstable,” he explains. “So we’re trying to understand if a gas giant planet could form at very large radii given gravitational instability. Then this ties into the whole question of migration. If gas giant planets were to form at 100 or 200 AU, how could they move much closer to the central star and not get accreted on to the central star? It will be very interesting to see what the results show.”

Project at a glance

Team members
Scott Michael, Indiana University
Richard H. Durisen, Indiana University
Thomas Y. Steiman-Cameron, Indiana University
Aaron C. Boley, University of Florida
Megan K. Pickett, Lawrence University


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