Saving the Earth with dynamical simulations

Model suggests how protoplanets kept a safe distance from the sun

5:06pm, January 8, 2010
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A new model keeps the solar system safe for the young Earth and other infant planets by preventing them from spiraling into the sun.

When astronomers simulate the formation of the solar system, disaster strikes: no planets survive. Under most models’ assumptions, protoplanets would have collided with the parent star before they had a chance to fully form.

“This contradicts basic observational evidence: the fact that we are here,” said Mordecai-Mark Mac Low of the American Museum of Natural History at a press briefing January 7 at the winter meeting of the American Astronomical Society.

Planets form from a disk of gas and dust swirling around a young star. When the disk begins to coalesce into protoplanets, the gravity of those protoplanets pulls clumps of gas around the disk with them as they orbit the star. Gravitational perturbations from the clumps, in turn, can push the nascent planets into orbits closer to the parent star.

Previous calculations found that the asymmetries in clumping gas would push protoplanets into the star within 1 million years — far shorter than the time it takes for a protoplanetary disk to mature into a set of planets.

But those models assumed constant temperatures within a disk. Other theoretical calculations have found that differences in the disk’s transparency would make the disk radiate heat more efficiently in some areas than in others, and this would cause temperatures to vary. Recent work by Mac Low’s collaborator Sijme-Jan Paardekooper of the University of Cambridge in England showed that including these temperature variations allowed a planet to migrate sometimes toward the parent star, and sometimes away from it. Because gas expands when it is heated, temperature variations can create asymmetries in where the gas clumps and how those clumps move. Gas clusters that push the protoplanet outward can sometimes exert stronger forces than those that push inward.

To determine whether outward migration could save the Earth, Mac Low and colleagues ran simulations of a protoplanetary disk evolving over millions of years, this time including the effects of temperature variations. The team found that at some positions in the disk, planets would be pushed inward, and that at other positions, planets would be pushed outward. The zones of inward and outward migration would meet at stable equilibrium points.

“Planets move to these equilibrium radii, and then they more or less sit there,” Mac Low said. “They get stuck at these radii, because if they go in either direction, they’ll migrate right back.”

The stable radii do move inward toward the star, but much more slowly, Mac Low said. Also, the gas disk gets thinner and has less gravitational pull as protoplanets accrete more material and grow into full-sized planets. In this model, the disk thins out faster than it pushes planets inward.

“Regions of outward migration allow planets and planetoids to survive,” Mac Low said. “That finally explains how the planets — both in our own solar system and the ones we observe all across the galaxy — survive.”

Lee Hartmann of the University of Michigan, an expert in protoplanetary disk evolution, says the work is an important step. “Migration is the biggest issue in understanding planet formation these days,” he said. “This is an important and detailed attempt to find a mechanism which avoids the potential of catastrophic migration — where all the planets that are formed get accreted into the central star.”

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