Wandering Worlds

Saving newborn planets from a fiery demise is just one step in the quest to understand the mysterious planetary systems around other stars.

Before 1995, it was widely assumed that other planetary systems would be like ours. Small rocky planets like Venus and Earth would live near their sun. Large gaseous planets like Jupiter and Saturn would live farther out. And all of them would have nearly circular orbits. Never mind the fact that, at that time, there was no observational evidence for the existence of even a single planet orbiting another Sun-like star. (A few appeared to orbit around pulsars, but pulsars are generally considered to be "dead" stars.)

Perhaps that evidence seemed too difficult to come by. Detecting a dim and comparatively tiny planet right next to a much bigger and brighter object—its parent star—many light years away would be like spotting a dust grain next to a jet airliner glinting in the Sun at 37,000 feet.

Or perhaps the evidence for other planets didn't seem necessary. Our solar system made so much sense that you could simply expect others like ours to exist. According to standard theory, our solar system (and presumably others) began with the young Sun at the center of a swirling disk of gas and dust. Over time, gravity caused the dust to accumulate to form the cores of emerging planets, which then kept roughly the same nearly circular orbits that the disk material had. Near the Sun, the disk is too hot and lacks sufficient gas to form giant planets. Only farther away could you get a gas giant resembling Jupiter. And just like that, you've built a solar system with nothing more than basic physics: gravity, Newtonian motion, and a little thermodynamics. What could be wrong with that?

Exoplanet Pic

Most extrasolar planets are too dim to see with today's technology. But in this image, an infrared telescope was able to reveal an exoplanet (top left) together with its parent star, because the planet hasn't yet cooled from its initial formation.
CREDIT: Gemini Observatory, D. Lafreniere, R. Jayawardhana, M. van Kerkwijk (University of Toronto).

Pesky Planets

Unfortunately, all it takes is one good measurement to spoil a perfectly sensible theory. In 1995, astronomers discovered the first of what would grow to be a whole fleet of planets outside of our solar system—extrasolar planets, or exoplanets for short. (At the time of this writing, 528 exoplanets have been confirmed.) This first exoplanet, discovered around a Sun-like star called 51-Pegasi, turned out to be a gas giant at least half the mass of Jupiter, but the size of its orbit is one-sixth that of our Sun's innermost planet, Mercury. And a year on this exoplanet lasts only four Earth days. Perhaps researchers imagined that 51-Pegasi's planet would prove to be a rare oddity in an otherwise sensible galaxy. Instead, hundreds of similar exoplanets have since been discovered, implying that such "hot jupiters" are the rule, not the exception.

To be fair, astronomers admit that their prevailing planet detection method is biased in favor of finding massive planets orbiting close to their stars, because such planets have a strong gravitational effect on their stars, and that effect is what's observed. Planetary systems like our own, with only small planets near the Sun and massive planets far away, would generally go unnoticed. Nonetheless, whether hot jupiters are genuinely common, or just selectively picked up by the biased methodology, many do exist. They are pervasive and need to be explained.

The trouble is, attempts to explain hot jupiters lead to other vexing questions. Because gas giants can't form in the heat near a star the most logical possibility is that these planets formed in cooler regions away from the star and then somehow moved inward. This is called migration. Scientists began to explore migration by calculating how a surrounding disk of matter might pull a planet inward. They found that migration should indeed happen, but would happen so quickly that a planet would move all the way inward, even into the central star, long before its orbit could stabilize (the way Earth's orbit is stable now). Even our own Earth should not exist.

Clearly, some other factor is at work here. Something must be saving planets from migrating into their suns. But what is that something? Scientists have proposed several new mechanisms, including the effects of magnetic fields, turbulent motions, or altered densities in the disk. One or more of these ideas may indeed do the trick. But here at Los Alamos National Laboratory, astrophysicist Hui Li and computational scientist Shengtai Li (no relation) have conducted high-resolution supercomputer simulations of another possibility—one that shows just how these planets might naturally be saved under realistic conditions in the disk.

young star photo

Planets are born from a disk of gas and dust swirling around a young star, like this one. The disk appears black because its dust obscures light coming from behind it.
CREDIT: D. Johnstone (CITA), J. Bally (U. Colorado) et al., WFPC2, HST, NASA..

Shock and Stall

A planet migrates as a result of a complex interaction between the planet and the gas in the disk. The planet's gravity disturbs the material in the disk, creating two density waves—one propagating inward and the other propagating outward. Because of standard differential rotation, in which orbiting matter revolves faster when it's closer to the center, the disturbances wrap into spirals. These spiral waves are visible in the output from the Los Alamos team's simulations (see figure below).


In this simulation, a planet (at the 9-o'clock position) has gravitationally disturbed the surrounding disk, creating waves that propagate inward and outward. The rotation of the disk material is faster toward the center, so the waves wrap around into the spiral seen here. Red and yellow indicate higher density, as seen in the spiral waves. Blue indicates lower density, as seen in the circle of the planet's orbit, from which the planet has already driven disk material away.

The waves gravitationally tug on the planet but will only cause the planet to migrate inwards if the interaction permanently drains angular momentum from the planet's orbit. (Angular momentum is momentum associated with motion around an axis.) That means the waves must dissipate angular momentum into the disk. This happens naturally if the disk has sufficient resistance to flow—that is, if it has enough viscosity. Unfortunately, the disk around a young star is made from a very dilute gas, so it has very little viscosity in the normal sense: it's not at all sticky like honey. What it does have, as has long been postulated, is turbulent viscosity, resulting from the gas thickening in some regions, thinning in others, and moving about and mixing in a haphazard way. Thus, the amount of migration depends on how turbulent the disk is.

Conventional models portray the disk as plenty turbulent: migration is rapid, and planets don't survive. But there are hints that the turbulence may be lower. Some observations of young stars support this possibility. If so, then the lower turbulence would lead to lower viscosity. A less viscous disk would dissipate less of the planet's orbital angular momentum, leading to slower migration. In fact, Li and Li's research has shown that the nature of the dissipation becomes quite different in a low-viscosity disk.

The spiral waves that drain and dissipate angular momentum from a planet's orbit are actually shock waves—waves that travel faster than the speed of sound. That is to be expected, because the cold, dilute gas in the disk has a relatively slow sound speed. The spiral shock waves cause an irreversible exchange of angular momentum between the planet and the disk material. Normally, this shock-based dissipation is a minor effect when compared to the viscous dissipation. But the simulations reveal that if the viscosity is about one-tenth the value that conventional disk models suppose, then shock dissipation produces a greater angular momentum exchange than viscous dissipation. In that case, migration mediated by shock waves determines a planet's fate.

The simulations reveal that the amount of time needed for migration dominated by shock physics in a low-viscosity disk is appreciably longer than the time needed for viscous migration in a conventional disk. The actual time depends on the mass of the planet, but the result is generally ten million to a hundred million years (107 to 108)—much longer than the hundred thousand years (105) suggested by higher-viscosity simulations. The extended time afforded by the low-viscosity scenario is long enough, because even though stars like the Sun live for several billion years (109), the disk around a young star only survives for about 107 years. The disk will vanish by photoevaporation under the intense radiation of the parent star, allowing the planet's orbit to stabilize before the planet migrates all the way inward. Once the disk is gone, so is the tendency for planets to migrate.

dead zone picture

In the dead zone—the region of a disk that's shielded from ionizing radiation (wavy arrows)—the disk's viscosity is much lower. As a result, turbulence in the disk's surface layers has a diminished influence over the motion of a planet in this region, essentially eliminating the planet's migration. Sources of ionizing radiation include the star, the magnetically active region around the star, and cosmic rays from the rest of the galaxy.

So it seems that Li and Li have solved the migration problem, if indeed the disks that form around young stars have very little turbulent viscosity. In theory, this should be the case within a disk's dead zone, the part of the disk where ultraviolet radiation from the central star, and other high-energy radiation from elsewhere, do not reach (see figure above). Ultraviolet radiation is energetic enough to ionize the gas in the disk, causing electrons to abandon their atoms. The resulting charged ions and electrons, unlike electrically neutral atoms, are affected by magnetic fields in the disk, so they enable magnetic forces to stir the gas and generate the turbulence that gives rise to turbulent viscosity. The dead zone, however, being shielded from ionizing radiation, would have far less turbulence. Planets formed in the dead zone would suffer only shock-based migration forces, saving them from an untimely demise.

Not Exactly Physics 101

Evidently, understanding the dynamics of exoplanetary systems requires a detailed understanding of the intricate physical processes involved. But even with simulations of shock waves and calculations of turbulent viscosity, much remains unknown. For example, how would adding a third, vertical dimension to the simulations affect the results? How would spiral density waves propagate and steepen into shocks in such systems? And what about more complex disks? Might different amounts of dissipation at different locations occasionally tip the delicate balance of gravitational influences, sometimes causing young planetary bodies to migrate outward instead of inward?

Even if such improvements are made to the simulations, the original dilemma persists: the existence of gas giant planets demands that the Earth-sized planetary cores from which they grew must have been surrounded by an abundance of gas, yet this very abundance of gas significantly increases their migration rate and thereby threatens their survival. Figuring out how to slow down the migration becomes a trickier business when you're trying to make the planet grow at the same time.

While the work of Li and Li and others in the field appears to explain how the migration of Earth-sized cores can be stopped, young planetary systems are still quite complex. Other key processes that operate over the same time span as the slowed planetary core migration include the formation of gas giants by accumulating the surrounding gas and the photoevaporation of that gas by the central star. Thus, the interplay of three essential processes—planet formation, planet migration, and disk evaporation—must conspire in complex ways to produce the vast diversity of exoplanet masses and orbital properties detected so far. This interplay begs for further research with ever-more-sophisticated simulations, which Li and Li already have underway.

In one generation, exoplanets have gone from little more than a mainstay of science fiction to a richly varied reality. While a complete picture of their evolution remains elusive, Li and Li and others in the exoplanet astrophysics community are hopeful that these enigmatic extraterrestrial systems are destined to be understood.

— Craig Tyler

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