FEATURE ARTICLE
Are Planetary Systems Filled to Capacity?
Computer simulations suggest that the answer may be yes. But observations of extrasolar systems will provide the ultimate test
Steven Soter
Making Worlds Is a Messy Business
These ideas fit naturally into the prevailing theory of solar system formation, originally proposed by the philosopher Immanuel Kant in 1755. According to his nebular accretion theory, the solar system and other planetary systems formed by the condensation and accumulation of dust and gas in flattened disks of debris orbiting around young stars. The theory has found strong support in modern observations: Astronomers today routinely detect such debris disks around newborn stars.
The dust-sized particles in such a disk first coagulate to form trillions of rocky asteroids and icy comets a few kilometers in diameter, called planetesimals. These objects in turn gently collide and grow to produce scores to hundreds of Moon- to Mars-sized bodies called planetary embryos, orbiting amid the swarm of remaining planetesimals. Some embryos in the outer parts of the disk grow large enough for their gravity to capture the abundant gas from the nebula, giving rise to giant planets.
As long as the planetesimals retain most of the mass in the disk, their gravity locally exerts a damping effect (called dynamical friction) on the motion of the larger embedded embryos, and the whole system remains dynamically well behaved. The embryos grow by capturing material from so-called feeding zones in the disk, and their orbits become rather evenly spaced. But once the embryos have swept up most of the mass from the disk, the damping effect becomes too feeble to keep the system under control. The gravitational tugs that the embryos exert on one another can then pump up their orbital eccentricities without limit. At that point, to use the vernacular, all hell breaks loose. In this final stage of planet formation, the orbits of the planetary embryos begin to intersect, and the whole system erupts into large-scale anarchy. Entire worlds collide and merge, while others are flung capriciously out into the Galaxy.
The observational evidence makes it clear that the worlds formed in the young solar system were subjected to intense bombardment, their surfaces being saturated with craters. Many of them are still covered with enormous impact scars. Some moons and asteroids look like they were entirely blown apart and reassembled from fragments. A Mars-sized planetary embryo evidently collided with and entirely melted the proto-Earth, explosively throwing off a great splash of debris, some part of which reassembled to form the Moon.
As the growing planets swallowed up planetesimals from the debris disk, they were also ejecting countless others to great distances. Many of those objects had enough energy to escape to interstellar space, where they now drift between the stars. Others, flung without quite enough velocity to escape, reached the outermost fringes of the solar system, where the gravitational influence of nearby stars and the Galaxy itself could circularize their orbits. Hundreds of billions of these icy objects now populate the distant Oort cloud, loosely bound by the Sun's gravity. Some of them, further nudged by passing stars and galactic tides, re-enter the inner solar system as spectacular long-period comets.
Theorists today use computer models to simulate the late stages of planetary formation. They can follow the dynamical evolution of such systems, using a range of starting conditions to represent different debris disks. Some of the simulations generate planets with orbits and masses that resemble those in our solar system. Others produce systems with giant planets in more eccentric orbits. In such simulations, collisions and ejections reduce the number of growing planets and increase the average spacing between them. The planets effectively compete for space, "elbowing" each other apart.
These numerical experiments confirm that the formation of planets is exquisitely sensitive to initial conditions. For example, the displacement of only one in a hundred starting embryos along its orbit by only one meter, keeping everything else the same in a simulation, can make the difference between ending up with three terrestrial planets or five. Such results strongly suggest that a trivial chance encounter determined the very existence of Earth.
Astronomers are now getting the chance to check whether such simulations reflect reality. For more than a decade, observers have been discovering and charting the configuration of other planetary systems, which were long assumed to exist. Planet hunters have already detected more than 240 worlds orbiting around other stars, more than 60 of them in systems having two or more known planets. So far, the observing techniques are limited to detecting giant planets, in most cases at least 10 times more massive than Earth. Smaller terrestrial planets undoubtedly exist around many of those stars, but current measurements cannot yet reveal them.
Astronomers were surprised to learn that most of the known extrasolar planets have orbits much more eccentric than those of the giant planets in our solar system. It was generally assumed that the other systems would resemble our own, with planets in nearly circular orbits. Perhaps, some argued, our solar system is exceptional and most planetary systems were formed in a different way. This now looks unlikely.
Mario Juric and Scott Tremaine at Princeton University recently ran thousands of computer simulations to follow the dynamical evolution of 10 or more giant planets in a disk undergoing collisions, mergers and ejections. For simulations that begin with planets relatively close together, the ones that survive to the end have a distribution of orbital eccentricities that beautifully matches the data for the observed extrasolar planets. For simulations that begin with the planets farther apart, leading to fewer interactions, the surviving giant planets have lower orbital eccentricities, more like our own solar system. Most of the simulations end up with two or three giant planets, after the ejection of at least half of the initial population. This result suggests that free-floating planets, unattached to any star, are very common in the Galaxy.
Other studies confirm that many of the worlds initially populating a planet-forming disk, if not most of them, end up being tossed out into interstellar space. The largest worlds left behind continue to grow by sweeping up smaller objects that remain bound to the central star. Making planets thus seems to be an extremely messy business. A growing planetary system resembles an overly energetic infant learning to eat cereal with a spoon: Some is consumed, but much of it ends up on the floor, walls and ceiling.
Most of the known extrasolar planets are more massive and have shorter periods and more eccentric orbits than the planets of our solar system. However, that does not necessarily mean that our system is anomalous. Current observational techniques strongly favor the discovery of massive planets with orbital periods of only a few years or less, and even the giant planets of our solar system, with their longer orbital periods, would be near the limits of detection if observed from the distance of a nearby star.
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