Twenty-eight Ways to Build a Solar System

Brett Gladman

Ever since their discovery, extrasolar planets have challenged standard ideas about planet formation. Faced with increasing numbers of 'unusual' planetary systems, astronomers are now developing models that attempt to explain these giant planets around Sun-like stars.

A bewildering variety of extrasolar planetary systems are now known. Although the systems that have been discovered are heavily biased (by the methods used to detect them) towards planets at least as large as Jupiter very near their stars, we are already glimpsing the diversity of solar systems¹. Some have Jupiter-like planets in circular orbits both near (closer than Mercury) and far (roughly the same as Jupiter) from their stars. Some planets have highly elliptical orbits, perhaps suggesting gravitational interactions with other large planets, although there are alternative explanations. It is believed that these newly discovered planets are 'gas giants', meaning that although they may have a solid core, most of the mass consists of hydrogen and helium. Writing in the Astronomical Journal, Levison and colleagues² have modeled a variety of possible 'outer solar systems'.

One general scheme for giant-planet formation consists of forming a set of' 'embryos' (Mars- to Earth-size) by the aggregation of kilometre-sized 'planetesimals' from the disk-like nebula that swirls around a young star. The planetesimals form out of whatever solid material can locally condense from the nebula, depending largely on the local temperature. The embryos then come together to build giant-planet 'cores' with masses of 5-20 Earth masses; only then can cores suck up vast quantities of nebular gas and grow into gas giant planets³ before the remaining nebular gas is dispersed when the central star lights up. If this description seems vague, then the reader has caught on. The physics of these processes is very poorly known. It is not really understood how planetesimals form or what the physical conditions (temperature, mass and density as a function of solar distance) of the nebulae are. Other mysteries include how long gas disks remain around forming stars before being blown away, how planets accrete gas, or how the presence of all that gas in the disks affects the orbits of the embryos. There are, of course, reasonable guesses.

Levison et all have made a brave attempt to study the diversity of possible planetary systems by performing 28 numerical simulations of the aggregation of planetary embryos. Because the important physical parameters are unknown, they chose ranges that probably encompass the 'real' values. After constructing plausible initial distributions of embryos surrounding the star, they compute the orbital evolution of these protoplanets as they interact with each other, sometimes coalescing and sometimes throwing each other out of the system. Of particular importance (or perhaps concern) is the modeling of huge gas cocoons around the embryos to make them coalesce more easily as they pass each other. This was done to prevent the known problem of the strong gravity of the protoplanets sling-shorting each other to high-velocity orbits and then bashing each other to bits before they get large enough to accreted gas.

Simulations continue until the orbits stabilize, and produce a wide variety of final planetary systems. Some have a few widely spaced planets, others have many Uranus-sized planets evenly spaced, while yet others have big planets closely packed together. Some even look like our Solar System. Interestingly, the simulations do not produce the most prevalent class of known extrasolar planets — Jupiter-sized objects very close to their stars — indicating that some crucial piece of physics is missing. The authors observe that even the higher growth rates they use (produced by the gas cocoons) do not sufficiently damp the planetary velocities to produce solar systems like our own with nearly circular planetary orbits. This problem is also observed in simulations of inner- planet formation, but because most of the accumulation is presumed to occur after the gas has vanished, it is not clear that gas is the culprit in removing the dynamical excitation.

The variety found in these simulations raises two issues. One is that the range of physical parameters used (due largely to our ignorance) is far wider than the Universe actually produces in protoplanetary nebulae, implying that the diversity found is larger than would be observed in reality. For example, the authors double the gas mass of large cores on a timescale that varies by four orders of magnitude; perhaps real disks have much less variation, producing a smaller range of final planetary masses than emerge from these models.

The second issue is that of predictability for theories of solar system formation. The dynamical evolution of a small number of embryos is highly chaotic, giving variable locations and numbers for the resulting planets. Levison et al. find stable systems ranging from one to seven planets. So it is unreasonable to demand that planet-formation theories produce our Solar System in detail; rather, some of the time at least, they must provide systems similar to ours from what are thought to be plausible starting conditions. This is in contrast to more 'regularist' thinking of 10-20 years ago, when it was popular to postulate that most solar systems would have a Jupiter analogue just outside the 'snow line'. This is the distance beyond which the temperature has dropped enough that icy solids condense, and greatly increase the surface mass-density of solids and thus local accretion rates.