Pedagoguery

Twenty years ago, scientists had only one example of how planets formed: our own solar system. Since then, an extraordinary deluge of discoveries have revealed dozens of solar systems, each one unique. The incredible diversity of solar systems out there have revealed some of the heretofore unknown complexities of planetary formation and evolution.

It all starts with a giant cloud of gas and dust. Dust in this context are tiny grains, typically micron-sized, of heavier elements: carbonates, silicates, and iron, typically, along with various ices such as water, carbon dioxide, and ammonia. These grains form in the outer atmospheres of red giant stars. The deep convecting layers of such stars dredge up elements formed in the latter stages of nuclear fusion and the strong stellar winds of the stars blow the elements away to cooler realms where they condense. The cloud starts to collapse. In the center, a protostar forms, while the remainder of the collapsing cloud forms a disc of gas and dust around it. The ratio of gas to dust in the disc varies in both time and space. The farther away from the protostar, the more gas. In addition, as the protostar ages and starts its transition into a star, the radiation it gives off tends to blow the gas out of the disc. So, the older the disc, the less gas it has. For the case of planetary formation, however, we can consider the starting point as early, when there is still plenty of gas around.

When the star is about a million years old, the protoplanetary disc surrounding it starts to sort itself out. The dust grains therein collide, sometimes sticking together, sometimes breaking apart. Those hit by direct sunlight re-radiate the energy as heat, ensuring that even the darkest areas of the disc get heated. The temperature, density, and pressure of the gas generally decrease as you get further from the star. Because of the balance of these forces, the disc tends to rotate more slowly than an independent body at the same distance would. Smaller dust grains get swept along with the gas, but larger grains, those more than about a millimeter in size, want to rotate faster, and thus experience something of a “headwind”, which causes them to spiral inward. Depending on the size of the star, there is a point, usually from 2 to 4 astronomical units away, where ices, especially water ice, start to vaporize. This is referred to as the “snow line”. The snow line is important for a number of reasons. It separates the inner, volatile-poor part of the disc from the outer, volatile-rich part. As dust grains cross that line, its volatiles boil off, typically causing an accumulation of water right at the snow line. It also causes a drop in pressure inside the snow line. This drop in pressure causes the gas to rotate more quickly, and thus dust grains experience a tail wind causing them to spiral out. So, at the snow line, you get an accumulation of dust particles, along with a slush of ices and organic molecules, which encourage the dust particles to stick together. Eventually, the dust grains pack themselves into kilometer-sized planetesimals. Planetesimals form throughout the disc, but the formation is much quicker at the snow line, and the interactions there will frequently throw them into irregular orbits that land them far inside or outside the snow line.

Once most of the mass of dust is bound up in planetesimals, another process takes over. Elliptical orbits tend to circularize due to drag effects of the gas. The planetesimals collide and grow, with larger ones sweeping up a zone and capturing smaller ones in that zone. How big they can grow depends on where they are. In the inner parts of the disc, these planetary embryos would top out at about 0.1 earth masses, while in the outer parts, they could easily top 4 earth masses. Planetesimals can also grow larger at the snow line or on the edges of gaps within the disc, where planetesimals tend to accumulate. Interactions between the embryos will tend to thin the herd quite a bit, with some thrown clear of the burgeoning solar system, and others thrown on collision courses with the central star. What you eventually get is an oligarchy of moon- to earth-sized planetary embryos.

The defining moment in the formation of any planetary system is the formation of a Jupiter-mass planet. Such a planet typically starts as an embryo about the size of the earth that accumulated 300 times its mass in gas. There are a few competing processes that affect this. The first is the fact that infalling gas heats up. In order for it to settle on the growing planet, it must cool off. The efficiency of the cooling depends on a number of factors, not least of which is the composition of the gas and the opacity of the outer layers. Competing against this is the fact that a planetary embryo of this size generates waves in the surrounding gas. These waves generate an unbalanced torque on the planet, slowing it down and causing it to spiral inward. Since the inner areas of the disc are both poorer in gas and warmer, this poses problems. First of all, there is less gas to accumulate, and secondly, cooling is less efficient in warmer surroundings. The inward spiraling does tend to stall at the snow line, where the gas head wind turns into a tail wind. The accumulation of material here also helps to encourage planetary growth. This may well be the reason why Jupiter is where it is, since the snow line in the early solar system would be just inside its current orbit. The bottom line on gas giant formation is that embryo growth, embryo migration, and gas depletion within the disc would all tend to occur at roughly the same rate, and which wins out is determined largely by the luck of the draw. Only about 10% of sun like stars examined so far have gas giants around them. Once the gas giant reaches a certain point, growth accelerates at a rapid rate. Within 1000 years, a Jupiter-mass planet can gain half of its eventual mass. The planet stabilizes when it becomes massive enough that it moves the disc rather than the disc moving it. Gas interior to the planet gets pulled back by the planet's gravity, causing it to spiral inward, while the opposite happens with gas exterior to the planet. Thus the planet clears a channel in the disc, slowing or stopping planetary growth. How big it gets depends on the density of the disc and the timing of when the planet forms.

The formation of the first gas giant has profound affects on the system as a whole. First of all, it can trigger the formation of additional gas giants, as well as terrestrial planets. The gas giant clears out a gap in the disc at its orbit. This gap acts as a moat, allowing material to pile up outside its orbit and thus encouraging the formation of an additional gas giant right there. Gas giants also help to foster the formation of terrestrial planets. Planetary embryos, when they form, have nearly circular orbits. However, since there is little gas in the inner disc, the only way terrestrial planets can grow is for the embryos to coalesce. The gas giant can foster this process by perturbing the orbits of the embryos, or by flinging planetesimals from the outer disc into the inner disc.

Many of the planetary systems we have observed contain gas giants very close to their parent stars – so close that they could not possibly have formed there. How did they get there? The most likely explanation is that the disc did it. Friction within the disc can cause it to slow down and spiral in. This spiraling can drag the gas giant with it, until it is so close to the star that tidal affects circularize and stabilize its orbit.

The final process that takes place during the formation of a planetary system, is the clean-up. When most of the gas has been blown away, and most of the planetesimals have been absorbed into planets, there is still quite a lot of debris left over. Gravitational interactions between the debris and the plants take car of this. The debris either gets flung out of the system entirely, or it gets flung into the inner system where it either hits a planet or the central star. These interactions cause the planets orbits to migrate, and the migration could very well cause an instability that wildly relocates a planet, perhaps even ejects it from the system entirely. It could easily take a billion years before thing settle down to a state similar to what we have in our solar system.

Next time, does quantum theory predict a Big Bounce?