Spiral Waves in Proto-planetary Disks

Very recent observations indicate that in some proto-planetary disks, there are spiral waves. This has some interesting implications.

One thing to remember is that these waves are caused by a gravitational instability in shearing, thin, self-gravitating disks. The only other known example is spiral galaxies. If they are the same in proto-planetary disks as in galaxies, these are waves of density, not material, and it is not some selected subset of the matter in the disk which has formed into a rotating spiral, but instead it is like waves on the surface of the ocean. The seawater does not travel along the surface, just in loops near the surface. The wave is an instability formed by the shearing of the air over the ocean surface. The energy in the wind is tapped to form waves, and interestingly enough, waves are non-linear, in that having some waves creates more wind friction, coupling more energy into the water, until some saturation point is reached. The saturation point can involve huge expanses of oceans, as deep-water waves do not dissipate rapidly. If gravitational density waves are analogous, the energy in the shearing of the rotating disk couples into the wave instability, and probably having some unevenness in the density of the disk makes the shearing couple better, up to a point where it saturates.

If this phenomena has some implications for planetary formation, the timing is important. In galaxy spiral density waves, the formation time of stars is short enough so that they can get started in the time it takes the spiral wave to pass by. For solar system spiral density waves, a planet must get started in the time it takes the spiral wave to pass by, or else there is no effect. We do not know the propagation speed of solar system spiral density waves, but galaxy spiral density waves move quite slowly around the galaxy. If solar system waves are also slow, planets might get started as they pass. It may just be that the rotation rate of the spiral density wave is the same as the rotational rate at some radius, perhaps a radius located about half-way out the spiral structure. If this is the case, then the motion of matter through the wave is zero at the key radius, and slow on either side of that.

This has two possible implications. One is that, assuming they are more likely dual spiral waves with two arms rather than three or four, two giant planets might form about simultaneously. This requires that the initial condensation of the planets happen very quickly. Times in condensation are typically quick if there is no angular momentum to keep things spread out. Freefall times for a planet are measured in minutes and for a star, in tens of days, or from far out in the solar system, hundreds of days. The spiral wave does not eliminate the angular momentum that slows down the collapse, but it mitigates it. Thus, if a planetary orbit is 10 years, collapse could be a fraction of that. In other words, the proto-planet could form during the passage of the spiral density wave.

In a two-pronged spiral wave, two planets could form. If the wave was in the densest part of the proto-planetary disk, and there was enough total mass in it, two gas giants could form, and begin to accumulated surrounding matter. Planet formation is quick, once the disk becomes non-uniform. A solar system with two gas giants, which lock into perturbations around some commensurate orbital times, seems to provide a very stable home for other, smaller planets.

It would be expected that the spiral density wave was symmetric, in that both sides had about the same condensation and the same mean density. Even so, since two planets by themselves, meaning with no other larger planets to stabilize them, are unstable if in the same orbit or close to it, they would swap angular momentum and move apart. With some luck related to accidental close approaches, they would reach a stable equilibrium. One interesting question is how likely is this dispersion? Do most planet pairs formed by a spiral wave or anything else at very similar radii tend to chuck one out of the solar system or do they tend to drift into a stable pair of orbits. Some intensive but simple simulation of planetary orbits might help answer this question. The effect of the residual proto-planetary disk at inner radii or outer radii, relative to the planet pair, might be beneficial, but that will have to be thought out in more detail.

Let’s turn the situation on its head. If there are two large gas giants in stable orbits, just recently formed, and the inner residual of the proto-planetary disk has not yet collapsed into its own planets, would these outer planets induce a spiral wave in the inner residual disk? If the spiral density wave is a near stable phenomena, then it should be preferentially induced by any regular perturbation. To say this a different way, if disks tend to respond to some forcing by creating spiral density waves, then a dual planet system might provide such forcing. Ocean waves do not form because they are manipulated by the wind, as the wind has only a very simple forcing effect on the ocean. Waves are a natural oscillation of the system, but they die out without some forcing. The wind shearing over the surface of the ocean provides that forcing. Similarly, if gravitational spiral waves are a natural oscillation of a proto-planetary disk, lots of things might provide a forcing, including planets orbiting beyond it.

This leads to the second implication. If a residual inner proto-planetary disk is put into spiral wave motion, then there again might be a dual pair of condensation centers formed, one in each spiral arm. Then these dual planets, being formed in a much less dense part of the proto-planetary disk, might form smaller planets. If there is a composition gradient, they could be more metallic that the outer ones. But the interesting part is that they are in opposition, one being at one of the Lagrangian points of the other. If proto-Earth and Theia, the hypothetical planetesimal that impacted the proto-Earth to form the moon, and perhaps assist in the origination of life, did have their collision, these spiral waves provide one speculative cause of the pair. Again, some simple but extensive simulations of planetary orbits would be needed to determine if this is anything more that a wild idea, but wild ideas sometimes become less wild, and since this fits in with what we know so far, it might be worth thinking about.