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Is this a consequence of planet formation in accretion disks ?

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  • $\begingroup$ A bit facetiously: Because if it weren't, it would be a binary star system. $\endgroup$ – Ilmari Karonen Dec 13 '14 at 18:09
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I feel that HDE gives a good start of an answer, but stops short of the important part. We have seen in HDE's answer the formation of a star at the center of the collapsing molecular cloud. When the star begins to fuse lighter elements, the protoplanetary disk has several forces acting on it:

  • The momentum of the particles in the disk.
  • The gravity of the star in the center and other particles of the protoplanetary disk on the other side.
  • The gravity of the particles of the protoplanetary disk opposite the sun (outward).
  • The radiation pressure of the new star.

Interestingly, the second and third forces pretty much cancel out when the disk is still uniform in distribution. But once large clumps of matter accumulate those large masses (protoplanets) gravitationally pull at the other matter in inconsistent and sometimes violent ways, especially when multiple protoplanets align (once per orbit of the inner body).

Thus, the area of the protoplanetary disk is being 'swept up' of all the mass: some is pulled into the sun by gravity and loss of momentum due to collisions, some is pushed out of the solar system by radiation, and whatever matter was not disturbed by one of those processes is then subject to being disturbed by the gravity of the protoplanets themselves. The protoplanets will, over time, either absorb that matter or gravitationally slingshot that matter out of the system or too it's very edges.

In short, the protoplanetary disk within a few tens of AU of the star in the center is a chaotic mess of a place. Not much matter can form a stable orbit there.

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  • $\begingroup$ Regarding the last part: So the central stuff is generally either absorbed by the Sun, pushed into another orbit or chucked out completely? $\endgroup$ – HDE 226868 Dec 13 '14 at 16:20
  • $\begingroup$ @HDE226868: From what I understand, during the early stages of planetary formation (such as that which Vega is undergoing right now) things are too chaotic (i.e. too many random gravitational encounters and collisions) to really have a stable orbit for any accretions of matter without significant mass. I'm not sure how long this stage lasts, but I do believe that we can observe it for quite a few stars (such as the afore-mentioned Vega). So the accretions of matter which have not-significant mass are constantly having their orbits perturbed. $\endgroup$ – dotancohen Dec 13 '14 at 16:29
  • $\begingroup$ Any idea what the cut-off limit is for an object to not have a greatly-perturbed orbit? $\endgroup$ – HDE 226868 Dec 13 '14 at 16:35
  • $\begingroup$ I don't have any idea, but I should imagine (warning: speculation following) that there is more of a continuum than a cutoff point. A dust particle may be perturbed by a passing Theia and thus be ejected by gravitational slingshot. However, two fist-sized objects would interact in a more uniform fashion and neither would have enough momentum to eject the other. I don't believe that we have the technology to observed this in nature yet, nor do we have the technology to perform Monte Carlo planet-formation experiments just yet. $\endgroup$ – dotancohen Dec 13 '14 at 17:11
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    $\begingroup$ Vega has a debris disc. It is not a proptoplanetary disc. Vega is not a young star. It has nothing to do with this question. All the planets formed "within a few tens of au" of the Sun, so what do you mean that matter can't "form a stable orbit there"? $\endgroup$ – Rob Jeffries Dec 13 '14 at 17:14
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It's because of the Sun.

It might be good if I give a quick overview on star formation before I get to the meat of the issue. Here's star formation in a few simple steps:

  1. Giant Molecular Cloud forms. A large region of gas and dust, essentially a dense version of the interstellar medium, coalesces into an interstellar cloud. GMCs can be tens or hundreds of light-years across, enough to give birth to many stars. Within the GMC, some regions will be slightly denser than others.
  2. A portion of the cloud collapses. A certain region of the GMC collapses, generally due to an outside disturbance. The most commonly cited cause is a supernova shockwave that compresses portions of the GMC, although close passes between galaxies have been known to incite star formation. My favorite example is the Cartwheel galaxy.
  3. The region heats up. There is quite a lot of matter pressing in on what has now become a protostar, and so it heats up. Eventually, conditions become such that hydrogen fusion is possible. The protostar, now a pre-main-sequence star, begins to shine.
  4. A protoplanetary disk forms. At this point, the star dominates this region of the GMC. Matter nearby is pulled towards it by the force of gravity, and a circumstellar disk forms. It may be composed of gas and dust. Eventually, small grains of dust collide and form bigger grains. Planetesimals form, then protoplanets, and finally planets.

The reason that there isn't more matter in a given stellar system is that the star dominates the surrounding area. It pulls in nearly everything around it during its early life. Much of the region of the collapsing cloud is made of molecular $H_2$, and so it is pulled in and used for fusion.

Now the question translates to 'Why isn't the protoplanetary disk more massive'? The answer is that when the disk formed, much of the matter that was in its inner reaches spiraled into the Sun. This is partly due to the Poynting-Robertson effect, where photons from the Sun pull dust grains in. Over billions of years, the star can accumulate much of the matter than was originally close to it in the disk.

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  • $\begingroup$ Nice answer, but I feel that you stop right where it gets interesting! I pick up where you left off in another answer. If you feel that this should be a single answer you can edit my answer into yours. $\endgroup$ – dotancohen Dec 13 '14 at 16:20
  • $\begingroup$ @dotancohen No, I like yours. Let's keep it separate. $\endgroup$ – HDE 226868 Dec 13 '14 at 16:20
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Are you asking why there isn't more mass in the planetary system?

The reasons go back to the collapse and fragmentation of the protostellar cloud and the subsequent accretion (from a pseudo-spherical envelope) of the bulk of the protostellar material. It has little to do with subsequent processes occurring in the accretion disc.

If the disc had too much mass it becomes unstable to further fragmentation and this is one of the ways in which binary systems are formed.

In general discs around stars rarely exceed about a tenth of the stellar mass. But of course there are lots of binary systems.

If instead you mean why didn't more of the protoplanetary disc end up in the planets - the main two reasons are: (i) a large fraction of the protoplanetary disc was accreted. We see class II T-Tauri stars with mass accretion rates of $10^{-9}-10^{-8}$ solar masses per year and this appears to persist for a few million years. (ii) The disc gets photoevaporated by the high energy radiation coming from the star and possibly from external sources too. This drives a disc wind that will deplete the disc of material.

Planet formation is in competition with these processes. The popular "core accretion" model for the formation of giant planets (there aren't enough rocks in the protoplanetary disc for rocky planets/asteroids et al. to make any difference) has a timescale of 5-10 million years for the accretion of gas, so most of the raw materials can easily have disappeared before much accretion of material into giant planets has occurred.

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