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I couldn't find an answer to this question.

Suppose a dust ring around a new star contains relatively uniform dust particles.

What's the process by which they aggregate into larger bodies?

I can understand that there's a velocity distribution, so they can collide, but what makes them stick together? If they collide at low velocity, they should just bounce. If they collide at high velocity, heat energy would be released, but the fragments would just fly away.

I could see particles of opposite charge sticking together, but the result would have little charge, so it would not attract more particles.

Gravity could not become an attractant until sizable bodies could be formed.

Could it be that if a volume of space contained a large enough concentration of dust, that volume would itself have enough gravity to be an attractant?

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  • $\begingroup$ I've heard that it's a combination of static electricity, and gravity. The idea being that the static clumps the dust, and gravity clumps the bigger stuff. $\endgroup$
    – CoilKid
    Commented Mar 14, 2015 at 16:26
  • $\begingroup$ @CoilKid: I wonder if clouds that are otherwise neutral become charged just by flowing past each other, the same way charges build up in a thundercloud or a volcano cloud (Van de Graaf generator), and if that could provide the charge necessary to form clumps. $\endgroup$ Commented Mar 14, 2015 at 16:58
  • $\begingroup$ Pretty sure that's the idea :) $\endgroup$
    – CoilKid
    Commented Mar 14, 2015 at 17:14

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Any colloid, whether it's clay particles on water, fat globules in milk or dust clouds in a vacuum, is inherently unstable because chunks of matter attract other chunks of matter due to Van der Waals forces (mostly the London dispersion force in a dust cloud). This is quite general and applies to every form of solid (or liquid) particle, so a colloid will flocculate unless there is some mechanism to stabilise it. In clay dispersions the stability comes from electrostatic forces, and in milk the stability comes from a combination of electrostatic and steric stabilisation.

So any cosmic dust cloud will flocculate unless some mechanism stabilises it. However the London forces are very short range, so two dust grains will basically only aggregate if they collide. The rate of aggregation is then determined by the collision frequency. And this is where gravity comes in, because gravitational collapse of the dust cloud as a whole increases the dust particle density and therefore increases the collision frequency and hence the aggregation.

I've used the escape clause unless some mechanism stabilises it several times. In a cosmic dust cloud the only mechanism I can think of is charge, but it's hard to see how this could work because the cloud would be overall neutral.

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  • $\begingroup$ I hadn't thought of Van der Waals force. That's interesting. $\endgroup$ Commented Mar 14, 2015 at 16:43
  • $\begingroup$ @MikeDunlavey: I started my professional scientific life as a colloid scientist, and understanding the forces between colloidal particles is the bread and butter of the trade. Fortunately the colloidal dispersions we work with are rather more accessible than interstellar dust :-) $\endgroup$ Commented Mar 14, 2015 at 16:47
  • $\begingroup$ Is it possible that the formation of polar molecules like water naturally want to clump, even though they are overall neutral? I'm thinking of "dirty snowballs" (like I have out my window :) $\endgroup$ Commented Mar 14, 2015 at 16:47
  • $\begingroup$ Water molecules have a large (by molecular standards) electric dipole, so the forces between water molecules are high. However in ice the dipoles cancel out so an ice particle doesn't have a large net dipole and there won't be much of a long range force. However once the ice particles collide there will be very strong short range forces that make them adhere. $\endgroup$ Commented Mar 14, 2015 at 16:49
  • $\begingroup$ Do you suppose the clumping charge could come from Van de Graaff action? $\endgroup$ Commented Mar 14, 2015 at 17:04
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It's exactly as you say in your last sentence. Gas clouds can become big or dense enough to collapse on themselves. The page on Jean's instability has the relevant collapse requirements along with a lot of other good information. The following arguments are taken right from The Physics of Stars, by A.J. Phillips.

The gravitational energy of a cloud of gas can be evaluated with $$ E_{GR} = - \int_{m=0}^{m=M} \frac{Gm(r)}{r}dm \Rightarrow -f\frac{GM^2}{R},$$

where $f$ is a constant that depends on the mass distribution. For a spherically symmetric cloud, $f=\frac{3}{5}$, but it will be higher if the center of the cloud is more concentrated. For the rest of a rough calculation the book assumes $f=1$. The thermal kinetic energy of the cloud is just $\frac{3}{2}NkT $. The condition for onset of condensation is $|E_{GR}| \gt E_{KE}$. This implies a gas cloud of radius $R$ can condense if the mass exceeds $$ M_J = \frac{3kT}{2G\bar{m}}R.$$ It also implies a cloud of mass $M$ can condense if the average density exceeds $$ \rho_J= \frac{3}{4\pi M^2} \left[\frac{3kT}{2G\bar{m}} \right]^3.$$

The text plugs in some numbers for a quick example. A cloud of molecular hydrogen at 20 K with a mass of $2\times10^{33}$kg, or 1000 solar masses, condenses with a density of $10^{-22}$kgm$^{-3}$, or $10^5$ molecules per cubic meter. The critical density of a cloud with only 1 solar mass is a million times higher.

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  • $\begingroup$ OK, that's a big help. I wonder if it extends to planetary dust clouds. I mean, we see things like comets. I wonder how they are formed. Rather than, say, disintegrated? $\endgroup$ Commented Mar 14, 2015 at 15:46
  • $\begingroup$ Yeah a collapsing dust cloud explains the gas giants, but not so much the smaller bodies. I'm not sure what specifically happens there. Maybe the heavier elements are just 'sticky' enough so they clump through random collisions, as opposed to gases. $\endgroup$ Commented Mar 14, 2015 at 15:58
  • $\begingroup$ Jean's analysis as written here is incomplete for the matter of planetary formation because of the tidal influence of the primary. Presumably this just skews the shape of the collapsing region (to a oblate spheroid with the short axis pointing through the primary?) and adds a correction term to the requisite mass density without effecting the overall sweep (heh!) of the argument. $\endgroup$ Commented Mar 14, 2015 at 17:15

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