In a dust cloud around a star, what causes bodies to form?

Question

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?

Answer 1

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.

Answer 2

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.