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Why do protostellar discs spin?


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I'm trying to get my head around this. So far what I've looked at (admittedly, here and wikipedia), and I can't find an explanation. Is it down to subtle differences in density in the cloud? If so must such differences in density exist on such a scale, necessitating rotation?

If anyone can point me in the right direction, or indeed a cosmologist can answer my question, that'd be just grand. :)

John

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The dust clouds from which protostars form are turbulent and will therefore have a certain angular momentum. As the cloud collapses, its dimensions shrink by many orders of magnitude, but its angular momentum must be conserved, therefore it must start to spin faster & faster - the usual analogy is a skater's spin accelerating as she pulls her arms in, but the effect is much stronger as a dust cloud parsecs in extent collapses to the dimensions of a protostellar disc.

In some ways the miracle is that the spin isn't so strong as to prevent the gravitational collapse altogether.

Once the disc acquires a reasonable density, frictional heating is able to radiate rotational energy out of the system, allowing strict conservation of angular momentum to be violated and allowing the gravitationally driven collapse to continue to the point where a stellar core can form.

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as a large, initially rotating gas cloud collapses under its own gravity (jeans criterion), must speed up as its radius decreases to conserve angular momentum...

why the gas cloud rotates in the first place?

maybe with the various forces pulling at the particles of the gas, predominantly hydrogen, there is bound to be some sort of motion which may be initially small. Of course, space offers no resistance to this motion hence the particles will not come to rest....

if the gas cloud is perturbed, with the size of the pertubation being larger that the jeans length, meaning the mass contained with the length (volume) is greater than the jeans mass, then the self gravity overcomes the outward pressure, and the cloud will collapse.

the gas particles will now be attracted toward the centre of the now fragmented gas cloud. The radius will become smaller, and particles will travel faster to maintain the angular momentum...

the jeans theory isnt quite correct, and infact star formation is still poorly understood. as we were told in 3rd year, the pressure from the gas heating up during contraction should out weigh the gravitaional force....halting collapse. Clearly this doesnt happen as we stars...

if its not cloudy

hope that was of help, but why gas clouds initially rotate, im not sure

but certainly a rotating gas cloud will speed up during contraction to maintain angular momentum.....

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That makes sense, but I still don't understand the initial conditions in the cloud. Am I right in thinking that the angular momentum of the cloud is related (directly) to an integral of the vector field of angular momenta about the centre of the cloud? So, the velocity of the particles of the cloud at any given point in the cloud always have a component tangent to a sphere enclosing the core, and irrespective of any other considerations this momentum must be conserved as the cloud shrinks around a common point?

This might make very little sense as my understanding of the curl of vector fields is pretty limited. If i'm waffling nonsense just ignore me, lol.

John

Edited by astoc
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I think - bit rusty, that rotation is due to differences of pressures and temperatures of the gases along with different densities which cause mutual gravitational effects within the various pockets of the cloud which eventually start the process of spinning/rotating around a point relative to their densities.

Probably haven't made any sense there :)

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Clouds acquire angular momentum from the tidal influence of other clouds (or matter in general) - this works at the level of protogalactic clouds as well as protostellar ones.

Edited by acey
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the pressure from the gas heating up during contraction should out weigh the gravitaional force....halting collapse. Clearly this doesnt happen

It's not as simple as that ... low velocity collisions between dust grains which are slightly "sticky" reduces the particle count, therefore contraction can occur without as much increase in pressure as you'd expect. The energy of the collisions is expelled in long wavelength radiation (microwaves) which don't interact much with matter in the low densities associated with collapsing dust clouds, so effectively the collisions radiate away much of the gravitational energy associated with the collapse in the early low density, low pressure, low temperature stages of the event. Later on, kinetic energy of the infall starts to play a major effect.

We don't understand perfectly but simulations based on known physics show pretty clearly what happens.

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The formation of a star at the centre of a collapsing cloud is believed to require two stages of collapse. In the early stages the cloud is transparent to heat emission wavelengths from dust grains in the cloud. The source of the heat comes from compressional heating of the cloud during collapse. Hence cooling of the cloud through thermal emission dominates, keeping the cloud at a low temperature ~10K.

When the cloud becomes dense enough, it become opaque to thermal emission resulting in the formation of an adiabatic core that gets increasingly hotter through continued collapse. Adiabatic basically means it heats up as it compresses.

Once it heats up to ~2000 K, molecular hydrogen starts to split apart (dissociate) reducing the value of the adiabatic exponent, which triggers the second collapse phase that eventually results in the formation of the protostar at the centre of the cloud.

The spinning protoplanetary disc is, as others have said, the result of conservation of angular momentum. From a crude perspective, the differential rotation of the galaxy can impart a slight spin to the interstellar cloud, so that the outer edge of the cloud moves slightly slower than the inner edge, but I've never seen this mentioned anywhere in literature. The reality is that interstellar molecular clouds are turbulent shock-filled entities which collapse in phases as different stars form in different parts of the cloud. Messy, very messy :)

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