Why do nebulae tend to collapse into discs?

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Main Question or Discussion Point

As far as I understand it, a nebula initially tends to have a small amount of rotation (on average) and then as it collapses under its own gravity this rotation increases significantly due to conservation of angular momentum (assuming that there is no external torque,right?!). What I'm unsure about, is why do nebulae tend to end up as rotating discs (after starting from an initial, potentially arbitrary shape)?
Is it somewhat analogous to the reason why the Earth is an oblate sphere, i.e. due to the effects of rotation, because the top and bottom parts of the Earth have a smaller tangential velocity and are therefore more heavily influenced by the force of the Earth's own gravity, whereas near the equator the tangential velocity is much higher (since it is proportial to the radius) causing the Earth to bulge outwards?!
 

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D H
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why do nebulae tend to end up as rotating discs (after starting from an initial, potentially arbitrary shape)?
A nebula starts its life with some amount of angular momentum. A bit of a disk shape starts forming as the nebula starts to collapse gravitationally. As stuff that isn't orbiting this pre-disk crosses that plane, it collides. That stuff collides because it interacts electromagnetically as well as by gravitation. In addition to occasionally colliding, that stuff that forms the nebula occasionally emit photons. Compare with dark matter, which does not interact electromagnetically and doesn't clump the way baryonic matter does. Dark matter has no mechanism (or possibly a very weak mechanism; we don't know what dark matter is) for getting rid of energy.

There's a general principle at work here, which is the minimum energy principle. This says that a closed system (a system that exchanges energy but not mass with the external environment) that has a constant entropy will tend to seek a configuration where energy is at its minimum if there's a pathway to that minimum energy collision. There is a pathway thanks to those collisions and photon emissions. This is a consequence of the second law of thermodynamics. In fact, so much energy is carried away that the collapsing nebula loses entropy. There's no violation of the laws of thermodynamics here; the entropy of the gas cloud and the rest of the universe increases.
 
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A bit of a disk shape starts forming as the nebula starts to collapse gravitationally
Why is this the case though?

As stuff that isn't orbiting this pre-disk crosses that plane, it collides. That stuff collides because it interacts electromagnetically as well as by gravitation. In addition to occasionally colliding, that stuff that forms the nebula occasionally emit photons. Compare with dark matter, which does not interact electromagnetically and doesn't clump the way baryonic matter does. Dark matter has no mechanism (or possibly a very weak mechanism; we don't know what dark matter is) for getting rid of energy.
Is the point then, that the disc shape is energetically favourable - anything that is not in (or near) the plane of the disc will collide with one another due to their random motions, doing so until they eventually end up in the orbital plane of the disc, or radiate away as electromagnetic radiation?
 
Chronos
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Take a christmas snow globe, shake it up to get a blizzard going then set it down and spin it. What happens to the blizzard inside the glass ball?
 
Bandersnatch
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Why is this the case though?
First imagine a nebula composed of particles uniformly (same angular velocity) rotating around some axis.*

As a particle attempts to collapse under the gravity of the cloud, it will experience centrifugal force perpendicular to the rotation axis, and no such force parallel to the rotation axis. The centrifugal force will act to prevent a complete collapse in the direction towards the axis, but no such restriction will exist parallel to the axis, so particles must end up moving in a way that will form a flat disc - before passing through and to the other side. Some particles will collide as they pass each other in the disc plane, exchanging their opposite momenta along, and eventually most particles will end up with no, or nearly no velocity in the direction parallel to the rotation axis.**


*Any actual nebula will have a slew of particles going every which way, but as long as there is some net angular momentum it's in the end equivalent to the aforementioned idealised scenario since for every particle going against the overall rotation you will have another that goes with it faster (or is larger), and their eventual collision will exchange momenta leading to roughly uniform rotation.

** The program linked below simulates such a uniformly rotating collapsing cloud (with some extra interactions tangent to this topic). You can see how the disc forms in the first seconds of the simulation. It has very simplified collisions, though, so you won't see nice long-term evolution (maybe if you fiddle with the parameters).
https://www.khanacademy.org/computer-programming/challenge-modeling-accretion-disks/1180451277
 
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Take a christmas snow globe, shake it up to get a blizzard going then set it down and spin it. What happens to the blizzard inside the glass ball?
I don't have a snow globe handy, but I'm guessing the blizzard will eventually settle into a spinning disc, but what I don't quite understand is the physics behind why this happens?!

As a particle attempts to collapse under the gravity of the cloud, it will experience centrifugal force perpendicular to the rotation axis, and no such force parallel to the rotation axis. The centrifugal force will act to prevent a complete collapse in the direction towards the axis, but no such restriction will exist parallel to the axis, so particles must end up moving in a way that will form a flat disc - before passing through and to the other side. Some particles will collide as they pass each other in the disc plane, exchanging their opposite momenta along, and eventually most particles will end up with no, or nearly no velocity in the direction parallel to the rotation axis.**
Thanks for the link to the simulation.

I don't quite understand why the particles experience a centrifugal force perpendicular to the axis of rotation (I assume that this description is in the accelerated reference frame of the particle)? Wouldn't gravity act as a centripetal force towards the centre of mass of the nebula (which isn't necessarily perpendicular to the axis of rotation)?
Is the point that as the cloud collapses under its own gravity angular momentum is conserved and so the particles start to rotate faster and faster around their common centre of mass. The particles further from the centre of mass of the nebula will experience a smaller gravitational force and so will tend to bulge outwards (since their high tangential velocity will increase size of their orbits), whereas those nearest the centre will collapse further under the influence of gravity (since the force will be greater there and furthermore, as tangential velocity increases with radius, their velocities will be lower and hence won't be able to overcome the effects of gravity as much) and so will be "squashed" towards the centre of gravity, and hence the nebula will tend towards a disc shape?!
 
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don't quite understand why the particles experience a centrifugal force perpendicular to the axis of rotation (I assume that this description is in the accelerated reference frame of the particle)? Wouldn't gravity act as a centripetal force towards the centre of mass of the nebula (which isn't necessarily perpendicular to the axis of rotation)?
Apologies about this bit. I've since thought about it a bit more and see that the rotation axis will always be perpendicular to the gravitational force (well at least from thinking about a simplified 2D example of a vertical spinning wheel in which the gravitational force will point "downwards" in the plane and the axis of rotation will point out of the plane).
 
Bandersnatch
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In the 3D case it's just a matter of splitting the gravity vector into its components parallel and perpendicular to the axis.
 
Chronos
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Bear in mind, in empty space, the most meaningful direction is towards the nearest center of gravity.
 

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