Why gas clouds collapse if the forces are conservative?

[fbs7]

Hello all,

You all have always kindly helped me as I remember questions I have accumulated since high school days, and have never been answered. Eventually I gave up and forgot them, but as I grow old for some odd reason these things pop back up in my mind, like old ghosts from 35 years ago.

So here's a ghost: if you have two small objects in space, they will not collapse. They will just fly around each other (or go in whatever orbit) forever, for the reason that gravity is a conservative force. If you have three small objects, same thing, they will not collapse.

Now give me a trillion trillion trillion hydrogen molecules flying in space. Due to the sheer number, some will come close together. But, they will never actually touch each other, as they will repel and just change directions. Electromagnetism is also a conservative force, so if two molecules have some speed when they are a certain distance before that "collision", then after they collide they will have speeds that add up to the same momentum when they reach that distance. So, before collision and after collision the sum of kinetic + gravity potential + electromagnetic potential will be the same.

Plus, there are no chemical reactions. If two H2 molecules come very close together, they will not form a H4 molecule, so it's impossible for them to aggregate due to some chemical reaction.

Therefore, for the simple fact that energy is conserved, even if a hydrogen cloud starts to collapse, it must bounce back into a cloud, as there's nothing holding it together.

So my old 14 years old self came to the conclusion that the movies showing a gas cloud "collapsing under the effect of gravity" must be false (or at least quite incomplete), because gravity and electromagnetism are conservative and there are no chemical reactions in a gas cloud. But I know that gas clouds do collapse, so where did my 14 years old self go wrong with that conclusion?

 

[Charles Kottler]

I think what happens is that over time the size of the clouds will increase as more matter gets caught in the gravitational field. This causes an increase in pressure and therefore heat in the centre. Eventually the pressure and heat will become sufficient to ignite a fusion reaction which reduces the total number of molecules, allowing the cloud to reduce in size leading to greater pressure, heat etc. and so it goes on...

 

[jbriggs444]

If you have three small objects, same thing, they will not collapse.

The three body problem is not that simple.

 

[russ_watters]

So here's a ghost: if you have two small objects in space, they will not collapse. They will just fly around each other (or go in whatever orbit) forever, for the reason that gravity is a conservative force.

What if they are initially stationary with respect to each other?

 

[A.T.]

So here's a ghost: if you have two small objects in space, they will not collapse. They will just fly around each other (or go in whatever orbit) forever, for the reason that gravity is a conservative force.

Not quite. They will radiate gravitational waves, loosing energy. If they are charged they will radiate EM waves with the same effect.

Electromagnetism is also a conservative force, so if two molecules have some speed when they are a certain distance before that "collision", then after they collide they will have speeds that add up to the same momentum when they reach that distance.

Total momentum is conserved, kinetic energy is not. The EM interactions produce EM radiation as well.

 

[Dale]

But, they will never actually touch each other, as they will repel and just change directions.

This is the key mistake. The hydrogen atoms have internal degrees of freedom, so their collisions are not elastic. When they have a plastic collision they do not just change directions. They lose KE to those internal degrees of freedom and collapse gravitationally. Those internal degrees of freedom then exchange energy and the cloud becomes hot.

 

[russ_watters]

This is the key mistake. The hydrogen atoms have internal degrees of freedom, so their collisions are not elastic. When they have a plastic collision they do not just change directions. They lose KE to those internal degrees of freedom and collapse gravitationally. Those internal degrees of freedom then exchange energy and the cloud becomes hot.

Interesting, I thought star formation was a largely adiabatic/ideal gas process, converting GPE into heat and pressure. You're saying a significant portion of the heat and resulting density is due to non-ideal gas behavior? Is that because the process takes a long time, allowing the particles to have more collisions and lose more energy to non-ideal/inelastic behavior?

Either way, isn't this beyond the scope of the OP though? Star formation starts when there isn't a stable equilibrium between gravity and pressure...or is it long term, slow heat loss due to those inelastic collissions that results in the instability in the first place?

 

[anorlunda]

@Dale got there first with the answer. The particles do collide.

I used to think like the OP that gas clouds were so thin that collisions almost never happen, but then I saw clear pictures of shock waves from supernovae passing through galactic dust clouds. You can't have a shock wave without particle collisions, and you can't have a shock wave without exceeding the speed of sound. So then I learned about the speed of sound in those galactic gas clouds. You can't have sound without collisions.

Most fun, in a different post, I was directed to this delightful paper, The Potato Radius: a Lower Minimum Size for Dwarf Planets that talks about asteroids, planets, rings, disc shaped galaxies, and spherical clouds all as instances of the same question the OP asked about.

You can think of Saturn's rings as a intermediate case. Many more than 3 particles, but many fewer particles than a gas cloud. How did the ring shape evolve?

Most fun, was the same idea applied to dark matter. Q: Why don't dark matter halos collapse into the same shape as the rest of the galaxy? A: Because if they can not radiate away their energy, they can't collapse.

I think if you read that paper linked above, you'll find interesting answers to your questions.

 

[Dale]

Interesting, I thought star formation was a largely adiabatic/ideal gas process, converting GPE into heat and pressure.

You probably know more on the topic than I do, but I don't think that either of these are in conflict with each other. Thermal energy is just energy in some internal degree of freedom. In an ideal gas the individual particles don't have the internal degree of freedom, but the gas as a whole does. As long as there is some internal degree of freedom you get the loss of KE and PE to heat, regardless of the details.

 

[fbs7]

This is the key mistake. The hydrogen atoms have internal degrees of freedom, so their collisions are not elastic. When they have a plastic collision they do not just change directions. They lose KE to those internal degrees of freedom and collapse gravitationally. Those internal degrees of freedom then exchange energy and the cloud becomes hot.

Ahhhh... most excellent! Now I get it.

So I can't prove a star is formed purely by applying gravitation laws, right? In order to do that I need to know the structure of the molecules, in order to conclude the collisions are not elastic... that does it.

So, same thing if I had 1 trillion planets in a cloud - their collisions would also make them lose a little kinetic energy, and they would tend to heat up, even if they don't actually touch each other, right?

Most surprising argument! Thanks again!
Fernando.

ps: hmmmm... does that mean that all gravitational collisions actually lose some kinetic energy, even if very little?

 

[fbs7]

Hmm... I thought I got it, but I'm down in the hole again...

A cloud of hydrogen gas in space... its pressure is very very very small, so the density is very very very small too... the distances (compared to the size of the hydrogen atom) are, as Trump says, yuuuuuge... and the atoms are very very very very light, so the gravitational force is incredibly small. Then two hydrogen atoms pass close by; that "close by" will be much bigger than the distance between the nucleus and the electrons.

That distance can't be small, because electromagnetism will prevent it. Then, given that the distance between the proton and electron is much much much smaller than the distance between the atoms, for gravity the atoms will then be just like points. So how is it possible that the atoms would lose any (significant) kinetic energy due to gravitational effects?

Therefore, is the "collision" between two hydrogen atoms will be dominated by electromagnetic force, not by gravitational force? So that energy loss must be due mainly to electromagnetic iteration between the two atoms, not by gravity?

So I can't really collapse any gas cloud by using gravity laws alone, right?

 

[Nugatory]

A cloud of hydrogen gas in space... its pressure is very very very small, so the density is very very very small too...

This is true, but consider what happens because the pressure is very low. There's is nothing to prevent one of the outer atoms from falling towards the center, increasing its kinetic energy as it does. However, jbriggs444 has already pointed out that this isn't the simple two-body case; the atom is not in going to follow an elliptical orbit that eventually brings it back to its original height with the increased kinetic energy traded in for a return of the original potential energy. Instead, it collides with one or more other atoms. The energy gained in the fall is shared out among these so we end up with a bunch of atoms, all of which have increased their kinetic energy but none of which have enough energy to climb back to the original height. Thus, the cloud becomes smaller, denser, and hotter, and the pressure increases.

That's gravitational collapse, and it continues until the pressure increases enough to halt it. It's really nothing more than realizing that the original uncollapsed cloud is not in equilibrium; internal pressure pushing up does not balance gravitational force pulling down. The cloud will collapse until the pressure increases enough produce that balance.

So I can't really collapse any gas cloud by using gravity laws alone, right?

You can, as I just described. However other interactions (electromagnetic and chemical until the center reaches temperatures and pressures sufficient for nuclear fusion reactions) will come into play as the cloud becomes hotter and denser. Many of these will create additional degrees of freedom as Dale describes.

 

[256bits]

largely adiabatic

As AT stated, radiation would carry energy away. so it isn't actually adiabatic.

 

[DrStupid]

As AT stated, radiation would carry energy away. so it isn't actually adiabatic.

At least in case of visible matter. Without this emission the collapse stops when the conditions of the virial theorem are reached. That's the reason for the different dimensions of visible matter distributions and the corresponding dark matter halos.

In the late state of the colapse angular momentum becomes an additional problem.

 

[fbs7]

Wow, this whole thing is really fascinating. I always see in the TV something like "the gas cloud collapses" and that's it, but actually that seems to be a pretty complicated process, uh?

So, say that I have a spaceship, and I'm flying through the center of a cloud of water vapor (not hydrogen) that is on the verge of becoming a star. I'll probably see all kinds of different things, right? say:

* some very cold, low density H2O molecules in the outer edges
* maybe some very cold, very sparse ice crystals somewhere?
* maybe some liquid water droplets somewhere? maybe even something akin to a large water pond floating in that region?
* lots of increasing pressure, increasing temperature steam in some inner edge
* then the vapor will dissociate into H2 and O2, and have some super heated gas in the center
* then plasma at the very center, just ready to ignite

That sounds correct? Should be a fascinating sight to see a lot of superheated steam in this water-based sun!

 

[my2cts]

Ahhhh... most excellent! Now I get it.

So I can't prove a star is formed purely by applying gravitation laws, right? In order to do that I need to know the structure of the molecules, in order to conclude the collisions are not elastic... that does it.

So, same thing if I had 1 trillion planets in a cloud - their collisions would also make them lose a little kinetic energy, and they would tend to heat up, even if they don't actually touch each other, right?

Most surprising argument! Thanks again!
Fernando.

ps: hmmmm... does that mean that all gravitational collisions actually lose some kinetic energy, even if very little?

Planetary interaction is inelastic because of tidal heating.
Of course gravitational waves are als emitted but at an extremely low power.