Does galaxy formation conserve mass and angular momentum?

In summary, the galaxies closest to us, the ones formed from the original gas cloud, have a significantly different total mass and total angular momentum.
  • #1
fbs7
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Last week I posted in General Physics some questions about what happens in a collapsing gas cloud, and I was advised that total angular momentum is conserved. I thought of asking for extra clarification here, as that seems really amazing -- I apologize for asking the same thing twice. I use a galaxy to ask the question. Our galaxy has a huge momentum today, and in the past it was just a huge gas cloud. So, what astronomers believe is closest approximation to the formation of our galaxy?

(a) The original gas cloud and our galaxy have about the same mass and total angular momentum
(b) The original gas cloud and our galaxy have significantly different total mass and total angular momentum

If (a) is true, then why these equations fail to explain that; say a particle just on the outskirts of a circular gas cloud, and it is collapsing with the gas cloud, and after it collapses it remains at the outskirts of the galaxy; then, for the particle:

Force gravity = Centripetal force
G.M.m/r^2 = m.v^2/r = m.w^2.r
w = GM/r^3
L = I.w = mr^2.w = G.M.m/r

M = mass of the gas cloud, which per (a) is the same, but r has decreased, so the angular momentum of the particle on the outskirts of the gas cloud increases, therefore angular momentum of one particle cannot be the same, and (a) is impossible... the only way for L to be preserved is by decreasing M...

Where is the equation wrong?
 
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  • #2
fbs7 said:
Where is the equation wrong?

For any closed system you have Newton's Third Law, which guarantees conservation of total linear and angular momentum - of the system. Individual particles in the system may change their linear and/or angular momentum, but the total of all particles is constant.
 
  • #3
The initial gas cloud is not a galaxy, you particles don't make nice circular orbits around it. Otherwise it wouldn't be a gas cloud.
 
  • #4
PeroK said:
For any closed system you have Newton's Third Law, which guarantees conservation of total linear and angular momentum - of the system. Individual particles in the system may change their linear and/or angular momentum, but the total of all particles is constant.

Correct, but a collapsing gas cloud can eject mass. That would allow the resulting galaxy to have equal, larger or smaller angular momentum than the original cloud, right? Of course, if higher then it would have to be compensated by some ejected mass with opposing angular momentum.

Is it possible that the collapsing gas cloud ejects a significant portion of its mass? Or, if not, then how to conserve the angular momentum?
 
  • #5
fbs7 said:
Or, if not, then how to conserve the angular momentum?

The gas cloud has no choice about conservation of angular momentum: it must obey Newton's Third Law.
 
  • #6
mfb said:
The initial gas cloud is not a galaxy, you particles don't make nice circular orbits around it. Otherwise it wouldn't be a gas cloud.

Hmm... that's a good point... so you mean that while the gas cloud is collapsing into a galaxy then that process will preserve mass and angular momentum, but when the galaxy organizes and the particles follow more or less circular orbits, then angular momentum is no longer preserved?
 
  • #7
PeroK said:
The gas cloud has no choice about conservation of angular momentum: it must obey Newton's Third Law.

Precisely, provided that no mass is ejected, precisely. But do we know that most of the mass of the gas cloud will indeed collapse into a well ordered, nicely rotating galaxy (assuming it's spiral, of course)?
 
  • #8
PeroK said:
For any closed system you have Newton's Third Law, which guarantees conservation of total linear and angular momentum - of the system. Individual particles in the system may change their linear and/or angular momentum, but the total of all particles is constant.
Careful. To me, galaxy formation is a GR process, and your statements are not true for it. Even tracking mass/energy flow carrying momentum and angular momentum away from the cloud as it collapses, you can still have failure of conservation of the order of GW momentum (unless the cloud is alone in an asymptotically flat universe, and you measure the GW at infinity).
 
  • #9
PAllen said:
Careful. To me, galaxy formation is a GR process, and your statements are not true for it. Even tracking mass/energy flow carrying momentum and angular momentum away from the cloud as it collapses, you can still have failure of conservation of the order of GW momentum (unless the cloud is alone in an asymptotically flat universe, and you measure the GW at infinity).

Fair enough, but the OP is analysing things with Newtonian equations of motion.

So, it's a good point, whether Newton's law apply in the first place is another matter.
 
  • #10
Ohhhh... I see... so the gas cloud is just too big to analyze with those simple principles. Maybe it doesn't even make sense to talk about a total angular momentum of the galaxy? That's awesome, I always thought of a galaxy being somewhat similar to a pancake, but I guess the equations are very different, uh?

How about a gas cloud collapsing into a star? Do we believe that most of the mass of the gas cloud collapses into the star, or do we believe that a good part of it is expelled?

If a part of the star's gas cloud is ejected, then can we say at all that the angular momentum of the start and the angular momentum of the gas cloud are similar?
 
  • #11
Stellar formation is not really my area of expertise, but my understanding is that the "nett" angular momentum of the initial dust cloud is conserved. Which is to say that collisions between counter-rotating particles (opposite angular momenta) cancel most, but not all, of the apparent rotation of the dust cloud. This conservation of the "residual" angular momentum is what leads to the formation of the dust disc around the proto-star. As the particles in the disc coalesce into planets they retain the angular momentum. Unless I am mistaken, the Sun contains most of the mass of the Solar System but Jupiter contains most of the angular momentum.
Presumably something similar applies to galactic formation except on a much larger scale (and somehow we must account for Dark Matter). My guess is that the stars in the spiral arms account for most of the galactic angular momentum. (Can anyone confirm/contradict this?) I have no idea about the distribution of mass or angular momentum in elliptical galaxies. And of course all this should be detailed with General Relativity.
 
  • #12
fbs7 said:
Maybe it doesn't even make sense to talk about a total angular momentum of the galaxy?
It makes good sense to talk about the total angular momentum of a galaxy. It makes good sense to talk about the total angular momentum of a gas cloud from which it condensed. Going from the one state to the other, angular momentum is conserved.

You seem to perceive a contradiction in all of this but have not stated that contradiction plainly. Perhaps you reason that...

"The starting gas cloud is simply a random clump of gas and should have no rotation on average. After it condenses into a galaxy, the galaxy is observed to rotate and clearly has significant angular momentum. But angular momentum is conserved. How can this be?"

Is that your question?
 
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  • #13
fbs7 said:
Maybe it doesn't even make sense to talk about a total angular momentum of the galaxy?
Talking about angular momentum (and other conserved quantities) is still valid when relativity is in play: it is just the rules (equations) are slightly different.
 
  • #14
jbriggs444 said:
"The starting gas cloud is simply a random clump of gas and should have no rotation on average. After it condenses into a galaxy, the galaxy is observed to rotate and clearly has significant angular momentum. But angular momentum is conserved. How can this be?"

Is that your question?
Thank you! That's precisely the question! Very precisely put! How come something that looks very random and statistically should add to zero angular momentum end up so well organized and with a huge angular momentum. I can only imagine that mass is expelled and the expelled mass compensates (so that the total angular momentum of the galaxy + the expelled matter should still be zero, even if the galaxy itself is non-zero).

This is a question that dogged me for maybe 20 years; every time I see one of those science programs that shows a cloud collapsing into a rotating star (or galaxy, for the matter) I always think - "riiiiiight... there must be something missing there, but what is it"
 
  • #15
fbs7 said:
Thank you! That's precisely the question! Very precisely put! How come something that looks very random and statistically should add to zero angular momentum end up so well organized and with a huge angular momentum.
It starts with the same huge angular momentum it ends with.

The attractive statistical argument might be to imagine a bunch of constituent particles all with independent linear and angular momenta. By the law of large numbers, we might naively expect the total angular momentum to scale as individual angular momentum times the square root of the number of particles. But that expecation would be incorrect. The angular momenta are not independent. They are correlated. In any case, one would not expect the starting angular momentum to be precisely zero. It is sure to be non-zero.

In the final state, the galaxy is smaller in radius than the cloud of gas it originated from. The result is a higher spin rate for the same angular momentum.
 
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  • #16
Ohhhhhhh... that's amazing!

My thinking error is that I thought that after the big bang you would have a more or less uniform gargantuan cloud of gas... so any point you chose and any region you selected, the average average angular momentum would be about zero with minor fluctuations... but instead you need to have huge fluctuations everywhere in order for rotating galaxies to form, right?

What caused those big fluctuations in angular momentum over vast areas, that were needed for the first rotating galaxies to form?
 
  • #17
fbs7 said:
Ohhhhhhh... that's amazing!

My thinking error is that I thought that after the big bang you would have a more or less uniform gargantuan cloud of gas... so any point you chose and any region you selected, the average average angular momentum would be about zero with minor fluctuations... but instead you need to have huge fluctuations everywhere in order for rotating galaxies to form, right?

What caused those big fluctuations in angular momentum over vast areas, that were needed for the first rotating galaxies to form?

Take a look here

http://www.as.utexas.edu/astronomy/education/fall04/komatsu/lec_07.pdf

It also occurs to me that if a very large cloud of particles condenses into a much smaller object, then any relatively small component of angular momentum of the original cloud will magnify (in terms of rotational speed). And, in fact, the AM of the solar system may be relatively small. If you were to map that AM onto a huge cloud of dust, then the variation from a uniform distribution of AM among the constituent particles may be small.

In addition, if the dust cloud formed from two or more sources (with the particles coming in different directions), then that would naturally lead to a significant non-zero AM.
 
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  • #18
I see! So, it's like this, right? From A, a very smooth universe, to B, big blobs of gas with angular momentum, then to C, with well organized rotating galaxies?

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I understand how it goes from B to C, it's just gravity and conservation of angular momentum (with whatever corrections from general relativity). But how does it go from A to B, that is, from a smooth and uniform universe to one filled with galaxy-size blobs with random angular momentum? Can we explain that with gravity alone or do we need to introduce other tricks like dark matter to explain how it fluctuated that way?
 

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  • #19
Random initial fluctuations tend to grow over time as denser parts attract even more matter in a positive feedback loop. If the infalling matter is not perfectly isotropic it will in general lead to some angular momentum for the denser parts. Gravity and the randomness of quantum mechanics in the very early universe are enough to produce the structures we see today.
Dark matter plays a big role, sure, but not different from regular matter in that aspect. Dark matter clumps on the scale of galaxies and galaxy clusters, regular matter goes where the dark matter is.
 
  • #20
Ohhh... wow... I never thought of that! "If the falling matter is not isotropic!"... but I cannot visualize it, oh no!

The only way I can imagine this is by things flying by, say as a big blob A sitting quietly in some corner, then a trio of blobs B, C, D all fly by nearby and only C is captured by the gravity of A:

p1.png


As C is now in orbit around A, A got some rotation, while by conservation B and D will also somehow get some rotation around each other - so A would eventually form a galaxy rotating counterclockwise, while B creates one rotating clockwise. Is it something like this, but with gases? My diagram looks very much like turbulence caused by winds. So the early universe would need to have some kind of turbulence or some gas flows, both in vast scales, in order for these rotations to develop, is that right?
 

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  • #21
fbs7 said:
As C is now in orbit around A, A got some rotation, while by conservation B and D will also somehow get some rotation around each other
That is not how angular momentum conservation works.

Start by picking a reference axis. Any reference axis will work. Angular momentum is conserved no matter what axis you choose. Around this axis, A, B, C and D will all have some amount of angular momentum (possibly zero). Their angular momentum is computed based on two things.

1. How much angular momentum they individually have due to their own spin.

In this case, we can assume that A, B, C and D are not spinning. They have zero angular momentum from their own spin.

2. The vector cross product of their distance from the reference axis times the tangential component of their velocity relative to that axis.

In this case, A, B, C and D are all moving relative to one another. Unless one chooses a reference axis carefully, they will each have some non-zero angular momentum based on their linear motion.

Conservation of angular momentum means that if you add up the angular momenta for each object in a closed system about a fixed axis and avoid external torques the total will remain unchanged.
 
  • #22
Right, the total angular momentum of the system A+B+C+D will be exactly the same before, during and after the flyby, whatever coordinate system.

But the diagram referred to the angular momentum of the region around A relative to the center of A. Before that flyby the angular momentum of the region is zero, because it only includes A, and A doesn't rotate. After the flyby and B+D moves far away, the region around A now has A+C, and the angular momentum is now non-zero, because C is rotating around A. So that region went from zero angular momentum to a non-zero angular momentum, due to gravity alone, and that's compensated by a change in the angular momentum of the region around B.

So, before the flyby, if the region around A should collapse into a galaxy, that would be a galaxy with zero or very small angular momentum, but after the flyby and capture of C, if the region around A collapses into a galaxy, that would be a nicely rotating galaxy, as that region now has a good angular momentum provided by the "falling" of C into the region A.

That kind of off-center collision is the only way I can visualize a scenario that "infalling matter that is not perfectly isotropic causes an increase in angular momentum for the denser parts". What a wonderful and mysterious statement! I wish the Science Channel would have some programs that would show that, instead of just going from "voila that was a blob of gas, now it's a rotating galaxy!".

By the way, I appreciate everybody's patience and kindness with me old fool here.
 
  • #23
fbs7 said:
But the diagram referred to the angular momentum of the region around A relative to the center of A. Before that flyby the angular momentum of the region is zero, because it only includes A, and A doesn't rotate. After the flyby and B+D moves far away, the region around A now has A+C, and the angular momentum is now non-zero, because C is rotating around A. So that region went from zero angular momentum to a non-zero angular momentum, due to gravity alone, and that's compensated by a change in the angular momentum of the region around B.
The region went from zero angular momentum to a non-zero angular momentum because we are not dealing with a closed system. We drew lines around the system such that C flew in and did not fly out. [Obviously, system B+C+D lost an equal amount of angular momentum when C went away and it became system B+D]

Gravity did not do that. Under the influence of gravity alone, C would [in this case] have flown back out. Something must have acted to slow C down while it was near A.
 
  • #24
I see... invalid scenario then. How about this one: a small mass is falling into a gas cloud A, and once it's inside the gas cloud it is slowed down by the gas. If it was all, then the gas cloud A wouldn't change it's angular momentum as the small mass would fall straight to the center.

But, if there's another gas cloud B in the path of that small mass, then the mass will not fall into the center of A, but off-center as B will pull it a little bit. With this the little mass is falling into A, will become part of A as it slows down due to friction, but because the blob B pulled it off-center, that will increase the angular momentum of gas cloud A (although the total angular momentum of the whole universe remains the same). Does this show how a "non-isotropic falling mass increases the angular momentum of the denser parts"?

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  • #25
fbs7 said:
I see... invalid scenario then. How about this one: a small mass is falling into a gas cloud A, and once it's inside the gas cloud it is slowed down by the gas. If it was all, then the gas cloud A wouldn't change it's angular momentum as the small mass would fall straight to the center.
OK. In this case you have the mass falling directly radially inward so that its angular momentum is zero to begin with. So even though we have drawn the lines around our system so that it is open, the addition of A to the system does not change its total angular momentum.
But, if there's another gas cloud B in the path of that small mass, then the mass will not fall into the center of A, but off-center as B will pull it a little bit. With this the little mass is falling into A, will become part of A as it slows down due to friction, but because the blob B pulled it off-center, that will increase the angular momentum of gas cloud A (although the total angular momentum of the whole universe remains the same).
So this time the mass started off radially infalling with zero angular momentum. It was deflected by B and picked up some clockwise angular momentum. By Newton's third law, B was also deflected and picked up some counter-clockwise angular momentum. The mass gets captured by A and A's angular momentum increases as a result. Meanwhile, B flies off carrying away its counter-clockwise angular momentum.
Does this show how a "non-isotropic falling mass increases the angular momentum of the denser parts"?
I am not sure. It seems like loaded phrasing.

We definitely saw how adding something with clockwise angular momentum to something with zero angular momentum yielded something with clockwise angular momentum.
 
  • #26
Yay! Now I can visualize how mass falling into a big glob of gas will cause that gas to rotate! It seems this has two parts to it:

(a) The falling stuff needs to have some kind of off-center assymetry
(b) The falling stuff needs to be slowed down by the gas in order for it to be captured by the gas

So,

variations in density in the gas + gravity + slowdown due to friction = rotating mass of gas --> rotating galaxy!

That's excellent! I learned something! Thanks so much! You think that "slowdown due to friction" is really necessary for that?
 
  • #27
The process is more effective if the additional mass is caught (doesn’t have to be actual friction, scattering of stuff works as well) but you can have a transfer of angular momentum even if the whole object escapes again: Torque from the gravitational interaction and tidal effects make it possible.
 
  • #28
I see! Now I kinda start to get it!

Thank all again! This whole thread was full of excellent-level explanations, without the need to be accepted into a university for them! That's fantasitc!
 
  • #29
fbs7 said:
How about a gas cloud collapsing into a star? Do we believe that most of the mass of the gas cloud collapses into the star, or do we believe that a good part of it is expelled?
...
Most of the gas cloud is ejected. Giant molecular clouds can have million of solar mass. The biggest star we have found is R136a1 which has a little over 300 solar mass.
Herbig-haro objects are worth reading about.
 
  • #30
I see; so there are multiple reasons why these gas clouds end up rotating into a star or a galaxy?

(a) The original gas cloud has some initial angular momentum, which is conserved and increases rotation as the radius decreases
(b) Infalling material has attrition with the gas and slows down, which causes the gas rotate
(c) Non-symmetry of infalling material causes rotation all by itself
(d) Material is ejected (or scattered) with angular momentum, and that also causes rotation in the cloud
(e) The whole thing is relativistic, so these are not easy equations

The whole thing seems quite complicated now! No wonder the Science Channel just shows "big blob of gas" then "zap, rotating star or rotating galaxy!".. the "zap" thingie seems quite complex!
 
  • #31
And I was hoping I could just say... L = m.r.v... a-ha, I caught you! :D... I'm wiser now
 
  • #32
fbs7 said:
(e) The whole thing is relativistic, so these are not easy equations
Relativistic effects should be negligible.
 

1. What is galaxy formation?

Galaxy formation refers to the process by which galaxies, the large-scale structures in the universe, are created. It involves the merging of smaller structures, such as gas clouds and stars, to form larger and more complex systems.

2. Does galaxy formation conserve mass and angular momentum?

Yes, galaxy formation does conserve mass and angular momentum. This is due to the laws of conservation of mass and conservation of angular momentum, which state that these quantities cannot be created or destroyed, only transferred or transformed.

3. How does galaxy formation conserve mass and angular momentum?

Galaxy formation conserves mass and angular momentum through various physical processes, such as gas accretion, star formation, and mergers. Gas accretion involves the accumulation of gas from the surrounding environment, which contributes to the overall mass of the galaxy. Star formation also adds to the mass of the galaxy, while mergers between galaxies can transfer mass and angular momentum between them.

4. Are there any exceptions to the conservation of mass and angular momentum in galaxy formation?

While galaxy formation generally follows the laws of conservation, there are some exceptions. For example, in rare cases, galaxy collisions can result in the ejection of material from the galaxies, which can disrupt the conservation of mass and angular momentum. However, these cases are not the norm and do not significantly impact the overall conservation of these quantities.

5. Why is it important to study the conservation of mass and angular momentum in galaxy formation?

Studying the conservation of mass and angular momentum in galaxy formation is important because it helps us understand the fundamental laws of physics that govern the universe. It also allows us to better understand the processes that shape and evolve galaxies, which can provide insights into the formation and evolution of the universe as a whole.

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