Why are galaxies flat since it's an unstable configuration in 3d?

Question

I'll probably have to delete this question because someone's already asked it, but what accounts for the stable 2-d structure of spiral galaxies in three dimensional space (assuming random starting vectors)? The traditional centrifugal force answer doesn't account for the fact that purely Newtonian $n$-body simulations never evolve into flat disks.

Is it actually suggested that there is some non-Newtonian process to account for this? Or that spinning galaxies throw out stars from the center? I keep hearing a lot of bullshit.

[Edit: I'm keeping this answer for now as it is spurring some interesting discussion.]

Why do you say n-body simulations give the wrong results? The EAGLE simulation has done very well in producing the observed galaxy structures. — John Rennie, Sep 25 '15 at 05:30
Well, I've run n-body simulations in 3-d. Anything above 2 bodies gives non-planar results and is unstable. — Mark Janssen, Sep 25 '15 at 05:33
Well, like I say, anything above n=2 gives non-planar results. — Mark Janssen, Sep 25 '15 at 05:37
No, the values of $n$ you've used give non-planar results. Large scale simulations such as EAGLE give realistic results. Note that EAGLE use billions of particles. You won't get a decent treatment of phenomena like dynamical friction unless you work at this scale. — John Rennie, Sep 25 '15 at 05:40
See also Why doesn't my particle simulation end in a flat disc? and Why do 3d spheres and gravity tend to rotating discs on one plane? I'll note that galaxies consist of hundreds of billions of stars, so $n=3$ or even $n=1000$ isn't realistic. Also, there are all sorts of subtleties in the numerics (did you expect perfect flatness? are you using the right integrator? did you soften the potential?). — , Sep 25 '15 at 05:40
EAGLE is not just an N-body simulation, it is a _hydro_simulation, meaning that energy can dissipate from hydroforces, relaxing the galaxies into disks. Pure N-body cannot do that (which is what I think TheDoctor is referring to), since the particles only interact graviationally, so they can only relax kinematically. This is much less efficient, so the halos tend to stay spherical-ish. — pela, Sep 25 '15 at 08:09
Note too that it isn't a "2D structure" -- it's flattened, not flat, and even that is more a density function than a constraint. — keshlam, Sep 25 '15 at 10:07
@pela: What principle of Newtonian Mechanics allow galaxies to "relax" into disks? — Mark Janssen, Sep 25 '15 at 11:23
@keshlam: Of course it's not a constraint. That's part of my point. — Mark Janssen, Sep 25 '15 at 11:26
Voting to close as a duplicate, as the accepted answer here carefully explains that your few-body simulations are missing the dust component that will produce the results you expect. — Emilio Pisanty, Sep 25 '15 at 11:41
@TheDoctor: There are several mechanisms that can come into play; phase mixing, chaotic mixing, violent relaxation, and Landau damping. I wrote an answer about this at some point, but I can't seem to find it. But have a look at Sec. 5.5 in Mo, Bosch, & White's Galaxy Formation and Evolution about collisionless relaxation. — pela, Sep 25 '15 at 12:17

score 0 · Answer 1 · answered Sep 25 '15 at 12:01

This answer possibly isn't at the level that you would like, but I'm inclined to write it anyway because it's a good introductory answer. In the event that that this question does merge as duplicate, I'll probably just move my answer over there (as this is slightly different than the posted answers).

First, watch this Minute Physics video as it provides a great explanation of why any rotating, disc-like object (the Solar System, galaxies, etc) tend to be roughly two-dimensional (disc-like). The bodies begin as a collection of rotating, colliding particles. Because the momentum in the $z$-direction is roughly zero, collisions among particles will conserve the $z$-momentum at zero. The preferred way for a system to do this is for the particles to collapse into a flatter distribution. However, Conservation of Angular Momentum dictates that the matter continues to rotate.

So this answers your question as stated, but you seem to actually be more concerned with why this can't be well-modeled. I suppose the unsatisfying answer is that the universe, and the matter within it, is a much more complex place than what your typical $n$-body simulation is capable of producing. The Milky Way galaxy contains 100 billion stars, not to mention other types of objects as well.

Thank you. However, why the assumption that there is hardly any momentum in the z-direction? In simulation, the bodies start with a random initial (3-d) vector. But do agree (and can only conclude) that the Universe is indeed a much more complex place than physics has imagined. — Mark Janssen, Sep 25 '15 at 12:09
An n-body simulation with 100 billion stars would not collapse to a disc because they do not (often) collide. Hence elliptical galaxies. — ProfRob, Sep 25 '15 at 15:56

Why are galaxies flat since it's an unstable configuration in 3d?

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