If gravity is attractive, why doesn't the Milky Way contract?

Question

Einstein introduced the cosmological constant because without it, one cannot get a static universe - gravity would cause the universe to contract.

Given that, why is the Milky Way not contracting? For that matter, why isn't the Solar System contracting? It can't be because of dark energy, because dark energy's effect shouldn't manifest within over such short distances.

I'm guessing that the answer has something to do with rotation - after all both the Solar System & the Milky Way are rotating. However, the obvious "to conserve angular momentum" answer doesn't seem applicable, since the Milky Way (Solar System) could both collapse and conserve angular momentum as long as there is a very fast-rotating central black hole (Sun).

Answer 1

Both energy and angular momentum must be conserved.

In the case of the Milky Way (and the Solar System), a more compact configuration would have a numerically smaller gravitational potential energy.

This means that get to the more compact configuration would require the system to lose energy. The question then, is how can that energy be lost and on what timescale?

In neither the cases of the Milky Way, where stars orbit in a collisionless fashion through a very sparse interstellar medium, or the Solar System, where planets orbit without direct interaction, is there an energy loss mechanism that is rapid enough to bring about significant contraction on interesting timescales.

In terms of cosmology - the idea of introducing a cosmological constant to get a static universe applies on cosmological scales when the matter is assumed to be isotropic and homogeneous and it only considers gravitational interactions. The applicability of some sort of scaled expansion or contraction of the universe on scales smaller than gravitationally bound structures is questionable and you can find several duplicates of that on Physics SE. However, we do know that energy within a closed system like the Solar System or the Milky Way must be conserved, so any contraction must be "paid for" by shedding that energy somewhere.

As a final point, both energy and angular momentum must be conserved. In Newtonian physics and GR, the components of the Milky Way and Solar System cannot move into more compact configurations without losing angular momentum as well as energy. Even the hypothesis that the Solar System could ultimately turn into a fast-spinning black hole requires both energy and angular momentum to be lost. The angular momentum of the Sun is about $J = 2\times 10^{41}$ kg m$^2$ s$^{-1}$. A maximally spinning black hole has $J = GM^2/c$, which is $ 8\times 10^{41}$ kg m$^2$ s$^{-1}$ for the mass of the Sun. Thus, whilst the Sun could collapse to a black hole whilst conserving angular momentum, it could not take the rest of the Solar System with it, because there is about 4 orders of magnitude more angular momentum in the Solar System as a whole, with very little additional mass.

Answer 2

If all the planets in our solar system, and all the stars in the Milky Way, were to all contract into a smaller volume, we would have a huge loss of energy and angular momentum. These are conserved quantities, and so what you suggest would contradict the laws of conservation of energy and angular momentum.

First, you are correct in that planets continue to orbit the sun to conserve angular momentum. It is thought that the solar system began with a cloud of essentially gas and dust that over time condensed to form the planets and our sun. As this cloud began to collapse inward, all this matter began to settle into a spinning disc with a big lump in the center: the Sun. Further collapsing caused the formation of the planets. This process is called accretion. The point is, there was angular momentum present back then, and so there still is (conserved) now, meaning that the planets must maintain their stable orbits (and the sun keeps its own rotational angular momentum, as do all the planets as well).

The formation and motion of the Milky Way also relies on conservation of angular momentum (and energy and linear momentum), for objects in motion within it, though their formation is more complicated, and this time we have many stars (and perhaps planets revolving around them) revolving around the center of a black hole. Universal expansion probably has a little to do with the galaxy itself expanding from its center, though relative to the general expansion of the universe (that causes galaxies to move away from each other), the Milky Way is moving at $\approx 600 km/s$.

Whether dark energy is a significant contributing factor is unknown (I am not aware of any experiments or data that suggest dark energy causes some of the stability - or even expansion - of our galaxy or solar system), though its behavior on cosmological scales is more obvious (if it truly exists).

since the Milky Way (Solar System) could still collapse as long as there is a very fast-rotating central black hole (Sun).

A black hole is destructive only when bodies are close to the event horizon. A black hole from a great distance away is just like any other object that has the same mass. It will not crush things into it from such distances. Its gravitational force behaves the same as anything else with similar mass. If the sun was suddenly turned into a black hole, apart from darkness, nothing else would happen, and the Earth and all planets would continue to orbit it in exactly the same way as before this happens. The same logic would also apply to our galaxy with a black hole in the center of it. Black holes are destructive (in the sense of crushing things into them) only in regions close too, or at the event horizon.

Answer 3

One can think of a galaxy as an oversized accretion disk of its central black hole.

Eventually, in quite distant future, inner part of the galaxy matter will be accreted, outer part of it will carry away the extra angular momentum. Possibly, some of the matter will be thrown away by the polar jets. The extra energy will be radiated away as heat.

On the other hand, the timescale of this process is way longer than the presently accepted universe age.