# The most simple explanation for origination of spiral galaxies?

1. ### Edward Solomo

72
We know that there exists no such thing as a "rigid" substance in relativity.

Now suppose we had a disc of uniform density the size of the Milky Way. When the "core" of the galaxy starts to rotate, the effects (tidal and gravitational) of this rotation propagate at the speed of light, which is VERY slow compared to the size of entire galaxy. It takes 40,000 years for the effects of the core to be felt by the extremities of the arms!

Thus, even the most rigid solid possible, neutronium or quark/strange matter, would experience a "bending", resulting in the disc deforming in a spiral fashion. However, this alone doesn't account for the observed spiral structure, but it provides for the "first half" of the theory. We still haven't accounted for the diminishing effect of gravity/tidal forces from the core to the surface via distance.

Now, if we consider the galaxy as it actually was, a disc of gas, gas is very far from being rigid, the only "container" of the gas is the gravity of the entire mass as whole. When the core of this disc starts to rotate, and the effects of the core also DIMINISH with distance by the inverse square, we don't result with a continuous set co-centric rings orbiting the core at different speeds, whose speeds decrease linearly with the radius, but we end up with co-centric rings whose orbiting speeds decrease with the inverse square of the radius.

As the co-centric rings merge and separate from their neighboring co-centric rings, they will form into "arms" whose segments will be orbiting at different speeds about the core, becoming more and more spiral, with each revolution widening the total spiral arc of each arm. Initially, there should be MANY arms.

After enough revolutions (old galaxies), different arms will come in close proximity, causing a local gravitational effect, causing arms to collide and merge, decreasing the number of observed arms, and creating VERY WIDE ARCS. These would be BARRED SPIRAL GALAXIES. Eventually you should be left with two "parallel" arms.

What's nice is that we don't need this fictional dark matter to explain these structures, just stir a cup of coffee from the center, and observe its spiral structure. This is where I got the idea. The liquid of the coffee was from from being rigid, sot he kinetic transfer between the cylindrical axis of the cup to the cylindrical surface area of the cup took quite some time. Now replace Kinetic energy with gravity/tidal forces and you can see how it would effect entire galaxies in a similar way.

### Staff: Mentor

40000 years are extremely fast relative to the evolution of galaxies, which happens at the timescale of billions of years.
There is no non-rotating galaxy, where a core could suddenly "start" to rotate.
In addition, gravity does not care about (slow) rotations, there would be no reason for the other parts to join the rotation.
You do not need special relativity to argue that the galaxy is not rigid - the galaxy is mainly empty space with a few particles inside. It is very close to an ideal gas.

Consider the rotation speed, given by the condition that gravity provides the centripetal acceleration for a circular motion: in general, the angular velocity will depend on the radius. Something spiral-like is quite natural, if you have some initial density fluctuations.

3. ### bossman27

204
As far as I know, spiral galaxy structure is not cited as direct evidence for dark matter to begin with. In addition to several other areas of observation, however, DM provides a particularly nice solution for the galaxy rotation problem. For a generic spiral galaxy, assume we can derive the amount of luminous matter, $M_{lum}(R)$ enclosed at a radius $R$. We can then write:

$v_{lum}^2(R) = \frac{GM_{lum}(R)}{R}$
[this is a simplification since luminous matter really has an oblate distribution, but it works in this context]

For a circular orbit at radius $R$ which lies outside a large portion of the mass distribution, we would expect to approach the Keplerian case where $v_{lum}(R) \propto \frac{1}{\sqrt{R}}$. What we actually observe is that $v_{c}$ is constant out to a very large radius. The corresponding "flatness" of the rotation curve is depicted here (sorry for the size, I'm not sure how to scale a picture from a link):

If we write the first Keplerian equation above for total mass and velocity, we have:

$v_{c}^2(R) = \frac{GM_{tot}(R)}{R}$

Then combining the two with $M_{dark}(R) = M_{tot}(R)- M_{lum}(R)$ gives the DM distribution:

$M_{dark}(R) = \frac{R}{G} \left[v_{c}^2(R) - v_{lum}^2(R)\right]$

The sharp rise and then constant value of $v_{c}$ implies a flat density profile of DM in the inner region, becoming $\rho \propto R^{-2}$ at larger radii. This also gives a corresponding halo mass profile of $M \propto R$, usually extending at least past the edge of the visible matter disk, so that we can only estimate a lower bound for the size of the halo.

With regard to spiral galaxy structure, it's actually thought that spiral arms are quasi-stationary density waves, whose velocity does not coincide with the rotational velocity of the stars. An analogy might be sound waves, where the velocity of the pressure wave is by no means the velocity of air molecules.

Side Note:
There's a formulation of gravity called MOND that accounts for rotation curves without dark matter by modifying Newtonian gravity when acceleration is less than a constant $a_{0} \approx 10^{-10} m/s^{2}$. You might find it interesting, but know that most astrophysicists don't take it very seriously -- it doesn't account for gravitational lensing or any of the other observational evidence for DM, and it's essentially derived from data fitting, without giving any explanation of an underlying mechanism that could account for it.

4. ### Chronos

10,133
The primordial gas cloud which became the milky way was already rotating as it coalesced, as noted by mfb. This is an inevitable consequence of gravitational collapse. Assuming the dark matter halo was already in place [which appears probable], it is reasonable to assume its rotation was approximately the same as it is now by the time it reached its current size. The initial gas cloud was probably a spheroid that gradually flattened out into a disc.