How do stars or galaxies get their spin?

It is my understanding that when a star, a planetary disk, or a galaxy forms, the rotational momentum of the whole system is conserved.

Due to the smaller size of the resulting object, it will spin with a significantly higher speed than the original nebula.

What I do not understand is where the original rotation comes from. Why should a random dust cloud have an overall spin? Wouldn't the impulses of all particles in the cloud tend to average each other out?

Is there some alternative source of spin or a reason why nebula have an inherent spin?

You could start from the premise that there was no net angular momentum in the universe at all; but it would still be the case that everything of interest was spinning.

On the scales of stars and planets there are (at least) two important mechanisms that result in individual systems having angular momentum. The first is turbulence. If you take a parcel of turbulent gas from a giant molecular cloud it will always possess some angular momentum, even if the total cloud does not. As the parcel collapses to form a star/planets conservation of angular momentum $J$ and dissipative interactions result in an ncrease in spin rate and collapse towards a planar geometry.

Second, stars form in clusters. There is interaction between stellar systems early in their lives. Again, the cluster may have little net J, but groups of stars can, relative to their own centre of mass frame.

On bigger scales (galaxies) the second of these explanations becomes more important. The interaction and accretion of galaxies is what gives individual galaxies a spin, even if the clusters they are born in have much less or even no net angular momentum.

As an example of how turbulent velocity fields lead to gravitational condensations containing angular momentum you could do worse than study the star formation simulation performed by Matthew Bate and collaborators. These simulations start off in clouds with zero net angular momentum, yet produce a host of stars with swirling accretion disks, binary systems of all shape and sizes etc. An example journal paper can be found here: http://adsabs.harvard.edu/abs/2009MNRAS.392..590B Here is a web page where you can download the animations and study them at length http://www.astro.ex.ac.uk/people/mbate/Cluster/cluster500RT.html

Turbulent clouds are by their nature random and stochastic in terms of their motions. Often the velocity field is defined in terms of a power law dependence on spatial scale. The formation of vortices is a characteristic of turbulent media. They can be produced in the absence of external forces. The vortices contain angular momentum.

It is also worth noting that not all galaxies have an appreciable spin. Spiral galaxies do, but many elliptical galaxies have little net rotation. See https://physics.stackexchange.com/questions/93830/why-the-galaxies-forms-2d-plane-or-spiral-like-instead-of-3d-ball-or-spherica

Any gaseous object has some spin, usually acquired by interactions with other objects. For example, (proto-)galaxies torque each other to acquire a low rate of angular momentum. Initially, this spin is rather low in the sense that it does not dominate the dynamics: the energy in rotational motion is small compared to other energies, typically by a factor $\sim100$.

However, energy can be lost via dissipation (and ultimately radiated away), while angular momentum (spin) is much harder to get rid off. That's why rotating gaseous objects eventually form a disc-like configuration (galactic and proto-stellar discs). In these discs, the kinetic energy is dominated by the rotation. Such systems can only significantly evolve if angular momentum can be exchanged and/or transported. For example, the formation of a star from a proto-stellar disc is promoted by (outwards) angular-momentum transport within the disc. The newly born star retains some residual spin, but that is no longer dominating its energy (otherwise the star wouldn't be near-spherical by disc-like). The same essentially holds for planets.

• I guess I do not see how an arbitrary gaseous object can have spin. Wouldn't random interactions with other objects tend to cancel out? It seems similar to expecting large-scale objects to move because of brownian motion. – HugoRune Jan 25 '15 at 19:40
• @HugoRune I edited the question somewhat, but yes, it is somewhat similar to the Brownian motion, except that the expectation value is much larger. Don't forget that the ISM is not smooth, but has structure on many scales (while a gas has only the molecular structure and is smooth on larger scales up to macroscopic scales, when there may be structure again). – Walter Jan 26 '15 at 8:44