What is the origin of spin of celestial objects?

I asked the question because I did not believe in the accepted answer that has been sitting for more than 3 years.

I have my own understanding, but since it is not good practice to put it with the question, I am posting it as one possible answer.

My problem is that I do not believe the first statement quoted in the question which is contradicted by the second quoted statement. If there is such a thing as angular momentum conservation, I do not see why assymetry alone should produce angular momentum on the assymetric structure.

If the cloud is isolated, it should collapse - period. The assymetry may possibly create some internal spinning (adding to zero angular momentum), but certainly not any global spinning, no global angular momentum, as clearly stated in this first statement.

What can induce spinning in the collapsing cloud is (gravitational) interaction with other external structures. And it is a fact that such external structures always exist. That may be obvious for the author of the answer, or professional astrophysicists, but it is certainly not obvious for laypeople. Hence I do consider this answer misleading at best.

Furthermore, if such external interacting structures exists as they must, then the asymmetry hypothesis is no longer needed, as it will be created by these interactions.

Angular momentum can be "created" only by exchanging angular momentum with another body, so that each gets one of two opposite angular momenta, that sum to no momentum. Then each can go its own way. Of couse, there is globally no creation of angular momentum.

I am not quite sure about the dynamics of the phenomenon, but I can see no other explanation. This kind of interaction is frequent between moving bodies, for example through tidal effect.

Restarting from this questionable answer, I have been wondering whether it can occur within a structure of clouds with asymmetries, initially at rest, both internally and with respect to each other.

What follows is intuitive and speculative, as I do not know how to deal with the problem mathematically.

My own idea of how it could occur, very intuitively and informally, is that when two clouds are both collapsing to their own centers of mass, gravitational attraction of cloud A will slow down the collapse of the closest parts of cloud B (and conversely), so that the center of mass will move, and the the velocity of the collapsing cloud components going no longer through the center of mass, they have acquired angular momentum with respect to that center of mass, which does initiate the spining. Then indeed, the collapse will increase the spin. The symmetry of the phenomenon with respect to the median plane (assuming symmetrical clouds to simplify) applies also to the angular momenta induced in each cloud, so that they get opposite angular momenta, and opposite spin.

So all you need to get started would be inhomogeneity in a motionless cosmic cloud, that lead to collapse of subparts to their center of mass, while being distorted by neigboring subparts. This create spin, from which we get higher speeds as the cloud parts keep collapsing.

This is my own intuitive reconstruction. Hence do not trust me unless it is confirmed by professionals. My problem is finding one who would address/answer this question

There is an angular momentum problem with regard to star formation, but you have the sense of the problem completely backwards. The problem is not where the angular momentum arises. The problem is where does it go.

Gas clouds a tenth of a parsec across have been routinely been observed to rotate at about one revolution every five or ten million years or so ($\Omega \approx 3\times10^{-14}$ radians/second). That's about 30 or 40 times faster than the mean galactic rotation rate. Those interstellar gas clouds interact gravitationally with one another and with nearby stars. The gravity gradient torque across a tenth of a parsec exerted by a nearby gas cloud or star can easily build up that tiny rotation rate.

That rotation rate sounds tiny, but it's not. Were the entire gas cloud to shrink to a star and conserve angular momentum along the way, the star would necessarily be spinning at about two revolutions per minute. The star could not form! This is the crux of the angular momentum problem.

The old nebular hypothesis (from the mid 18th century) regarding the formation of the solar system had huge problems with angular momentum, so huge the theory was discarded. The revived version of the hypothesis (1970s) is now the dominant theory regarding star and planetary formation because it has solved the angular momentum problem to some extent. The solution isn't complete; some problems with angular momentum remain. "Where does it go?" remains a partially unanswered question.

You could start from the premise that there was not 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... I'm not repeating all this.

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 (not my field) I think 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 J.

Edit: 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.