How do globular clusters stay globular?

Michael Richmond
Dec 10, 2000

Originally posted to sci.astro on Dec 10, 2000.

Robert Lane writes:

> ... how do globular clusters stay globular? 
>    So, ok, the primordial cloud was inhomogeneous, had turbulence 
> (from what?). If that primordial cloud, in toto, had any net 
> rotational velocity, it seems to me the resulting globular cluster 
> would have collapsed by now into a disk--like solar systems and 
> spiral galaxies. GCs haven't collapsed into disks, so their 
> primordial clouds had no net rotational velocity. 

This is not quite true. We can observe the motions of stars within globular clusters, and we find that some globular clusters _do_ have a significant net rotational velocity, while others do not.

Why didn't the rotating globular clusters collapse into disks? The magic word is "dissipation". A rotating cloud of gas consists of particles which

  1. interact strongly with each other (colliding physically) on relatively short timescales
  2. can radiate away some of their energy and momentum by emitting photons

For both of these reasons, a dense cloud of rotating gas _will_ collapse to form a rotating disk, on timescales of, um, something like 10^5 to 10^7 years -- shorter than the age of the universe so far.

On the other hand, if the gas in a cloud forms stars very quickly, so that the particles in it are _stars_ rather than atoms, then these stellar "particles"

  1. do not interact strongly on short timescales (the time between direct collisions for a star in a globular cluster is > 10^10 years)
  2. can NOT radiate away their energy and momentum by emitting photons; they can emit gravitational radiation, but that's not as effective

For these reasons, a spherical cluster of stars will remain spherical for very long periods of time; much longer than the current age of the universe.

> 1) There oughta be, or have been, "disk clusters", mini-spirals, 
>    representing primordial clouds that had some net rotational velocity.

Perhaps you mean "clouds of gas which collapsed into disks, and then formed stars." We don't see any "flat" clusters, as far as I know. I suspect that a) star formation may not work very well in a flat disk of the typical globular cluster mass (just a wild guess), and b) small flattened systems of stars aren't dynamically stable on timescales of 10^10 years (not a wild guess).

> 2) Assuming it's possible to measure proper motion in GCs, the 
>    elliptical orbits oughta be detectable.

Oh, yes, we can measure the proper motions of stars in some globular clusters -- with a lot of work. Go to the ADS Abstract Service:

and search for "globular cluster proper motion stellar" in the "Abstract Text" box. One of the articles you will see is "Internal Motions in Globular Clusters", by Ivan King and Jay Anderson at UC Berkeley (Hi, Jay, if you're reading this!). From the abstract:

Recent advances in astrometric techniques now make it possible to use HST WFPC2 images to measure proper motions of individual stars in many globular clusters. These proper motions have an important impact both on the dynamics of the clusters and on their distance scale.

Previously, only radial velocities were available. From them two of the three components of the cluster's rotation can be measured, and anisotropy of the velocity ellipsoid of the brighter stars can be estimated from a comparison of observed velocity dispersions with those predicted by a model that is based on isotropic velocities. From proper motions, however, anisotropy can be measured directly by comparing proper-motion dispersions in the radial and transverse directions. Moreover, such measurements can be extended to low-mass stars for which anisotropy measurements have not previously been possible. Radial variations of the radial-direction dispersion also offer a further check on the modeling. Finally, measurement of the mean velocity of cluster stars with respect to distant background objects gives the plane-of-the-sky component of cluster rotation.