Ken G said:
I wonder if the main cause is just randomness, or if there is a systematic trend.
There is a systematic trend.
The main kinds of galaxy scale structures can be strictly arranged in order of galaxy mass with almost no overlap between the catagories - dwarf galaxies always have less mass than spiral galaxies which always have less mass than elliptical galaxies which always have less mass than galactic clusters.
For spiral galaxies, this is the Tully-Fisher relation,
https://en.wikipedia.org/wiki/Tully–Fisher_relation and for ellipical galaxies it is the Faber-Jackson relation,
https://en.wikipedia.org/wiki/Faber–Jackson_relation The formal relations relate rotational velocity to luminosity. But, luminosity is an excellent proxy for aggregate baryonic matter (because the vast majority of mass in a galaxy is from stars and the amount of non-star matter is roughly proportional to star matter) and the amount of inferred dark matter in a halo can be inferred from a galaxy's rotational speed. There is also systemic deviation from the Faber-Jackson relation based upon the extent to which an ellipical galaxy is spherical or not. Less spherical elliptical galaxies have more dark matter than more spherical ones relative to their baryonic matter. There are also characteristic proportions of dark matter relative to baryonic matter in galactic clusters and in dwarf galaxies (where the proportion is particularly high).
Romanowsky notes more systemic relationship.
http://arxiv.org/pdf/1207.4189.pdf as does Disney
http://www.nature.com/nature/journal/v455/n7216/abs/nature07366.html
There are two ways of explaining dark matter phenomena.
One is to modify the law of gravity in a way that corresponds to the observed systemic relationships more or less directly. In this case, the modification to the laws of gravity produces a precise amount of dark matter equivalent impact on gravitational dynamics for any given ordinary matter distribution. Roughly speaking, dark matter effects are observed below a particular threshold of weakness in weak gravitational fields.
The other is to hypothesize that there is dark matter and to devise a way that a universe with the right amount of dark matter naturally tends to produce a spectrum of galaxies in which the size and the shape of the galaxy is related to the amount of dark matter in that galaxy because of the role that dark matter and gravitational interactions between dark matter and ordinary matter (which go both ways) have on the evolution of galaxies of a particular size.
One heuristic way to describe this process is that a certain amount of baryonic matter in a particular configuration can anchor a certain amount of dark matter, and the baryonic matter tends to push the dark matter towards a non-spherical distribution, while the dark matter tends to shape galaxies of a particular size into a particular form. But, there is not a full consensus on the dynamical process that causes dark matter and ordinary matter to co-evolve their structure in a way that shows such pronounced systemic trends. There are serious criticisms of the way that this in models in the computer models used to compare how the universe would look with a particular kind of dark matter in it to the observed universe.
