[antognini]

I had not seen that xkcd article before! Thanks! It's the most lucid explanation of the problem that I've seen.

The only other interesting surface-brightness-related fact I can think of at the moment is that surface brightness fluctuations can be used to measure the distance to galaxies. This is one of the cases where it helps to have a really big telescope.

The basic idea is that although galaxies are extended sources, they're really just a collection of point sources --- they're just a bunch of stars grouped together in an area of the sky. Now suppose you have two similar galaxies (at least they have similar stellar densities) and one of them is close by and the other is far away. The nearby galaxy will have relatively few stars per pixel and the distant galaxy will have many more stars per pixel. Since the stars are randomly distributed, the number of stars in any given pixel will be given by a Poisson distribution. A consequence of this is that in the nearby galaxy there will be a lot of variation in the flux from one pixel to the next, whereas in the distant galaxy the image will be much more smooth. So even though the average flux per pixel from both galaxies is the same, you can still tell which one is close and which one is distant based on the surface brightness fluctuations.

[sandworm101]

But without actually imaging stars, how do you know that two galaxies have similar stellar densities? The OP was about low-star/high-darkmatter galaxies. I guess you would have to hope that the entire thing was rotating, and at an angle, that doppler effects could determine the size/mass.

[antognini]

That's where you have to make some assumptions given the galaxy type. As with a lot of distance techniques in astronomy, there is a lot of uncertainty. This is one of the reasons that surface brightness fluctuations are not a very popular method.