, where h=3.8 kpc, and Σ_{0}=6.725 x 10^{7} solar luminosities/kpc^{2}.

h is some scale height.

Σ

What does that mean?

Let's start from the beginning.

You have your galaxy, NGC 2742:

Obviously, it gets dimmer towards the edge. We are dealing with surface brightness here, which is how much light comes from some area of the galaxy. It is typically assumed that surface brightness can be modeled with a decaying exponential. That means that going out one particular radius, the brightness in each same sized area patch dims as you move outwards. It starts from some high point, Σ

To create our integrated surface brightness profile, we need to integrate that function over radius. Since we're taking account all the brightness inside, we also need to take into account the fact that the galaxy is a disk. That means integrating over the entire circle (thus the 2πr in the below integral).

If you know more math than I do, you will see that this can be integrated by parts and the result is:

(Sorry about all the math, that's just the easiest way to explain the curve in this case.)

In particular, Σ

Persic, M., Salucci, P. 1988, MNRAS, 234, 131

Yep, we took the easy way out. Andrew West claims that you could use pictures from the Sloan Digital Sky Survey (SDSS) to create a surface brightness profile. While I admit that it wouldn't be hard to just plot how the brightness falls off with area (thereby getting real values for our two parameters), it would be a trigonometric mess to try to photometrically integrate over the concentric rings to find an integrated surface brightness profile. There might be some simple trick that aleviates the problem I'm talking about. Anyways, it was reasonably easy to look on NED to find the reference mentioned above.