The de Vaucouleurs' Profile (or de Vaucouleurs' Law, or R To The 1/4 Law) is a relation between the Surface Brightness of a point on an Elliptical Galaxy and that point's distance from the Galaxy's center.
ln ΣR = ln Σ0 - k R1/4
This is an empirical relation and unfortunately it has limited use for determining other information, but is a relation that any theory of elliptical galaxies had best reproduce. I believe some models of Galaxy Mergers appear to produce galaxies with such a relation, consistent with the notion that elliptical galaxies are often the result of mergers.
Other such empirical relations regarding galaxy surface brightness have been devised.