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.