de Vaucouleurs' profile

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 (i.e., a surface brightness profile). The relation:

ln ΣR = ln Σ0 - k R1/4

• R - radius, a distance from the center of the galaxy.
• Σ_R - surface brightness at that radius.
• Σ₀ - surface brightness at the center.
• k - a constant.

This is an empirical relation (based upon observation) 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. The de Vaucouleurs' profile is an example of a Sérsic profile, a more general profile formula that specifies an exponent of R^1/n, with n, a small number, for which various values might be used for various galaxy classes.