De Vaucouleurs's law
In astronomy, de Vaucouleurs's law, also known as the de Vaucouleurs profile or de Vaucouleurs model, describes how the surface brightness I {\displaystyle I} of an elliptical galaxy varies as a function of apparent distance R {\displaystyle R} from the center of the galaxy: ln I ( R ) = ln I 0 − k R 1 / 4 . {\displaystyle \ln I(R)=\ln I_{0}-kR^{1/4}.} By defining Re as the radius of the isophote containing half of the total luminosity of the galaxy, the half-light radius, de Vaucouleurs profile may be expressed as: ln I ( R ) = ln I e + 7.669 [ 1 − ( R R e ) 1 / 4 ] {\displaystyle \ln I(R)=\ln I_{e}+7.669\left[1-\left({\frac {R}{R_{e}}}\right)^{1/4}\right]} or I ( R ) = I e e − 7.669 [ ( R R e ) 1 / 4 − 1 ] {\displaystyle I(R)=I_{e}e^{-7.669\left[\left({\frac {R}{R_{e}}}\right)^{1/4}-1\right]}} where Ie is the surface brightness at Re.