Half light radius Re encloses half of the total light emitted by an object

The effective radius ($R_e$) of a galaxy is the radius at which half of the total light of the system is emitted.[1][2] This assumes the galaxy has either intrinsic spherical symmetry or is at least circularly symmetric as viewed in the plane of the sky. Alternatively, a half-light contour, or isophote, may be used for spherically and circularly asymmetric objects.

$R_e$ is an important length scale in de Vaucouleurs $\sqrt[4] R$ law, which characterizes a specific rate at which surface brightness decreases as a function of radius:

$I(R) = I_e \cdot e^{-7.67 \left( \sqrt[4]{\frac R {R_e}} - 1 \right)}$

where $I_e$ is the surface brightness at $R = R_e$. Note that at $R = 0$,

$I(R=0) = I_e \cdot e^{7.67} \approx 2000 \cdot I_e$

Thus, the central surface brightness is approximately $2000 \cdot I_e$.