Galaxy effective radius

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

Galaxy effective radius or half-light radius ($R_e$) is the radius at which half of the total light of a galaxy is emitted. 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 $\sqrt[4]{R}$ term in de Vaucouleurs's law, which characterizes a specific rate at which surface brightness decreases as a function of radius: $$I(R)=I_e\cdot e^{-7.67(\sqrt[4]{R/R_e}-1)}$$ where $I_e$ is the surface brightness at $R=R_e$. At $R=0$, $$I(R=0)=I_e\cdot e^{7.67}\approx 2000\cdot I_e$$

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