Galaxy effective radius

Galaxy effective radius or half-light radius (${\displaystyle R_{e}}$) is the radius at which half of the total light of a galaxy 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.

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

${\displaystyle R_{e}}$ is an important length scale in ${\displaystyle {\sqrt[{4}]{R}}}$ term in de Vaucouleurs law,[3] which characterizes a specific rate at which surface brightness decreases as a function of radius:

$${\displaystyle I(R)=I_{e}\cdot e^{-7.67\left({\sqrt[{4}]{R/{R_{e}}}}-1\right)}}$$

where ${\displaystyle I_{e}}$ is the surface brightness at ${\displaystyle R=R_{e}}$. At ${\displaystyle R=0}$,

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

Thus, the central surface brightness is approximately ${\displaystyle 2000\cdot I_{e}}$.