Effective radius

The effective radius or half-light radius (${\displaystyle R_{e}}$) 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.

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

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

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

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 ${\displaystyle 2000\cdot I_{e}}$.