Galaxy effective radius or half-light radius ( R e {\displaystyle 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 {\displaystyle R_{e}} is an important length scale in R 4 {\displaystyle {\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 ⋅ e − 7.67 ( R / R e 4 − 1 ) {\displaystyle I(R)=I_{e}\cdot e^{-7.67\left({\sqrt[{4}]{R/{R_{e}}}}-1\right)}}
where I e {\displaystyle I_{e}} is the surface brightness at R = R e {\displaystyle R=R_{e}} . At R = 0 {\displaystyle R=0} ,
I ( R = 0 ) = I e ⋅ e 7.67 ≈ 2000 ⋅ I e {\displaystyle I(R=0)=I_{e}\cdot e^{7.67}\approx 2000\cdot I_{e}}
Thus, the central surface brightness is approximately 2000 ⋅ I e {\displaystyle 2000\cdot I_{e}} .
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