Galaxy effective radius

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 law, which characterizes a specific rate at which surface brightness decreases as a function of radius: $$ I(R) = I_e \cdot e^{-7.67 \left( \sqrt[4]{ R/ {R_e}} - 1 \right)} $$ 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 $$2000 \cdot I_e$$.