Effective radius

The effective radius ($R\_e$) of a galaxy is the radius at which one half of the total light of the system is emitted interior to this radius. This assumes the galaxy is circularly symmetric. This is an important length scale in de Vaucouleurs $sqrt\; [4]\; R$ law which is given as:

:$I(R)\; =\; I\_e\; cdot\; e^\{-7.67\; left(\; sqrt\; [4]\; \{frac\; R\; \{R\_e\; -\; 1\; ight)\}$

where $I\_e$ is the surface brightness at $R\; =\; R\_e$. Note that at $R\; =\; 0$,

:$I(R=0)\; =\; I\_e\; cdot\; e^\{7.67\}\; approx\; 2000\; cdot\; I\_e$

Thus the central surface brightness is approximately $2000\; cdot\; I\_e$.