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Half light radius R_e represents the half of the total galaxy light emitted

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 spherically symmetric. This is an important length scale in de Vaucouleurs ${\sqrt[{4}]{R}}$ law which is given as:

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

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 $2000\cdot I_{e}$.

References

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