# Effective radius

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This article is about astronomy. For cloud drops, see Cloud drop effective radius.
Half light radius Re encloses half of the total light emitted by an object

The effective radius ($R_e$) of a galaxy is the radius at which half of the total light of the system is emitted.[1] This assumes the galaxy is spherically symmetric. Alternatively, a half-light contour may be used for spherically asymmetric objects.

$R_e$ 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

1. ^ "Half-light Radius". Swinburne University. Retrieved 22 May 2013.