Effective radius

Half light radius R_e 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][2] 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 de Vaucouleurs ${\sqrt[ {4}]R}$ law, which characterizes a specific rate at which surface brightness decreases as a function of radius:

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

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 $2000\cdot I_{e}$.

See also

• Airy disk
• Elliptical galaxy
• Globular cluster
• Open cluster
• Point spread function
• Sersic profile

References

1. "Half-light Radius". Swinburne University. Retrieved 22 May 2013.
2. Binney, James; Tremaine, Scott (2008). Galactic Dynamics (Second ed.). Princeton Series in Astrophysics. p. 21. ISBN 9780691130279.