// Workers AI · dad joke modeWhat did the galaxy effective radius say? I'm a big circle of influence.

Half light radius R_e encloses half of the total light emitted by an object

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's 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 $2000\cdot I_{e}$.

See also

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