Physics:Galaxy effective radius

Short description: Radius which encloses 50% of the total light of a galaxy

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

Galaxy effective radius or half-light radius ([math]\displaystyle{ R_e }[/math]) 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.

[math]\displaystyle{ R_e }[/math] is an important length scale in [math]\displaystyle{ \sqrt[4] R }[/math] term in de Vaucouleurs law, which characterizes a specific rate at which surface brightness decreases as a function of radius: [math]\displaystyle{ I(R) = I_e \cdot e^{-7.67 \left( \sqrt[4]{ R/ {R_e}} - 1 \right)} }[/math] where [math]\displaystyle{ I_e }[/math] is the surface brightness at [math]\displaystyle{ R = R_e }[/math]. At [math]\displaystyle{ R = 0 }[/math], [math]\displaystyle{ I(R=0) = I_e \cdot e^{7.67} \approx 2000 \cdot I_e }[/math]

Thus, the central surface brightness is approximately [math]\displaystyle{ 2000 \cdot I_e }[/math].