Half-Light Radii for Various Profiles
Written by
Taro Sato,
on .
Tagged:
astro
math
For a radial profile of , the enclosed flux within the radius is given by
I’m only concerned about azimuthal symmetric cases, so . The idea is to solve
for .
Gaussian Profile
Say the Gaussian intensity profile is given by
The enclosed flux within is given by
Hence
Exponential Profile
The radial surface-brightness profile of a disk galaxy is often fitted by the exponential profile:
where is the disk scale length. The flux enclosed within the radius is given by
Solving for the half-light radius leads to the following:
A relevant numerical solution is
Sersic/de Vaucouleurs Profile
The radial surface-brightness profile of a spheroidal galaxy is often fitted by the Sersic (de Vaucouleurs when profile):
where (Capaccioli 1989). This expression explicitly parametrizes the profile in terms of half-light radius.