# Effective radius from astropy sersic profile

I would like to integrate the 2d Sérsic profile of the astropy library to check the half light radius, but I have some issues.

First, I create a simple profile:

theta_rad = 0
r_eff = 4
x_cen = 0
y_cen = 0
ellip  = 0
Amplitude = 2
model = Sersic2D(Amplitude, r_eff, 1, x_cen, y_cen, ellip, theta_rad)


Then I want to calculate the total flux, so I do the integral over all the Cartesian Space:

l = lambda x, y: model(x, y) *2 * np.pi * np.sqrt(x**2 + y**2)
max_flux = integrate.dblquad(l, -np.inf, np.inf, lambda y: -np.inf, lambda y: np.inf)


When I want to integrate only the flux inside the half light radius, I don't recover the r_eff = 4 I set initially. For example, I obtain this curve:

with this code:

inte= []
for i in np.linspace(0,20,100):
inte.append(integrate.dblquad(l, -i, i, lambda y: -i, lambda y: i)[0])


I think that the mistake is on the integral limits and how to define the x and y for doing the integral. In this case, this is easy because the ellipticity = 0 and x=y but what happens when it is not?

• I'm pretty sure your integral is wrong; the $2 \pi r$ term doesn't belong there (why are you multiplying the intensity by the circumference?). You should probably have " l = lambda y x: model(x,y) " Feb 15 at 0:24