Moffat

Usage

moffat  
  x1c       # x-coordinate of centroid  
  x2c       # y-coordinate of centroid  
  q         # axis ratio (minor/major)  
  pa        # position angle (in radians; counter-clockwise from +x)  
  Amp       # amplitude (normalisation; peak surface brightness)  
  alpha     # structural parameter (controls width of the profile)  
  beta      # structural parameter (controls the wings of the profile) 

Surface Brightness Profile

After rotating by $-\text{pa}$ into the frame aligned with the light profile (major axis along $x_1$, minor along $x_2$), define:

$r^2 = x_1^2 + \frac{x_2^2}{q^2}$

The Moffat intensity is given by:

$I(r) = A \cdot \frac{\beta - 1}{\pi \alpha^2} \cdot \left(1 + \frac{r^2}{\alpha^2}\right)^{-\beta}$

where:

• $A$ is the amplitude (Amp), the peak surface brightness
• $\alpha$ sets the core width
• $\beta$ controls the steepness of the wings
• $q$ is the axis ratio