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8.1.3 Profile magnitude ¶

To find the profile’s total magnitude, (see Brightness, Flux, Magnitude and Surface brightness), it is customary to use the 2D integration of the flux to infinity. However, in MakeProfiles we do not follow this idealistic approach and apply a more realistic method to find the total magnitude: the sum of all the pixels belonging to a profile within its predefined truncation radius. Note that if the truncation radius is not large enough, this can be significantly different from the total integrated light to infinity.

An integration to infinity is not a realistic condition because no galaxy extends indefinitely (important for high Sérsic index profiles), pixelation can also cause a significant difference between the actual total pixel sum value of the profile and that of integration to infinity, especially in small and high Sérsic index profiles. To be safe, you can specify a large enough truncation radius for such compact high Sérsic index profiles.

If oversampling is used then the pixel value is calculated using the over-sampled image, see Oversampling which is much more accurate. The profile is first built in an array completely bounding it with a normalization constant of unity (see Galaxies). Taking \(V\) to be the desired pixel value and \(S\) to be the sum of the pixels in the created profile, every pixel is then multiplied by \(V/S\) so the sum is exactly \(V\).

If the --individual option is called, this same array is written to a FITS file. If not, only the overlapping pixels of this array and the output image are kept and added to the output array.