flux_fraction_contaminant

tessilator.contaminants.flux_fraction_contaminant(pix_sep, s, d_thr=5e-06)

Quantify the flux contamination from a neighbouring source.

Calculates the fraction of flux from a neighbouring contaminating source that gets scattered into the aperture. The analytic function uses equation 3b-10 from Biser & Millman (1965), which is a double converging sum with infinite limits, given by

\[f_{\rm bg} = e^{-t} \sum_{n=0}^{n\to{\infty}} {\Bigg\{\frac{t^{n}}{n!}\bigg[1-e^{-s}\sum_{k=0}^{n} {\frac{s^{k}}{k!}}} \bigg]\Bigg\}\]

To solve the equation computationally, the summation terminates once the difference from the nth iteration is less than some given threshold value, d_thr.

Parameters:

pix_sepfloat

The pixel distance between a contaminant and the aperture centre.

sfloat

For a given aperture size, rad (in pixels) and an FWHM of the TESS PSF, exprf (set at 0.65 pixels), \(s = {\rm rad}^2/(2.0*{\rm exprf}^2)\)

d_thrfloat, optional, default=5.e-6

The threshold value to stop the summations. When the next component contributes a value which is less than d_thr, the summation ends.

Returns:

frac_flux_in_aperturefloat

Fraction of contaminant flux that gets scattered into the aperture.