pUgm

zdm.optical.pUgm(mag, mean, width)[source]

Return the probability that a galaxy is undetected as a function of magnitude.

Models the survey detection completeness as a logistic function that transitions from ~0 (bright, always detected) to ~1 (faint, never detected) with a smooth rolloff centred on mean:

p(U | m) = 1 / (1 + exp((mean - m) / width))

Parameters:

  • mag (float or np.ndarray) – r-band apparent magnitude(s) at which to evaluate the detection-failure probability.

  • mean (float) – magnitude at which p(U | m) = 0.5 (the 50% completeness limit of the survey).

  • width (float) – characteristic width of the completeness rolloff in magnitudes. Smaller values give a sharper transition.

Returns:

probability of non-detection at each

magnitude in mag, in the range [0, 1].

Return type:

pU (float or np.ndarray)