Histogram of the number of isolated galaxies (orange line) compared to the total number of galaxies (red line), as a function of apparent r-band magnitude mr. The dashed vertical line represents the magnitude mbright, below which all satellites with a luminosity fraction larger than fL ≡ Lsat/Llens = 0.1 compared to the lens are still detected. Beyond this limit, the fraction of isolated galaxies (blue line) slightly increases because satellites fainter than the flux limit are not detected, which can cause lenses close to the magnitude limit (mlim = 20 mag) to be falsely identified as isolated.
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