Detection Thresholds for Diffuse Cluster Light: Limiting Surface Brightness as Surface Density and Missed Light

Every measurement of intracluster light is silently a statement about a surface-brightness limit: light fainter than the limit is not measured, and for an extended diffuse profile the unmeasured part is a calculable fraction of the whole. This paper converts four representative limits, 28.5, 29.5, 30.5, and 31.5 magnitudes per square arcsecond in V, into physical terms and applies them to a fiducial exponential profile of central brightness 26.0 magnitudes per square arcsecond and scale length 60 kpc. The limits correspond to luminosity surface densities of 0.1448, 0.0577, 0.0230, and 0.0091 solar luminosities per square parsec, and to stellar mass surface densities of 0.434, 0.173, 0.069, and 0.027 solar masses per square parsec at a mass-to-light ratio of 3. Against the fiducial profile, whose total light is 3.28e+10 solar luminosities, the four limits truncate the detectable profile at 138, 193, 249, and 304 kpc, leaving fractions 0.330, 0.168, 0.082, and 0.038 of the total diffuse light below the limit. A survey reaching only 28.5 therefore misses about a third of a typical cluster's diffuse light before any other systematic is considered.