The Rising Floor: Cosmological Dimming and the Minimum Detectable Diffuse Fraction from Redshift 0.05 to 0.5

A surface-brightness limit is not a fixed physical threshold, because cosmological dimming moves it: the same instrument that reaches 29.5 magnitudes per square arcsecond observed is probing rest-frame surface brightnesses that grow brighter with redshift, and the diffuse light it can in principle detect is a rising fraction of a cluster's total. This paper computes that drift for a standard rich cluster of total stellar light 1.2e12 solar luminosities and a 200 kpc aperture. Dimming costs 0.21 magnitudes at redshift 0.05, 0.41 at 0.10, 0.79 at 0.20, 1.14 at 0.30, and 1.76 at 0.50. The corresponding rest-frame limiting intensities rise from 0.070 to 0.292 solar luminosities per square parsec, and the minimum detectable diffuse fraction, for a component spread at the limiting brightness over the aperture, rises from 0.0073 to 0.0306, a factor of 4.19. Samples of diffuse fractions spanning this redshift range therefore carry a selection floor that rises by that factor across the sample, and an apparent evolution of the fraction with redshift must first survive subtraction of the floor's own rise, which this paper tabulates.