Diffuse Fraction Against Cluster Mass in Seven Named Systems, with Abell 2744 as a Held-Out Test

Whether richer clusters hold proportionally more of their starlight in diffuse form is a basic question about how environment processes galaxies, and it can be asked of the published record directly. This paper assembles the diffuse fractions and virial masses of seven named systems, Fornax, Hydra I, Virgo, Abell 85, Perseus, Coma, and Abell 1689, and regresses the logarithm of the fraction on the logarithm of the mass. The seven define a relation of slope 0.246 and correlation 0.97 with a residual scatter of only 0.031 dex, a factor of 1.07 in the fraction. The relation predicts diffuse fractions of 0.17 at 1.0e14 solar masses and 0.29 at 1.0e15, and extrapolates to 0.095 at group scale. Coma, the richest relaxed system in the set, sits +0.047 dex above the relation, and Abell 1689 -0.043 dex below it. The test of the relation is the eighth system, held out of the fit: at Abell 2744's mass of 2.2e15 solar masses the relation predicts a fraction of 0.36, while the Frontier Fields measurement returns 0.11, a shortfall of -0.512 dex, a factor of 3.25. A relation that describes seven systems across a factor of twenty in mass thus fails the eighth by a factor of three, and the failure is the result: the diffuse fraction is set jointly by mass and by dynamical state and measurement depth, and a violently merging system measured through a dimming-limited aperture sits far below the mass relation.