Joint Fit of Galaxy Cluster Scaling Relations from Individual Weak Lensing Data: Comparison with Stacked Analysis and a Real Data Test

Stacking is the standard route to signal-to-noise in cluster weak lensing, but it destroys the cluster-by-cluster information that scaling-relation studies need. We instead fit every cluster's individual ΔΣ profile simultaneously, tying its mass and concentration to its own richness, redshift and magnitude gap, and compare with two stacked analyses of the same data: a forward-modelled stack sharing the same model and priors, and the standard two-step analysis. The magnitude gap (the BCG-to-brightest-satellite magnitude difference) enters the concentration, which the fossil-group picture ties to earlier assembly and more relaxed systems. On mock populations with triaxial haloes and miscentering, at DES Y3-like and LSST-like density, all three analyses recover the injected gap slope γ cm with uncertainties that match the scatter between realisations, but not equally precisely: the joint fit scatters 1.2--1.3 times less than the forward-modelled stack, and 2 (DES-like) to 6.5 (LSST-like) times less than the two-step analysis, which is also biased in several other scaling-relation parameters. Applied to WaZP clusters with DES Y3 shears, the joint and forward-modelled fits agree on the gap coupling once the mass at fixed richness also depends on the gap, γ cm = 0.065 plus or minus 0.033 (forward-modelled) and 0.007+0.032-0.033 mag-1 (joint); the joint value is consistent with no coupling, so neither is a detection. The mass--concentration slope is consistent with zero in both, as expected from the upturn of the relation over this mass range. A gap coupling obtained in a model where the gap enters only the concentration need not survive a modest extension of that model.