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

Abstract

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 $γ_{\mathrm{cm}}$ 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, $γ_{\mathrm{cm}} = 0.065 \pm 0.033$ (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 \citet{diemer2019} 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.