β − T_dust distribution for the z-GAL sources (black squares) compared to the BEARS sources (orange diamonds; Bendo et al. 2023). The solid black line is the fitted relation we find for the z-GAL sources with α = 0.69 ± 0.04 (see Sect. 6.4) and the shaded region is the confidence level. We over-plot the trend found by Yang & Phillips (2007) for local LIRGs in black dashed line. The 1σ level distribution of the MCMC chains is represented by the red contours for a few sources, that demonstrate a high level constraint. The lighter pink contour demonstrates one of the few cases where the 1σ level shows large degeneracy.