Comparison of the observed Y_gas versus mass relations within R₅₀₀ with different hydrodynamical simulations. The color code for each dataset is indicated in each panel. The light orange squares show the stacked points of Fig. 4, while the black line shows our best-fit relation. The bottom subpanels show the residuals of each dataset to our best fit. These are expressed in dex (log(f_gas)−log(fit)). Top-left panel: Comparison of Y_gas–M₅₀₀ relation with the predictions of the BAHAMAS (Salcido et al. 2023) and FLAMINGO (Schaye et al. 2023) simulations. The blue shaded region indicates the 1σ uncertainty of the relation in FLAMINGO as reported in the corresponding paper. These two simulations use similar galaxy evolution models and feedback implementations. Top-right panel: Comparison of Y_gas–M₅₀₀ relation with the predictions of the IllustrisTNG (Pillepich et al. 2019) and of MillenniumTNG (Pakmor et al. 2023) simulations. For IllustrisTNG we show the individual estimates (pink points) and the mean relation (purple squares). For MillenniumTNG we report the mean relation (green squares) retrieved in the corresponding paper. These two simulations use similar galaxy evolution models and feedback implementations. Bottom-left panel: Comparison of Y_gas–M₅₀₀ relation with the predictions of the Magneticum (Dolag et al. 2016). The pink points indicate the individual estimates, while the purple squares indicate the mean relation. Bottom-right panel: Comparison of Y_gas–M₅₀₀ relation with the predictions of the Simba (Davé et al. 2019) and Illustris (Genel et al. 2014).