Similar to Fig. 3, we show cumulative distribution functions for L_x and T_x within R₅₀₀. For a better comparison with observations, we estimated the X-ray luminosity in the band 0.1–2.4 keV for every cluster using SMAC. In the top panel, the bin values range from 10⁴⁴ erg × s⁻¹ to 10⁴⁵ erg × s⁻¹, with increments of 10. Uneven spacing between higher-value bins has to do with the inherent limitations of small number statistics within our cosmological box (see Sect. 5.2 for a deeper discussion). The bottom panel presents the cumulative distribution function from the X-ray temperature in R₅₀₀. We estimated this temperature using SUBFIND. The bin values range from 2 keV to 9 keV, with increments of 1 keV.