Simulations showing the observed values of β and L₁ obtained using the method described in Sect. 3.1 as a function of the known input values, assuming a fixed width of σ_L = 0.25 and AGN contamination following Sabater et al. (2019). The best-fit relations between the two sets of values are shown as the dashed grey lines, and they are parameterised as in the text. The dotted line in each panel shows the 1:1 relation.