Top: Predicted mass-luminosity relationship near the convective transition for the nominal parameters of NGC 6397 ([M/H]= − 1.9, [O/M] = 0.3, Y = 0.25, T = 12.6 Gyr, α_MLT = 1.82, E(B − V) = 0.22, distance of 2.458 kpc, and α = 0). The points represent individual MESA models. Bottom: Corresponding predicted luminosity function. The best-fit empirical model introduced in Sect. 7.1 is also shown. The physical model of the luminosity function features a spike in star counts at the faint edge of the gap due to the abrupt discontinuity in the mass-luminosity relationship. It does not matter whether the spike is a genuine feature of the cluster or a modelling artefact, as its range of magnitudes is too narrow to be detected in the observed luminosity function.