Total mass of the star versus mass of the convective core in the Pop III case. Solid red lines indicate the limit of stability for hylotropic models with μ = 0.6 and T_c = 1.5−2 × 10⁸ K. The GENEC models of Haemmerlé et al. (2018a, 2019) at zero metallicity are plotted with the indicated rates. The identity corresponds to polytropes of different masses, and is shown as a grey line. The final masses obtained in Haemmerlé (2020) are marked by star-like symbols. The dotted red line is the limit of stability for hylotropes with μ = 0.6 and the exact central temperature of the GENEC model at 10 M_⊙ yr⁻¹ at the onset of instability (T_c = 1.78 × 10⁸ K).