tokens: core-helium burning in the blue part of the HRD or crosses the HRD and starts core-helium burning as a RSG. This depends on a variety of parameters, which can be interdependent, such as the following: rotation (and its implementation), mass-loss rates, chemical gradients in the radiative zones, activity of the intermediate H-burning shell ( Langer Maeder 1995 ; Maeder Meynet 2001 ). Models at low metallicity tend to remain in the blue region of the HRD longer (e.g. Georgy et al. 2013 ), and this is also what we observe in the computations used in this work. A similarity between our models at both metallicities is that the luminosity of the hydrogen burning-shell at the onset of shell hydrogen-burning is systematically higher for models computed with the Schwarzschild criterion compared to models computed with the Ledoux one (see Fig. 4 ). This is due to chemical gradients in the region which was previously occupied by the hydrogen burning-core during the MS (the region below the dot-dashed line in Fig. 3 ), which prevent a convective zone from appearing at the same location where hydrogen is burnt. Since hydrogen-shell burning starts in a radiative condition with the Ledoux criterion, there is no refueling in fresh hydrogen by convection and then the energy production remains lower. In the Ledoux models, the convective zone appears higher inside the star, where no burning occurs. It then grows at a deeper level by eroding the chemical gradient below the convective zone. The difference between solar and LMC metallicity is that at solar metallicity, the first crossing of the HRD can be fast: All the Ledoux models and the Schwarzschild 25 M ⊙ models ignite central helium burning on the RSG branch after a quick crossing of the HRD. Only the Schwarzschild 20 M ⊙ model starts burning its helium as a BSG before slowly crossing the HRD for the first time: The luminosity of the intermediate hydrogen-burning shell is sufficient to maintain the model on the blue side of the HRD, and it remains almost constant; whereas in other cases, it decreases over time. Figure 4 shows the time-evolution of the shell luminosity for 3 × 10 5 years after the end of the MS. Three different kinds of behaviours can be seen. The first type are models with an abrupt decrease in the shell luminosity shortly after the shell ignites (Ledoux models at solar metallicity). These are the models which cross the Hertzsprung gap very quickly after the end of the MS. The second type are models with a slow decrease in the shell luminosity over time (models at Z = 0.006 and Schwarzschild solar metallicity 20 M ⊙ model). These models ignite core-He burning in the blue part of the HRD and cross the gap slowly. The third type is the model with an intermediate behaviour (Schwarzschild solar metallicity 25 M ⊙ model). This model crosses the HRD quite quickly, but not as fast as the first type of models. For the models that are quickly crossing the HRD, the intermediate convective zone of the
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