tokens: corresponding to the position of the hydrogen-burning shell that is slowly moving outwards in mass as the helium core continues to grow. The surface chemical composition is the same as obtained at 7 R ⊙ since, in the absence of any additional mixing process, there is no change in the surface composition after the RGB-bump (see Table C.2 ). Age differences remain at the same level as they were at 7 R ⊙ (cf., Fig. 2 ) and are sustained in the subsequent evolution towards the RGB tip. 5.2. Evolution of 1.5 M<sub>⊙</sub>, 2.0 M<sub>⊙</sub>, and 2.5 M<sub>⊙</sub> models Using the same initial composition as in the 1 M ⊙ case, we calculated and compared tracks and stellar structures at higher masses: 1.5 M ⊙ , 2.0 M ⊙ , and 2.5 M ⊙ . The first and most evident difference with respect to the lower-mass case is the existence of a convective core during the main-sequence evolution, whose extent as a function of age is depicted in Fig. 6 . Although all codes rely on the Schwarzschild criterion for defining the core convective boundary there are differences in the predicted core size of the order of 10% across codes. Fig. 6. Evolution of the convective-core size during the main-sequence phase as a function of age for the 1.5 M ⊙ ( left ), 2.0 M ⊙ ( centre ), and 2.5 M ⊙ ( right ) solar-radius calibrated models. In many cases a saw-tooth profile is visible at the edge of the core as a consequence of changes in its chemical composition throughout the evolution. Nuclear burning produces changes across the chemically homogeneous central region of the model. In the case of growing convective cores (1.5 M ⊙ ), the sharp increase in density at the edge of the core increases the opacity, which consequently increases the radiative temperature gradient in that position. As evolution proceeds and the discontinuity becomes larger, the radiative gradient outside the core surpasses the value of the adiabatic gradient turning that additional layer convectively unstable. The core suddenly increases in size as is revealed by the sharp spikes in the core profiles (see left panel in Fig. 6 ), and the subsequent fast decrease in the core extent occurs once the composition of the layer is homogenised to the core value. The radiative temperature gradient then decreases as a result of the opacity decrease and the layer becomes convectively stable again (see e.g. Silva Aguirre et al. 2011 ; Gabriel et al. 2014 ). The existence of these “peaks” in the core size as a function of time are the result of the numerical implementation of the Schwarzschild criterion in evolutionary codes, and the behaviour of the core boundary is expected to be smooth as a function of time in real stars. For the higher-mass cases (2 M ⊙ and 2.5 M ⊙ ) the evolution of the convective-core size is indeed smoother as it reaches it maximum extension at the beginning of the main sequence and contracts throughout the core hydrogen-burning phase. One of the expected consequences of the different
ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Tag O B-Tag O O B-Tag O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-EntityOfFutureInterest O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O