Evolution in the HeBurning Phase and Dredgeup

Let us further follow the evolution in the giant phase (Fig. 26.1) for stars which do not experience the He flash (cf. Sect. 25.3.2), i.e., for stellar masses above about 2.3M0.

D-E, Red giant branch, first dredge-up: the low Teff resulting from envelope expansion produces very large opacities, which in turn favor convection. The external convective envelope becomes very deep and may cover 90% of the stellar radius (Fig. 5.8). The deep convective envelope reaches the layers processed by the CNO cycle and brings excesses of 14N, 13C and He to the surface together with a 12C depletion. This is the first dredge-up. Figure 26.3 illustrates the predicted changes of the abundance ratios 14N/12C and 13C/12C along the red giant branch as functions of the luminosity for various stellar masses. The enrichment is first rapid and then there is a plateau, because the convective envelope does not get much deeper. More massive stars generally have stronger enrichments in the products of CNO burning, because the external convective envelopes reach deeper layers. The enrichments in 4He are modest of the order of few percentage. The amplitude of 14N and 13C surface enrichments and the luminosity at which they appear on the red giant branch are powerful tests of the internal mixing.

Observations are in rough agreement with models for M > 2.5 M®. However, there is a disagreement below this mass, in the sense that the observations show much more CNO-processed elements than predicted (e.g., 14N and the 13C/12C ratio are too large [207, 220]). This suggests an additional mixing between the convective envelope and the H shell. Conservation of the angular momentum in red giant envelopes favors large differential rotation and shear mixing at the base of the envelope [118, 455]; however it does not seem sufficient to account for low-Z red giants.

Core contraction goes on until the temperature of central He ignition is reached. The energies from the core and the shell now contribute to increase the luminosity. The density profile of the star is more and more peaked at the center with an extended thin envelope.

E-F, He burning, blue loops: the temperature of He ignition depends on the density like q-2. Thus, He ignition occurs at a slightly lower central T for smaller masses, i.e., Tc = 108 K at 2 M0 and 1.6 x 108 K at 20 M0 (Fig. 26.9). The highly sensitive rate of £ produces a steep T gradient and a convective core appears within the central regions (Fig. 26.1) converting He into 12C and 16O. The contraction of the core is stopped and the core expands producing a decrease of L, surface convection recedes and the star leaves the Hayashi line. This is again the "mirror effect",

Fig. 26.3 Top: evolution of the surface ratio X (14N) /X (12C) as a function of the luminosity on the red giant branch for different masses. Bottom: the same for X(13C)/X(12C). From the author and G. Meynet [363]

Fig. 26.3 Top: evolution of the surface ratio X (14N) /X (12C) as a function of the luminosity on the red giant branch for different masses. Bottom: the same for X(13C)/X(12C). From the author and G. Meynet [363]

but in the opposite way as between C and D. Core expansion produces envelope contraction, the stellar radius decreases and the star moves, first rapidly and then slowly toward point F, which is near the middle of the He phase. The core represents a much smaller mass fraction than during the MS phase. Overshooting for a given ratio dover/HP produces a smaller core increase than during the MS phase, because the pressure gradient is steeper. The H shell progressively looses its energetic importance and its outward migration slows down.

Fig. 26.4 The lifetimes (yr) for the H- and He-burning phases as a function of the mass on the ZAMS for Z = 0.02, Y = 0.30 and for Z = 0.001 and Y = 0.243, with an overshooting of 0.20 HP from the core. From G. Schaller et al. [513]

Fig. 26.4 The lifetimes (yr) for the H- and He-burning phases as a function of the mass on the ZAMS for Z = 0.02, Y = 0.30 and for Z = 0.001 and Y = 0.243, with an overshooting of 0.20 HP from the core. From G. Schaller et al. [513]

The duration of the He phase for the 7 M0 model is 4.7 x 106 yr, i.e., 10% of the MS phase (this ratio is determined by L, the core sizes and the energy available per nucleon). Figure 25.17 indicates where most of the He-burning phase is spent, while Fig. 26.4 shows the lifetimes in the H- and He-burning phases for different masses for Z = 0.02 and Z = 0.001.

During its motion in the HR diagram from E to G, the star describes the blue loops, which are more extended for more massive stars (Fig. 25.17). The blue loops appear between about 3 and 12 M0 (at standard composition); they are sensitive to most model ingredients (Sect. 26.2.4). During sufficiently extended blue loops, the stars cross the "Cepheid instability strip" (Sect. 15.5.2) where they pulsate radially and are observed as Cepheids. Most Cepheids occur in the slow part of the blue loop (near point F), if it lies within the instability strip. The blueward or redward evolution within the instability strip is responsible for the secular changes of some Cepheids. Cepheids no longer have the initial He and CNO compositions (Fig. 26.3), the He-surface mass fraction being a few percentage higher than the initial one. F-G, End of central He burning: core He burning goes on after point F. When the central abundance Yc of helium declines, the nuclear rate decreases (e ~ Yc3) and central contraction again occurs. The mirror effect produces an expansion of the envelope and the star evolves to point G. In the second half of the He-burning phase, the reaction 12C(a, y)16O (with e ~ X(4He)X(12C)) becomes dominant over

Fig. 26.5 Evolution of the carbon and oxygen abundances in the core of a 7 [email protected] during the He-burning phase. The mass fraction of 12C and 16O is given as a function of the central helium content Yc

Fig. 26.5 Evolution of the carbon and oxygen abundances in the core of a 7 [email protected] during the He-burning phase. The mass fraction of 12C and 16O is given as a function of the central helium content Yc

4He(2a, y)12C, so that the core content in 12C decreases (Fig. 26.5). At the end of He burning, the C and O abundances in the center of the 7 M0 model are X(12C)=0.30 and X(160)=0.67. The fraction of 16O is higher in higher mass stars.

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