The Evolution of the

The evolution of the Sun in the HR diagram is illustrated in Fig. 25.11. It also shows all the various evolutionary phases discussed in other chapters. From the emergence of the Sun at the end of the protostellar stage (Chap. 19) characterized by the dynamical timescale 106 yr), the pre-main sequence proceeds at the Kelvin-Helmholtz timescale (tKH ~ 3 x 107 yr), first descending along the Hayashi branch and then joining the MS after a small hook due to the settling of the CN cycle to equilibrium. The H-burning or main sequence phase proceeds very slowly with a luminosity increase of about 7% per Gyr. The Sun with an age of 4.57 Gyr is presently near the middle of the MS phase, which ends at central H exhaustion at an age of 11.0052 Gyr.

After central H exhaustion, the nuclear H burning continues in a shell surrounding the extinct He core, which contracts making the pressure of degenerate electrons more important. The shell adds new He to the core and progressively migrates outward (Fig. 25.10). During these phases, the star leaves the MS phase and becomes a red giant. On the red giant branch, an outer convection zone develops and becomes deeper as the star becomes more luminous, at some stage its lower boundary penetrates the H-burning shell. This brings nuclear-processed materials to the surface, a process known as "dredge-up"; this is the first dredge-up. Being mostly convective

70% of the mass), the star lies close to the Hayashi branch (Sect. 20.2.1). The slow outward migration of the H-burning shell brings it to the chemical discontinuity let by the convective envelope at its deepest point. The decrease in the mean molecular weight ^ makes a drop in luminosity, before L further increases again. This temporary slowing down of the brightening produces a small accumulation of stars in the sequence of old clusters in the HR diagram. In its further evolution, the stellar luminosity essentially depends on the mass of the degenerate He core, a property which also applies to more massive stars in the advanced stages (Fig. 26.14). As the core grows, the rising of the luminosity on the red giant branch accelerates, as well as the radius inflation which reaches 10, then 100 and finally 234 R0 at the tip of the red giant branch at an age of 13.210735 Gyr. About 0.3 M0 is lost by stellar winds during the brightest part of this evolution.

At the point marked by a star at the top of the red giant branch, the so-called He flash occurs. The He-temperature ignition is reached in the core which is highly degenerate, with a central density of 1.02 x 106 g cm-3. This produces a violent nuclear instability (Sect. 3.5). Due to strong neutrino cooling, the maximum T is at some distance of the center (Mr/M « 0.1), where degenerate He burning starts. Energy is radiated both toward the interior (where it is then evacuated by neutrinos) and the exterior. The high energy production by the flash drives a new temporary convective layer, which rapidly dies out without merging with the outer convective envelope. The He flash with its violent divergence of the nuclear energy production rate has for main effect to release the internal electron degeneracy in the core. At an age of 13.212520 Gyr, i.e., in about 1.8 x 106 yr, the star readjusts to non-degenerate central conditions. During these events, the central He content has decreased by about 5% from yc = 0.986 to 0.936. Then the star starts its non-degenerate phase of central He burning (point marked by a star at logL/L0 « 1.85 in Fig. 25.11).

Fig. 25.11 HR diagram of the solar evolution with the best fit composition X = 0.72, Y = 0.266 and Z = 0.014 from the emergence of the dust cloud at the top of the Hayashi branch (taken here as zero age) to the evolution toward the planetary nebulae. Ages are indicated along the track (the composition being slightly different from that of Fig. 25.10, the timescales are also slightly different). The two 4-pike stars show the beginning and end of the He flash, which leads to the central He-burning sequence. From data by C. Charbonnel [119]

Fig. 25.11 HR diagram of the solar evolution with the best fit composition X = 0.72, Y = 0.266 and Z = 0.014 from the emergence of the dust cloud at the top of the Hayashi branch (taken here as zero age) to the evolution toward the planetary nebulae. Ages are indicated along the track (the composition being slightly different from that of Fig. 25.10, the timescales are also slightly different). The two 4-pike stars show the beginning and end of the He flash, which leads to the central He-burning sequence. From data by C. Charbonnel [119]

L/Ls jiinn

L/Ls jiinn

13.32.4 Qjt

Fig. 25.12 The variations of luminosity and radius of the Sun through the ages. Same source [119] as in Fig. 25.11

13.32.4 Qjt

1000

Fig. 25.12 The variations of luminosity and radius of the Sun through the ages. Same source [119] as in Fig. 25.11

The star enters a phase of non-degenerate He burning. The luminosity slightly decreases up to an age of 13.25893 Gyr where the central He content is yc = 0.3620 and He burning makes the star brightening again. For lower metallicity Z stars, this corresponds to the so-called horizontal branch (Sect. 26.5); at solar or higher Z, the corresponding accumulation of stars in the HR diagram is known as "the clump". The brightening and radius increase bring the star to the asymptotic giant branch (AGB), which joins asymptotically the red giant branch. This complex phase is studied in more detail in Sect. 26.6. Central He is exhausted at an age of 13.3196 Gyr. Most of the time between the end of central H burning and He ignition (2.314 Gyr) is spent in the H-shell burning on the red giant branch, while the duration of the quiet central He-burning lifetime is only 1.07 x 108 yr (plus 1.8 x 106 for the He flash). This is much shorter (by a factor of 102!) than the MS lifetime, this is due to the smaller nuclear energy available per nucleon, but even more because the star is much brighter than on the MS (Fig. 25.12).

After central He exhaustion, He burning goes on in a thin shell. As seen in Sect. 3.5.1, nuclear burning in very thin shells is unstable. This gives the so-called thermal pulses at the top of the AGB phase. This phase is called the TP-AGB phase (Sect. 26.6), while the early AGB phase is called E-AGB. The star gets a maximum radius of 312 R0. It experiences increasing mass loss, the mass at the top of the TP-AGB phase is estimated to be about 0.6 M0. During the last thermal pulses, the star in the post-AGB phase (Sect. 26.6.4) gets rid of its H-rich envelope and becomes a planetary nebula with a central white dwarf with a mass of about 0.55 M0.

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