The asymptotic giant branch (AGB) phase

When the core is exhausted of helium the star enters the AGB phase and becomes a red giant again (Fig. 2.2 point E-G). This is called the second ascent of the giant branch. At this stage the degenerate core is made of carbon and oxygen, and there is now a thin helium-burning shell, at the base of the helium-shell, surrounding the C-O core and above the He-shell, a thin hydrogen-burning shell, at the base of the outer hydrogen-rich shell. The outer hydrogen zone contains a deep convective envelope which, in stars with
M_star > ~4M , transports the products of hydrogen-burning to the surface when the star reaches the base of the AGB (``second dredge-up''). The energy-producing nucleosynthetic processes are confined to two regions (the He-burning shell and the H-burning shell) containing less than 3% of the total stellar mass. One of the characteristics of the AGB phase is the thermally unstable He-burning shell. This shell periodically produces a hundred to a million times the energy produced by the H-burning shell on a time-scale of several tens of years. These energy bursts manifest themselves as thermal pulses and hence this phase is known as the thermally pulsing-AGB or TP-AGB phase. These pulses typically happen every 10<sup>4</sup> years or so for a C-O core mass of ~0.6-O.8M, during which time the star is quiescent (the ``interpulse'' phase; Mowlavi 1998). The pulses create convective zones in the He-burning shell. The consequences of the pulses are important to both the chemistry and the structure of the stars. The material manufactured in the He-burning shell is convectively mixed and transported to close to the base of the H-burning shell, where the products of these two shells can be involved in further nucleosynthesis. Furthermore, after the extinction of the He-burning thermal pulse, the outer convective zone then penetrates deep into the hydrogen and helium burning shells where, eventually, it can transport carbon to the surface. This is called the ``third dredge-up''. It is clear that, since the thermal pulses are repeated periodically, the third dredge-up event can happen many times. Eventually, enough carbon can be transported to the surface that the initial cosmic C/O ratio of ~0.4 is raised to >1 and a carbon star is formed due to the transformation of the surface chemistry.

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