Hydrogen-shell burning deposits helium onto a geometrically thin helium layer. Once helium ignites, the strong temperature dependence of the <Triple-alpha process> and the shell's initially weak expansion response produce the <Härm–Schwarzschild instability>. The resulting <AGB thermal pulse> drives a short-lived intershell convection zone, expands the layers above it, and temporarily extinguishes the hydrogen-burning shell before the cycle restarts.

Toward the upper end of the mass range, neutrino cooling keeps the centre cooler than an off-centre shell, so <carbon burning> can ignite off-centre under partial <electron degeneracy pressure>. Repeated flashes and an inward-moving carbon flame consume most carbon and leave a degenerate <oxygen-neon-magnesium core>, surrounded by helium- and hydrogen-burning shells.

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 317 / 1 / iv / Solution

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The Härm–Schwarzschild instability is the thin-shell thermal instability of helium burning in an asymptotic-giant-branch star. Heating greatly raises the nuclear rate while the geometrically thin shell initially expands too little to provide stabilizing cooling.


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 Incoming links: Härm–Schwarzschild instability