A -- main sequence star burns hydrogen mainly through the CNO cycle. Its strong temperature sensitivity produces a convective core, which leaves a helium-rich core with a relatively sharp composition discontinuity as it retreats. After central hydrogen exhaustion, hydrogen burning continues in a shell while the helium core contracts and the envelope expands toward the red-giant branch.
When the core becomes hot enough, the Triple-alpha process starts core helium burning. Alpha capture on the newly made carbon also produces oxygen, so central helium exhaustion leaves a carbon-oxygen core. The star then enters the Asymptotic giant branch with an inert core, a helium-burning shell, a hydrogen-burning shell, and a deep convective envelope. At the high-mass end, off-centre carbon burning converts the carbon-oxygen core into an oxygen-neon-magnesium core.
The Schönberg-Chandrasekhar limit is the largest mass fraction that an approximately isothermal inert core can have while remaining matched in hydrostatic and thermal equilibrium to a hydrogen-rich envelope. For a simple isothermal core and polytropic envelope,Because a helium core has larger mean molecular weight than its hydrogen-rich envelope, the limiting fraction is typically near ten per cent. Once shell burning grows the core beyond this limit, no neighboring equilibrium with an isothermal core exists: the core contracts and heats by Kelvin-Helmholtz contraction, the hydrogen-burning shell brightens, and the envelope expands rapidly toward a red giant.
During first dredge-up, the convective envelope deepens on the red-giant branch and brings CNO cycle-processed material to the surface, increasing helium and nitrogen while reducing carbon and changing isotopic ratios. After central helium exhaustion, second dredge-up occurs in this intermediate-mass range: the envelope penetrates into layers processed by hydrogen and sometimes helium burning, lowers the hydrogen-exhausted core mass, and further enriches the surface in helium and nitrogen.
During the thermally pulsing Asymptotic giant branch, a helium-shell flash can be followed by third dredge-up. The envelope then reaches the intershell and may expose newly synthesized carbon and slow-neutron-capture products. In the more massive objects, hot-bottom burning at the base of the convective envelope can convert some dredged-up carbon into nitrogen.
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.
The exact initial-mass boundaries depend on metallicity, convective overshooting, rotation, and mass loss, but stars near the upper intermediate-mass range, roughly --, can become Super-AGB stars. They ignite carbon but do not immediately ignite neon hydrostatically throughout the core.
Their final fate is set by competition between shell-driven core growth and envelope loss. If a stellar wind removes the envelope first, the remnant is an oxygen-neon, or oxygen-neon-magnesium, white dwarf. If the degenerate core grows toward the Chandrasekhar mass, electron captures on magnesium and neon reduce the electron pressure and can trigger an electron-capture supernova, leaving a neutron star. Slightly higher-mass stars can ignite further fuels and proceed to ordinary iron-core collapse.
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