Schönberg-Chandrasekhar limit

The Schönberg-Chandrasekhar limit is the maximum stable isothermal mass of the helium stellar core formed from fusion in a main sequence star. A core is isothermal (same temperature throughout) if the energy source (fusion) surrounds it (i.e., forming a shell) and everything is sufficiently stable that the core falls into and essentially remains at equilibrium. Given a stellar mass within a specific range (the exact range depending upon metallicity), a star develops such an isothermal core that is below the Schönberg-Chandrasekhar limit with a surrounding hydrogen burning shell, and undergoes limited expansion into a subgiant. As the fusion adds helium to the core, the limit may be reached, at which time the core collapses, becoming degenerate, and the temperature rise due to the collapse (Kelvin-Helmholtz mechanism) leads to additional CNO fusion, and the star expands into an RGB star. The limit depends upon characteristics of the star's interior:

Mcore/M ≈ 0.37(μenv/μcore)²

• M_core/M - the limit (believed to fall generally in the 10-15% range).
• M_core - mass of the core.
• M - mass of the whole star.
• μ_core - mean molecular mass of the core.
• μ_env - mean molecular mass of the envelope, the rest of the star.

The above limit is not the same as the Chandrasekhar limit (the maximum mass of a white dwarf), though the two would seem to be related.