The validity of the Schoenberg-Chandrasekhar limit in describing stellar evolution

We discuss the Schoenberg-Chandrasekhar limit in the light of the modern theory of stellar evolution. We find it remains a valid concept with the numerical value of the limiting fractional mass of the He core lying in a relatively narrow range of 0.09--0.11 for stars in the mass range of 1.4--$7M_\odot$. Crossing this limit is associated with some restructuring of the star, which manifests itself by a characteristic kink (first a decrease then an increase) in the evolution of the radius vs.\ time. This also coincides with the moment the star moves from the subgiant branch to the red giant branch. The crossing is associated with some acceleration of the rate of the growth of the stellar radius and luminosity, but this acceleration is not substantial and the evolution does not change qualitatively. Therefore, the Schoenberg-Chandrasekhar limit, while remaining a valid concept, is not a particularly useful tool in constraining the evolutionary status of a specific object.