The Schoenberg-Chandrasekhar limit: A polytropic approximation

The existence of a maximum isothermal core mass fraction (q_max), the Schoenberg-Chandrasekhar limit, is one of the classic results from the theory of stellar structure. This limit can be demonstrated through a simplified composite polytrope model in which an isothermal core is surrounded by ann=1 polytrope envelope. While this model underestimatesq_mas by 25% in the homogeneous case, it is accurate to within 5% in the more realistic inhomogeneous situation.