The **Schönberg-Chandrasekhar Limit** is the maximum mass of a non-fusing, isothermal core that can support an enclosing envelope. $ P_{\rm max}(r_{\rm c}) \ge P_{\rm env}(r_{\rm c}) \hspace{1cm} \Rightarrow \hspace{1cm} \frac{m_{\rm c}}{M} \lesssim 0.37 \left(\frac{\mu_{\rm env}}{\mu_{\rm c}}\right) $ This limit is the upper bound on the ratio between the mass of a stellar core ($m_{\rm c}$) and the total stellar mass ($M$) such that [[Stellar Structure#Hydrostatic Equilibrium|hydrostatic equilibrium]] of the core is maintained. > [!important] > The **Schönberg-Chandrasekhar Limit** applies to stars with $M \sim 2 \; {\rm M_{\odot}}$. > - Lighter stars develop a partially non-relativistic degenerate core before reaching this limit, providing additional pressure support. However, these degenerate cores still shrink as mass is added ($R \propto M^{-1/3}$). > - Heavier stars will exceed this limit, causing the core will collapse on the [[Timescales#Thermal Timescale|thermal timescale]] allowing gravitational contractions to be primary energy source.