Stellar core ($M_c=m(R_c)$)

A stellar core is the central region distinguished from the surrounding envelope by its composition, energy generation or thermodynamic state. A core boundary at radius $R_c$ encloses mass $M_c=m(R_c)=4\pi {\int }_0^{R_c}\rho (r)r^{2}dr$. In a hydrogen-shell-burning red giant, a helium-rich core can be inert while a narrow surrounding layer supplies the luminosity. Core mass and core radius are separate variables: the relation between them must come from a structural model, such as a polytropic mass-radius relation, rather than from the word core alone.