A small contribution to the giant problem

We present a simple analytic model of a composite polytropic star, which exhibits a limiting Schönberg-Chandrasekhar core mass fraction strongly analogous to the classic numerical result for an isothermal core, a radiative envelope and a μ-jump (i.e. a molecular weight jump) at the interface. Our model consists of an n_c=5 core, an n_e=1 envelope and a μ-jump by a factor >=3 the core mass fraction cannot exceed 2/π. We use the classic UV plane to show that composite models will exhibit a Schönberg-Chandrasekhar limit only if the core is `soft', i.e. has n<sub>c</sub>>=5, and the envelope is `hard', i.e. has n_e<5 in the critical case (n_c=5), the limit only exists if the μ-jump is sufficiently large, >=6/(n_e+1).