Stellar Structure: the Eddington Standard Model

A full stellar-structure playground built on the Eddington standard model (an $n = 3$ polytrope; Carroll and Ostlie Ch. 10; Hansen and Kawaler). The Lane-Emden equation is integrated from the regular centre by RK4 to its first zero ($\xi_1 = 6.89685$), then scaled to the chosen mass and composition to give $\rho(r)$, $P(r)$, $T(r)$ (ideal gas plus radiation), $m(r)$ and $L(r)$ from the pp, CNO and triple-alpha rates, with the Schwarzschild criterion deciding where the star is convective. Panel A is a pseudo-3D sliced star coloured by temperature with its burning core, radiative and convective zones and photosphere; Panel B is the run of $T$, $\rho$, $P$ and $L$; Panel C is the energy generation and the HR position on the ZAMS. The Lane-Emden surface values, the solar central pressure and temperature within the Eddington-model tolerances, the Schwarzschild convective-versus-radiative split, and the pp/CNO/triple-alpha hierarchy along a monotone zero-age main sequence are the physical content.