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.
WHAT TO TRY
- Drag the mass up: the star brightens steeply (L grows as about M^3.5), the central temperature climbs, and in the energy-generation panel the CNO cycle overtakes the pp chain, its much steeper temperature dependence concentrating the burning into a tiny central core.
- Drag the mass down: the core cools, the pp chain dominates, and the luminosity drops by orders of magnitude across the main-sequence range.
- Watch the HR panel: as the mass changes, the model slides along the zero-age main sequence, the locus every star starts on.
- Change the hydrogen fraction X: the mean molecular weight shifts, moving the central temperature and the luminosity.