After the Main Sequence

Part 6: Putting the Full Low-Mass Path Together

The combined HR-diagram evidence from clusters and field stars shows a path: main-sequence turnoff, subgiant branch, red giant branch, horizontal branch or red clump, AGB stars, planetary nebulae, white dwarf cooling sequence. These are the observable signposts of low-mass stellar evolution.

The physical chain is now complete:

1. Core hydrogen is exhausted.
2. The helium core contracts and heats by the virial theorem.
3. Hydrogen shell burning ignites around the inert core.
4. The envelope expands because shell luminosity and transport bottlenecks reorganize the outer star.
5. Helium ignites when the core reaches $T \sim 10^8~\text{K}$.
6. A helium flash occurs if the core is degenerate.
7. Core helium burning creates carbon, and some carbon captures helium to form oxygen.
8. The carbon-oxygen core contracts after helium is exhausted.
9. Double-shell burning on the AGB drives instability and mass loss.
10. The envelope is ejected as a planetary nebula.
11. A white dwarf remains, supported by electron degeneracy pressure.

The overall timing is also part of the model:

These timescales reflect the basic rule $t \sim (\text{available energy})/L$, so long phases have large fuel reservoirs and modest luminosities, while short phases are either high-luminosity burning stages or brief transient transitions.

Low-mass stars do not end by catastrophic collapse, and the HR diagram does not show unrelated classes of stars scattered by chance. It shows a physically connected sequence of structural states that low-mass stars pass through after core hydrogen exhaustion.