Red Giant Envelope Expansion

Evolutionary Stage

Subgiant → RGB tip 0%

Playback speed 1.0×

Shell-burning rate 1.0×

Star State

Subgiant — hydrogen shell ignites around an inert helium core.

Radius

1.6 R☉

Luminosity

1.3 L☉

Surface temp.

4910 K

Core mass

0.150 M☉

How it works

After core hydrogen exhaustion the helium core is electron-degenerate and inert; a thin hydrogen shell around it keeps burning. As the shell dumps helium ash, the core mass Mc grows and — because degenerate matter obeys an inverse mass–radius law — the core contracts even as it gains mass:

R_core ∝ Mc^(-1/3)          (degenerate core, mirror principle)

The shell's luminosity depends almost entirely on the core mass beneath it (Paczyński's core-mass–luminosity relation), so a small rise in Mc drives a huge rise in L:

L ≈ C·(Mc − 0.15 M☉)^4      (steep, approximate)

The envelope stays on a nearly vertical track in the Hertzsprung–Russell diagram — its surface temperature barely changes — so almost all of the extra luminosity must escape through a much larger surface. From the Stefan–Boltzmann law L = 4πR²σT⁴:

R/R☉ = √(L/L☉) · (T☉/Teff)²

This is the "mirror principle": the core shrinks while the envelope swells by a factor of ~50–100, cooling and reddening the star into a red giant. The whole inflated envelope also becomes convective (shown as the translucent turbulent shell), carrying the shell's energy to the surface by bulk motion rather than radiation.

Evolutionary stage slider — scrubs the star from subgiant to the tip of the red-giant branch (helium flash threshold, Mc ≈ 0.48 M☉).
Play evolution — advances the stage automatically at the chosen playback speed.
Shell-burning rate — how fast the core accretes ash from the shell (steepens or flattens the whole track).
Cutaway view — slices the envelope open to show the tiny, contracting degenerate core inside (drawn enlarged for visibility — the true size ratio is roughly 1:10,000).

Photosphere Convective envelope Degenerate He core

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.