Stellar Core Fusion: pp-Chain vs CNO Cycle

Core Conditions

Core temperature T 15.7 MK

Hydrogen fraction X 0.70

Metallicity Z 0.0200

Reaction Balance

pp-chain 100%CNO 0%

ε total (ε☉ = 1)

1.00

Crossover T

21.2 MK

ε(pp) rel.

0.985

ε(CNO) rel.

0.015

How it works

A star's core fuses hydrogen into helium through two competing chains whose energy-generation rates ε (energy per unit mass per unit time) scale very differently with core temperature T:

ε_pp  ∝ ρ X²        T^4     (proton-proton chain)
ε_CNO ∝ ρ X Z_CNO    T^18    (carbon-nitrogen-oxygen cycle)

Calibrated to the Sun's core (T ≈ 15.7 MK, X ≈ 0.70, Z ≈ 0.02, where the pp-chain supplies ≈98.5% of the luminosity and the CNO cycle only ≈1.5%), this simulation evaluates:

ε_pp  = 0.985 · (X/0.7)² · (T/15.7)^4
ε_CNO = 0.015 · (X/0.7) · (Z/0.02) · (T/15.7)^18

Because the CNO term climbs with the 18th power of temperature, it overtakes the pp-chain very abruptly once the core is hot enough — the crossover temperature (solved live from the two expressions above) marks where a star's energy budget flips from pp-dominated to CNO-dominated. Solar-mass stars sit below it and shine on the pp-chain; stars somewhat more massive than the Sun (roughly F-type and hotter, ≳1.3 M☉) sit above it and are CNO-powered. Sparks in the 3D core are proton-proton events (blue) and CNO-cycle events (orange); their relative numbers track ε_pp and ε_CNO directly, so the core visibly flips color as you cross the threshold.

Core temperature — the single biggest lever; a small increase swings the CNO term by orders of magnitude.
Hydrogen fraction X — both channels need protons, but pp scales as X² and CNO only as X, so raising X favors pp slightly.
Metallicity Z — the CNO cycle needs carbon/nitrogen/oxygen as catalysts; a metal-poor (Population II) star has almost no CNO channel at any temperature.

pp-chain event CNO-cycle event

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