What main characteristic of a star's central temperature dictates whether it primarily uses the proton-proton chain or the CNO cycle to burn hydrogen into helium?

The main characteristic of a star's central temperature that dictates whether it primarily uses the proton-proton chain or the CNO cycle to burn hydrogen into helium is the *absolute value of that temperature*, which directly determines the kinetic energy available to overcome the specific Coulomb barriers associated with each fusion pathway.

The proton-proton (PP) chain is a nuclear fusion process where four protons (hydrogen nuclei) combine to form one helium nucleus, releasing energy. This process is dominant in stars with lower central temperatures, typically below about 15 million Kelvin. The fundamental step in the PP chain involves two protons fusing. Since protons each carry a single positive charge, the electrostatic repulsive force between them, known as the Coulomb barrier, is relatively low. This lower barrier requires less kinetic energy from the colliding nuclei to overcome, making the PP chain efficient at comparatively lower temperatures.

The CNO cycle (Carbon-Nitrogen-Oxygen cycle) is another nuclear fusion process that also converts four protons into one helium nucleus, releasing energy. This cycle becomes dominant in stars with higher central temperatures, typically above about 17 million Kelvin. The CNO cycle utilizes carbon, nitrogen, and oxygen nuclei as catalysts. A catalyst is a substance that facilitates a reaction without being consumed; it participates but is regenerated. The initial and critical steps in the CNO cycle involve protons fusing with these heavier catalyst nuclei (e.g., carbon has six positive charges). The electrostatic repulsion, or Coulomb barrier, between a proton and a carbon nucleus (or nitrogen or oxygen) is significantly higher due to the larger positive charge of the heavier nucleus. Overcoming this much higher Coulomb barrier demands substantially greater kinetic energy from the reacting particles, which is only available at higher central temperatures.

Crucially, the reaction rate of the CNO cycle is far more sensitive to temperature changes than the PP chain. A small increase in temperature dramatically increases the probability of overcoming the higher Coulomb barrier in the CNO cycle, causing its energy production rate to rise very steeply. This heightened temperature sensitivity means that once the central temperature crosses a certain threshold, the CNO cycle quickly becomes the overwhelmingly dominant mechanism for hydrogen burning, even though the PP chain is still occurring.