Enough fuel was only half the problem
A star looks steady from night to night, yet it loses energy continuously as light. Replacing that energy for billions of years requires far more than ordinary chemical burning can provide. Gravitational contraction can heat a star and is important during its formation, but it cannot supply the Sun’s present luminosity throughout its long life. A successful explanation needed both a large energy source and a mechanism that released it slowly enough.
Combining hydrogen into helium supplies the energy scale. The helium nucleus is more tightly bound, so the final system has less mass than the corresponding initial particles. Roughly seven parts in a thousand of the starting mass can emerge as energy in the overall conversion. This is a huge improvement over chemical energy. But knowing the difference in mass does not say which reactions occur inside a star, or how often they happen. Those were central questions in Hans Bethe’s work of 1938–1939.
The available fuel also has to be located where reactions can occur. Most of a main-sequence star’s material is not all burning at the central rate at once. The hot core provides the conditions for appreciable fusion, and its size and supply of material affect the lifetime. Stellar structure therefore determines where the fuel can burn and how long the supply can last.
The nuclei usually miss their opportunity
Hydrogen nuclei are protons and carry positive charge, so they repel one another. The interior of a main-sequence star is hot, but a typical thermal proton still has too little energy to climb classically over the electric barrier. Quantum tunneling gives a small chance to penetrate it. Faster particles in the thermal distribution tunnel more readily, although they are less common. The useful reaction rate comes from combining these two tendencies.
A reaction rate describes how many reactions occur in a given amount of material and time. It depends on temperature, density, the abundance of the reacting nuclei and the energy-dependent probability of their interaction. A plausible reaction that happens too rarely cannot power the observed star; one that consumes its fuel too rapidly cannot explain the star’s lifetime. Bethe brought nuclear calculations into contact with these astronomical requirements.
The first step of the proton–proton chain has an additional reason to be slow. Two protons must form deuterium, a nucleus containing one proton and one neutron. One proton changes into a neutron through the weak interaction, with a positron and a neutrino emitted. This rare step helps explain why the enormous quantity of hydrogen in a star can be used gradually. Bethe and Charles Critchfield calculated the proton-combination process in 1938.
Carbon could help hydrogen burn
Another route uses nuclei already present in the star as intermediates. In the carbon–nitrogen–oxygen cycle, protons are captured through a sequence of nuclear changes and decays. At the end of the main cycle, a carbon nucleus is restored and a helium nucleus has been produced. The carbon participates like a catalyst: it helps turn hydrogen into helium and becomes available to take part again.
Bethe’s 1939 paper developed this cycle as a source of stellar energy; Carl Friedrich von Weizsäcker also developed the carbon-cycle idea independently. The route is strongly temperature-sensitive. It becomes especially important in hotter main-sequence stars when the needed catalyst nuclei are present. The proton–proton chain dominates in the Sun. The contrast is about rates under different conditions, not a choice of two unrelated kinds of fuel.
This rate-based view makes stellar observations useful tests. A theory of nuclear reactions must work together with a model of the stellar interior to account for luminosities and how they vary among stars. Later measurements of solar neutrinos added a much more direct view of the reactions occurring in the core. The familiar diagram of a fusion chain is the starting point; the rate calculation asks whether that diagram can actually keep a star shining.
Gravity helps the reaction rate regulate itself
Why does the star not immediately run away once a reaction is possible? In a main-sequence star, gravity and pressure link the temperature to the structure. If extra heating causes the central region to expand, it tends to cool; nuclear rates then fall. If the region contracts, it tends to heat, and the rates rise. The star’s response can stabilize its energy output over long periods. This description applies to ordinary stable burning; other stages, including burning in degenerate matter, can respond differently.
Bethe’s 1967 Nobel prize recognized contributions to nuclear reactions, especially stellar energy production. It came long after the 1938–1939 work. The achievement was to turn a possible energy source into a calculable physical explanation. Hydrogen supplied enough stored energy, tunneling and weak interactions set usable rates, and the star’s structure connected those rates to a long-lived glow. Each part was needed to explain the steady light crossing the night sky.