Physics 1939

Energy Production in Stars

Hans A. Bethe

Why stars shine: a carbon catalyst quietly fuses hydrogen into helium.

Choose your version

In depth · the introduction

The Sun has blazed for billions of years — and a pinch of carbon, used over and over without ever being used up, is part of how.

The big idea

The Sun makes its light by fusing hydrogen into helium deep in its core, where everything is crushingly hot and dense. Hans Bethe worked out the exact nuclear recipes — there are two. In light, cooler stars, hydrogen nuclei simply collide and stick. In stars as hot as the Sun and hotter, a more roundabout route dominates: the carbon–nitrogen cycle.

In that cycle, a single carbon nucleus grabs hydrogen nuclei one at a time, changing into nitrogen and oxygen forms along the way, and at the end it spits out a brand-new helium nucleus and turns back into exactly the carbon it started as — ready to go round again. The carbon is never consumed; it's a catalyst, a matchmaker. The net result is that four hydrogen nuclei become one helium nucleus, releasing the energy that, after a long climb, leaves the Sun as light.

How it came about

For a long time nobody could say what kept the Sun burning. The best idea — that the Sun slowly shrinks under its own gravity, heating as it falls — could power it for only a few tens of millions of years. But rocks and fossils showed the Earth was billions of years old, so that idea fell short by a hundredfold. In the 1920s Arthur Eddington insisted the answer had to lie in the atom itself.

The pieces came together in 1938. After a small conference in Washington gathered the astronomers' numbers and the physicists' new nuclear data, Bethe — back at Cornell — worked out the carbon–nitrogen cycle in a matter of weeks. The German physicist Carl Friedrich von Weizsäcker had found the same cycle independently at almost the same time. Bethe's 1939 paper laid out the full accounting, and nearly thirty years later it won him the 1967 Nobel Prize in Physics.

Why it mattered

It answered one of the oldest questions there is — why does the Sun shine, and how can it keep shining for so long — and in doing so it founded the science of how stars work. From this grew our understanding that stars are furnaces that forge the chemical elements, and the startling realization that the carbon, oxygen and iron in our own bodies were cooked inside stars long ago.

A way to picture it

Think of the carbon nucleus as a bricklayer's hod — a carrier that ferries bricks but is never built into the wall. Four times over it picks up a brick (a proton) and shuffles it along the line, through nitrogen and oxygen; at the end it drops off one finished block (a helium nucleus) and walks back empty to fetch the next load. Because the hod itself is never consumed, a tiny amount of carbon can help burn an enormous amount of hydrogen — that is exactly what makes it a catalyst.

Where it sits

Eddington had guessed that stars run on subatomic energy; Bethe supplied the exact reactions, and with them nuclear astrophysics began. The story ran on from here: in 1957 a famous paper by Burbidge, Burbidge, Fowler and Hoyle (B²FH) showed how the heavier elements are forged in a star's later life, and in 2020 physicists finally caught the ghostly neutrinos streaming out of the Sun's carbon cycle — eighty years after Bethe predicted the cycle was there.

The original document

Original source text

H. A. Bethe · Physical Review 55 (1939): 434–456

The paper sets a sharp problem: which nuclear reactions can supply the energy that ordinary stars radiate, given central temperatures of order ten to twenty million degrees and material that is mostly hydrogen? Gravitational contraction alone could power the Sun for only tens of millions of years — far too short — so the source must be nuclear.

Which reactions can occur

Bethe surveys the reactions of protons with the light nuclei and asks which proceed fast enough at stellar temperatures, where particles must tunnel through the electrical repulsion of the nucleus. A key conclusion: building nuclei heavier than helium this way is blocked, because no stable nucleus exists at mass 5 or mass 8 — so proton capture self-limits at helium, and the energy comes from turning hydrogen into helium.

Two routes from hydrogen to helium

Two processes dominate the main sequence. In the lightest, coolest stars, hydrogen burns by the direct proton–proton chain (worked out by Bethe with Critchfield). In stars as hot as the Sun and hotter, the leading process is a catalytic cycle running on carbon and nitrogen.

The carbon–nitrogen cycle

Bethe's reaction scheme for the cycle is: ¹²C + H → ¹³N + γ ; ¹³N → ¹³C + ε⁺ + ν ; ¹³C + H → ¹⁴N + γ ; ¹⁴N + H → ¹⁵O + γ ; ¹⁵O → ¹⁵N + ε⁺ + ν ; ¹⁵N + H → ¹²C + ⁴He. The original ¹²C reappears unchanged at the end, so carbon and nitrogen serve only as catalysts; the net effect is to combine four protons (and two electrons) into one ⁴He nucleus.

Temperature dependence and conclusion

Because the reaction rate climbs very steeply with temperature, a star's energy output is governed chiefly by its central temperature and its content of carbon and nitrogen. Bethe concludes that the carbon–nitrogen cycle is the principal source of energy in the Sun and in brighter main-sequence stars. (Later work, with better opacities and a lower solar central temperature, reassigned most of the Sun's output to the proton–proton chain — see the introduction.)

[ … ]

Cornell University, Ithaca, New York · 1939