Field · Emerged 1920 – 1957

Stellar Astrophysics

What makes the stars shine, and where do the chemical elements come from?

5 chapters4 min read6 turning points 1 open problem

Branched from: Astronomical Spectroscopy + Quantum Mechanics
Branched into: Compact Objects + Exoplanetary Science + Fusion Energy
Figures: Arthur Eddington, George Gamow, Robert d'Escourt Atkinson, Fritz Houtermans, Hans Bethe, Carl Friedrich von Weizsäcker, Fred Hoyle, William Fowler, Margaret Burbidge, Geoffrey Burbidge, Alastair Cameron

In brief

Stellar astrophysics explains how stars work: how they hold themselves up against gravity, where their energy comes from, how long they last and how they change as they age. A star is a ball of gas in balance. Gravity pulls inwards, the pressure of hot gas pushes outwards, and nuclear fusion in the core supplies the energy that keeps the gas hot.

In the nineteenth century no known energy source could keep the Sun shining for as long as geology and evolution required. The answer, fusion of hydrogen into helium, needed Einstein's $E = mc^2$ and quantum tunnelling, and was worked out between 1920 and 1939. By 1957 the same physics explained how stars forge nearly every element heavier than helium, including the carbon and oxygen in our bodies.

Key ideas

Hydrostatic equilibriumEnters 1920: At every depth in a star, the pressure of the gas balances the weight of the layers above. It fixes how hot and dense the core must be.
Nuclear fusionEnters 1938 – 1939: Light nuclei joining to form heavier ones, releasing energy because the product weighs slightly less than the ingredients. The Sun turns about 4 million tonnes of mass into energy every second.
Quantum tunnellingEnters 1928 – 1929: Protons repel each other and, by classical physics, the Sun's core is far too cool for them to touch. Quantum mechanics lets them tunnel through the barrier, rarely but often enough.
Stellar nucleosynthesisEnters 1957: The making of heavier elements inside stars and in their explosions: carbon and oxygen by fusion in giants, iron in massive stars, and heavier elements by neutron capture.

Chapter I

Not Enough Fuel

By the 1850s physicists knew the Sun radiates an enormous power, and asked what supplies it. Burning coal would last a few thousand years. William Thomson and Hermann von Helmholtz proposed that the Sun shines by slowly shrinking, turning gravitational energy into heat. That could last a few tens of millions of years. Geologists and Darwin wanted hundreds of millions. Thomson used his estimate to argue against Darwin's timescale for evolution, and the physicists seemed to have the stronger case.

Chapter II

Mass Into Energy

The answer came from a new kind of physics. In 1920 Francis Aston measured that a helium atom weighs about 0.7% less than four hydrogen atoms. Arthur Eddington saw what this meant. By Einstein's $E = mc^2$ , turning hydrogen into helium would release that missing mass as energy, enough to keep the Sun shining for billions of years. Critics objected that the Sun's core, at around 15 million degrees, was far too cool for protons to overcome their electrical repulsion. Eddington told them to go and find a hotter place.

Quantum mechanics settled the matter. In 1928 George Gamow showed that particles can tunnel through energy barriers they could not classically cross, and in 1929 Robert Atkinson and Fritz Houtermans applied it to stars. Protons fuse rarely, but a star has enough of them. In 1938–39 Hans Bethe worked out the actual reactions, the proton–proton chain and the carbon–nitrogen–oxygen cycle, and Carl Friedrich von Weizsäcker found the second independently.

Chapter III

Forging the Elements

If stars make helium, might they make the rest? The Big Bang made mostly hydrogen and helium. Fred Hoyle argued that everything heavier was cooked in stars. One step seemed impossible: three helium nuclei must meet almost at once to make carbon, and the rate was far too low. In 1953 Hoyle predicted that carbon has an energy level at about 7.65 MeV that makes the reaction resonant, and persuaded William Fowler's sceptical group at Caltech to look. It was there.

In 1957 Margaret Burbidge, Geoffrey Burbidge, Fowler and Hoyle set out how stars build almost every element: fusion up to iron in the cores of massive stars, then slow neutron capture in ageing giants and rapid neutron capture in violent explosions. Alastair Cameron reached similar conclusions independently. The calcium in bones and the iron in blood were made in stars that died before the Sun formed.

Chapter IV

A Closer Look: How Long Can the Sun Shine?

The Sun radiates $L = 3.83 \times 10^{26}$ watts. By $E = mc^2$ , that is a loss of mass of

\frac{L}{c^2} = \frac{3.83 \times 10^{26}}{(3.00 \times 10^{8})^2} \approx 4.3 \times 10^9 \text{ kg per second} ,

over four million tonnes every second, converted from matter into sunlight.

How long can that go on? Fusing hydrogen into helium converts 0.7% of the mass into energy. Only the core, about a tenth of the Sun's mass of $2 \times 10^{30}$ kg, gets hot enough to fuse. So the available energy is

E = 0.007 \times 0.1 \times 2 \times 10^{30} \times (3.00 \times 10^8)^2 \approx 1.3 \times 10^{44} \text{ J} ,

and dividing by the power output gives about $3.3 \times 10^{17}$ seconds, roughly 10 billion years. The Sun is about 4.6 billion years old, so it is around halfway through its life on the main sequence. Detailed models agree.

Compare Kelvin's source, gravitational contraction. The energy a shrinking Sun can release is about $GM^2/R$ , which divided by the Sun's power gives about 30 million years. Kelvin's own estimates, from 1862 onwards, fell from about 100 million years to a few tens of millions. Nuclear energy gives more than 300 times as much. The physicists had not made a mistake in their calculation, only in assuming they knew all the sources of energy. When radioactivity was discovered, the rocks themselves showed the Earth to be billions of years old.

Chapter V

Stellar Lives

Stellar astrophysics now explains the Hertzsprung–Russell diagram from spectroscopy as a map of stellar lives. Stars spend most of their time on the main sequence burning hydrogen, swell into giants when the core's hydrogen runs out, and end in ways set by their mass, the subject of compact objects. Neutrinos from the Sun's core, detected since 1968 and from the CNO cycle since 2020, confirm that fusion is happening there now. The origin of the heaviest elements, gold and uranium among them, is still being settled.

Turning points6

1920PARADIGM-SHIFT
Eddington proposes subatomic energy
Francis Aston has just measured that a helium atom weighs slightly less than four hydrogen atoms. Arthur Eddington, addressing the British Association, argues that turning hydrogen into helium would release enough energy, through $E = mc^2$ , to power the Sun for billions of years. His 1926 book on the internal constitution of the stars became the foundation of the subject.
Arthur Eddington
› Sources (2)
- Eddington, A. S. (1920). The internal constitution of the stars. The Observatory 43: 341–358.
- Eddington, A. S. (1926). The Internal Constitution of the Stars. Cambridge University Press.
1928 – 1929DISCOVERY
Tunnelling makes fusion possible
George Gamow explains radioactive alpha decay as quantum tunnelling through a barrier. Robert Atkinson and Fritz Houtermans apply the idea in reverse: protons in a star's core can tunnel into nuclei and fuse at temperatures far below those that classical physics requires. Critics had told Eddington the Sun was too cool for fusion. He replied that they should go and find a hotter place.
George Gamow, Robert d'Escourt Atkinson, Fritz Houtermans
› Sources (2)
- Gamow, G. (1928). Zur Quantentheorie des Atomkernes. Zeitschrift für Physik 51: 204–212.
- Atkinson, R. d'E. & Houtermans, F. G. (1929). Zur Frage der Aufbaumöglichkeit der Elemente in Sternen. Zeitschrift für Physik 54: 656–665.
1938 – 1939DISCOVERY
Bethe's fusion cycles
Hans Bethe works out the two chains of nuclear reactions by which stars turn hydrogen into helium: the proton–proton chain, with Charles Critchfield, which dominates in the Sun, and the carbon–nitrogen–oxygen cycle, which dominates in heavier stars. Carl Friedrich von Weizsäcker found the CNO cycle independently. Bethe received the 1967 Nobel prize.
Hans Bethe, Carl Friedrich von Weizsäcker
› Sources (1)
- Bethe, H. A. (1939). Energy production in stars. Physical Review 55(5): 434–456.
1953EXPERIMENTContested
The carbon resonance
Carbon forms in stars when three helium nuclei fuse, which seemed far too slow to make the carbon observed. Fred Hoyle predicts that carbon must have an excited state at about 7.65 MeV that speeds the reaction. He persuades William Fowler's group at Caltech to look, and they find it almost exactly where predicted.
What is disputed
The episode is often told as the first successful "anthropic" prediction, deduced from the existence of carbon-based life. Historians such as Helge Kragh have argued that Hoyle reasoned from the observed abundance of carbon, not from life, and that the anthropic framing was added decades later.
Fred Hoyle, William Fowler
› Sources (2)
- Dunbar, D. N. F., Pixley, R. E., Wenzel, W. A. & Whaling, W. (1953). The 7.68-MeV state in C12. Physical Review 92(3): 649–650.
- Kragh, H. (2010). When is a prediction anthropic? Fred Hoyle and the 7.65 MeV carbon resonance. PhilSci Archive.
1957PARADIGM-SHIFTContested
The elements are made in stars
Margaret Burbidge, Geoffrey Burbidge, William Fowler and Fred Hoyle publish a hundred-page paper, known as B²FH, showing how stars build nearly every element heavier than helium, through fusion and through slow and rapid neutron capture. Alastair Cameron reached many of the same conclusions independently the same year. Apart from hydrogen and most helium, the atoms of the Earth were forged in stars.
What is disputed
Of the four authors, only Fowler received a Nobel prize, in 1983, shared with Subrahmanyan Chandrasekhar for other work. The omission of Hoyle, whom many regarded as the intellectual driving force, surprised many. Some have attributed it to his public clashes with the scientific establishment, though the committee's reasons are not known. Cameron's parallel work is less often remembered.
Fred Hoyle, William Fowler, Margaret Burbidge, Geoffrey Burbidge, Alastair Cameron
› Sources (2)
- Burbidge, E. M., Burbidge, G. R., Fowler, W. A. & Hoyle, F. (1957). Synthesis of the elements in stars. Reviews of Modern Physics 29(4): 547–650.
- Cameron, A. G. W. (1957). Stellar evolution, nuclear astrophysics, and nucleogenesis. Chalk River Report CRL-41.
2020EXPERIMENT
Neutrinos from the CNO cycle
The Borexino detector under the Gran Sasso mountain in Italy detects neutrinos from the carbon–nitrogen–oxygen cycle in the Sun's core, eighty years after Bethe predicted it. Both of his fusion chains have now been observed directly.
› Sources (1)
- Borexino Collaboration (2020). Experimental evidence of neutrinos produced in the CNO fusion cycle in the Sun. Nature 587: 577–582.

Applications

Where it is used

Evolution↗ Biology · Evolutionary Biology
Enough time for evolution
Kelvin's estimate of the Sun's age, a few tens of millions of years, seemed to leave too little time for natural selection, and Darwin worried about it. Nuclear fusion gave the Sun billions of years, and radioactive dating gave the Earth 4.5 billion, ample time for evolution.
› Sources (1)
- Burchfield, J. D. (1975). Lord Kelvin and the Age of the Earth. Science History Publications.
Energy
Fusion power on Earth
Fusion reactors try to reproduce the Sun's energy source on Earth, at much higher temperatures because they cannot rely on the Sun's gravity and size. In 2022 the National Ignition Facility produced more fusion energy from a fuel capsule than the laser energy delivered to it, for the first time.
› Sources (1)
- Abu-Shawareb, H. et al. (2024). Achievement of target gain larger than unity in an inertial fusion experiment. Physical Review Letters 132(6): 065102.

Open problems

Where the map runs out

Open

Where are the heaviest elements made?

Open as of 2026. Neutron-star mergers are known to contribute, but whether they are the main source is debated.

About half the elements heavier than iron, including gold, platinum and uranium, are made by rapid neutron capture, which needs extreme densities of free neutrons. The 2017 neutron-star merger GW170817 showed such mergers produce them. Whether mergers account for all of them, or supernovae of rare kinds contribute too, is unresolved.

Why it is hard: The nuclei involved are too unstable to study easily in laboratories, and mergers are rare and brief. The timing of heavy elements in the oldest stars seems to require a source that acts earlier than mergers typically can.
What resolving it unlocks: The origin of the gold and uranium on Earth, and a test of nuclear physics at conditions no laboratory can reach.

› Sources (1)

Kasen, D., Metzger, B., Barnes, J., Quataert, E. & Ramirez-Ruiz, E. (2017). Origin of the heavy elements in binary neutron-star mergers from a gravitational-wave event. Nature 551: 80–84.