Nucleosynthesis in stars

What powers a star?

In the 1800s, the best idea was that the Sun was slowly shrinking, turning gravitational potential energy into heat. Lord Kelvin calculated that this could keep it shining for only about 30 million years, far less than geologists needed for the Earth's rocks and Darwin needed for evolution.

In 1920 Arthur Eddington pointed out that four hydrogen atoms have about 0.7% more mass than one helium atom. If the Sun could fuse hydrogen into helium, that mass difference would be released as energy, enough for billions of years. Cecilia Payne's 1925 result that the Sun is mostly hydrogen supplied the fuel, and in 1938–39 Hans Bethe worked out the reaction steps.

The proton–proton chain

Fusion needs nuclei to get close enough (about $10^{-15}$ m) for the strong nuclear force to act, despite their electrostatic repulsion. That needs extremely high temperatures: about 10 to 15 million K in the Sun's core. Even then, most protons don't have enough kinetic energy to get over the repulsion. Fusion only happens because of quantum tunnelling, which gives a small chance of getting through the barrier.

In stars up to about 1.3 solar masses, including the Sun, most energy comes from the proton–proton (p–p) chain:

$$^1_1\text{H} + {}^1_1\text{H} \rightarrow {}^2_1\text{H} + {}^0_{+1}e + \nu_e$$

$$^2_1\text{H} + {}^1_1\text{H} \rightarrow {}^3_2\text{He} + \gamma$$

$$^3_2\text{He} + {}^3_2\text{He} \rightarrow {}^4_2\text{He} + 2\,{}^1_1\text{H}$$

The first step is extraordinarily slow, because one proton has to turn into a neutron by the weak interaction while the two protons are briefly close. An average proton in the Sun's core waits billions of years for it. That slowness is why the Sun lasts 10 billion years instead of exploding. The positrons annihilate with electrons immediately, adding their energy to the core.

Overall: $4\,{}^1_1\text{H} \rightarrow {}^4_2\text{He} + 2\,{}^0_{+1}e + 2\nu_e + 2\gamma$, releasing 26.7 MeV once the positrons have annihilated. A small fraction (about 2%) is carried away by the neutrinos, which pass straight out of the Sun.

The CNO cycle

In stars more massive than about 1.3 solar masses, with core temperatures above about 17 million K, hydrogen is fused mainly through the carbon–nitrogen–oxygen (CNO) cycle. Carbon-12 acts as a catalyst: it captures protons one at a time, goes through nitrogen and oxygen isotopes with two β⁺ decays, and is returned at the end along with a new helium-4 nucleus.

$$^{12}\text{C} \xrightarrow{+p} {}^{13}\text{N} \xrightarrow{\beta^+} {}^{13}\text{C} \xrightarrow{+p} {}^{14}\text{N} \xrightarrow{+p} {}^{15}\text{O} \xrightarrow{\beta^+} {}^{15}\text{N} \xrightarrow{+p} {}^{12}\text{C} + {}^{4}\text{He}$$

The net reaction is the same as for the p–p chain, $4\,{}^1\text{H} \rightarrow {}^4\text{He} + 2e^+ + 2\nu_e$, so the same mass is converted and the same total energy is released. The difference is the rate. Each step has to push a proton into a nucleus with charge +6 or +7, so the electrostatic barrier is much higher. The CNO rate rises extremely steeply with temperature (roughly as $T^{17}$ or more, compared with about $T^4$ for the p–p chain). Below about 17 million K, the p–p chain wins; above it, the CNO cycle takes over.

In the Sun the CNO cycle supplies only about 1% of the energy. In 2020 the Borexino detector in Italy detected neutrinos from the Sun's CNO cycle for the first time, confirming Bethe's prediction directly.

Post-main-sequence nucleosynthesis

When a star's core hydrogen runs out, the core contracts and heats up. At about 100 million K, helium nuclei can fuse by the triple-alpha process:

$$^4_2\text{He} + {}^4_2\text{He} \rightleftharpoons {}^8_4\text{Be}, \qquad {}^8_4\text{Be} + {}^4_2\text{He} \rightarrow {}^{12}_{\ 6}\text{C} + \gamma$$

Some carbon captures another helium nucleus to make oxygen: $^{12}\text{C} + {}^4\text{He} \rightarrow {}^{16}\text{O} + \gamma$. This is where almost all the carbon and much of the oxygen in the universe was made, including the atoms in your body.

In stars above about 8 solar masses the sequence continues, each stage needing a higher temperature and lasting a shorter time:

Fusion stops at iron and nickel because nuclei around mass number 56 have the highest binding energy per nucleon (page 8K). Fusing them further would absorb energy, not release it.

Making elements heavier than iron

Elements beyond iron are made by adding neutrons, which have no charge and so feel no repulsion. A nucleus captures neutrons until it becomes unstable, then β⁻ decays, turning a neutron into a proton and moving up one element.

• The s-process (slow neutron capture) happens in AGB stars over thousands of years. Each capture is usually followed by a β⁻ decay before the next capture. It makes about half the heavy elements, including much of the strontium, barium and lead.
• The r-process (rapid neutron capture) needs an enormous flood of neutrons, so that many are captured within seconds. It happens in neutron-star mergers and possibly some rare supernovae. In 2017 the merger GW170817 was detected by gravitational waves and then observed by telescopes worldwide, including Australian ones; its glow showed signs of freshly made heavy elements. Much of the gold, platinum and uranium in the universe was made this way.

Supernovae and stellar winds return all these elements to space, where they mix into new gas clouds. The Sun, formed 4.6 billion years ago, inherited elements made by generations of earlier stars. As astronomers like to say, we are made of star stuff.