Advanced Burning, the Iron Peak, and the s/r Processes

A star of more than about $8M_{\odot }$ does not stop at carbon and oxygen. Its core contracts and heats through a succession of burning stages, each fusing the ashes of the last, until it assembles an iron core that can release no further energy. The sequence is governed by two curves met earlier: the Coulomb barrier, which raises the ignition temperature of each heavier fuel, and the binding energy per nucleon, which peaks at iron and marks the end of energy-releasing fusion. Everything heavier than the iron peak is built not by fusion but by capturing neutrons.

Advanced burning stages

After core helium burning leaves a carbon–oxygen core, contraction raises the central temperature through the ignition points of successively heavier fuels. Each stage has a higher Coulomb barrier and therefore a higher ignition temperature, following the Gamow scaling of reaction rates.

• Carbon burning ($\sim 8\times 10^8\text{K}$): ${}^{12}\text{C}+{}^{12}\text{C}$ yields ${}^{20}\text{Ne}+\alpha$, ${}^{23}\text{Na}+p$, and other channels.
• Neon burning ($\sim 1.5\times 10^9\text{K}$): photodisintegration ${}^{20}\text{Ne}+\gamma \to {}^{16}\text{O}+\alpha$ precedes ${}^{20}\text{Ne}+\alpha \to {}^{24}\text{Mg}+\gamma$. Neon burns before oxygen because its photodisintegration sets in at a lower temperature than oxygen fusion.
• Oxygen burning ($\sim 2\times 10^9\text{K}$): ${}^{16}\text{O}+{}^{16}\text{O}$ produces ${}^{28}\text{Si}$, ${}^{31}\text{P}$, ${}^{31}\text{S}$, and ${}^{32}\text{S}$.
• Silicon burning ($\sim 3\times 10^9\text{K}$): the Coulomb barrier for ${}^{28}\text{Si}+{}^{28}\text{Si}$ is too high to fuse directly. Instead, energetic photons photodisintegrate some silicon into alpha particles, protons, and neutrons, which are recaptured onto other nuclei, gradually rearranging the composition toward the iron peak.

Each stage releases less energy per unit mass than the last, and neutrino losses grow steeply with temperature, so the burning lifetimes collapse. For a $20M_{\odot }$ star the durations run from millions of years for hydrogen down to a few days for silicon.

Because each fuel ignites in the core and then continues burning in a shell around the newly formed heavier core, the star develops a layered onion-shell structure, with the heaviest ash at the center and hydrogen still burning at the outer edge.¹

The iron peak and the end of fusion

At temperatures above $\sim 4\times 10^9\text{K}$ the forward fusion and reverse photodisintegration reactions come into balance, and the composition relaxes to nuclear statistical equilibrium (NSE). Under equilibrium the abundances are fixed by a Saha-like relation that favors the most tightly bound nuclei, which are the iron-peak species around ${}^{56}\text{Fe}$, ${}^{54}\text{Fe}$, and ${}^{56}\text{Ni}$. Silicon burning drives the core into this state, and the core becomes iron.

The reason iron is the endpoint is the binding energy per nucleon,

which measures how much energy is released when $A$ free nucleons assemble into a nucleus. This curve rises steeply from hydrogen, reaches a broad maximum of about $8.8\text{MeV}$ per nucleon near $A\approx 56$–$62$, then declines gently toward uranium. Fusion releases energy only when it moves nuclei toward the peak, that is, when $B/A$ increases. Fusing iron-peak nuclei into anything heavier would decrease $B/A$ and therefore absorb energy. The core can extract no more nuclear energy, loses its pressure support, and is left to collapse, the trigger for a core-collapse supernova.

Neutron capture beyond iron

Elements heavier than the iron peak cannot be built by charged-particle fusion: the Coulomb barrier is prohibitive and the reactions are endothermic. They are assembled instead by neutron capture, which has no Coulomb barrier. A nucleus absorbs a neutron, $(Z,A)+n\to (Z,A+1)$; if the product is stable it waits for another neutron, and if it is unstable it ${\beta }^{-}$ decays, $(Z,A)\to (Z+1,A)+e^{-}+{\bar{\nu }}_e$, raising the atomic number. The path a nucleus takes through the chart of nuclides depends entirely on the ratio of the neutron-capture rate to the beta-decay rate, which splits nucleosynthesis into two regimes.

The slow (s) process operates when neutron capture is slow compared with beta decay. After each capture, an unstable nucleus decays back to stability before the next neutron arrives, so the path hugs the valley of beta stability, stepping from one stable isotope to the next. It occurs in thermally pulsing asymptotic-giant-branch stars, where the reactions ${}^{13}\text{C}(\alpha ,n){}^{16}\text{O}$ and ${}^{22}\text{Ne}(\alpha ,n){}^{25}\text{Mg}$ supply modest neutron densities of order $10^7$–$10^{11}{\text{cm}}^{-3}$. The s-process builds nuclei up to bismuth, where an alpha-decay cycle terminates the chain.

The rapid (r) process operates when neutron capture is fast compared with beta decay. A nucleus captures many neutrons in quick succession, driving it far to the neutron-rich side of stability toward the neutron drip line, and only when the neutron flux ends does the highly unstable product beta-decay back to stability. It requires enormous neutron densities, of order $10^{22}$–$10^{24}{\text{cm}}^{-3}$, reached only in explosive sites: the neutrino-driven winds of core-collapse supernovae and, decisively, the ejecta of neutron-star mergers. The r-process makes the heaviest nuclei, including thorium and uranium.

Because the two processes reach the neutron magic numbers $N=50,82,126$ at different proton numbers, they leave distinct fingerprints in the abundance pattern: the s-process abundance peaks (at $A\approx 88,138,208$) sit at slightly higher mass than the r-process peaks (at $A\approx 80,130,195$), because the r-process reaches a magic neutron number while still neutron-rich and the nuclei only later decay to lower mass along an isobar. The double-peaked abundance curve of the heavy elements is direct evidence that both processes contribute.

The origin of the elements

Assembling these mechanisms accounts for the cosmic abundance pattern across the periodic table:

• Hydrogen, helium, and a trace of lithium were made in Big Bang nucleosynthesis in the first minutes.
• Carbon through the iron peak are forged by fusion in stellar cores, the lighter of these also by low-mass stars and the iron-peak nuclei predominantly in the explosive burning of supernovae.
• Most nuclei heavier than iron are built by neutron capture, split between the s-process in AGB stars and the r-process in supernovae and neutron-star mergers.
• Lithium, beryllium, and boron are largely produced by cosmic-ray spallation of heavier nuclei in the interstellar medium, filling a gap the stellar processes skip.

The nuclear physics of this module fixes where each element comes from and when. The Gamow peak set the ignition temperatures that order the burning stages; the binding-energy curve fixed the iron endpoint that ends fusion and collapses the core; and neutron capture, in its slow and rapid forms, builds everything heavier. The collapse of the iron core and the explosive nucleosynthesis that accompanies it are taken up in core-collapse supernovae, and the r-process ejecta of merging neutron stars are confirmed observationally in multimessenger astronomy.