How Do Stars Make Heavier Elements? The B²FH Paper Explained

Our explainer How Did the First Elements Form? ends with the universe a few minutes old, made almost entirely of hydrogen and helium, the work of our Primordix sticker. So where did the carbon, oxygen, iron and gold come from? The answer is the stars, and our Relativity & Cosmos tees celebrate the furnaces that do it. The roadmap was published in 1957 by Margaret Burbidge, Geoffrey Burbidge, William Fowler and Fred Hoyle, in a paper so famous it is known by its initials: B²FH.

What did the B²FH paper show?

Titled “Synthesis of the Elements in Stars”, the 104-page review opens with a line from King Lear: “It is the stars, The stars above us, govern our conditions” (Burbidge, Burbidge, Fowler & Hoyle 1957^[1]). Its central claim is that, to explain all the features of the cosmic abundance curve, “at least eight different types of synthesizing processes are demanded, if we believe that only hydrogen is primeval”. The same year, A. G. W. Cameron published his own account, “Nuclear Reactions in Stars and Nucleogenesis” (Cameron 1957^[2]). Fowler later shared the 1983 Nobel Prize in Physics “for his theoretical and experimental studies of the nuclear reactions of importance in the formation of the chemical elements in the universe” (NobelPrize.org^[3]).

The eight processes, as B²FH named them:

1. Hydrogen burning: makes helium, and is “responsible for the majority of the energy production in the stars”.
2. Helium burning: makes carbon from helium, then oxygen and neon.
3. α process: adds helium nuclei to neon to make magnesium, silicon, sulfur, argon and calcium.
4. e process: an “equilibrium process” at very high temperature and density that makes the iron peak (vanadium to nickel).
5. s process: slow neutron capture.
6. r process: rapid neutron capture.
7. p process: proton capture, for a few rare proton-rich isotopes.
8. x process: for deuterium, lithium, beryllium and boron, which stars destroy rather than make.

Step 1: hydrogen to helium

A star spends most of its life fusing hydrogen into helium. The net reaction is

4 ¹H → ⁴He + 2e⁺ + 2νₑ

where ¹H is a proton, ⁴He a helium-4 nucleus, e⁺ a positron and νₑ an electron neutrino. Four protons end up as one helium nucleus that is slightly lighter than the four separately, and that mass difference becomes the star’s energy through E = mc². How the Sun pulls this off despite the protons’ electric repulsion is covered in How Does the Sun Actually Work?.

Step 2: the carbon bottleneck

Once the core runs out of hydrogen it shrinks and heats. OpenStax explains that once it reaches 100 million K, “three helium atoms can begin to fuse to form a single carbon nucleus. This process is called the triple-alpha process” (OpenStax Astronomy 2e, §22.4^[4]):

3 ⁴He → ¹²C

This step only works at a useful rate because carbon-12 has an excited state at just the right energy. In 1957 Cook, Fowler and C. C. and T. Lauritsen measured it: a state with spin-parity 0⁺ at an excitation energy of 7.653 ± 0.008 MeV, lying only 372 ± 4 keV above the combined energy of three helium-4 nuclei (Cook et al. 1957^[5]). This resonance is often called the Hoyle state, after Fred Hoyle, whose 1954 paper on reactions in very hot stars laid out how elements from carbon to nickel could be built (Hoyle 1954^[6]).

Step 3: carbon to iron, and why it stops

In stars much more massive than the Sun, burning continues in stages. OpenStax describes how carbon fusion products can be converted into silicon, sulfur, calcium and argon, and these, heated further, “can combine to produce iron”. Just before collapse the core “resembles an onion”, with an iron core surrounded by layers of silicon and sulfur, oxygen, neon, carbon, helium and hydrogen (OpenStax Astronomy 2e, §23.2^[7]).

Then the chain stops. The reason is nuclear binding energy. Plotted against mass number A, the binding energy per nucleon “peaks very near iron (Fe, A = 56)”, which OpenStax notes is “why nuclear fusion in the cores of stars ends with Fe” (OpenStax University Physics, §10.2^[8]). Fusing lighter nuclei toward iron releases energy; fusing iron into anything heavier costs energy. With no energy source left, the core collapses.

Step 4: beyond iron, by neutron capture

Neutrons carry no charge, so they are not repelled by the nucleus and can be absorbed even by heavy nuclei. A nucleus that absorbs too many neutrons beta-decays, turning a neutron into a proton and becoming the next element up. B²FH identified two speeds:

• s process (slow): neutron capture on a long time-scale, where “the neutron captures occur at a slow (s) rate compared to the intervening beta decays”. An unstable nucleus usually has time to decay before the next neutron arrives.
• r process (rapid): neutron captures occur “at a rapid (r) rate compared to the beta decays”. B²FH assigned to it a large number of isotopes in the range 70 ≤ A ≤ 209, “and also for synthesis of uranium and thorium” (B²FH 1957^[1]).

Where does the gold come from? (still debated)

The r process needs a huge flood of neutrons in seconds, and where in the universe that happens has, in the words of one 2017 paper, “long been uncertain”. In 2017, the gravitational-wave event GW170817, a merger of two neutron stars, was followed by a glowing “kilonova”. Daniel Kasen and colleagues modelled its light and argued that it came from freshly made r-process elements, with one component of light (A < 140) and one of heavy (A > 140) elements, and concluded that “such mergers are a dominant mode of r-process production in the Universe” (Kasen et al. 2017^[9]). Whether mergers are the only important site, or whether some kinds of exploding stars also contribute, is still an open question, so we label this one debated.

FAQ

Are we really made of star stuff?

Mostly, yes. The hydrogen in your body’s water dates from the Big Bang, but your carbon, oxygen, calcium and iron were made by fusion in stars that lived and died before the Sun formed. For the woman who first showed what stars are made of, see Cecilia Payne.

Why didn’t the Big Bang make heavy elements?

The early universe cooled and thinned out within minutes, too fast to get far past helium. Our post on the first elements explains the timing; stars, by contrast, can burn helium for a long time at 100 million K.

What does “B²FH” stand for?

Burbidge, Burbidge, Fowler and Hoyle: Margaret and Geoffrey Burbidge, William Fowler and Fred Hoyle, the four authors of the 1957 paper.

References

1. E. M. Burbidge, G. R. Burbidge, W. A. Fowler & F. Hoyle (1957), “Synthesis of the Elements in Stars,” Rev. Mod. Phys. 29, 547–650 (DOI 10.1103/RevModPhys.29.547; free to read at APS). https://journals.aps.org/rmp/pdf/10.1103/RevModPhys.29.547
2. A. G. W. Cameron (1957), “Nuclear Reactions in Stars and Nucleogenesis,” PASP 69, 201 (DOI 10.1086/127051; metadata verified via Crossref). https://doi.org/10.1086/127051
3. NobelPrize.org, The Nobel Prize in Physics 1983 (Chandrasekhar, Fowler). https://www.nobelprize.org/prizes/physics/1983/summary/
4. A. Fraknoi, D. Morrison & S. C. Wolff, Astronomy 2e (OpenStax, Rice University), §22.4 “Further Evolution of Stars”. https://openstax.org/books/astronomy-2e/pages/22-4-further-evolution-of-stars
5. C. W. Cook, W. A. Fowler, C. C. Lauritsen & T. Lauritsen (1957), “B¹² , C¹²* and the Red Giants,” Phys. Rev. 107, 508–515. https://journals.aps.org/pr/abstract/10.1103/PhysRev.107.508
6. F. Hoyle (1954), “On Nuclear Reactions Occurring in Very Hot Stars. I. The Synthesis of Elements from Carbon to Nickel,” ApJS 1, 121 (DOI 10.1086/190005; metadata verified via Crossref). https://doi.org/10.1086/190005
7. A. Fraknoi, D. Morrison & S. C. Wolff, Astronomy 2e (OpenStax, Rice University), §23.2 “Evolution of Massive Stars: An Explosive Finish”. https://openstax.org/books/astronomy-2e/pages/23-2-evolution-of-massive-stars-an-explosive-finish
8. S. J. Ling, J. Sanny & W. Moebs, University Physics Volume 3 (OpenStax, Rice University), §10.2 “Nuclear Binding Energy”. https://openstax.org/books/university-physics-volume-3/pages/10-2-nuclear-binding-energy
9. D. Kasen, B. Metzger, J. Barnes, E. Quataert & E. Ramirez-Ruiz (2017), “Origin of the heavy elements in binary neutron-star mergers from a gravitational-wave event,” Nature 551, 80–84. https://www.nature.com/articles/nature24453

Written by Pixelated Physics. Every factual claim is linked to the source we checked; points that are still debated are labelled open.