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The B2FH paper, named after the initials of the authors of the paper, Margaret Burbidge, Geoffrey Burbidge, William A. Fowler, and Fred Hoyle, is a landmark paper on the origin of the chemical elements published in Reviews of Modern Physics in 1957.[1] The title of that paper is "Synthesis of the Elements in Stars", but as that paper grew in influence, it came to be referred to only as "B2FH". The B2FH paper spread stellar nucleosynthesis theory widely in the scientific community, especially among astronomers who saw everyday relevance to their quest, at a time when it was appreciated by only a handful of experts in nuclear physics. But it did not create the theory of stellar nucleosynthesis as much as bring it vividly to life.

The paper comprehensively outlined and analyzed several key processes that are responsible for the nucleosynthesis of the elements heavier than iron and their relative abundance by the capture within stars of free neutrons. It advanced much less the understanding of the synthesis of the very abundant elements from silicon to nickel. A puzzle about that is that despite Hoyle's coauthorship of B2FH and being its chief conceptual architect, the paper did not include the carbon-burning process, the oxygen-burning process and the silicon-burning process, each of which contributes massively to the growth of stellar metallicity from magnesium to nickel in the interstellar gas. The supernova nucleosynthesis that achieves that had been published by Hoyle in 1954.[2]Donald D. Clayton has attributed the severe undercitations of Hoyle's 1954 paper relative to the voluminous citations of B2FH to several factors: the advanced difficulty of digesting Hoyle's 1954 paper even for his B2FH coauthors, as it proved to be for the world of astronomy generally; to Hoyle's having described its key equation only in words[3] rather than writing it prominently in his paper; and finally to a lack of careful review by Hoyle himself of the B2FH draft written by two junior coauthors who had themselves not adequately digested Hoyle's paper.[4]

Physics in 1957

At the time of the publication of the B2FH paper, George Gamow advocated a theory of the universe according to which virtually all elements, or atomic nuclei, were synthesized during the Big Bang. The implications of Gamow's nucleosynthesis theory (not to be confused with present-day nucleosynthesis theory) would be that nuclear abundances in the universe are largely static. Together, Hans Bethe and Charles L. Critchfield had derived the Proton proton chain (pp-chain) in 1938,[5] and Carl von Weizsäcker[6] and Hans Bethe[7] had independently derived the CNO cycle in 1938 and 1939, respectively, to show that the conversion of hydrogen to helium by nuclear fusion could account for stellar energy production. Thus, it was known by Gamow and others that the abundances of hydrogen and helium were not perfectly static. Small production of helium would add marginally to its abundance left by the Big Bang. But stellar nuclear power was not a compelling step toward stellar nucleosynthesis. The elements from carbon upward remained a mystery. Gamow advocated the theory that all elements were residual from the Big Bang, also allowing for slight changes in the ratios of hydrogen and helium.

Then Fred Hoyle, initially in 1946 and later in 1954,[2] and his three collaborators who authored B2FH gave a different account for the origin of heavy elements. They claimed that all other atomic nuclei heavier than lithium had to have been synthesized in stars rather than during the Big Bang, if a Big Bang had in fact occurred (as was later confirmed). Both theories agreed that some light nuclei (hydrogen, helium and a relatively tiny mass of lithium) were not created in stars, and this contributed to the now-accepted theory of Big Bang nucleosynthesis of H, He and Li.

Physics in the paper

Because the idea of origin of the atoms of the chemical elements within stars is that a majority of all elements (all except for hydrogen, helium and the tiny amount of lithium) must come from stars, that idea is called the theory of stellar nucleosynthesis.[8] The key difference between this theory of stellar nucleosynthesis and all previous accounts for the origin of the elements is that it predicted chemical evolution of the universe, which is testable by astronomers' measuring stellar spectral lines. Quantum mechanics explains why different atoms emit light at characteristic wavelengths and so, by studying the light emitted from different stars, one may infer the atmospheric composition of individual stars. Upon undertaking such a task, observations indicate a strong negative correlation between a star's initial heavy element content (metallicity) and its age (red shift). More recently formed stars tend to have higher metallicity.

Big Bang nucleosynthesis tells us that the early universe consisted of only the light elements, and so one expects the first stars to be composed of hydrogen, helium, and lithium, the three lightest elements. Stellar structure and the Hertzsprung-Russell diagram indicate that the length of the lifetime of a star depends greatly on its initial mass, so that massive stars are very short-lived, and less massive stars are longer-lived. B2FH argues that as a star dies, it will enrich the interstellar medium with 'heavy elements' (in this case all elements heavier than lithium, the third element), from which newer stars are formed. This account is consistent with the observed negative correlation between stellar metallicity and red shift.

The theory presented by the authors of B2FH also described key aspects of the nuclear physics and astrophysics involved in how stars achieve this creative act. By carefully scrutinizing the table of nuclides, they were able to characterize the existence of different stellar environments that could produce the observed isotopic abundances and the nuclear processes that must occur in these stars. In this paper the authors described creatively the existence of the p-process, r-process, and s-process to account for the elements heavier than iron. The abundances of these heavy elements and their isotopes are roughly 100,000 times less than those of the major elements, which Hoyle (1954)[2] had explained three years earlier by nuclear fusion within the burning shells of massive stars.

Writing of the paper

Margaret Burbidge and Geoffrey Burbidge wrote the first complete draft of the paper in 1956 at Caltech, incorporating an earlier draft of material by Fowler and Hoyle and adding extensive astronomical observations and experimental data to support the theory. Both of the Burbidges had temporary positions created for them in 1956 at Caltech by W. A. Fowler for this purpose. Hoyle and Fowler had worked extensively on the early draft in 1955 when all four coauthors were temporarily together in Cambridge U.K. The original theory of stellar nucleosynthesis had been created earlier in published research papers in 1946 and 1954 by Fred Hoyle in Cambridge. Geoffrey Burbidge has asserted that it is a misconception some have had to presume that Fowler was the leader of the group because the writing and submission for publication were done at Caltech in 1956. But Fowler, though an accomplished nuclear physicist, was still actively learning Hoyle's theory in 1955 while on sabbatical leave from Caltech and later stated emphatically[9] that Hoyle was the intellectual leader of this effort. Both Burbidges were also learning Hoyle's theory during 1954-55 in Cambridge. And yet "There was no leader in the group," G. Burbidge puzzlingly wrote in 2008, "we all made substantial contributions".[10] Fowler appeared to be their leader only by virtue of getting the paper written and submitted at Caltech, and Fowler asserted that Hoyle was the leader. So Burbidge's remarks could validly be questioned.


Because B2FH firmly focused scientific attention onto the field of nuclear astrophysics, it has frequently been said to have founded that field, which exaggerates its importance to the history of science considerably. Although the scientific theory had clearly been started by Fred Hoyle's 1946 and 1954 published papers as well as by his attracting to Cambridge U.K. the B2FH team, Hoyle's own papers did not attract the scientific following that the B2FH paper quickly achieved. Some writers have erroneously stated William A. Fowler was awarded half of the 1983 Nobel Prize in Physics for his contributions to B2FH, but that prize was clearly stated instead[11] to have been for Fowler's work on evaluating for decades experimental nuclear physics papers for rates of thermonuclear reactions in stellar cores. Fowler's contributions to B2FH can clearly also seen in the nuclear expertise of the details of the s-process and the r-process, which were its major new creative theories which captured the excitement of astronomers. Some believe that Fred Hoyle also deserved similar Nobel Prize recognition for his scholarship creating the theory, and they contend that his unorthodox views concerning the Big Bang played a role in his not being awarded a share of the Nobel Prize.[12]

Geoffrey Burbidge wrote in 2008, "Hoyle should have been awarded a Nobel Prize for this and other work. On the basis of my private correspondence, I believe that a major reason for his exclusion was that W. A. Fowler was believed to be the leader of the group."[10] Burbidge stated that this perception is not true and also points to Hoyle's earlier papers from 1946 as indicators of Hoyle's role in the authorship of the theory of stellar nucleosynthesis[13] and 1954.[2] Burbidge said that "Hoyle's work has been undercited in part because it was published in an astrophysical journal,[2] and a new one at that (the very first volume, in fact), whereas B2FH was published in a well-established physics journal, Reviews of Modern Physics. When B2FH was first written, preprints were widely distributed to the nuclear physics community. Willy Fowler was very well known as a leader in that community, and the California Institute of Technology already had a news bureau that knew how to spread the word."

In 2007 a conference was held at Caltech in Pasadena, California to commemorate the 50th anniversary of the publication of B2FH.[14] The opening session on July 23 was titled Historical Perspective, but only G. R. Burbidge and Donald D. Clayton, Fowler's research student during 1956-1961, actually presented talks on that topic. Burbidge posted a lengthy text that included his remarks on the writing of B2FH, but also on several other topics that seem to be part of a longer multi-purpose text that exceeded his remarks at the conference. Clayton[15] on the other hand posted both his power point slides and his comments on his historical opinion of cultural reasons for the great fame achieved by B2FH. He pointed specifically to the high praise among astronomers owing to B2FH citing more than a hundred astronomy papers that thrilled astronomers by their referring to observational signs of stellar nucleosynthesis. These brought new headline purpose to astronomers' research, whereas Hoyle's 1954 paper focused only on his nucleosynthesis theory.

Cultural revolution: computers

The papers of Hoyle (1946) and Hoyle (1954) and of B2FH (1957) were written by those scientists before the advent of the age of computers. They used hand calculations, deep thought, physical intuition, and thorough familiarity with details of nuclear physics. Brilliant as these founding papers were, a cultural disconnect emerged with a younger generation of workers who began to construct computer programs[16] that would eventually yield numerical answers for the advanced evolution of stars[17] and the nucleosynthesis within.[18][19] Most of this new generation did not digest Hoyle (1954) carefully and in any case forgot what they had read in their focus on the immense task of computerizing massive stars. They usually did not cite Hoyle (1954) but did cite B2FH, which became a needed default citation for stellar nucleosynthesis. This cultural revolution began in late 1960s. The upshot in regard to the confusion over Hoyle and B2FH that followed was made possible by the B2FH review's failing to review Hoyle's picture. Understandable therefore was the new generation's feeling of discovering themselves the picture that Hoyle had presented, albeit with huge numerical details. The computer models of massive stars demonstrated that core burning in massive stars occurred in smaller cores than the previous burning phase had. This shrinking of successive cores yielded an onion shell model of the sequence of burning phases, a shell model that was necessary for Hoyle's 1954 picture to work as simultaneous ejection of the abundances from each burning phase. Understanding this cultural revolution of computing takes one far in understanding why Hoyle (1954) was forgotten and B2FH appeared to have been the work that founded stellar nucleosynthesis, as many even claimed.

See also

Further reading

  • Burbidge, E. Margaret; Burbidge, G. R.; Fowler, William A.; Hoyle, F. (1957). "Synthesis of the Elements in Stars". Reviews of Modern Physics. 29 (4): 547-650. Bibcode:1957RvMP...29..547B. doi:10.1103/RevModPhys.29.547.


  1. ^ E. M. Burbidge; G. R. Burbidge; W. A. Fowler; F. Hoyle (1957). "Synthesis of the Elements in Stars" (PDF). Reviews of Modern Physics. 29 (4): 547. Bibcode:1957RvMP...29..547B. doi:10.1103/RevModPhys.29.547.
  2. ^ a b c d e F. Hoyle (1954). "On Nuclear Reactions Occurring in Very Hot Stars. I. The Synthesis of Elements from Carbon to Nickel". Astrophysical Journal Supplement. 1: 121. Bibcode:1954ApJS....1..121H. doi:10.1086/190005.
  3. ^ Donald D. Clayton (2007). "Hoyle's Equation". Science. 318 (5858): 1876-1877. doi:10.1126/science.1151167. PMID 18096793.
  4. ^ See footnote 1 in Donald D. Clayton (2008). "Fred Hoyle, primary nucleosynthesis and radioactivity". New Astronomy Reviews. 32: 360-363.
  5. ^ H. A. Bethe; C. L. Critchfield (1938). "The Formation of Deuterons by Proton Combination". Physical Review. 54 (4): 248. Bibcode:1938PhRv...54..248B. doi:10.1103/PhysRev.54.248.
  6. ^ C. F. von Weizsäcker (1938). "Über Elementumwandlungen in Innern der Sterne II". Physikalische Zeitschrift. 39: 633.
  7. ^ H. A. Bethe (1939). "Energy Production in Stars". Physical Review. 55 (5): 434. Bibcode:1939PhRv...55..434B. doi:10.1103/PhysRev.55.434.
  8. ^ G. Wallerstein; et al. (1997). "Synthesis of the elements in stars: forty years of progress" (PDF). Reviews of Modern Physics. 69 (4): 995-1084. Bibcode:1997RvMP...69..995W. doi:10.1103/RevModPhys.69.995. hdl:2152/61093. Archived from the original (PDF) on 9 September 2011.
  9. ^ "William A. Fowler - Nobel Lecture: Experimental and Theoretical Nuclear Astrophysics; the Quest for the Origin of the Elements". Nobelprize.org. Nobel Media AB 2014. Web. 29 Mar 2018. http://www.nobelprize.org/nobel_prizes/physics/laureates/1983/fowler-lecture.html (see Biographical)
  10. ^ a b G. Burbidge (2008). "Hoyle's Role in B2FH". Science. 319 (5869): 1484. doi:10.1126/science.319.5869.1484b. PMID 18339922.
  11. ^ "William A. Fowler - Facts". Nobelprize.org. Nobel Media AB 2014. Web. 28 Mar 2018. http://www.nobelprize.org/nobel_prizes/physics/laureates/1983/fowler-facts.html "William A. Fowler - Nobel Lecture: Experimental and Theoretical Nuclear Astrophysics; the Quest for the Origin of the Elements". Nobelprize.org. Nobel Media AB 2014. Web. 29 Mar 2018. http://www.nobelprize.org/nobel_prizes/physics/laureates/1983/fowler-lecture.html
  12. ^ R. McKie (2 October 2010). "Fred Hoyle: the scientist whose rudeness cost him a Nobel prize". The Guardian. Retrieved 2013.
  13. ^ F. Hoyle (1946). "The Synthesis of the Elements from Hydrogen" (PDF). Monthly Notices of the Royal Astronomical Society. 106 (5): 343. Bibcode:1946MNRAS.106..343H. doi:10.1093/mnras/106.5.343.
  14. ^ "Nuclear Astrophysics: 1957-2007 - Beyond the first 50 years". California Institute of Technology. July 2007. Archived from the original on 2011-05-07. Retrieved .
  15. ^ http://www.na2007.caltech.edu/Talks/ClaytonCommentsNA2007.doc
  16. ^ Donald D. Clayton, Principles of Stellar Evolution and Nucleosynthesis, McGraw-Hill (1968) Chapter 6. Calculation of Stellar Structure
  17. ^ For example, Iben, Icko, Jr. (1967). "Stellar Evolution. VI. Evolution from the Main Sequence to the Red-Giant Branch for Stars of Mass 1 M, 1.25 M, and 1.5 M". The Astrophysical Journal. 147: 624. Bibcode:1967ApJ...147..624I. doi:10.1086/149040.
  18. ^ Woosley, S. E.; Weaver, Thomas A. (1995). "The Evolution and Explosion of Massive Stars. II. Explosive Hydrodynamics and Nucleosynthesis". The Astrophysical Journal Supplement Series. 101: 181. Bibcode:1995ApJS..101..181W. doi:10.1086/192237.
  19. ^ Thielemann, Friedrich-Karl; Nomoto, Ken'ichi; Hashimoto, Masa-Aki (1996). "Core-Collapse Supernovae and Their Ejecta". The Astrophysical Journal. 460: 408. Bibcode:1996ApJ...460..408T. doi:10.1086/176980.

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