John Faulkner is Professor Emeritus of Astronomy and Astrophysics at the University of California, Santa Cruz. He was one of Fred Hoyle's many graduate students from 1960 to 1964, subsequently spent two stimulating years as a postdoctoral fellow in William A. Fowler's Kellogg Laboratory at CalTech, and in 1966 returned to Hoyle's fledgling Institute of Theoretical Astronomy, Cambridge. In 1969, after receiving an offer he couldn't refuse, Faulkner moved to UC Santa Cruz.
On a Sunday evening in late February or early March 1964, I witnessed a remarkable sight at Fred Hoyle's home in Clarkson Close, Cambridge. I had just reported to him the results of computing the helium content of the universe from a presumed hot big bang origin. Those computations were performed according to a prescription Fred had lain out in full in a lecture only the previous morning.
For a wide range of initial conditions, the results showed what we at least regarded as a "high" helium content. (That characterization has to be understood in the context and against the particular prejudices of those days.) Fred reacted ecstatically to the news I had brought him. He got up from his armchair in the study alcove where he invariably read, wrote and talked with students, and walked triumphantly about the adjacent living room, shaking his fist in the air and declaring, "We've disproved the big bang!"
Within a short time (see Narlikar's contribution), Fred came to realize instead that he might well have found some of the best supporting evidence then possible for the big bang (short of observing the CMBR itself). Here I try to describe what led up to Hoyle's remarkable moment of mistaken euphoria, and explain it in its historical context.
I became Fred Hoyle's graduate student after obtaining a distinction in Part III of the Cambridge Mathematical Tripos. The grueling Part III year was the traditional hurdle for those wishing to be admitted as graduate students the next year. Those allowed to take it (only those students with first or high upper second class degrees in Part II of the Tripos) were neither fish nor fowl - no longer undergraduates but not yet admitted as graduate students. We all knew that at least our Cambridge research futures hung on how we did in the six end-of-year exams. A distinction (a "star") would guarantee success, a mere pass would lead to uncertainty. (We were however assured that as already highly selected graduates, we could all simply walk into an appropriate graduate program at any other university fortunate enough to have us apply!)
After the exam results were announced, those interested in pursuing research on the applied side were asked to meet in the sacred small lecture room on the first floor (second floor US) of the Arts School, where, despite its deceptive name, physics and astrophysics luminaries like Dirac, Hoyle, Mestel, and later Sciama gave their high-powered Part III lectures. G. K. Batchelor, the chairman of the recently established DAMTP, read out some pertinent sentences: "Professor Hoyle would like to see the following students tomorrow morning at his home ... At 9 o'clock, J.V. Narlikar, at 10 o'clock, J. Faulkner, at 11 o'clock, S. M. Chitre." Thus did we learn the order in which we had finished in the exams.
When I arrived at 10 o'clock, Fred congratulated me on my Part III performance, and then showed me a handwritten list of potential research areas, inviting me to make my preference known. I pointed to Relativity and Cosmology. "Oh, that's a pity," he said, "because Narlikar just chose that, and I would rather not have two students in any one area. Is there anything else that takes your fancy?" "Well," I replied, "I've also found myself quite interested this past year in Stellar Structure and Evolution." "Oh, very good," said Fred. "There's still a lot to be done in that area. I think you'll find it a good choice."
So that's how I became a stellar theorist. When I look back now on how things developed for me in the next decade or so, I believe that this rather brief and informal research selection process did result in a choice of field that best suited my capabilities.
Jayant Narlikar and I had often studied in the same library areas during our Part III year. We were on pleasant nodding terms, but it was not until we found ourselves both graduate students of Fred's that we became very good friends. Jayant knew of my originally expressed interest in relativity and cosmology. Early in 1961 he learned of a summer school on "Evidence for Gravitational Theories," to be held in Varenna on the shores of Lake Como, and asked if I would be interested in attending it with him. Lake Como? Italy? I jumped at the chance.
That summer school was memorable for several reasons. Most importantly, I saved Barbara Hoyle from drowning, and was by that singular event admitted to the Hoyle family's inner circle. I briefly mentioned this in my after-dinner speech at Cardiff's memorial meeting for Fred Hoyle (Faulkner 2003). The circumstances are described more completely in Simon Mitton's (2005) biography of Fred.
There I also met, for the first time, relativists of world class like Bondi, Dicke, Schild, and Weber. While I enjoyed their lectures immensely, I also learned a lot in informal conversations. I shall have to recount Alfred Schild's amazing wartime saga elsewhere; it involves his mother in England receiving the first postcard he was allowed to send her, as an alien internee in Canada, a year after she thought that he had died - he had been declared officially lost to a bombing at sea, en route from England.
One more amusing memory of these noted relativists stands out. A group of eight or ten lecturers and students had taken a ferry across the lake for dinner. Walking back along the far shore road as darkness fell, we saw that there were clearly some planets visible in the sky. An argument broke out among the senior relativists as to which planets they were. I knew what they were, and said so, but they were all skeptical. In an attempt to resolve the matter, they fed some lire into a scenery-viewing telescope mounted on a lakeshore post, and attempted to elevate it so that they could look at those planets. I regret that I didn't own a camera in those impecunious days - a photograph of some of the world's leading relativists kneeling, in full observing mode, would have been priceless.
Apart from a death-defying ride at more than 100 mph through lakeside galleria in my hotel room-mate R. U. Sexl's convertible Porsche (in which he claimed he had beaten the known driving speed record from Vienna to Como), one other memory remains quite vivid. In one of the cosmology lectures, a question arose about the consequences of a certain possible observational selection effect for the deduced acceleration parameter of the universe, q0. Suppose that as the redshift z became larger, one increasingly failed to see galaxies occupying the less bright tail of the intrinsic luminosity distribution. Then in practice, instead of viewing an average and unvarying "intrinsic standard candle" among the galaxies one actually could observe, one's assumed standard candle would in fact become intrinsically more luminous with z. What would be the effect of such a selection bias with increasing z on the deduced q0? After some hand-waving discussion, all the big shots agreed on the answer.
Something bothered me about their conclusion. That evening, while Sexl was out impressing the local young women, I went through an analysis that assumed a simple dependence of Lgal on z. I found that in their hand-waving discussion, the pundits had only considered something that was but part of the full effect. When properly evaluated, the conclusion was reversed! Sexl chortled at my result when I showed it to him later that night. I gave Fred my analysis after breakfast the next morning. He immediately saw the point and accepted what I had done. He made an announcement before the lectures proper started that day, saying (in paraphrase) "We all thought yesterday that the effect would be such and such, but my student John Faulkner (whose main research area is stellar evolution) has shown that it's just the opposite, and here's why " In the break several people came up to me and ruefully patted me on the back.
Fred suggested that I write up my analysis as a letter to The Observatory Magazine. Back in Cambridge I literally did that, in careful fountain pen handwriting. This was in the days BP - before the photocopier existed. I naively gave Fred that sole copy of what I had written, asking for his opinion before I sent it off. (I was only a first year student; I had never published anything.) First weeks, then months went by. I eventually asked him what he had thought of it. He said it had had been fine, and asked whether I had submitted it. When I told him he had the only copy, he was sure he must have given it back to me. The missing account never did show up, however, and I was so far into my stellar work by then, I was loth to take time to reconstruct the now fading argument. Some time later, a slightly extended version of what I had done was published by someone else - and in The Observatory, to rub salt into the wound. Thus my first independent piece of research had all come to naught. I have sometimes found myself wondering whether Fred's reluctance to have two research students working in the same general area was somehow subconsciously involved in his misplacing or losing that manuscript of mine. (Shortly after this book was sent to press, my long lost manuscript and the cover letter that had accompanied it were both found, after 47 years, among Fred Hoyle's preserved papers in the library of St John's College, Cambridge.)
What I'm now going to write may surprise those who know of my long distaste for computing and distinct preference for analytical work. Nevertheless, I fairly rapidly became one of Fred's two best computing students, the other being Sverre Aarseth. Fred had pioneered the automatic computation of stellar evolution, first coding in inscrutable machine line instructions with
Brian Haselgrove on the original Cambridge Maths Lab Edsac I computer. Several months into my first year as his student, Fred returned from an extended visit to the US with an IBM program now coded in FAP, essentially mnemonically written IBM machine instructions. He had developed a severe distrust of systems programmers, claiming that every time he returned with a working code to any machine, they had made it harder to run. He used specially-written FAP subroutines for all his needed mathematical functions. His printing subroutine came from someone he trusted at Westinghouse; its main snag was that all minus signs were printed as ampersands! We all became quite accustomed to reading them that way. The Westinghouse program also had very limited output formatting. I came across a Fortran manual, realized the potential advantages of using it, taught myself Fortran from that manual, and then bided my time.
In those days, for Fred's group computing meant commuting. (Fred had quarreled with Maurice Wilkes, director of the Cambridge Maths Lab, and forbad us from having anything to do with it. I nevertheless first learned Edsac II machine code surreptitiously, and later Edsac Autocode, which I still claim was one of the most practical programming languages in which to become quickly proficient and productive.) So instead of computing in Cambridge, Fred had us do our work on what was then the first IBM 7090 in Europe. The problem was that it was in Wardour Street, off Oxford Street in London. That meant a draining commute from Cambridge several days a week. We started with revised FAP programs. However, the day came when Fred said he desperately needed both some fairly standard and more complicated functions and integrals to be evaluated for a variety of input values. I coded the whole thing up in Fortran, and went up with it to London the next day. Hard to believe, but it worked first time! I returned with a sheaf of beautifully formatted results. When I showed them to Fred the next day, he first admired the clear formatting, then pointed at the now visible minus signs. "What are these?" he asked. "They're minus signs," I replied. He looked at me, blinking. "Well, this is obviously the way to go, isn't it?" And the instruction went out to the other students to learn and use Fortran from now on.
There were various other ways in which Fred realized that I was at that time unusually good at computing, which has a bearing on this unfolding story. Basically, he learned that he could trust what I did.
I am now approaching the main topic of this contribution, the computation of the helium content of the universe. But before I get to that, I also need to lay out what the understanding of the helium content in various objects was when the 1960s began. That requires going back even a bit earlier. (I have found that many of today's cosmologists have very little idea of this history; a certain local physicist is a case in point.) Much of what I shall summarize is laid out more completely in my contribution to The Scientific Legacy of Fred Hoyle (Gough 2005).
The brief story is that until the end of World War II, astronomers thought that stars contained either very little, or no more than 35% or so hydrogen content (X) by mass. In 1946, Fred Hoyle swung the hydrogen pendulum over to 99% or more. This was before the steady state theory was a glimmer in its originators' eyes.
Hoyle's very interesting and significant paper (Hoyle 1946) changed forever the former notion that less than half of stellar material was hydrogen, and that the"metal content" Z of many stars exceeded 10%. This paper does not now receive anywhere near the attention it deserves. At the time Fred wrote it, many people, in particular those generally interested in stellar structure, still believed that the initial hydrogen content of the Sun was quite low -between about 0.35 and 0.50 by mass fraction. Schwarzschild (1946) had published a model of the Sun just a little earlier; it still had X = 0.47, and a huge amount of metals (Z = 0.12). That was the standard picture at that time. In his own 1946 paper Fred noted that there were growing indications in other astronomical areas - in studies of both the interstellar medium and stellar atmospheres - that the previously reigning view could not be right. He then pointed out, in paraphrase, "You get a much better fit of model main sequences to the observations if instead of something like 35% hydrogen and huge amounts of metals, you assume that the stars generally contain less than about 1% by mass in the form of heavy elements and a really substantial amount of hydrogen."
As one sees by looking at his figures, the fits for low metals and a value for I (the mean molecular weight) between 0.5 and 1, and indeed closer to 0.5, pass through or closer to the general run of most of the points than those of the earlier presumed compositions. Thus Fred was the first stellar theorist to champion what with some modification is essentially the present picture -metals of no more than a few percent, the rest predominantly hydrogen -quite a revolutionary point to be making at that time, and one in which he perhaps went to extremes. (Indeed, in the summary of his paper he stated, "The data suggest that at the time of condensation of the stars at least 99 per cent by mass must be in the form of hydrogen." He would employ such a figure for Population II stars as late as 1959, and urge it on his students in the early 1960s; see below.)
That particular year, 1946, was of course two years before the emergence of the steady state theory. In that theory, it was philosophically satisfying and convenient to have all the newly created material be hydrogen, that is of the simplest conceivable atomic form. I'm inclined to think that Fred's desire to have a unified picture, together with his argument from stellar structure (as just presented), really led him to largely favor a high hydrogen content (and indeed, a very high hydrogen content) in the oldest stars in particular, for quite some time. He still favored that point of view when I became his student in 1960.
In two stellar evolution papers (Haselgrove and Hoyle 1959; Hoyle 1959a) Fred still used and promoted additional arguments for preferring a hydrogen content of 99% for the oldest Population II stars. With a badly needed revision in the CNO energy generation rate, Haselgrove and Hoyle laid the foundation for an oft-quoted result in Fred's immediately following paper (Hoyle 1959a). From his computations, and a rather involved argument invoking the brightness of RR Lyrae stars, he first announced to the world a result that he knew would be considered startling at the time: that "the age of the Galaxy must be in excess of 1010 years." Fred's paper has often been quoted for this eye-catching result (it is printed in italics), but no one who does so ever seems to note (or even notice?) that such a large value for the age of the galaxy (again, "large" at that time) was only obtained for input parameters that would raise eyebrows today: X = 0.99, helium mass fraction Y = 0.009, and currently evolving masses quite a bit above a solar mass (M > 1.3M©). For X = 0.75, much closer to today's understanding of the hydrogen content of Population II stars, he obtained only t ~ 4.8 x 109 years, a value his additional RR Lyrae argument led him to reject. I've always felt it was a little naive or disingenuous for later authors to quote the much higher age with great approval, without even the tiniest caveat paying attention to Fred's choice of input parameters.
In the end, of course, Fred was right about the age of the galaxy, but not for the range of parameters or the argument he had used. To go further here is beyond the scope of this contribution.
In lectures and conversation from 1960 onward, the idea we stellar students received from Fred was "Of course, the helium content of the oldest stars is very low." (When we undertook extensive main sequence calculations in 1962, he suggested we calculate our Population II models for X = 0.985.) I did not once hear such ideas questioned. Indeed, I began to notice a curious thing. Roger Tayler had returned to Cambridge in 1961, originally to act as an intermediate mentor for Fred's many students. He started giving a number of voluntary but meticulously prepared lectures on a wide variety of topics. (The reputation he so gained was partly how he became a regular DAMTP faculty member.) Yet, even when the course was on "The
Abundances of the Elements," the topic of the helium content of the oldest stars seemed to be skirted, in much the manner that Fred would skirt it. It was always explained that helium absorption lines can only be seen in very hot stars, and that all such presumably pristine main sequence stars of Population II had regrettably evolved away to other parts of the color-magnitude (or HR) diagram. By the time any subsequent descendants were hot enough to display helium lines again, one could not be sure whether or not they were (indeed they all probably had been) contaminated by the products of nuclear burning welling up from their deep interiors. Thus was argued away the very possibility that their surface abundances reflected their original compositions in any direct way.
Yet, ironically, Geoff and Margaret Burbidge had already been responsible for planting a questioning seed in my mind at the outset of my research studies.
Fred was away in the US for the first few months of my contemporaries' research careers. Before leaving, he suggested some useful reading, certainly more than enough to keep me fully occupied. In addition to Burbidge, Burbidge, Fowler and Hoyle (1957), of course, he suggested long articles from the classic Volume 51 of the Handbuch der Physik (Arp 1958; Burbidge and Burbidge 1958). Chip Arp's article first introduced me to his wonderful comparative work on globular clusters, and the correlation between their metal contents and the form of their horizontal branches in the HR diagram. The article by the Burbidges was dense with useful information. Within it I found an intriguing argument spelled out in only a few sentences. They pointed out that if the luminosity of the Milky Way Galaxy had been essentially constant during its presumed lifetime, then attributing that luminosity to hydrogen burning would have resulted in an average enrichment of the galactic helium content by at most 1 or perhaps 2%. That simple but profound argument had a strong impact upon me. In another paper (Burbidge 1958), Geoff remarked that this approach would be capable of producing the observed Population I helium contents, only if, for example, the Galaxy had been 100 times brighter in the first tenth of its lifetime. (But even he seemed to find that particular sleight of hand unconvincing.)
The Burbidges hadn't taken the argument to the point that it necessarily implied a much higher primeval helium content in the oldest stars. Nevertheless, I was left with that thought planted in my mind by their original argument. Perhaps there had been a fairly "high" helium content initially, one that had only been modestly altered subsequently. That thought was ever present in my mind even though I don't recall ever voicing it to Fred.
I have to say, looking back, that we in Cambridge seem to have remained remarkably ignorant of the impact of the work on helium abundances by Osterbrock and Rogerson (1961), among others. It is particularly surprising as Fred certainly made known to us his appreciation of Don's work in explaining the radii of low-mass main sequence stars. I simply cannot explain it, apart from the fact that we appear to have been in our own insular bubble at that time. (The self-satisfaction that was part of the Cambridge scene is well known.) As Osterbrock reported in his contribution (and as he discussed with me shortly before his untimely death), this failure to take note of what was being found out about helium at that time in other areas of research was apparently common to most stellar structure investigators, including the two men Don seemed to admire more than all others, Schwarzschild as well as Hoyle.
In the Lent (winter) term of 1964, Fred Hoyle gave a remarkable series of lectures solely intended for a graduate audience, on Extragalactic Astronomy and Cosmology. These nonexaminable lectures took place in the usual Part III venue, from 11 am to noon on a Tu.-Th.-Sat. schedule. Several faculty (including Tayler and Lynden-Bell) and most astronomical postdocs, as well as then current graduate students, attended that course. I was known for taking rather verbatim notes; the following summary is taken from my notebook. [Here and in what follows I shall enclose clarifying insertions or essentially editorial comments in square braces.]
Narlikar presented a couple of early lectures when Fred was unavoidably absent, but the bulk of the course consisted of Fred apparently working his way through problems that were then of particular interest to him. My notes say that Fred described these as "conversation classes," rather than lectures. The course began by discussing quasars, with much quoting of Maarten Schmidt's work. It went on to radio galaxies, massive objects, cosmic rays, etc.
Cosmology proper entered at Lecture 15. Half way through it, Fred mentioned "Gamow's addition" of nuclear reactions to a hot beginning, and said (because Gamow started with pure neutrons), "You're balanced on a razor edge in this problem." [He meant that with a pure neutron beginning, the density at a given starting temperature could be neither too low nor too large.] He then stated "The empirical evidence is that He/H by mass is ~1/2." [I found myself wondering where that came from, since it seemed at odds with what he had promoted in Population II stars. He must have been meaning, in Population I.] Near the end of the lecture, without explicitly giving his own view, he remarked that "Schmidt has a thing about
He4/H by number being about 0.13 in almost all things ever examined. For example, the number (whatever it may be) is constant over the face of Andromeda. Galaxies would have to be considerably brighter than they are to give this ratio." [Aha! That otherwise gnomic remark indicates that he was thinking of the problem of enriching an originally low universal helium content.] He finished the lecture with a remark that when he went through the corresponding analysis to Gamow's but with no assumption about density, he actually found that he wound up with a number ratio of about 0.13, independently of any density consideration. [At that stage, he really didn't indicate what the differences might be in the other physical assumptions.] He ended with two questions. "Are stars only negligible changers?" "Is the composition largely determined by, say, massive star nuclear reactions?"
At the start of Lecture 16, Fred declared that he now had a pedagogical dilemma. He had done something more carefully than the previous time, with startling results! But first he needed to complete something else he had left hanging. He switched gears abruptly at the end of the lecture, asking out of the blue if anyone could tell him the form of the cross section for positron plus neutron going to proton plus antineutrino. He remarked that he could get it by detailed balancing for the (electron, proton) cross section from a preprint on that by Bahcall, but he had concerns about two factors in it before deducing what he wanted.
The key lecture, number 17, took place on a Saturday morning. Fred now explained that because of the presence of electron-positron and various neutrino-antineutrino pairs the analysis would differ from Gamow's attack. He reduced the problem to a fairly simple differential equation for n/(n+p). [Here n and p are the neutron and proton number densities. He was taking account of the reactions in equation (3.9) on page 32 that determine the abundance of neutrons that could end up in helium.] He concluded that the "critical quantity" n/(n+p) would "freeze out" at a value of about 0.135. He said he had calculated this for one chosen starting condition, using Simpson's rule and counting squares on graph paper. However, it clearly needed to be done for a number of starting conditions, to check both the value he had obtained and the expected insensitivity to initial conditions above a certain initial starting temperature.
He was looking at me as he said this, and I took it as an open invitation to do just that. As had happened before, I thought that he had no other way of quickly obtaining detailed desired results for varied initial conditions. Indeed, I was then working on an analogous but rather more complicated computing problem with him and Narlikar, which resulted in a paper submitted soon afterward, in May (Faulkner, Hoyle and Narlikar 1964). [I had almost finished my thesis work, and was employed that year as a research assistant to Fred on a DSIR grant.] I do not recall Fred saying at that time that he was working with anyone else on the helium problem; up to that point, there is no mention of Roger Tayler in my notes. Fred then remarked in his lecture that the odd factors that still concerned him could result in a final value for n/(n + p) of about 0.15 so that one could end up with about 30% helium, and "this is a pretty good number." [In this context the final neutron fraction f = n/(n + p) at freeze-out is a much more convenient variable than the number density ratio N = He/H, the beloved variable of interstellar medium or planetary nebula investigators. Under the assumption of negligible heavy element concentrations, and assuming each surviving neutron combines with a proton to ultimately produce helium, Y becomes simply 2f. So values of f in the range 0.135-0.15 imply Y = 0.27-0.30. That simple doubling appears to be what he consistently used in this context.] He concluded by saying "If we didn't know about massive objects, we would unavoidably come to the conclusion that we live in a radiation universe." [In retrospect, this struck me as an attempt to "save the phenomenon" - the phenomenon being his preference for virtually no helium to begin with. How could he explain away observed "high helium" at apparently an expected Big Bang value?!]
My reaction to the end of the lecture was to have a quick lunch and then head over to the Maths Lab. One could run one's own programs there. The equations to be integrated were relatively simple, and I was sure that with luck I could complete the needed work later that same day, or on Sunday if need be. I wrote the necessary autocode program and punched it onto the input paper tape, which I unfortunately tore in my excitement. After necessary repairs and backtracking, more paper tapes bearing the results spewed out of Edsac and I hurried over to a reader to interpret them. The results were a tribute to Fred's simple methods. For the input values from which Fred had obtained n/(n+p) ~ 0.135, I found 0.1337! I rather self-consciously inscribed "Helium content of the Universe" on my copies of the tapes, waved them triumphantly at some grad students I knew, and headed home. [Those tapes followed me on several moves until I lost track of them. They could still be somewhere, very brittle by now, in old packing cases in my garage.]
At that time Fred, who had fallen out severely with G. K. Batchelor, was rarely to be seen in the DAMTP. [He tended to just give his lectures in the Arts School near the old Cavendish Laboratory, perhaps drop in afterward to the DAMTP in the far corner of the Cavendish to see people fleetingly and pick up any mail, and then go home.] So, I made the usual arrangement by phone to see him at his home. The allotted time was shortly before dinner on Sunday. I arrived by bicycle as predinner martinis were being served. I gave him a copy of my program and of the results. His reaction, described at the start of this contribution, surprised and indeed disturbed me. Did he really think that there was somehow reliable evidence for old stars having very little helium? What could it be? [I had concluded that any other astronomers who might still think this had been bowled over by the power of Fred's own personality - even if they were otherwise philosophically opposed to the steady state theory - but I didn't dare say so! As several people could confirm, I've expressed this viewpoint to confidants over the years.] I came out of this brief reverie to hear Fred now saying something about the lowest values being most relevant as a test, and that O'Dell had observed number ratios N = He/H as low as about 0.09. [In fact, that lowest result was indicated to be extremely uncertain, though it would have implied a value for f of about 0.13, or of Y about 0.26. Most of what O'Dell considered his more reliable results were substantially larger than this.] I felt confused and unsure of my grounds for feeling that what I had witnessed was a little bizarre. I knew that O'Dell had written a paper the previous year about helium abundances in rather bright field planetaries (O'Dell 1963), but those results were not necessarily relevant. There was nothing in those studies that would necessarily link them to an old population. However, I thought I had seen a very recently arrived preprint by a collaboration including O'Dell; that was probably more relevant. I left thinking that I needed to find that preprint.
I found it the next morning in the small DAMTP library. It was a very recently submitted paper, and had probably been received only in the last week or so, which meant that Fred might not have seen it yet. [The published paper - O'Dell, Peimbert and Kinman (1964) - shows that it was submitted to The Astrophysical Journal on February 10, 1964.] The authors reported what as far as I knew was a truly remarkable and ground-breaking analysis, namely that of the first planetary to be observed in a truly classical globular cluster. They had found that the planetary nebula K648 in M15 had N = He/H (by number) = 0.18 ± 0.03. Yet oxygen was low relative to solar values by a factor of about 60! Here then was an incredibly "high" helium value (corresponding at face value to Y ~ 0.41 ± 0.04) coupled with a typically low "metal" content characteristic of the oldest Population II stars. While it could still be argued that this truly high helium represented some kind of nuclear "dredge-up," was it likely that the oxygen content could remain apparently so pristine? The authors thought not, and I tended to agree with them, although one could still argue that the case was entirely circumstantial.
I became further alarmed at the thought that Fred might be going out on a limb of his own making. Yet who was I to make this point? I decided to talk with Roger Tayler, whose office was just down the corridor from mine. (Though by then a regular faculty member, Roger continued to act as an intermediary with Fred.) Roger understood my concerns, and said he would speak with Fred about it; he told me he had already been discussing some aspects of the physics with Fred.
The next morning, at the start of Lecture 18, Fred reported that I had done the computations for a slew of initial starting temperatures, saying "John Faulkner's computations gave 0.1337 where I had 0.135!" [Malcolm Longair told me at Cambridge's memorial meeting for Fred that this announcement had had a strong effect on him.] Fred went on to discuss possible changes in some of the factors or coefficients, clarified the contribution to helium enrichment that stars could make from their characteristic lifetimes and luminosities, and then turned to massive stars. He reinterpreted time-reversed cosmological results in terms of collapsing massive star matter densities rather than expanding radiation-dominated energy densities. His reconstructed table from this exercise still included my computed value of 0.1337 for n/(n + p), in a table that now had more variations in it. [How he had obtained those results was a mystery to me. They were all given to four significant figures. Surely these weren't from his square-counting method? Perhaps they were from a massive star mass-scaling of my original result, that was neither obvious to me then, nor now.]
He proceeded to do further "tidying up," as he called it, in the 19th and last lecture. This was very hard to follow, as changes in coefficients and consequences were flung about at dizzying speed. In the cosmological case he finally examined what limitations there might be for the assumptions to be consistent for a given temperature, concluding that at T = 3 x 109 K for example, the matter density needed to be between 10-3 and 103 gcm-3. The former limit came from the presumed current mean universal density with "an upper limit of T now to about 3 degrees." [! Fred had often mentioned in lectures that several current mean energy densities were effectively equivalent to the energy density in such an ambient temperature.]
Turning to massive objects, for which he declared "the situation is much simpler," he then made an intriguing statement that finally confirmed part of Roger Tayler's involvement in the problem: "Roger Tayler has pointed out that some of the approximations are not valid down at T9 ~ 0.4." [Here T = 109T9 K.] Fred concluded they were still good at T9 ~ 0.6, but that the radiation density factor would be off by a factor of about 2 at T9 ~ 0.3. Going back to helium abundances in stars again, he quoted Eggen as claiming that in the Hyades, the ratio of helium to hydrogen by mass was as high as 3/2. [I put a disbelieving "!" after this in my notes. As I wrote my thesis up, I showed that this conclusion and several others like it were based in part on far too naive interpretations of simplistic power-law homology results. However, I also realized that self-consistency meant that the Hyades stars were more distant than previously thought. Although that also had cosmological implications - the Hyades providing the first rung on the cosmic distance ladder - it's too convoluted a story to pursue here.] Fred also remarked "One really ought to get an unevolved subdwarf to see if it has far more, or far less helium than it should have ... but it's difficult to see what to do."
I heard no more about the progress of Hoyle and Tayler's work until their paper was published (Hoyle and Tayler 1964), as I was moving to Caltech that September. Looking at it more carefully than I was able to then, I find traces still remaining of what I took for a long time to be Fred's main motivation - to test and (he seems to have hoped) disprove the big bang picture. While that may be an overly strong conclusion, I can find no other way to explain his mistaken, ecstatic (and revealing?) moment of triumph when I showed him my computed results. Also, there are several numbers in it that I just don't recognize. Those include the leading coefficient in the factor determining the rate of change of the neutron fraction, the numerical value of the result attributed to me (although it could be at a different temperature cutoff point) and, correspondingly, the final fraction attributed to helium production in massive objects. [Both such quantities are quite a bit larger than Fred mentioned in his lectures, according to my notes.]
Until recently, I was under the delusion that Hoyle and Tayler thanked me in their paper for doing the computation I performed. I've been quite wrong about this. Instead, they simply wrote, "Mr. J. Faulkner has solved the equation for several starting temperatures."
Finally, the most peculiar oddity and indeed lacuna is this - what I believe to be the key preprint that brought down the low helium house of cards (O'Dell, Peimbert and Kinman 1964) is not referenced! Instead, the result from that paper is attributed (but only implicitly) to O'Dell's sole-author paper (O'Dell 1963), in which it does not appear. The dilemma Fred found himself in is contained and highlighted in two successive sentences in Hoyle and Tayler (1964) that assert "... low values of He/H are of more interest in relation to the original composition of the Galaxy than high values. However, O'Dell's high value of 0.18 ± 0.03 for the planetary nebula M 15 [meaning: in M 15] is of special interest because O'Dell also finds a low value for the ratio O/H . . .. "
For me, related scientific consequences followed from this 1964 brush with the big bang. I had become a primarily stellar theorist with the inside knowledge that the big bang would necessarily produce a "high" initial helium content in the oldest stars. I resolved to allow for the possibility of both high and low helium when I tackled the outstanding problem of understanding horizontal branch (HB) stars in globular clusters. (My results were ultimately published in Faulkner 1966.) The "high helium" models produced a far better fit to Arp's observations. In an immediately following paper (Faulkner and Iben 1966) Icko Iben and I showed that for Population II stars, "high helium" evolutionary tracks off the main sequence were much steeper than those for models containing low helium. This resolved yet another long-standing puzzle in stellar evolution. When a careful comparison of the best observed local subdwarfs with the Hyades main sequence also provided evidence for an initially high helium content (Faulkner 1967), it essentially completed the case for high helium from classical stellar structure alone.
My experiences in 1964, exciting though they briefly were, also helped to determine what I would not do in the near future. When I arrived at the Kellogg Laboratory in September with my first (and then only) "high helium" HB model almost burning a hole in my pocket, I rather brashly, reluctantly but firmly declined Willy Fowler's generous offer to become Bob Wagoner. As it turned out, of course, Bob Wagoner himself was far more suited to play that role.
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