View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server 1 Solar Models: An Historical Overview a John N. Bahcall ∗ aSchool of Natural Sciences, Institute for Advanced Study, Princeton, NJ, USA I will summarize in four slides the 40 years of development of the standard solar model that is used to predict solar neutrino fluxes and then describe the current uncertainties in the predictions. I will dispel the misconception that the p-p neutrino flux is determined by the solar luminosity and present a related formula that gives, in terms of the p-p and 7Be neutrino fluxes, the ratio of the rates of the two primary ways of terminating the p-p fusion chain. I will also attempt to explain why it took so long, about three and a half decades, to reach a consensus view that new physics is being learned from solar neutrino experiments. Finally, I close with a personal confession. 1. Introduction with a personal confession in Section 7. I will follow in this text the content of my talk at Neutrino2002, which occurred in Munich, May 2. Ray Davis 25-30, 2002. I begin in Section 2, as I did in Munich, with Before I begin the discussion of the standard so- a tribute to Ray Davis. In Section 3, I present lar model, I would like to say a few words about a concise history of the development of the stan- Ray Davis, shown in Figure 1. The solar neutrino dard solar model that is used today to predict saga has been a community effort in which thou- solar neutrino fluxes. This section is based upon sands of chemists, physicists, astronomers, and four slides that I used to summarize the devel- engineers have contributed in crucial ways to re- opment and is broken up into four subsections, fining the nuclear physics, the astrophysics, and each one of which describes what was written on the detectors so that the subject could become a one of the four slides. I describe in Section 4 precision test of stellar evolution and, ultimately, the currently-estimated uncertainties in the solar of weak interaction theory. neutrino predictions2, a critical issue for existing However, Ray’s role in the subject has been and future solar neutrino experiments. I show in unique. Any historical summary, even of solar Section 5 that the solar luminosity does not deter- models, would be grossly incomplete if it did not mine the p-p flux, although there are many claims emphasize the inspiration provided by Ray’s ex- in the literature that it does. I also present a for- perimental vision. Although Ray never was in- mula that gives the ratio of the rates of the 3He- volved in solar model calculations, and has always 3He and the 3He-4He reactions as a function of maintained a healthy skepticism regarding their the p-p and 7Be neutrino fluxes. These reactions validity, his interest in performing a solar neu- are the principal terminating fusion reactions of trino experiment was certainly the motivation for the p-p chain. In Section 6,I give my explana- my entering and remaining in the subject. More tion of why it took so long for physicists to reach importantly, for all of the formative years of the a consensus that new particle physics was being “solar neutrino problem”, Ray inspired everyone learned from solar neutrino experiments. I close who became involved with solar neutrinos by his conviction that valid and fundamental measure- ments could be made using solar neutrinos. We ∗[email protected] committed to a subject that did not attract main 2Where contemporary numbers are required in this review, I use the results from the BP00 solar model, ApJ 555 stream scientists because we believed in Ray’s (2001) 990, astro-ph/0010346. dream of measuring the solar neutrino flux. 2 3.1. 1962-1988 At the time Ray and I first began discussing the possibility of a solar neutrino experiment, in 1962, there were no solar model calculations of solar neutrino fluxes. Ray, who heard about some of my work on weak interactions from Willy Fowler, wrote and asked if I could calculate the rate of the 7Be electron capture reaction in the Sun. After I did the calculation and submitted the papertoPhysicalReview,Iwokeuptotheobvi- ous fact that we needed a detailed model of the Sun (the temperature, density, and composition profiles) in order to convert the result to a flux that Ray might consider measuring. I moved to Willy’s laboratory at CalTech, where there were experts in stellar modeling who were working on stellar evolution. We used the codes of Dick Sears Figure 1. Ray Davis preparing to pour liquid ni- and Icko Iben, and a bit of nuclear fusion input trogen into a dewar on a vacuum system of the that I provided, to calculate the first solar model type used for gas purification and counter filling prediction of solar neutrinos in 1962 1963. in the chlorine experiment. The glass object in The result was extremely disappointing− to Ray the foreground with the wire coming out that and to me, since the event rate from neutrino cap- blocks Ray’s left hand is an ionization gauge used ture by chlorine that I calculated from our first to measure the pressure in the vacuum system. flux evaluation was too small by an order of mag- nitude to be measured in any chlorine detector Ray and I have written three articles on the that Ray thought would be feasible. The situ- history of solar neutrino research (in 1976, 1982, ation was reversed in late 1963, when I realized and 2000, see http://www.sns.ias.edu/ jnb under that the capture rate for 8B neutrinos on chlorine the menu item Solar Neutrinos/History). It is would be increased by almost a factor of 20 over not feasible to present in a twenty minute talk my earlier calculations because of transitions to a balanced account of these three articles with the excited states of argon, most importantly the the appropriate acknowledgments of the impor- super-allowed transition from the ground state tant work of so many people. Therefore, I shall of 37Cl to the isotopic analogue state at about just describe some of the highlights regarding the 5 MeV excitation energy in 37Ar. This increase standard solar model from a very personal view. in the predicted rate made the experiment ap- I encourage the listeners who are interested in a pear feasible and Ray and I wrote a joint paper more balanced presentation to look back at the for Physical Review Letters proposing a practical earlier articles which provide references to criti- chlorine experiment, a paper that was separated cal work done by a large number of researchers. into two shorter papers to meet the space require- ments. During the period 1962 1968, the input data 3. The development of the “standard solar to the solar models were refined− in a number of model” for neutrino predictions important ways as the result of the hard work of I describe the development of the “standard so- many people. The most significant changes were lar model” for neutrino predictions in four subsec- in the measured laboratory rate for the 3He-3He tions, covering the period 1962-1988 (Section 3.1), reaction (changed by a factor of 3.9), in the the- 1988-1995 (Section 3.2), 1995-1997 (Section 3.3), oretically calculated rate for the p p reaction − and 1998-2002 (Section 3.4). (changed by 7%), and the observed value of the 3 heavy element to hydrogen ratio, Z/X (decreased lar models. For each of the 1000 models, the by a factor of 2.5). Unfortunately, each of the in- value of each input parameter was drawn from a dividual corrections were in a direction that de- probability distribution that had the same mean creased the predicted flux. and variance as was assigned to that parameter. Ray’s first measurement was reported in PRL The Monte Carlo results confirmed the conclu- in 1968. Our accompanying best-estimate solar sions reached using the partial derivatives. The model prediction (made together with N. A. Bah- uncertainty estimates made during this period are call and G. Shaviv) was about a factor of 2.5 the basis for the uncertainties assigned in the cur- times larger than Ray’s upper limit. But the rent neutrino flux predictions and influence infer- uncertainties in the model predictions were, in ences regarding neutrino parameters (like ∆m2, 1968, sufficiently large that I personally did not tan2 θ) that are derived from analyses that make feel confident in concluding that the disagreement use of the solar model predictions. between prediction and measurement meant that something fundamental was really wrong. 3.2. 1988-1995 As it turned out, the values of the stellar in- In the period 1990 1994, F. Rogers and J. Igle- terior parameters used in 1968 are in reasonably sias of the Livermore− National Laboratory pub- good agreement with the values used today. How- lished their detailed and improved calculations of ever, the uncertainties are much better known stellar radiative opacities and equation of state. now, after more than three decades of intense and Now almost universally used by stellar modelers, precise studies and refinements by many different this fundamental work resolved a number of long groups working all over the world. standing discrepancies between observations and The laboratory measurement of the predictions of stellar models. 7Be(p, γ)8B cross section was a principal source In the same 1988 RMP paper in which we pre- of uncertainty in the 1962 prediction, remained sented the Monte Carlo study of the uncertain- a principal uncertainty in 1968, and is still to- ties, Roger Ulrich and I also made comparisons day one of the two largest uncertainties in the between the predictions of our standard solar solar neutrino predictions.