Predicted versus measured sound speeds. The figure shows the excellent agreement between the calculated sound speeds for the Standard solar model (BP2000) and the helioseismologically measured (Sun) sound speeds. The horizontal line at 0.0 represents the hypothetical case in which the calculated sound speeds and the measured sound speeds agree exactly everywhere in the sun. The rms fractional difference between the calculated and the measured sound speeds is 0.10% for all solar radii between between 0.05 R and 0.95 R and is 0.08% for the deep interior region, r 0.25 R, in which neutrinos are produced. Taken from Figure 10 of ``Solar Models: current epoch and time dependences, neutrinos, and helioseismological properties'' (see below).

Standard solar models, helioseismology, and solar neutrinos: articles

You can find tables of solar models and helioseismologically inferred quantities (like sound speeds) at this url. See menu items like Solar Models, BP98 Sound Speeds, and Solar neutrino rates, fluxes, and uncertainties.

10,000 Standard Solar Models: A Monte Carlo Simulation
Author(s):John N. Bahcall, Aldo M. Serenelli, and Sarbani Basu
Journal: ApJ Suppl., 165, 400 (2006), astro-ph/0511337.

Abstract: We have evolved 10,000 solar models using 21 input parameters that are randomly drawn for each model from separate probability distributions for every parameter. We use the results of these models to determine the theoretical uncertainties in the predicted surface helium abundance, the profile of the sound speed versus radius, the profile of the density versus radius, the depth of the solar convective zone, the eight principal solar neutrino fluxes, and the fractions of nuclear reactions that occur in the CNO cycle or in the three branches of the p-p chains. We also determine the correlation coefficients of the neutrino fluxes for use in analysis of solar neutrino oscillations. Our calculations include the most accurate available input parameters, including radiative opacity, equation of state, and nuclear cross sections. We incorporate both the recently determined heavy element abundances recommended by Asplund et al. and the older (higher) heavy element abundances recommended by Grevesse & Sauval. We present best estimates of many characteristics of the standard solar model for both sets of recommended heavy element compositions.

Postscript file.     pdf file.

New Solar Opacities, Abundances, Helioseismology, and Neutrino Fluxes
Author(s):John N. Bahcall, Aldo Serenelli, and Sarbani Basu
Journal: ApJ, 621, L85 (2005), astro-ph/0412440.

Abstract: We construct solar models with the newly calculated radiative opacities from the Opacity Project (OP) and with recently determined (lower) heavy-element abundances. We compare the results from the new models with the predictions of a series of models that use OPAL radiative opacities, older determinations of the surface heavy-element abundances, and refinements of nuclear reaction rates. For all the variations we consider, solar models that are constructed with the newer and lower heavy-element abundances advocated by Asplund et al. disagree by much more than the estimated measuring errors with the helioseismological determinations of the depth of the solar convective zone, the surface helium composition, the internal sound speeds, and the density profile. Using the new OP radiative opacities, the ratio of the 8B neutrino flux calculated with the older and larger heavy-element abundances (or with the newer and lower heavy-element abundances) to the total neutrino flux measured by the Sudbury Neutrino Observatory is 1.09 (0.87) with a 9% experimental uncertainty and a 16% theoretical uncertainty, 1 σ errors.

Postscript file.     pdf file.

Helioseismological Implications of Recent Solar Abundance Determinations
Author(s):John N. Bahcall, Sarbani Basu, Marc Pinsonneault, and Aldo Serenelli
Journal: ApJ, 618, 1049 (2005), astro-ph/0407060.

Abstract: We show that standard solar models are in good agreement with the helioseismologically determined sound speed and density as a function of solar radius, the depth of the convective zone, and the surface helium abundance, as long as those models do not incorporate the most recent heavy element abundance determinations. However, sophisticated new analyses of the solar atmosphere infer lower abundances of the lighter metals (like C, N, O, Ne, and Ar) than the previously widely used surface abundances. We show that solar models that include the lower heavy element abundances disagree with the solar profiles of sound speed and density as well as the depth of the convective zone and the helium abundance. The disagreements for models with the new abundances range from factors of several to many times the quoted uncertainties in the helioseismological measurements. The disagreements are at relatively low temperatures and do not significantly affect solar neutrino emission. If errors in thecalculated OPAL opacities are solely responsible for the disagreements, then the corrections in the opacity must extend from 2 times 10^6 K (R = 0.7R_Sun)to 5 times 10^6 K (R = 0.4 R_Sun), with opacity increases of order 10%.

Postscript file.     pdf file.

What Do We (Not) Know Theoretically About Solar Neutrino Fluxes?
Author(s):John N. Bahcall and M. H. Pinsonneault
Journal: Phys. Rev. Lett., 92, Number 12, 121301 (2004), astro-ph/0402114.

Abstract:Solar model predictions of 8B and p-p neutrinos agree with the experimentally-determined fluxes (including oscillations): (pp)measured = (1.02 ± 0.02 ± 0.01)(pp)theory, and (8B)measured = (0.88 ± 0.04 ± 0.23)(8B)theory, 1 experimental and theoretical uncertainties, respectively. We use improved input data for nuclear fusion reactions, the equation of state, and the chemical composition of the Sun. The solar composition is the dominant uncertainty in calculating the 8B and CNO neutrino fluxes; the cross section for the 3He(4He,)7Be reaction is the most important uncertainty for the calculated 7Be neutrino flux.

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How Do Uncertainties in the Surface Chemical Composition of the Sun Affect the Predicted Solar Neutrino Fluxes?
Author(s):John N. Bahcall and Aldo Serenelli
Journal: ApJ, 626, 530 (June 10, 2005), astro-ph/0412096

Abstract: We show that uncertainties in the values of the surface heavy element abundances of the Sun are the largest source of the theoretical uncertainty in calculating the p-p, pep, 8B, 13N, 15O, and 17F solar neutrino fluxes. We evaluate for the first time the sensitivity (partial derivative) of each solar neutrino flux with respect to the surface abundance of each element. We then calculate the uncertainties in each neutrino flux using `conservative (preferred)' and `optimistic' estimates for the uncertainties in the element abundances. The total conservative (optimistic) composition uncertainty in the predicted 8B neutrino flux is 11.6% (5.0%) when sensitivities to individual element abundances are used. The traditional method that lumps all abundances into a single quantity (total heavy element to hydrogen ratio, Z/X) yields a larger uncertainty, 20%. The uncertainties in the carbon, oxygen, neon, silicon, sulphur, and iron abundances all make significant contributions to the uncertainties in calculating solar neutrino fluxes; the uncertainties of different elements are most important for different neutrino fluxes. The uncertainty in the iron abundance is the largest source of the estimated composition uncertainties of the important 7Be and 8B solar neutrinos. Carbon is the largest contributor to the uncertainty in the calculation of the p-p, 13N, and 15O neutrino fluxes. However, for all neutrino fluxes, several elements contribute comparable amounts to the total composition uncertainty.

Postscript file.    Pdf file.

How Accurately Can We Calculate the Depth of the Solar Convective Zone?
Author(s):John N. Bahcall, Aldo M. Serenelli, and Marc Pinsonneault
Journal: ApJ, 614, 464 (October 10, 2004), astro-ph/0403604.

Abstract: We evaluate the logarithmic derivative of the depth of the solar convective zone with respect to the logarithm of the radiative opacity. We use this expression to show that the radiative opacity near the base of the solar convective zone (CZ) must be known to an accuracy of +- 0.6% in order to calculate the CZ depth to the accuracy of the helioseismological measurement, R(CZ) = (0.713 +- 0.001)R(Sun). The radiative opacity near the base of the CZ that is obtained from OPAL tables must be increased by about 7% in the Bahcall-Pinsonneault (2004) solar model if one wants to invoke opacity errors in order to reconcile recent solar heavy abundance determinations with the helioseismological measurement of R(CZ). We show that the radiative opacity near the base of the convective zone depends sensitively upon the assumed heavy element mass fraction, Z. The uncertainty in the measured value of Z is currently the limiting factor in our ability to calculate the depth of the CZ. Different state-of-the-art interpolation schemes using the existing OPAL tables yield opacity values that differ by 4% . We describe the finer grid spacings that are necessary to interpolate the radiative opacity to 1%. Uncertainties due to the equation of state do not significantly affect the calculated depth of the convective zone.

Postscript file.    Pdf file.

Solar Models and Solar Neutrino Oscillations
Author(s):John N. Bahcall and and Carlos Peña-Garay
Journal: New Journal of Physics, 6, 63 (2004), hep-ph/0404061.

Abstract: We provide a summary of the current knowledge, theoretical and experimental, of solar neutrino fluxes and of the masses and mixing angles that characterize solar neutrino oscillations. We also summarize the principal reasons for doing new solar neutrino experiments and what we think may be learned from the future measurements.

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Does the Sun Shine by pp or CNO Fusion Reactions?
Author(s):John N. Bahcall, M. C. gonzalez-Garcia, and Carlos Peña-Garay
Journal: Phys. Rev. Lett., 90, 131301 (2003), astro-ph/0212331

Abstract: We show that solar neutrino experiments set an upper limit of 7.8% (7.3% including the recent KamLAND measurements) to the amount of energy that the Sun produces via the CNO fusion cycle, which is an order of magnitude improvement upon the previous limit. New experiments are required to detect CNO neutrinos corresponding to the 1.5% of the solar luminosity that the standard solar model predicts is generated by the CNO cycle.

Postscript file.    Pdf file.

`Solar Models: current epoch and time dependences, neutrinos, and helioseismological properties
Author(s):John N. Bahcall, M. H. Pinsonneault, and Sarbani Basu
Journal:The Astrophysical Journal, 555, 990-1012 (July 10, 2001), astro-ph/0010346.

Abstract: We contrast the neutrino predictions from a set of eight standard-like solar models and four deviant (or deficient) solar models with the results of solar neutrino experiments. We also present the time dependences of some of the principal solar quantities that may lead ultimately to observational tests of the predicted time evolution by studying solar-type stars of different ages. In addition, we compare the computed sound speeds with the results of p-mode observations by BiSON, GOLF, GONG, LOWL, and MDI instruments. For solar neutrino and for helioseismological applications, we present present-epoch numerical tabulations of characteristics of the standard solar model as a function of solar radius, including the principal physical and composition variables, sound speeds, and neutrino fluxes.

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Solar Models: An Historical Overview
Author(s):John N. Bahcall
Journal: in the Proceedings of Neutrino 2002, XXth International Conference on Neutrino Physics and Astrophysics, Nuclear Physics B (Proc. Suppl.), 118, 77, astro-ph/0209080.

Abstract: 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.

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Solar Models, Neutrino Experiments, and Helioseismology
Author(s):John N. Bahcall and Roger K. Ulrich
Journal: Reviews of Modern Physics, 60, No. 2, 297-372 (April 1988).

Abstract: The event rates and their recognized uncertainties are calculated for eleven solar neutrino experiments using accurate solar models. The same solar models are used to evaluate the frequency spectrum of the p and g oscillation modes of the sun and to compare with existing observations. A numerical table of the characteristics of the standard solar model is presented. Improved values have been calculated for all of the neutrino absorption cross sections evaluating the uncertainties for each neutrino source and detector as well as the best estimates. The neutrino capture rate calculated from the standard solar model for the 37Cl experiment is 7.9(1±0.33) SNU, which spans the total theoretical range; the rate observed by Davis and his associates is (2.0±0.3) SNU. The ratio of the observed to the predicted flux at Earth of neutrinos from 8B decay lies in the range 0 <= [φ (8B)observed/φ (8B)predicted] <= 0.5. The recent results from the Kamiokande II electron scattering experiment confirm this conclusion. This discrepancy between calculation and observation is the solar neutrino problem. Measurements of the energy spectrum of solar neutrinos can discriminate between suggested solutions of the solar neutrino problem. Nonstandard solar models, many examples of which are also calculated in this paper, preserve the shape of the energy spectrum from individual neutrino sources, whereas most proposed weak-interaction explanations imply altered neutrino energy spectra. Detailed energy spectra of individual neutrino sources are presented as well as a composite solar neutrino spectrum. hep neutrinos from the 3He + p reaction, probe a different region of the solar interior than do 8B neutrinos. Measurements of the very rare but highest-energy hep neutrinos are possible in proposed experiments using electron scattering, 2H, and 40Ar detectors. The standard solar model predicts p-mode oscillation frequencies that agree to within about 0.5% with the measured frequencies and reproduce well the overall dispersion relation of the modes. However, there are several small but significant discrepancies between the measured and observed frequencies. The complementarity of helioseismology and solar neutrino experiments is demonstrated by constructing a solar model with a drastically altered nuclear energy generation that eliminates entirely the important high-energy 8B and 7Be neutrinos, but which affects by less than 0.01% the calculated p-mode oscillation frequencies.

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How Much Do Helioseismological Inferences Depend Upon the Assumed Reference Model?
Author(s): Sarbani Basu, M. H. Pinsonneault and John N. Bahcall
Journal:The Astrophysical Journal, 529, No. 2, 1084-1100 (February 1, 2000); astro-ph/9909247

Abstract: We investigate systematic uncertainties in determining the profiles of the solar sound speed, density, and adiabatic index by helioseismological techniques. We find that rms uncertainties-averaged over the sun of ~ 0.2%-0.4% are contributed to the sound speed profile by each of three sources: 1)the choice of assumed reference model, 2) the width of the inversion kernel, and 3) the measurements errors. The density profile is about an order of magnitude less well determined by the helioseismological measurements. The profile of the adiabatic index is determined to an accuracy of about 0.2%. We find that even relatively crude reference models yield reasonably accurate solar parameters.

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How Uncertain Are Solar Neutrino Predictions?
Author(s): John N. Bahcall, Sarbani Basu, and M. H. Pinsonneault
Journal:Physics Letters B, 433, 1-8 (August 6, 1998); astro-ph/9805135

Abstract: Solar neutrino fluxes and sound speeds are calculated using a systematic reevaluation of nuclear fusion rates. The largest uncertainties are identified and their effects on the solar neutrino fluxes are estimated.

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Are standard solar models reliable?
Author(s): J. N. Bahcall, M. H. Pinsonneault, S. Basu, and J. Christensen-Dalsgaard
Journal: Physical Review Letters, 78, 171-174 (January 13, 1997); astro-ph/9610250.

Abstract: Solar models that include element diffusion agree with helioseismological measurements of the sound speed to typically 0.2% throughout essentially the entire sun. Models that do not include diffusion, or in which the interior of the sun is assumed to be significantly mixed, are ruled out by the helioseismology. Standard solar models predict the measured structure of the sun more accurately than is required for applications involving solar neutrinos.

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Localized helioseismic constraints on solar structure
Author(s): John N. Bahcall, Sarbani Basu, and Pawan Kumar
Journal: The Astrophysical Journal Letters, 485, L91-L94 (August 20, 1997); astro-ph/9702075.

Abstract: Localized differences between the real sun and standard solar models are shown to be small. The sound speeds of the real and the standard model suns typically differ by less than 0.3% in the solar core.

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Status of solar models
Author(s): J. N. Bahcall and M. H. Pinsonneault
Journal: Neutrino 96, Proceedings of the XVII International Conference on Neutrino Physics and Astrophysics, Helsinki, Finland, June 13--19, 1996, eds. Katri Huitu, Kari Enqvist, and Jukka Maalampi (World Scientific, Singapore, 1997), pp. 56-70; hep-ph/9610542

Abstract: The neutrino fluxes calculated from 14 standard solar models published recently in refereed journals are inconsistent with the results of the 4 pioneering solar neutrino experiments if nothing happens to the neutrinos after they are created in the solar interior. The sound speeds calculated from standard solar models are in excellent agreement with helioseismological measurements of sound speeds. Some statements made by Dar at Neutrino 96 are answered here.

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How well do standard solar models describe the results of solar neutrino experiments?
Author(s): John Bahcall
Journal: In The Inconstant Sun, 2nd Napoli Thinkshop on Physics and Astrophysics, Napoli, 18 March 1996, eds. G. Cauzzi and C. Marmolino, Memorie Della Societ\`a Astronomica Italiana, 68 N. 2, 1997, pp. 361--368. astro-ph/9606161

Abstract:The neutrino fluxes calculated from the 14 standard solar models published recently in refereed journals are inconsistent with the results of the 4 pioneering solar neutrino experiments if nothing happens to the neutrinos after they are created in the solar interior. The calculated fluxes and the experimental results are in good agreement if neutrino oscillations occur.

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Temperature dependence of solar neutrino fluxes
Author(s): John N. Bahcall and Andrew Ulmer
Journal: Physical Review D, 53, 4202-4225 (April 15, 1996); astro-ph/9602012.

Abstract: Using a one-zone model of the Sun, we derive expressions for the temperature dependence of the solar neutrino fluxes. The exponents of the scaling laws agree to within 20 percent or better with the exponents extracted from detailed solar models.

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Observational searches for solar g-modes: some theoretical considerations
Author(s): Pawan Kumar, Eliot J. Quataert, and John N. Bahcall
Journal: The Astrophysical Journal, 458, L83-L85 (February 20, 1996); astro-ph/9512091.

Abstract: We suggest that the most likely source of solar g-modes is turbulent stresses in the convection zone. The estimated surface velocity amplitude of low degree and low order g-modes resulting from this process is of order 0.01 cm per sec, interestingly close to the detection threshold of the SOHO satellite.

Solar g-modes are unlikely to have caused the discrete peaks in the power spectrum reported by Thompson et al. (1995). Using energy balance, the amplitudes given by Thompson et al. imply a surface velocity of at least 50 cm per sec, much larger than the existing observational upper limit (5 cm per sec).

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Solar models with helium and heavy element diffusion
Author(s): John N. Bahcall and M. H. Pinsonneault, with an Appendix on the Age of the Sun by G. J. Wasserburg
Journal: Reviews of Modern Physics, 67, 781-808 (October 1995); hep-ph/9505425.

Abstract: Helium and heavy-element diffusion are both included in precise calculations of solar models. In addition, improvements in the input data for solar interior models are described for nuclear reaction rates, the solar luminosity, the solar age, heavy element abundances, radiative opacities, helium and metal diffusion rates, and neutrino interaction cross sections. The effects on the neutrino fluxes of each change in the input physics are evaluated separately by constructing a series of solar models with one additional improvement added at each stage. The effective 1 uncertainties in the individual input quantities are estimated and used to evaluate the uncertainties in the calculated neutrino fluxes and the calculated event rates for solar neutrino experiments. The calculated neutrino event rates, including all of the improvements, are (9.3   +1.2-1.4) SNU for the 37Cl experiment and (137   +8-7) SNU for the 71Ga experiments. The calculated flux of 7Be neutrinos is 5.1 (1.00   +0.06-0.07) × 109 cm-2s-1 and the flux of 8B neutrinos is 6.6 (1.00   +0.14-0.17) × 106 cm-2s-1. The primordial helium abundance found for this model is Y = 0.278. The present-day surface abundance of the model is Ys = 0.247, in agreement with the helioseismological measurement of Ys = 0.242 ± 0.003 determined by Hernandez and Christensen-Dalsgaard (1994). The computed depth of the convective zone is R = 0.712R in agreement with the observed value determined from p-mode oscillation data of R = 0.713 ± 0.003R found by Christensen-Dalsgaard et al. (1991). Although the present results increase the predicted event rate in the four operating solar neutrino experiments by almost 1 (theoretical uncertainty), they only slightly increase the difficulty of explaining the existing experiments with standard physics (i.e., by assuming that nothing happens to the neutrinos after they are created in the center of the sun). For an extreme model in which all diffusion (helium and heavy element diffusion) is neglected, the event rates are (7.0   +0.9-1.0) SNU for the 37Cl experiment and (126   +6-6) SNU for the 71Ga experiments, while the 7Be and 8B neutrino fluxes are, respectively, 4.5 (1.00   +0.06-0.07) × 109 cm-2s-1 and 4.9 (1.00   +0.14-0.17) × 106 cm-2s-1. For the no-diffusion model, the computed value of the depth of the convective zone is R = 0.726R, which disagrees with the observed helioseismological value. The calculated surface abundance of helium, Ys = 0.268, is also in disagreement with the p-mode measurement. We conclude that helioseismology provides strong evidence for element diffusion and therefore for the somewhat larger solar neutrino event rates calculated in this paper.

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Do solar-neutrino experiments imply new physics?
Author(s): J. N. Bahcall and H. A. Bethe
Journal: Physical Review D, 47, 1298 (February 15, 1993); hep-ph/9212204.

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None of the 1000 solar models in a full Monte Carlo simulation is consistent with the results of the chlorine or the Kamiokande experiments. Even if the solar models are forced artifically to have a 8B neutrino flux in agreeement with the Kamiokande experiment, none of the fudged models agrees with the chlorine observations. The GALLEX and SAGE experiments, which currently have large statistical uncertainties, differ from the predictions of the standard solar model by 2 and 3 , respectively.

Standard Solar Models and the Uncertainties in Predicted Capture Rates of Solar Neutrinos
Author(s): John N. Bahcall, Walter F. Huebner, Stephen H. Lubow, Peter Parker, and Roger K. Ulrich
Journal: Reviews of Modern Physics, 54, 767 (July 1982).

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Abstract: The uncertainties that affect the prediction of solar neutrino fluxes are evaluated with the aid of standard solar models.   Full abstract

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