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.
Postscript
file. Pdf
file.
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.
Postscript
file. Pdf
file.
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.
Postscript
file. Pdf
file.
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.
pdf file
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.
pdf file
postscript file
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.
postscript
file pdf file
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.
pdf file
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.
pdf file
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.
postscript
file pdf file
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.
postscript
file pdf file
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.
pdf file
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.
pdf file
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).
postscript file pdf file
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.
pdf
file
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.
pdf file
Abstract:
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).
pdf file
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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