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The software available here was first described and used in "How do the uncertainties in the surface chemical composition of the Sun affect the predicted neutrino fluxes?," astro-ph/0412096, Bahcall and Serenelli. These data and software allow one to calculate uncertainties in solar neutrino fluxes and event rates taking account of the individual uncertainties in the abundances of different chemical elements on the surface of the Sun. |
The files accessible here are available for general use. I would
appreciate a note at your convenience telling me how you are using
them.
BS2005 This paper, (ApJ, 621, L83, March 2005) discusses the helioseismological implications of the new radiative opacity calculations by the OPAL (OP) opacity collaboration and the new (lower) heavy element abundances summarized by Asplund, Grevesse, and Sauval (2005). We also consider the effects of some refinements in nuclear reaction rates and the very small differences that arise from using two independent stellar evolution codes to calculate the solar models. Solar models constructed with the new Asplund et al. abundances disagree, by much more than the quoted measuring errors, with the helioseismological determinations of the depth of the solar convective zone, the solar sound speeds, the solar density profile, and the surface helium abundance. Our best model of this type is BS05(AGS,OP). Models constructed using the older (larger) heavy element abundances summarized by Grevesse and Sauval (1998) are in excellent agreement with the helioseismological data. Our preferred model with the older heavy element abundance is BS05(OP). Using the new OP radiative opacities, the ratio of the 8B neutrino flux calculated with the older heavy element abundances (or with the newer, 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 (solar model) uncertainty, 1 sigma errors.
Standard Solar Model BS05(AGS,OP)
Distribution of neutrino fluxes in the BS05(AGS,OP) standard solar model model
Distribution of neutrino fluxes in the BS05(OP) standard solar model model
Distribution of electron density in the BS05(OP) standard solar model
BP2004 This paper (Phys. Rev. Lett., 92, 121301, March 2004) is part of a series that spans more than 40 years. The goals of this series are to provide increasingly more precise theoretical calculations of the solar neutrino fluxes and detection rates and to make increasingly more comprehensive evaluations of the uncertainties in the predictions. We describe here two steps forward (improved accuracy of the equation of state of the solar interior and some of the nuclear fusion data) and one step backward (increased systematic uncertainties in the determination of the surface composition of the Sun). Using recent improvements in input data, we calculate the best-estimates, and especially the uncertainties, in the solar model predictions of solar neutrino fluxes. We compare the calculated neutrino fluxes with their measured values.We stress the need for further improvements in measurements of the surface composition of the Sun and of specific nuclear reaction rates.
For each spherical shell, the table presents the fraction of each neutrino flux that is produced in that shell. These data are necessary in order to compute accurately the MSW effect in the sun. The table also contains the 7Be mass density contained in each shell.
BP2000 This is the latest in the series that began in 1962 of successively refined standard solar models. The latest model appears in ApJ, 555, 990, 2001 authors John N. Bahcall, M. H. Pinsonneault, and Sarbani Basu. In this paper, 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.
The file gives the complete run of the logarithm of (electron density divided by Avrogadro's number) versus the radius of the sun. The density run that is shown is for the standard solar model, BP2000. However, the results are well fit for radii less than 0.9 of the solar radius by the exponential formula given in Eq. (4.2) of the book Neutrino Astrophysics (J. N. Bahcall, Cambridge Univ. Press, 1989), cf. Fig. 4.1 of this book. The table presented here for BP2000 is the first one we have published that contains precise values of the electron density in the outer region of the sun.
The file gives the complete run of the logarithm of the MSW number density (defined as the electron number density -0.5 times the neutron number density, all divided by Avrogadro's number) versus the radius of the sun. The MSW density run that is shown is for the standard solar model, BP2000. However, the results are well fit for radii less than 0.9 of the solar radius by a function with the same slope as the exponential formula given in Eq. (4.2) of the book Neutrino Astrophysics (J. N. Bahcall, Cambridge Univ. Press, 1989), cf. Fig. 4.1 of this book. The table presented here for the BP2000 solar model is the first one we have published that contains precise values of the MSW number.
This table gives details of the standard model, BP2000, as a function of the stellar radius, including mass fraction, temperature, density, pressure, and chemical composition. In order to determine the sensitivity of different quantities to the details of the solar models, you can use similar (but less numerically detailed) tables for the best standard solar models from 1998, 1995, 1992, 1988, and 1982, all of which are availabe under the menu item Solar Models on this page.
For each spherical shell, the table presents the fraction of each neutrino flux that is produced in that shell. These data are necessary in order to compute accurately the MSW effect in the sun. The table also contains the 7Be mass density contained in each shell.
This table gives at high resolution the computed sound speeds for the BP2000 model. Values of the sound speed are give at 875 radial positions from 0.0065 solar radii to 0.95 solar radii. The tabulated results can be compared with helioseismological measurements and with the computations made using other stellar evolution programs.
MSW
survival probabilities
These three files give the survival probabilities for electron type solar neutrinos as a function of neutrino energy for the LMA, SMA, and LOW MSW solutions. These best-fit MSW solutions include regeneration in the earth. Each file includes the day only, the day-night average, and the night only survival probabilities as a function of neutrino energy. The results were used to plot Figure 9 of the paper by Bahcall, Krastev, and Smirnov, Phys. Rev. D, 58, 096016 (1998). You can see a full explanation of how the probabilities were calculated in that paper.
Sound
speeds, density, and adiabatic index
This file contains a relatively dense grid of sound speeds, density, and adiabatic index that were derived from MDI data using a BP standard solar model. The table is taken from the paper ``How much do helioseismological inferences depend upon the assumed standard model?'' by S. Basu, M. H. Pinsonneault, and J. N. Bahcall, ApJ 529, 1084 (2000), astro-ph/9909247.
BP98
sound speeds
This file contains the sound speeds for the BP98 standard solar model. This solar model is described in ``How Uncertain Are Solar Neutrino Predictions'' by J. N. Bahcall, S. Basu, and M. H. Pinsonneault, Phys. Lett. B, 433, 1-8 (1998), astro-ph/9805135.
Hep
energy spectrum
The hep energy spectrum extends to 18.8 MeV, well beyond the endpoint
of the 8B neutrino energy spectrum. In principle, hep neutrinos may be
detectable in the SuperKamiokande and SNO solar neutrino experiments
(see discussion in Bahcall-Ulrich, RMP, 60, 297, 1988). The predicted
flux of the rare hep neutrinos is proportional to the low-energy cross
section for 3He + p
4He + e+ + 
e. Unfortunately, I
have been unable to find a reliable way of estimating an uncertainty
in this production cross section, since the reaction is forbidden and
the calculated value involves strong cancellation between terms from
different sources.
The spectrum given here includes the thermal fusion energy calculated in Phys. Rev. C, 56, 3391 (1997). The uncertainty in the shape of the hep energy spectrum is negligible in the context of solar neutrino research.
Solar
neutrino rates, fluxes, and uncertainties.
The code evaluates the uncertainties in the neutrino fluxes and the uncertainties in the predicted event rates. I used this code to calculate the rates and uncertainties in the recent paper ``What do we (not) know theoretically about solar neutrino fluxes?" by J. N. Bahcall and M. H. Pinsonneault (astro-ph/0402114, to be published in Phys. Rev Lett.). I keep this code current using the best-available values, and uncertainties, for neutrino cross sections and solar model input parameters (nuclear cross sections, element composition, solar luminosity, and age). The uncertainties due to radiative opacity and to elment diffusion are also included. A sample data file that illustrates how to take account of assymetric errors is included. The code describes with comment lines the best-estimates and their uncertainties and gives references for the sources of both the best-estimates and the errors.
Chlorine
neutrino absorption cross
sections as a function of energy.
The absorption cross sections as a function of energy for electron neutrinos incident on 37 Cl for energies from 1.0 MeV to 30.0 MeV. These improved values for the continuum cross sections are taken from Table 3 of Bahcall et al. Phys Rev C 54, 411 (1996). For the specific energies of the 7Be and pep solar neutrinos, cross sections are given in the book Neutrino Astrophysics.
Gallium neutrino absorption cross
sections as a function of energy.
The absorption cross sections as a function of energy for electron neutrinos incident on 71Ga for energies from 0.240 MeV to 30.0 MeV. I give at each energy the best estimate cross section and also the 3 sigma lower and upper limit cross sections. These cross sections can be used to calculate best-estimates, and uncertainties, for the solar neutrino capture rate in a gallium detector.
The
pp solar neutrino energy spectrum.
The normalized pp solar neutrino energy spectrum is given. This is the first time I have published the pp spectrum including the contribution of the kinetic energy of the colliding solar protons.
Zenith Angle Exposure Functions
For Kamioka, Sudbury, and Gran Sasso
The fractional number of solar neutrino events observed as a function of solar zenith angle is, for standard physics (no matter osccilations), determined only by the latitude of the neutrino detector. The number of events is largest for zenith angles at which the sun spends most of its time in its apparent motion around the earth. We refer to the normalized number distribution of events as the ``zenith angle exposure function''; this function describes the relative amount of time the detector is exposed to the sun at a fixed zenith angle. (For the full definition of the zenith angle exposure function, see under Some Recent Preprints and Reprints the paper by Bahcall and Krastev entitled ``Does the Sun Appear Brighter at Night in Neutrinos?''; Phys. Rev. C 56 , 2839, 1997.)
The table presented here gives the calculated zenith angle exposure functions for detectors located at Kamioka, Japan, Sudbury, Canada, and the Gran Sasso National Laboratory, Italy. Any departure of the measured zenith angle distribution function from the standard distribution functions given here would be a demonstration of the existence of matter regeneration in the earth, as suggested by the MSW effect.
Moments
of Electron Recoil Energy Spectra
The theoretical ingredients necessary for analyzing Superkaniokande and SNO solar neutrino observations are presented in tabular form as a function of neutrino energy. The ingredients include neutral and charged current cross sections on deuterium, the electron-neutrino scattering cross sections (electron and muon neutrinos), and the normalized standard neutrino spectrum.
The observable effects of solar neutrino oscillations in the Superkamiokande and SNO experiments can be summarized by the values of the measured average electron recoil energy and by the variance of the recoil energy. The data presented here permit the easy calculation of these first two spectral moments.
7Be
line shapeThe file contains the data used to plot Figure 2 and Figure 3 of “The 7Be Neutrino Line: A reflection of the central temperature of the Sun,” Phys. Rev. D 49 (1994) 3923.
B Neutrino Spectrum
The standard neutrino energy spectrum for the important
B
neutrinos. The table also contains energy spectra that differ from
the standard solar neutrino
spectrum by +/- three standard deviations, combined
theoretical and experimental uncertainties.
B
Neutrino Survival Probabilities
This table contains seven illustrative sets of solar neutrino survival probabilities as a function of energy. One set of survival probabilities represents the best-fit small mixing angle MSW solution to the measured results in the chlorine, Kamiokande, GALLEX, and SAGE experiments. The other sets of survival probabilities represent points on the periphery of the 95 percent C.L. solutions. The survival probabilities have all been averaged over the boron neutrino production region in the sun, which has a small influence on the numerical values.
CNO solar
neutrino energy spectra
These files contain the energy spectra for the three CNO solar neutrino sources, not previously published.
Survival Probabilities for ALL CNO
Solution
The survival probabilities as a function of energy for a remarkable MSW solution to the solar neutrino problems. In this solution, 99.95 percent of the solar energy is produced by CNO fusion reactions, with only negligible energy generation from pp reactions. The predictions of this model agree very well with the results from the chlorine, Kamiokande, GALLEX, and SAGE experiments. I do not believe this model is correct based upon what we know about standard solar models and their agreement with many electromagnetic observations. However, experiments that measure the energy of low energy solar neutrino events, such as BOREXINO or HELLAZ/HERON, are necessary to rule out this model via neutrino observations.
Exportenergy.f
This code calculates nuclear energy generation and neutrino fluxes in models of main sequence stars. The code is being used by different groups and is easily exportable, since it contains many comment lines. One can conveniently change the low energy cross sections for reaction rates in a single data file. The code has been applied to globular cluster stars as well as to Population I stars.
Solar Models
The most recent model contained here is the BP98 standard solar model. There are also tables of detailed solar models that were originally published in the Reviews of Modern Physics in 1982, 1988, 1992, and, 1995. Models with and without diffusion are included.
Deuterium Cross Sections
Contains an exportable set of subroutines and functions that calculate the charged current and neutral current cross sections on deuterium. The code is documented in detail and the physics has been described in a cited paper. The code can be used to calculate best-estimates for solar neutrino event rates in the SNO detector and also, as indicated, to estimate uncertainties due to our imperfect knowledge of the deuterium cross sections. The output of the code can be customized for a particular Monte Carlo simulation.
Diffusion Subroutine
This is an exportable subroutine that calculates rapidly the diffusion of any number of elements in stars. The subroutine solves exactly the Burgers equations. The code has been used successfully by a number of different groups; applications include diffusion in the sun and diffusion in globular cluster stars. Instructions for using the code are provided in a Read.me file.
Solar
Fusion Cross Sections
This is the version of the INT WorkShop paper on Solar Fusion reactions that was accepted for publication by the Reviews of Modern Physics. We are no longer able to make science changes, but the RMP editor has told me that we can send her a list of editorial changes (small) that add bibliographical information about papers that have been published since submission of this draft or to make editorial changes like correcting a number in a table or a misspelling. Please communicate as soon as possible your corrections to Maggie Best, best@sns.ias.edu, with a copy to me. Thanks very much. John
Logarithmic partial derivatives of fluxes with
individual abundances
These two tables are taken from Table 1 and 2 of astro-ph/0412096 . The entries represent the logarithmic partial derivatives of each neutrino flux with respect to each of the principal element abundances. The first table was computed using the solar model BP04 and the second table was computed using the solar model BP04+, both models taken from Bahcall-Pinsonneault, Phys. Rev. Lett., 92, Number 12, 121301 (2004), astro-ph/0402114.
Uncertainties in
neutrino fluxes and rates due to individual composition
uncertaintiesThis code calculates the uncertainties in solar neutrino fluxes and radiochemical event rates due to experimental uncertainties in the individual heavy abundances on the surface of the Sun.
compositionuncertainties.f compositionuncertainties.dat compositionuncertainties.output
Total event rates, and
total uncertainties in neutrino fluxes and event ratesThis code calculate the total capture rate in radiochemical experiments and the total uncertainties in the neutrino fluxes and radiochemical event rates.
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