Black and white figure (postscript)   Black and white figure (pdf)
Color figure (postscript)   Color figure (pdf)

For an explanation of this histogram, see J. N. Bahcall, Solar Models and Solar Neutrinos: Current Status, Proceedings of the Nobel Symposium 2004, Enkoping, Sweden, August 19-24, 2004, eds. L. Bergstrom, O. Botner, P. Carlson, P. O Hulth, and T. Ohlsson, hep-ph/0412068. The theoretical predictions have been updated to J. N. Bahcall, A. Serenelli, and S. Basu, ApJ Letters 621, L85 (2005). The experimental data include results reported up to April 20, 2005 (see the Salt Phase SNO paper, nucl-ex/0502021 and the GNO paper hep-ex/0504037 as well as references therein).

Solar Neutrino Viewgraphs

This page contains viewgraphs that I use in recent talks on solar neutrinos. The content of each figure is explained by the caption which is mainly taken from the paper in which the viewgraph appeared. The papers are available under Recent Preprints and Reprints or Popular Papers on my home page, as well as on the computer archives.

For many of the viewgraphs, there is an option of downloading either a color or a black and white version. For some browsers, the display of the black and white viewgraph will appear in color. It should, nevertheless, print out for you in black and white.

To see the explanation and a small version of a particular viewgraph, click on the title of that viewgraph.

I add and subtract viewgraphs to this page from time to time. I last altered this page on February 17, 2005.

Solar neutrino energy spectrum for the solar model BS05(OP). This is figure 2 of ``New Solar Opacities, Abundances, Helioseismology, and Neutrino Fluxes,'' ApJ, 621, L85 (2005).

Postscript (color)   PDF (color)    Postscript (black and white)   PDF (black and white)

Before and After Neutrino 2004

The two figures below show 1) the separate Before and After Neutrino 2004 solutions for the solar neutrino allowed regions (left panels) and the reactor allowed regions (right panels, KamLAND); 2) the globally allowed neutrino oscillation parameters Before and After Neutrino 2004. The results were obtained in a three neutrino fit to all the available solar, reactor, K2K, and atmospheric data (see hep-ph/0406294).

Separate solar and reactor allowed regionsGlobally allowed neutrino oscillation parameters
Postscript   PDFPostscript   PDF

Solar Models and Solar Neutrino Oscillations, New Journal of Physics, 6 (2004), 63
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 performing new solar neutrino experiments and what we anticipate from future studies.

Postscript     PDF

The predicted solar neutrino energy spectrum. The figure shows the energy spectrum of solar neutrinos predicted by the BP04 solar model. For continuum sources, the neutrino fluxes are given in number of neutrinos cm-2s-1 MeV-1 at the Earth's surface. For line sources, the units are number of neutrinos cm-2s-1. Total theoretical uncertainties are shown for each source. To avoid complication in the figure, we have omitted the difficult-to-detect CNO neutrino fluxes.

The Big News with solar neutrinos is that the p-p flux is determined to ± 2% by the analysis in hep-ph/0305159 of all of the existing solar neutrino experiments plus the luminosity constraint. The result agrees with the solar model prediction to 1% (with a theoretical uncertainty also of 1%). Low energy solar neutrino experiments are required to test whether the predicted transition from MSW oscillations at high energies to vacuum oscillations at low energies (typical transition energy ~ 2 MeV) actually occurs. If there is no new physics at the lower energies, then a 7Be solar neutrino experiment accurate to 5% will, together with the luminosity constraint, determine the p-p neutrino flux to 0.5%, making possible a precise measurement of the mixing angle 12 (see hep-ph/0305159).

A Road Map to Solar Neutrino Fluxes, Neutrino Oscillation Parameters, and Tests for New Physics, JHEP, 11(2003)004, hep-ph/0305159

Postscript     PDF

Vacuum-Matter transition.The figure shows the electron neutrino survival probability, Pee, as a function of neutrino energy for the (daytime) LMA oscillation solution. For small values of the parameter defined in equation (2) of hep-ph/0305159 [ is proportional to the electron number density times the energy divided by the square of the mass differences], the vacuum (kinematic) oscillation effects are dominant. For values of  greater than unity, the MSW (matter) oscillations are most important. For solar conditions, the transition between vacuum and matter oscillations occurs somewhere in the region of 2 MeV.

We show that solar plus reactor neutrino experiments set an upper limit of 7.3% to the fraction 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.

Does the Sun Shine by pp or CNO Fusion Reactions?

Postscript     PDF

The KamLAND experiment [Phys. Rev. Lett., 90 (2003) 021802] has confirmed decisively the LMA solution and enabled remarkably strong inferences, both about the 8B solar neutrino flux and about the physicsl characteristics of solar neutrinos. In recent lectures, I have presented the inferences from hep-ph/0212147 [JHEP 02(2003)009]. The most important of these conclusions are summarized in the two slides given here: 1) the principal inferences from a global solution including the KamLAND data; 2) the currently allowed region of neutrino oscillation parameters.

Solar neutrinos before and after KamLAND

Postscript     PDF Postscript     PDF

I gave three talks at the International Conference on Neutrinos and Subterranean Science, NESS02, Washington, D.C., September 19-21, 2002. Here are the viewgraphs for those talks in PowerPoint and in PDF files. The talks represent my latest thinking about the subjects covered. Individual slides from the talks may be useful to you in some of the talks you give.

Summary talk of the conference:   PowerPoint   PDF

The Waxman-Bahcall bound on extragalactic neutrino fluxes.:   PowerPoint   PDF

The standard solar model and experiments:   PowerPoint   PDF

High Energy Neutrino Viewgraphs

General viewgraphs

In general colloquia, I often show introductory material, including a schematic equation which summarizes how Nuclear burning of 4 protons to an alpha particle fuels the sun and the Original motivation for doing a solar neutrino experiment that Ray Davis and I gave in 1964. I also frequently show the Predicted solar neutrino fluxes as a function of time, for the last 33 years (since the first measurement of solar neutrino fluxes by Ray Davis). This historical viewgraph gives a feeling for the robustness of the predictions.

Have you ever wondered what was the origin of the term SNU? It is explained in the viewgraph SNU.

Nuclear fusion reactions

The p-p nuclear fusion reactions are shown on this viewgraph, p-p

The most important nuclear physics experiment for solar neutrino research is an accurate measurement of the low energy proton capture rate on 7Be. The largest astrophysical uncertainties in the calculation of the 8B neutrino flux are about 5 percent [Phys. Lett. B, 433, 1-8 (1998), astro-ph/9805135, and hep-ph/0111150]. Therefore, the low energy cross section for the production of 8B by proton capture on 7Be must be measured to an accuracy of 5 percent in order to prevent this nuclear physics measurement from dominating the error budget in inferring astrophysical and neutrino properties from solar neutrino experiments. This point of view is described in the viewgraph Most Important Nuclear Physics Experiment.

The 3He + 4He fusion cross section must also be measured more precisely. The uncertainties in this cross section dominate the uncertainties in the prediction of the 7Be neutrino flux and are also an important source of uncertainty in the prediction of the 8B neutrino flux (see Table 2 of hep-ph/0111150).

Where do solar neutrinos originate in the Sun?

This viewgraph shows where in the sun the different solar neutrino fluxes originate.

How uncertain are solar neutrino predictions?, Phys. Lett. B, 433, 1 (1998), astro-ph/9805135.

Two viewgraphs answer this question:

Predicted versus measured sound speeds, and Predicted solar neutrino fluxes with estimated uncertainties.

Neutrino energy spectra.

The shape of the neutrino energy spectrum from any individual neutrino source is determined by nuclear physics alone and is independent of any solar influence to an accuracy of 1 part in 105 (see Phys. Rev. D, 44, 1644-1651, 1991). The independence from any measurable influence of solar physics makes the shapes of neutrino energy spectra a key part of the subject of solar neutrinos and provides an opportunity for a "smoking gun" proof of new neutrino physics. There are 3 viewgraphs that illustrate particuarly well the role of solar neutrino energy spectra in different solar neutrino experiments They are:

The shape of the B energy spectrum is independent of solar conditions, Standard solar neutrino energy spectrum, and The best-estimate (standard) 8B neutrino spectrum , together with the spectra ± allowed by the maximum (± 3) theoretical and experimental uncertainties.

Neutrino oscillation experiments in the Events versus L/E plane.

This viewgraph shows neutrino oscillation experiments, including solar neutrino experiments, in the plane L/E versus Event Rate, where L is the source-detector separation and E is the neutrino energy.

Solar Models: Current Epoch and Time Dependences, Neutrinos, and Helioseismological Properties, ApJ, 555, 990-1012 (2001), astro-ph/0010346.
postscript    pdf

I use in talks the following viewgraphs:

Normalized solar luminosity vs. solar age. ; Depth of the convective zone as a function of age. ; Mass included within the convective zone as a function of age. ; Temporal evolution of the central temperature, density, pressure, and hydrogen mass fraction. ; Electron number density vs. solar radius. ; Predicted vs. measured sound speeds. ; Calculated solar sound speed vs. radius. ; and Six precise helioseismological measurements vs. BP2000.

I use in talks the following viewgraphs:

Global neutrino oscillation solutions for three different analysis strategies. ; Standard global oscillation solution (one panel). ; The neutral current to charged current double ratio, [NC]/[CC].; The percentage difference between the night and the day CC rates.; The currently allowed regions for the neutrino oscillation parameters that predict a neutral current to charged current double ration (left panel), and the currently allowed region that predicts a CC night-day difference (right panel).; The correlation between the neutral current to charged current double ration, and the charged current day-night effect.; The 7Be neutrino event rate.; and The percentage difference between the night and the day rates for recoil electrons with kinetic energies in the range 0.25 MeV < Te < 0.8 MeV.

What will the first year of SNO show? Phys. Lett. B, 477, 401-409 (2000), hep-ph/9911248.

I find the next two viewgraphs exciting. They show that the charged current rate in SNO may be a `smoking gun', distinguishing in one measurement between the `no-oscillation' expectation of 0.47 (relative to the combined standard model) and the different results predicted by the currently favored oscillation solutions. The measurement of this rate may well be the most important result that SNO will show in the first year.

     The charged current predictions for SNO versus the no oscillation hypothesis. The two figures are for a total electron energy threshold of 5 MeV and 8 MeV respectively. The shaded area is the no-oscillation prediction based upon the measured SuperKamiokande rate for -e scattering. The SNO charged current ratios (vertical axes) are shown for different neutrino oscillation scenarios. The error bars on the neutrino predictions represent the range of values predicted by the 99% CL allowed neutrino oscillation solutions.

Is Large Mixing Angle MSW the Solution of the Solar Neutrino Problems?, Phys. Rev. D, 60, 93001; hep-ph/9905220.

Plamen Krastev, Alexei Smirnov, and I argued that there is a good change that this is the solution. Hence, the title of the paper.

Three viewgraphs of observational effects are offered in support of this interpretation. The text provides more quantitative and theoretical arguments.

The predicted versus the observed zenith angle dependence of the total event rate,   Distortion of the 8B electron recoil energy spectrum,   The predicted seasonal dependence of the total event rate.

Gallium experiments

The four viewgraphs described below are based upon results given in ``Gallium Solar Neutrino Experiments: Absorption Cross Sections, Neutrino Spectra, and Predicted Event Rates," Phys. Rev. C, 56, 3391 (1997), hep-ph/9710491. The first viewgraph describes the relation between the calculated and the measured (by GALLEX and SAGE, references given on the viewgraph) neutrino absorption cross sections for the chromium test experiments. The second and third viewgraphs are Figure 3 and Figure 4 of the paper cited above and give the predicted gallium event rate versus year of publication (1962 to 1998) and the gallium neutrino absorption cross section versus energy. The fouth viewgraph describes the minimum rate that could be observed in the sun, given only that the sun shines by nuclear fusion in its interior and that nothing happens to the neutrinos after they are created. This limit is unrealistically since it involves setting equal to zero a number of nuclear cross sections that are measured in the laboratory to be significant and also ignores everything we know about the sun from solar models and heliosesimology.

The four viewgraphs are:

Measured versus calculated 51Cr neutrino absorption by 71Ga, Predicted standard model gallium neutrino event rate versus year of publication, Absorption cross sections for gallium as a function of energy, and The zero cross-section lower limit

The viewgraph 71Ga: Experiment versus Theory summarizes the comparison of the rates measured by GALLEX and SAGE with the predictions of the standard solar model.

Summary (1996 and 1998, prior to SNO)

My summary of the current situation in solar neutrino research is that there is no viable explanation of all the experiments that is based upon changing the solar model, but that a number of proposed particle-physics explanations do fit all the available data. A detailed justification for this summary is given in ApJ 467, 475 (1996), hep-ph/9512285; and more recently, in Phys. Lett. B, 433, 1-8 (1998), astro-ph/9805135.

Color Viewgraph        Black and White Viewgraph

Where do we stand with solar neutrino oscillations (in 1998)?, Phys. Rev. D, 58, 096016-2 - 096016-22 (1998), hep-ph/9807216.

There are five viewgraphs which summarize the allowed parameter regions for solar neutrino oscillations and illustrate the agreement (or disagreement) of the standard 8B neutrino energy spectrum with the spectral measurements made with the SuperKamiokande experiment.

The viewgraphs are:

Predictions of standard solar models since 1988,, Global fits: MSW solution,, Global fits for sterile neutrinos,, Global fits: vacuum solutions,, and Global best fits versus measured energy spectrum.

How well can one fit the solar neutrino data if one ignores all information from solar models? The answer is: ``Very poorly, unless one allows some new physics (like oscillations) to change the neutrino energy spectrum.'' The formal result of treating the neutrino fluxes as arbitrary parameters is summarized on the viewgraph No New Neutrino Physics.

SNO: Predictions for Ten Measurable Quantities, Phys. Rev. D, 62, 93004 (2000), hep-ph/0002293.

I use in my talks the following figures from this paper: survival probabilities for six global oscillation solutions, the CC electron recoil energy spectra, the fractional shift in the average electron recoil energy, the neutral current to charged current double ratio (5MeV), and 8 MeV, the neutrino-electron scattering to charged current double ratio, the percentage difference between the night and the day CC rates, and the neutral current to charged current double ratio versus the day-night asymmetry.

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