Standard Solar Model

Standard Solar Model

The Standard Solar Model (SSM) is the best current physical model of our sun. Very generally, in the Standard Solar Model the sun is a ball of mostly hydrogen plasma which is held together through self gravitation. At the core of the sun the temperature and density are large enough that hydrogen nuclei may be converted to helium through several different processes. The conversion of hydrogen to helium releases a large amount of energy, and also results in the production of two electron neutrinos. The energy continually produced in the core keeps the sun in equilibrium, neither exploding nor collapsing further. As the ratio of hydrogen to helium in the core changes, the core temperature and density also change, and this affects the size and luminosity of the sun. Like the Standard Model of particle physics and the standard cosmology the SSM changes over time in response to relevant new theoretical or experiment discoveries.

Neutrino production

Hydrogen is fused into helium through several different interactions in the sun. The vast majority of neutrinos are produced through the pp chain, a process in which four protons are combined to produce two protons, two neutrons, two electrons, and two electron neutrinos. Neutrinos are also produced by the CNO cycle, but that process is considerably less important in our sun than in other stars.

Most of the neutrinos produced in the sun come from the first step of the pp chain but their energy is so low (<0.425 MeV)cite web|first=John|last=Bahcall|authorlink=John N. Bahcall|url=|title=Solar Neutrino Viewgraphs|publisher=Institute for Advanced Study School of Natural Science|accessdate=2006-07-11] they are very difficult to detect. A rare side branch of the pp chain produces the "boron-8" neutrinos with a maximum energy of roughly 15MeV, and these are the easiest neutrinos to observe. A very rare interaction in the pp chain produces the "hep" neutrinos, the highest energy neutrinos produced in any detectable quantity by our sun. The hep neutrinos are predicted to have a maximum energy of about 18MeV.

All of the interactions described above produce neutrinos with a spectrum of energies. The inverse beta decay of Be7 produces neutrinos at either roughly 0.9 or 0.4MeV.

Neutrino detection

The weakness of the neutrino's coupling with other particles means that most neutrinos produced in the core of the sun can pass all the way through the sun without being absorbed. It is possible, therefore, to observe the core of the sun directly by detecting these neutrinos.


The first experiment to successfully detect cosmic neutrinos was Ray Davis's chlorine experiment, in which neutrinos were detected by observing the conversion of chlorine nuclei to radioactive argon in a large tank of perchloroethylene. This was a reaction channel expected for neutrinos, but since only the numbers of argon decays was counted, it didn't give any directional information, like where the neutrinos came from. The experiment found about 1/3 as many neutrinos as were predicted by the Standard Solar Model of the time, and this problem became known as the solar neutrino problem.

While it is now known that the chlorine experiment detected neutrinos, some physicists at the time were suspicious of the experiment, mainly because they didn't trust such radiochemical techniques. Unambiguous detection of solar neutrinos was provided by the Kamiokande-II experiment, a water Cerenkov detector with a low enough energy threshold to detect neutrinos through neutrino-electron elastic scattering. In the elastic scattering interaction the electrons coming out of the point of reaction strongly point in the direction that the neutrino was travelling, away from the sun. This ability to "point back" at the sun was the first conclusive evidence that the sun is powered by nuclear interactions in the core. While the neutrinos observed in Kamiokande-II were clearly from the sun, the rate of neutrino interactions was again suppressed. Even worse, the Kamiokande-II experiment measured about 1/2 the predicted flux, rather than the chlorine experiment's 1/3.

The solution to the solar neutrino problem was finally experimentally determined by the Sudbury Neutrino Observatory. The radiochemical experiments were only sensitive to electron neutrinos, and the signal in the water Cerenkov experiments was dominated by the electron neutrino signal. The SNO experiment, by contrast, had sensitivity to all three neutrino flavours. By simultaneously measuring the electron neutrino and total neutrino fluxes the experiment demonstrated that the suppression was due to the MSW effect, the conversion of electron neutrinos from their pure flavour state into the second neutrino mass eigenstate as they passed through a resonance due to the changing density of the sun. The resonance is energy dependent, and "turns on" near 2MeV. The water Cerenkov detectors only detect neutrinos above about 5MeV, while the radiochemical experiments were sensitive to lower energy (0.8MeV for chlorine, 0.2MeV for gallium), and this turned out to be the source of the difference in the observed neutrino rates at the two types of experiments.

hep neutrinos

The highest energy neutrinos have not yet been observed due to their small flux compared to the boron-8 neutrinos, so thus far only limits have been placed on the flux. No experiment yet has had enough sensitivity to observe the flux predicted by the SSM.

Future experiments

While radiochemical experiments have in some sense observed the pp and Be7 neutrinos they have measured only integral fluxes. The "holy grail" of solar neutrino experiments would detect the Be7 neutrinos with a detector that is sensitive to the individual neutrino energies. This experiment would test the MSW hypothesis by searching for the turn-on of the MSW effect. Some exotic models are still capable of explaining the solar neutrino deficit, so the observation of the MSW turn on would, in effect, finally solve the solar neutrino problem.

Core temperature prediction

The flux of boron-8 neutrinos is highly sensitive to the temperature of the core of the sun, phi(^8B) propto T^{25}.cite journal
last =Bahcall
first = John
title =How many σ’s is the solar neutrino effect?
journal = Physical Review C
year = 2002
volume = 65
doi = 10.1103/PhysRevC.65.015802
id = Arxiv|archive=hep-ph|id=0108147
pages =015802
] For this reason, a precise measurement of the boron-8 neutrino flux can be used in the framework of the Standard Solar Model as a measurement of the temperature of the core of the sun. This estimate was performed by Fiorentini and Ricci after the first SNO results were published, and they obtained a temperature of T_{sun} = 15.7 imes 10^6 K pm 1% .cite journal
last = Fiorentini
first = G.
coauthors = B. Ricci
year = 2002
title = What have we learnt about the Sun from the measurement of the 8B neutrino flux?
journal = Physics Letters B
volume = 526
issue = 3-4
pages = 186–190
doi = 10.1016/S0370-2693(02)01159-0
id = ArXiv|archive=astro-ph|id=0111334

ee also

* star
* stellar evolution


External links

* [ description of the SSM with many references, by David Guenther]

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