Standard Solar Model

# Standard Solar Model

Overview
The Standard Solar Model (SSM) refers to a mathematical treatment of the Sun as a spherical ball of gas (in varying states of ionisation, with the hydrogen in the deep interior being a completely ionised plasma
Plasma (physics)
In physics and chemistry, plasma is a state of matter similar to gas in which a certain portion of the particles are ionized. Heating a gas may ionize its molecules or atoms , thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions...

). This model, technically the spherically symmetric quasi-static
Quasistatic equilibrium
Quasistatic equilibrium is the quasi-balanced state of a thermodynamic system near to thermodynamic equilibrium in some sense or degree...

model of a star, has stellar structure
Stellar structure
Stars of different mass and age have varying internal structures. Stellar structure models describe the internal structure of a star in detail and make detailed predictions about the luminosity, the color and the future evolution of the star....

described by several differential equations derived from basic physical principles. The model is constrained by boundary conditions, namely the luminosity, radius, age and composition of the Sun, which are well determined. The age of the Sun cannot be measured directly; one way to estimate it is from the age of the oldest meteorites, and models of the evolution of the solar system. The composition in the photosphere of the modern-day Sun, by mass, is 74.9% hydrogen and 23.8% helium. All heavier elements, called metals
Metallicity
In astronomy and physical cosmology, the metallicity of an object is the proportion of its matter made up of chemical elements other than hydrogen and helium...

in astronomy, account for less than 2 percent of the mass. The SSM is used to test the validity of stellar evolution theory. In fact, the only way to determine the two free parameters of the stellar evolution model, the helium abundance and the mixing length
Mixing length theory
In fluid dynamics, mixing length model is a method attempting to describe momentum transfer by turbulence Reynolds stresses within a newtonian fluid boundary layer by means of an eddy viscosity. The model was developed by Ludwig Prandtl in the early 20th century...

parameter (used to model convection in the Sun), are to adjust the SSM to "fit" the observed Sun.
Discussion
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Encyclopedia
The Standard Solar Model (SSM) refers to a mathematical treatment of the Sun as a spherical ball of gas (in varying states of ionisation, with the hydrogen in the deep interior being a completely ionised plasma
Plasma (physics)
In physics and chemistry, plasma is a state of matter similar to gas in which a certain portion of the particles are ionized. Heating a gas may ionize its molecules or atoms , thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions...

). This model, technically the spherically symmetric quasi-static
Quasistatic equilibrium
Quasistatic equilibrium is the quasi-balanced state of a thermodynamic system near to thermodynamic equilibrium in some sense or degree...

model of a star, has stellar structure
Stellar structure
Stars of different mass and age have varying internal structures. Stellar structure models describe the internal structure of a star in detail and make detailed predictions about the luminosity, the color and the future evolution of the star....

described by several differential equations derived from basic physical principles. The model is constrained by boundary conditions, namely the luminosity, radius, age and composition of the Sun, which are well determined. The age of the Sun cannot be measured directly; one way to estimate it is from the age of the oldest meteorites, and models of the evolution of the solar system. The composition in the photosphere of the modern-day Sun, by mass, is 74.9% hydrogen and 23.8% helium. All heavier elements, called metals
Metallicity
In astronomy and physical cosmology, the metallicity of an object is the proportion of its matter made up of chemical elements other than hydrogen and helium...

in astronomy, account for less than 2 percent of the mass. The SSM is used to test the validity of stellar evolution theory. In fact, the only way to determine the two free parameters of the stellar evolution model, the helium abundance and the mixing length
Mixing length theory
In fluid dynamics, mixing length model is a method attempting to describe momentum transfer by turbulence Reynolds stresses within a newtonian fluid boundary layer by means of an eddy viscosity. The model was developed by Ludwig Prandtl in the early 20th century...

parameter (used to model convection in the Sun), are to adjust the SSM to "fit" the observed Sun.

A star is considered to be at zero age (protostellar) when it is assumed to have a homogeneous composition and to be just beginning to derive most of its luminosity from nuclear reactions (so neglecting the period of contraction from a cloud of gas and dust). To obtain the SSM, a one solar mass
Solar mass
The solar mass , , is a standard unit of mass in astronomy, used to indicate the masses of other stars and galaxies...

stellar model at zero age is evolved
Stellar evolution
Stellar evolution is the process by which a star undergoes a sequence of radical changes during its lifetime. Depending on the mass of the star, this lifetime ranges from only a few million years to trillions of years .Stellar evolution is not studied by observing the life of a single...

numerically to the age of the Sun. The abundance of elements in the zero age solar model is estimated from primordial meteorites. Along with this abundance information, a reasonable guess at the zero-age luminosity (such as the present-day Sun's luminosity) is then converted by an iterative procedure into the correct value for the model, and the temperature, pressure and density throughout the model calculated by solving the equations of stellar structure numerically assuming the star to be in a steady state
A system in a steady state has numerous properties that are unchanging in time. This implies that for any property p of the system, the partial derivative with respect to time is zero:...

. The model is then evolved numerically up to the age of the Sun. Any discrepancy from the measured values of the Sun's luminosity, surface abundances, etc. can then be used to refine the model. For example, since the Sun formed, the helium and heavy elements have settled out of the photosphere by diffusion. As a result, the Solar photosphere now contains about 87% as much helium and heavy elements as the protostellar photosphere had; the protostellar Solar photosphere was 71.1% hydrogen, 27.4% helium, and 1.5% metals. A measure of heavy-element settling by diffusion is required for a more accurate model.

## Numerical modelling of the stellar structure equations

The differential equations of stellar structure, such as the equation of hydrostatic equilibrium, are integrated numerically. The differential equations are approximated by difference equations. The star is imagined to be made up of spherically symmetric shells and the numerical integration carried out in finite steps making use of the equations of state
Equation of state
In physics and thermodynamics, an equation of state is a relation between state variables. More specifically, an equation of state is a thermodynamic equation describing the state of matter under a given set of physical conditions...

, giving relationships for the pressure, the opacity and the energy generation rate in terms of the density, temperature and composition.

## Evolution of the sun

Nuclear reactions in the core of the Sun change its composition, by converting hydrogen
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...

nuclei into helium
Helium
Helium is the chemical element with atomic number 2 and an atomic weight of 4.002602, which is represented by the symbol He. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas that heads the noble gas group in the periodic table...

nuclei by the proton-proton chain and (to a lesser extent in the Sun than in more massive stars) the CNO cycle
CNO cycle
The CNO cycle is one of two sets of fusion reactions by which stars convert hydrogen to helium, the other being the proton–proton chain. Unlike the proton–proton chain reaction, the CNO cycle is a catalytic cycle. Theoretical models show that the CNO cycle is the dominant source of energy in stars...

. This decreases the mean molecular weight in the core of the Sun, which should lead to a decrease in pressure. This does not happen as instead the core contracts. By the Virial Theorem half of the gravitational potential energy
Potential energy
In physics, potential energy is the energy stored in a body or in a system due to its position in a force field or due to its configuration. The SI unit of measure for energy and work is the Joule...

released by this contraction goes towards raising the temperature of the core, and the other half is radiated away. By the ideal gas law
Ideal gas law
The ideal gas law is the equation of state of a hypothetical ideal gas. It is a good approximation to the behavior of many gases under many conditions, although it has several limitations. It was first stated by Émile Clapeyron in 1834 as a combination of Boyle's law and Charles's law...

this increase in temperature also increases the pressure and restores the balance of hydrostatic equilibrium
Hydrostatic equilibrium
Hydrostatic equilibrium or hydrostatic balance is the condition in fluid mechanics where a volume of a fluid is at rest or at constant velocity. This occurs when compression due to gravity is balanced by a pressure gradient force...

. The luminosity of the Sun is increased by the temperature rise, increasing the rate of nuclear reactions. The outer layers expand to compensate for the increased temperature and pressure gradients, so the radius also increases.

No star is completely static, but stars stay on the main sequence (burning hydrogen in the core) for long periods. In the case of the Sun, it has been on the main sequence for roughly 4.6 billion years, and will become a red giant in roughly 6.5 billion years for a total main sequence lifetime of roughly 1010 years. Thus the assumption of steady state
A system in a steady state has numerous properties that are unchanging in time. This implies that for any property p of the system, the partial derivative with respect to time is zero:...

is a very good approximation. For simplicity, the stellar structure equations are written without explicit time dependence, with the exception of the luminosity gradient equation:

Here L is the luminosity, ε is the nuclear energy generation rate per unit mass and εν is the luminosity due to neutrino emission (see below for the other quantities). The slow evolution of the Sun on the main sequence is then determined by the change in the nuclear species (principally hydrogen being consumed and helium being produced). The rates of the various nuclear reactions are estimated from particle physics experiments at high energies, which are extrapolated back to the lower energies of stellar interiors (the Sun burns hydrogen rather slowly). Historically, errors in the nuclear reaction rates have been one of the biggest sources of error in stellar modelling. Computers are employed to calculate the varying abundances (usually by mass fraction) of the nuclear species. A particular species will have a rate of production and a rate of destruction, so both are needed to calculate its abundance over time, at varying conditions of temperature and density. Since there are many nuclear species, a computerised reaction network is needed to keep track of how all the abundances vary together.

According to the Vogt-Russel theorem, the mass and the composition structure throughout a star uniquely determine its radius, luminosity, and internal structure, as well as its subsequent evolution (though this "theorem" was only intended to apply to the slow, stable phases of stellar evolution and certainly does not apply to the transitions between stages and rapid evolutionary stages).
The information about the varying abundances of nuclear species over time, along with the equations of state, is sufficient for a numerical solution by taking sufficiently small time increments and using iteration to find the unique internal structure of the star at each stage.

## Purpose of the Standard Solar Model

The SSM serves two purposes:
• it provides estimates for the helium abundance and mixing length parameter by forcing the stellar model to have the correct luminosity and radius at the Sun's age,
• it provides a way to evaluate more complex models with additional physics, such as rotation, magnetic fields and diffusion or improvements to the treatment of convection, such as modelling turbulence, and convective overshooting.

Like the Standard Model
Standard Model
The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...

of particle physics
Particle physics
Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...

and the standard cosmology
Physical cosmology
Physical cosmology, as a branch of astronomy, is the study of the largest-scale structures and dynamics of the universe and is concerned with fundamental questions about its formation and evolution. For most of human history, it was a branch of metaphysics and religion...

model the SSM changes over time in response to relevant new theoretical
Theoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...

or experimental physics
Experimental physics
Within the field of physics, experimental physics is the category of disciplines and sub-disciplines concerned with the observation of physical phenomena in order to gather data about the universe...

discoveries.

## Energy transport in the Sun

As described in the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

article, the Sun has a radiative core and a convective outer envelope. In the core, the luminosity due to nuclear reactions is transmitted to outer layers principally by radiation. However, in the outer layers the temperature gradient is so great that radiation cannot transport enough energy. As a result, thermal convection occurs as thermal columns carry hot material to the surface (photosphere) of the Sun. Once the material cools off at the surface, it plunges back downward to the base of the convection zone, to receive more heat from the top of the radiative zone.

In a solar model, as described in stellar structure
Stellar structure
Stars of different mass and age have varying internal structures. Stellar structure models describe the internal structure of a star in detail and make detailed predictions about the luminosity, the color and the future evolution of the star....

, one considers the density
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...

, temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

T(r), total pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...

Luminosity
Luminosity is a measurement of brightness.-In photometry and color imaging:In photometry, luminosity is sometimes incorrectly used to refer to luminance, which is the density of luminous intensity in a given direction. The SI unit for luminance is candela per square metre.The luminosity function...

l(r) and energy generation rate per unit mass ε(r) in a spherical shell of a thickness dr at a distance r from the center of the star.

where κ is the opacity
Opacity (optics)
Opacity is the measure of impenetrability to electromagnetic or other kinds of radiation, especially visible light. In radiative transfer, it describes the absorption and scattering of radiation in a medium, such as a plasma, dielectric, shielding material, glass, etc...

of the matter, σ is the Stefan-Boltzmann constant
Stefan-Boltzmann constant
The Stefan–Boltzmann constant , a physical constant denoted by the Greek letter σ, is the constant of proportionality in the Stefan–Boltzmann law: the total energy radiated per unit surface area of a black body in unit time is proportional to the fourth power of the thermodynamic temperature.The...

, and the Boltzmann constant is set to one.

Convection is described using mixing length theory
Mixing length theory
In fluid dynamics, mixing length model is a method attempting to describe momentum transfer by turbulence Reynolds stresses within a newtonian fluid boundary layer by means of an eddy viscosity. The model was developed by Ludwig Prandtl in the early 20th century...

In thermodynamics, an adiabatic process or an isocaloric process is a thermodynamic process in which the net heat transfer to or from the working fluid is zero. Such a process can occur if the container of the system has thermally-insulated walls or the process happens in an extremely short time,...

convection) is:
where γ = cp / cv is the adiabatic index, the ratio of specific heats in the gas. (For a fully ionized ideal gas
Ideal gas
An ideal gas is a theoretical gas composed of a set of randomly-moving, non-interacting point particles. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics.At normal conditions such as...

, γ = 5/3.)

Near the base of the Sun's convection zone, the convection is adiabatic, but near the surface of the Sun, convection is not adiabatic.

## Simulations of near-surface convection

A more realistic description of the uppermost part of the convection zone is possible through detailed three-dimensional and time-dependent hydrodynamical
Fluid dynamics
In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...

simulations, taking into account radiative transfer
Radiative transfer is the physical phenomenon of energy transfer in the form of electromagnetic radiation. The propagation of radiation through a medium is affected by absorption, emission and scattering processes. The equation of radiative transfer describes these interactions mathematically...

in the atmosphere. Such simulations successfully reproduce the observed surface structure of solar granulation, as well as detailed profiles of lines in the solar radiative spectrum, without the use of parametrized models of turbulence
Turbulence
In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic and stochastic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time...

. The simulations only cover a very small fraction of the solar radius, and are evidently far too time-consuming to be included in general solar modeling. Extrapolation of an averaged simulation through the adiabatic
In thermodynamics, an adiabatic process or an isocaloric process is a thermodynamic process in which the net heat transfer to or from the working fluid is zero. Such a process can occur if the container of the system has thermally-insulated walls or the process happens in an extremely short time,...

part of the convection zone by means of a model based on the mixing-length description, demonstrated that the adiabat predicted by the simulation was essentially consistent with the depth of the solar convection zone as determined from helioseismology
Helioseismology
Helioseismology is the study of the propagation of wave oscillations, particularly acoustic pressure waves, in the Sun. Unlike seismic waves on Earth, solar waves have practically no shear component . Solar pressure waves are believed to be generated by the turbulence in the convection zone near...

. An extension of mixing-length theory, including effects of turbulent pressure and kinetic energy
Kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...

, based on numerical simulations of near-surface convection, has been developed.

This section is adapted from the Christensen-Dalsgaard
Jørgen Christensen-Dalsgaard
Jørgen Christensen-Dalsgaard is a Danish astronomer at Aarhus University in Denmark. He specializes in asteroseismology and helioseismology to which he has made significant contributions including predicting the oscillation of Sun-like stars in 1983...

review of helioseismology, Chapter IV.

## Equations of state

The numerical solution of the differential equations of stellar structure requires equations of state
Equation of state
In physics and thermodynamics, an equation of state is a relation between state variables. More specifically, an equation of state is a thermodynamic equation describing the state of matter under a given set of physical conditions...

for the pressure, opacity and energy generation rate, as described in stellar structure
Stellar structure
Stars of different mass and age have varying internal structures. Stellar structure models describe the internal structure of a star in detail and make detailed predictions about the luminosity, the color and the future evolution of the star....

, which relate these variables to the density, temperature and composition.

## Helioseismology

Helioseismology is the study of the wave oscillations in the Sun. Changes in the propagation of these waves through the Sun reveal inner structures and allow astrophysicists to develop extremely detailed profiles of the interior conditions of the Sun. In particular, the location of the convection zone in the outer layers of the Sun can be measured, and information about the core of the Sun provides a method, using the SSM, to calculate the age of the Sun, independently of the method of inferring the age of the Sun from that of the oldest meteorites. This is another example of how the SSM can be refined.

## 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 proton
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

s, two neutron
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...

s, two positron
Positron
The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1e, a spin of ½, and has the same mass as an electron...

s, and two electron neutrinos. Neutrinos are also produced by the CNO cycle
CNO cycle
The CNO cycle is one of two sets of fusion reactions by which stars convert hydrogen to helium, the other being the proton–proton chain. Unlike the proton–proton chain reaction, the CNO cycle is a catalytic cycle. Theoretical models show that the CNO cycle is the dominant source of energy in stars...

, 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
MEV
MeV and meV are multiples and submultiples of the electron volt unit referring to 1,000,000 eV and 0.001 eV, respectively.Mev or MEV may refer to:In entertainment:* Musica Elettronica Viva, an Italian musical group...

) they are very difficult to detect. A rare side branch of the pp chain produces the "boron
Boron
Boron is the chemical element with atomic number 5 and the chemical symbol B. Boron is a metalloid. Because boron is not produced by stellar nucleosynthesis, it is a low-abundance element in both the solar system and the Earth's crust. However, boron is concentrated on Earth by the...

-8" neutrinos with a maximum energy of roughly 15 MeV, and these are the easiest neutrinos to detect. A very rare interaction in the pp chain produces the "hep" neutrinos, the highest energy neutrinos predicted to be produced by our sun. They are predicted to have a maximum energy of about 18 MeV.

All of the interactions described above produce neutrinos with a spectrum
Spectrum
A spectrum is a condition that is not limited to a specific set of values but can vary infinitely within a continuum. The word saw its first scientific use within the field of optics to describe the rainbow of colors in visible light when separated using a prism; it has since been applied by...

of energies. The electron capture
Electron capture
Electron capture is a process in which a proton-rich nuclide absorbs an inner atomic electron and simultaneously emits a neutrino...

of 7Be produces neutrinos at either roughly 0.862 MeV (~90%) or 0.384 MeV (~10%).

## Neutrino detection

The weakness of the neutrino's interactions 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.

### History

The first experiment to successfully detect cosmic neutrinos was Ray Davis's
Raymond Davis Jr.
Raymond Davis, Jr. was an American chemist, physicist, and Nobel Prize in Physics laureate.-Early life and education:...

chlorine experiment
Homestake Experiment
The Homestake experiment was an experiment headed by astrophysicists Raymond Davis, Jr. and John N. Bahcall in the late 1960s. Its purpose was to collect and count neutrinos emitted by nuclear fusion taking place in the Sun. Bahcall did the theoretical calculations and Davis designed the experiment...

, in which neutrinos were detected by observing the conversion
Nuclear transmutation
Nuclear transmutation is the conversion of one chemical element or isotope into another. In other words, atoms of one element can be changed into atoms of other element by 'transmutation'...

of chlorine
Chlorine
Chlorine is the chemical element with atomic number 17 and symbol Cl. It is the second lightest halogen, found in the periodic table in group 17. The element forms diatomic molecules under standard conditions, called dichlorine...

nuclei
Atomic nucleus
The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...

Argon
Argon is a chemical element represented by the symbol Ar. Argon has atomic number 18 and is the third element in group 18 of the periodic table . Argon is the third most common gas in the Earth's atmosphere, at 0.93%, making it more common than carbon dioxide...

in a large tank
Chemical tank
Chemical tanks are storage containers for chemicals. They come in a variety of sizes and shapes, and are used for static storage, mixing, and transport of both raw materials and finished chemical products.-Design:...

of perchloroethylene. This was a reaction channel expected for neutrinos, but since only the number 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
Solar neutrino problem
The solar neutrino problem was a major discrepancy between measurements of the numbers of neutrinos flowing through the Earth and theoretical models of the solar interior, lasting from the mid-1960s to about 2002...

.

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
Water
Water is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...

Cerenkov detector with a low enough energy threshold to detect neutrinos through neutrino-electron elastic scattering
Elastic scattering
In scattering theory and in particular in particle physics, elastic scattering is one of the specific forms of scattering. In this process, the kinetic energy of the incident particles is conserved, only their direction of propagation is modified .-Electron elastic scattering:When an alpha particle...

. 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 compared to theory at the time. 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
Sudbury Neutrino Observatory
The Sudbury Neutrino Observatory is a neutrino observatory located 6,800 feet underground in Vale Inco's Creighton Mine in Sudbury, Ontario, Canada. The detector was designed to detect solar neutrinos through their interactions with a large tank of heavy water. The detector turned on in May 1999,...

. 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
Resonance
In physics, resonance is the tendency of a system to oscillate at a greater amplitude at some frequencies than at others. These are known as the system's resonant frequencies...

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
Chlorine
Chlorine is the chemical element with atomic number 17 and symbol Cl. It is the second lightest halogen, found in the periodic table in group 17. The element forms diatomic molecules under standard conditions, called dichlorine...

, 0.2MeV for gallium
Gallium
Gallium is a chemical element that has the symbol Ga and atomic number 31. Elemental gallium does not occur in nature, but as the gallium salt in trace amounts in bauxite and zinc ores. A soft silvery metallic poor metal, elemental gallium is a brittle solid at low temperatures. As it liquefies...

), 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
Sensitivity (electronics)
The sensitivity of an electronic device, such as a communications system receiver, or detection device, such as a PIN diode, is the minimum magnitude of input signal required to produce a specified output signal having a specified signal-to-noise ratio, or other specified criteria.Sensitivity is...

to observe the flux predicted by the SSM.

### CNO neutrinos

Neutrinos from a secondary cycle of solar energy generation -- i.e., the CNO-neutrinos -- are also expected to provide observable events below 1 MeV. They have not yet been observed due to experimental noise (background). Future ultra-pure scintillator detectors should allow us to probe the flux predicted by the SSM. This should be possible thanks to SNO+ and, on the longer term, thanks to LENA, two detectors that will be larger but will use the same principles of Borexino.

### Future experiments

While radiochemical experiments have in some sense observed the pp and Be7 neutrinos they have measured only integral fluxes. The "holy grail
Holy Grail
The Holy Grail is a sacred object figuring in literature and certain Christian traditions, most often identified with the dish, plate, or cup used by Jesus at the Last Supper and said to possess miraculous powers...

" 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
Exotic matter
In physics, exotic matter is a term which refers to matter which would somehow deviate from the norm and have "exotic" properties. There are several uses of the term....

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, . 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
Peer review
Peer review is a process of self-regulation by a profession or a process of evaluation involving qualified individuals within the relevant field. Peer review methods are employed to maintain standards, improve performance and provide credibility...

, and they obtained a temperature of .

## Lithium depletion at the solar surface

Stellar model
Stellar structure
Stars of different mass and age have varying internal structures. Stellar structure models describe the internal structure of a star in detail and make detailed predictions about the luminosity, the color and the future evolution of the star....

s of the Sun's evolution predict the solar surface chemical abundance pretty well except for lithium
Lithium
Lithium is a soft, silver-white metal that belongs to the alkali metal group of chemical elements. It is represented by the symbol Li, and it has the atomic number 3. Under standard conditions it is the lightest metal and the least dense solid element. Like all alkali metals, lithium is highly...

(Li).
The surface abundance of Li on the Sun is 140 times less than the protosolar
Protostar
A protostar is a large mass that forms by contraction out of the gas of a giant molecular cloud in the interstellar medium. The protostellar phase is an early stage in the process of star formation. For a one solar-mass star it lasts about 100,000 years...

value (i.e. the primordial abundance at the Sun's birth), yet the temperature at the base of the surface convective zone is not hot enough to burn - and hence deplete - Li. This is known as the solar lithium problem. A large range of Li abundances is observed in solar-type stars of the same age, mass and metallicity as the Sun. Observations of an unbiased sample of stars of this type with or without observed planets (exoplanets) showed that the known planet-bearing stars have less than one per cent of the primordial Li abundance, and of the remainder half had ten times as much Li. It is hypothesised that the presence of planets may increase the amount of mixing and deepen the convective zone to such an extent that the Li can be burned. A possible mechanism for this is the idea that the planets affect the angular momentum evolution of the star, thus changing the rotation of the star relative to similar stars without planets; in the case of the Sun slowing its rotation. More research is needed to discover where and when the fault in the modelling lies. Given the precision of helioseismic
Helioseismology
Helioseismology is the study of the propagation of wave oscillations, particularly acoustic pressure waves, in the Sun. Unlike seismic waves on Earth, solar waves have practically no shear component . Solar pressure waves are believed to be generated by the turbulence in the convection zone near...

probes of the interior of the modern-day Sun, it is likely that the modelling of the protostellar Sun needs to be adjusted.

• Star
Star
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...

• Stellar evolution
Stellar evolution
Stellar evolution is the process by which a star undergoes a sequence of radical changes during its lifetime. Depending on the mass of the star, this lifetime ranges from only a few million years to trillions of years .Stellar evolution is not studied by observing the life of a single...

• Stellar structure
Stellar structure
Stars of different mass and age have varying internal structures. Stellar structure models describe the internal structure of a star in detail and make detailed predictions about the luminosity, the color and the future evolution of the star....

• Protostar
Protostar
A protostar is a large mass that forms by contraction out of the gas of a giant molecular cloud in the interstellar medium. The protostellar phase is an early stage in the process of star formation. For a one solar-mass star it lasts about 100,000 years...

• Helioseismology
Helioseismology
Helioseismology is the study of the propagation of wave oscillations, particularly acoustic pressure waves, in the Sun. Unlike seismic waves on Earth, solar waves have practically no shear component . Solar pressure waves are believed to be generated by the turbulence in the convection zone near...