Standard solar model

The model is constrained by boundary conditions, namely the luminosity, radius, age and composition of the Sun, which are well determined.

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).

[2] 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.

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

This increases the mean molecular weight in the core of the Sun, which should lead to a decrease in pressure.

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).

Computers are employed to calculate the varying abundances (usually by mass fraction) of the nuclear species.

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–Russell 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).

[3] 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.

In the core, the luminosity due to nuclear reactions is transmitted to outer layers principally by radiation.

, temperature T(r), total pressure (matter plus radiation) P(r), luminosity 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 γ = cp / cv is the adiabatic index, the ratio of specific heats in the gas.

A more realistic description of the uppermost part of the convection zone is possible through detailed three-dimensional and time-dependent hydrodynamical simulations, taking into account radiative transfer in the atmosphere.

Extrapolation of an averaged simulation through the adiabatic 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.

[10] An extension of mixing-length theory, including effects of turbulent pressure and kinetic energy, based on numerical simulations of near-surface convection, has been developed.

[12] The numerical solution of the differential equations of stellar structure requires equations of state for the pressure, opacity and energy generation rate, as described in stellar structure, which relate these variables to the density, temperature and composition.

Neutrinos are also produced by the CNO cycle, but that process is considerably less important in the 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)[14] they are very difficult to detect.

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.

The detector SNO used scattering on deuterium that allowed to measure the energy of the events, thereby identifying the single components of the predicted SSM neutrino emission.

Finally, Kamiokande, Super-Kamiokande, SNO, Borexino and KamLAND used elastic scattering on electrons, which allows the measurement of the neutrino energy.

Neutrinos from the CNO cycle of solar energy generation – i.e., the CNO-neutrinos – are also expected to provide observable events below 1 MeV.

The Borexino Collaboration has confirmed that the CNO cycle accounts for 1% of the energy generation within the Sun's core.

[15] While radiochemical experiments have in some sense observed the pp and Be7 neutrinos they have measured only integral fluxes.

This estimate was performed by Fiorentini and Ricci after the first SNO results were published, and they obtained a temperature of

[17] Stellar models of the Sun's evolution predict the solar surface chemical abundance pretty well except for lithium (Li).

The surface abundance of Li on the Sun is 140 times less than the protosolar value (i.e. the primordial abundance at the Sun's birth),[18] yet the temperature at the base of the surface convective zone is not hot enough to burn – and hence deplete – Li.

A large range of Li abundances is observed in solar-type stars of the same age, mass, and metallicity as the Sun.

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.