Modello solare standard: differenze tra le versioni

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Il '''Modello Solare Standard''' (SSM) è il miglior modello disponibile per la descrizione del [[Sole]]. A grandi linee, nel Modello Solare Standard il Sole è una sfera composta prevalentemente di un [[Plasma (fisica)|plasma]] di [[idrogeno]] e tenuta insieme dalla [[gravità]]. Nel nucleo del Sole, la [[temperatura]] e la [[densità]] sono grandi abbastanza per consentire la conversione di [[nucleo atomico|nuclei]] di [[idrogeno]] in [[elio]] attraverso distinti processi di [[fusione nucleare]], i quali rilasciano una grande quantità [[energia]], producendo altresì due [[elettrone|elettroni]] e due [[neutrino|neutrini]] elettronici. L'energia è continuamente prodotta nel nucleo e mantiene il Sole in equilibrio: la tendenza a esplodere, dovuta alle reazioni di fusione, bilancia la tendenza a collassare a causa della gravità. Il modello inoltre descrive come, a causa dell'[[evoluzione stellare|evoluzione]] nel tempo del rapporto tra idrogeno e elio nel nucleo, cambino la temperatura e la densità del Sole e si modifichino le sue dimensioni e la sua [[luminosità]]. In maniera simile al [[Modello Standard]] in [[fisica delle particelle]] il SSM cambia nel tempo in funzione delle nuove teorie o scoperte sperimentali.

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==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]] of [[particle physics]] and the [[physical cosmology|standard cosmology]] model the SSM changes over time in response to relevant new [[theoretical physics|theoretical]] or [[Experimental physics|experimental physics]] discoveries.

==Energy transport in the Sun==

As described in the [[Sun]] 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]], one considers the [[density]] <math>\scriptstyle\rho(r)</math>, [[temperature]] T(r), total [[pressure]] (matter plus radiation) P(r), [[luminosity]] l(r) and energy generation rate per unit mass &epsilon;(r) in a spherical shell of a thickness dr at a distance r from the center of the star.

Radiative transport of energy is described by the radiative temperature gradient equation:

:<math> {\mbox{d} T \over \mbox{d} r} = - {3 \kappa \rho l \over 64 \pi r^2 \sigma T^3},</math>

where &kappa; is the [[opacity]] of the matter, &sigma; is the [[Stefan-Boltzmann constant]], and the [[Boltzmann constant]] is set to one.

Convection is described using [[mixing length theory]]<ref>{{citation|last=Hansen | last2=Kawaler | last3=Trimble | first=Carl J. | first2=Steven D. | first3=Virginia | publisher=Springer | edition=2nd | year=2004 | title=Stellar Interiors | isbn=0387200894}}</ref> and the corresponding temperature gradient equation (for [[adiabatic process|adiabatic]] convection) is:

:<math> {\mbox{d} T \over \mbox{d} r} = \left(1 - {1 \over \gamma} \right) {T \over P } { \mbox{d} P \over \mbox{d} r},</math>

where &gamma; = c_p / c_v is the [[adiabatic index]], the ratio of [[specific heat]]s in the gas. (For a fully ionized [[ideal gas]], &gamma; = 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 [[fluid dynamics|hydrodynamical]] simulations, taking into account [[radiative transfer]] in the atmosphere.<ref>{{cite journal

| author = Stein, R.F. and Nordlund, A.

| title = Simulations of Solar Granulation. I. General Properties

| journal = Astrophysical Journal

| year = May 1998

| volume = 499

| pages = 914-+

| doi = 10.1086/305678

| url = http://adsabs.harvard.edu/abs/1998ApJ...499..914S

}}</ref> Such simulations successfully reproduce the observed surface structure of [[solar granulation]],<ref>{{cite journal

|author = Nordlund, A. and Stein, R.

| title = Stellar Convection; general properties

| booktitle = SCORe'96 : Solar Convection and Oscillations and their Relationship

| year = December 1997

| series = Astrophysics and Space Science Library

| volume = 225

| editor = F.P. Pijpers, J. Christensen-Dalsgaard and C.S. Rosenthal

| pages = 79-103

| url = http://adsabs.harvard.edu/abs/1997ASSL..225...79N

}}</ref> as well as detailed profiles of lines in the solar radiative spectrum, without the use of parametrized models of [[turbulence]].<ref>{{cite journal

| author = Asplund, M. et al.

| title = Line formation in solar granulation. I. Fe line shapes, shifts and asymmetries

| journal = Astronomy and Astrophysics

| eprint = arXiv:astro-ph/0005320

| year = July 2000,

| volume = 359

| pages = 729-742

| url = http://adsabs.harvard.edu/abs/2000A%26A...359..729A

}}</ref> 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 process|adiabatic]] part of the convection zone by means of a model based on the mixing-length description, demonstrated that the [[adiabatic process#Graphing adiabats|adiabat]] predicted by the simulation was essentially consistent with the depth of the solar convection zone as determined from [[helioseismology]].<ref>{{cite journal

| author = Rosenthal, C.S. et al.

| title = Convective contributions to the frequencies of solar oscillations

| journal = Astronomy and Astrophysics

| eprint = arXiv:astro-ph/9803206

| year = November 1999

| volume = 351

| pages = 689-700

| url = http://adsabs.harvard.edu/abs/1999A%26A...351..689R

}}</ref> 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.<ref>{{cite journal

| author = Li, L.H. et al.

| title = Inclusion of Turbulence in Solar Modeling

| journal = The Astrophysical Journal

| eprint = arXiv:astro-ph/0109078

| year = March 2002

| volume = 567

| pages = 1192-1201

| doi = 10.1086/338352

| url = http://adsabs.harvard.edu/abs/2002ApJ...567.1192L

}}</ref>

This section is adapted from the Christensen-Dalsgaard review of helioseismology, Chapter IV.<ref>{{cite journal

| author = Christensen-Dalsgaard, J.

| title = Helioseismology

| journal = Reviews of Modern Physics

| eprint = arXiv:astro-ph/0207403

| year = November 2002

| volume = 74

| pages = 1073-1129

| doi = 10.1103/RevModPhys.74.1073

| url = http://adsabs.harvard.edu/abs/2002RvMP...74.1073C

}}</ref>

==Equations of state==

The numerical solution of the differential equations of stellar structure requires [[equation of state|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.

==Helioseismology==

{{Main|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.<ref name="bonannoetal2002">{{cite journal

| author = A. Bonanno, H. Schlattl, L. Paternò

| title = The age of the Sun and the relativistic corrections in the EOS

| journal = Astronomy and Astrophysics

| year = 2002

| url=http://adsabs.harvard.edu/abs/2002A%26A...390.1115B | volume = 390

| pages = 1115

| doi = 10.1051/0004-6361:20020749

}}</ref> This is another example of how the SSM can be refined.

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== Produzione di neutrini ==