Stellar structure

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The simplest commonly used model of stellar structure is the spherically symmetric quasi-static model, which assumes that a star is very close to an equilibrium state, and that it is spherically symmetric. It contains four basic first-order differential equations: two represent how matter and pressure vary with radius; two represent how temperature and luminosity vary with radius.

For conductive luminosity transport, the matter-pressure (or hydromechanical) equations, in Eulerian coordinates are:

- {\mbox{d} P \over \mbox{d} r} = { G m \rho \over r^2 }
{\mbox {d} m \over \mbox{d} r} = 4 \pi r^2 \rho

and the temperature-luminosity equations are:

- k {\mbox{d} T \over \mbox{d} r} = { l \over 4 \pi r^2 }
{\mbox{d} l \over \mbox{d} r} = 4 \pi r^2 \rho ( \epsilon - \epsilon_\nu )

where r is the distance from the star centre, m(r) is the cumulative mass inside of a sphere of radius r centred at the star centre, P(r) is the total pressure (matter plus radiation), ρ(r) is the matter density, l(r) is the luminosity (photons) at r, k is the thermal conductivity, T(r) is the temperature, assumed identical for matter and photons, ε(r) is the luminosity produced (from nuclear reactions) per unit mass, εν is the luminosity produced in the form of neutrinos (which usually escape the star directly from where they are generated) per unit mass, and G is the newtonian gravitational constant.

Similar equations for the case of radiative luminosity transport are obtained by replacing k with κ, the opacity of the material.

The case of convective luminosity transport is usually modelled by the more ad hoc mixing length theory.

Also required is the equation of state, relating the pressure to other local variables appropriate for the material, such as temperature, density, chemical composition, etc. Relevant equations of state may have to include the perfect gas law, radiation pressure, pressure due to degenerate electrons, etc.

Although nowday stellar evolution models describes the main features of Color-Magnitude Diagrams, important improvements have to be done in order to remove uncertainties which are linked to our limited knowledge of transport phenomena. The most difficult challenge remains the numerical treatment of turbulence. Some research teams are developing simplified modelling of turbulence in 3D calculations.

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[edit] References

  • Stellar Structure and Evolution, R. Kippenhahn and A. Weigert, Springer-Verlag, 1990.
  • Stellar Interiors, Carl J. Hansen, Steven D. Kawaler, Virginia Trimble, Springer, 2sd edition 2004.
  • Cox and Giuli's Principles of Stellar Structure, Achim Weiss, Wolfgang Hillebrandt, Hans-Christoph Thomas, H. Ritter, Cambridge Scientific Publishers[1], 2004.

[edit] External links

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