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Stellar structure

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, ε_ν is the luminosity produced by neutrinos per unit mass, and G is the newtonian gravitational constant.

Similar equations for the case of radiative luminosity transport are obtained by replacing k.

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

External links

Variational Principles for Stellar Structure, Dallas C. Kennedy, Sidney A. Bludman, 1996

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01-04-2007 01:21:04

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