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Concept
Radiation zone
Summary
A radiation zone, or radiative region is a layer of a star's interior where energy is primarily transported toward the exterior by means of radiative diffusion and thermal conduction, rather than by convection. Energy travels through the radiation zone in the form of electromagnetic radiation as photons.
Matter in a radiation zone is so dense that photons can travel only a short distance before they are absorbed or scattered by another particle, gradually shifting to longer wavelength as they do so. For this reason, it takes an average of 171,000 years for gamma rays from the core of the Sun to leave the radiation zone. Over this range, the temperature of the plasma drops from 15 million K near the core down to 1.5 million K at the base of the convection zone.
In a radiative zone, the temperature gradient—the change in temperature (T) as a function of radius (r)—is given by:
where κ(r) is the opacity, ρ(r) is the matter density, L(r) is the luminosity, and σB is the Stefan–Boltzmann constant. Hence the opacity (κ) and radiation flux (L) within a given layer of a star are important factors in determining how effective radiative diffusion is at transporting energy. A high opacity or high luminosity can cause a high temperature gradient, which results from a slow flow of energy. Those layers where convection is more effective than radiative diffusion at transporting energy, thereby creating a lower temperature gradient, will become convection zones.
This relation can be derived by integrating Fick's first law over the surface of some radius r, giving the total outgoing energy flux which is equal to the luminosity by conservation of energy:
Where D is the photons diffusion coefficient, and u is the energy density.
The energy density is related to the temperature by Stefan–Boltzmann law by:
Finally, as in the elementary theory of diffusion coefficient in gases, the diffusion coefficient D approximately satisfies:
where λ is the photon mean free path, and is the reciprocal of the opacity κ.
Official source
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