Editing Radiative zone (section)

==Temperature gradient==
In a radiative zone, the temperature gradient—the change in temperature (''T'') as a function of radius (''r'')—is given by:

: <math>\frac{\text{d}T(r)}{\text{d}r}\ =\ -\frac{3 \kappa(r) \rho(r) L(r)}{(4 \pi r^2)(16 \sigma_B) T^3(r)}</math>

where ''κ''(''r'') is the [[Opacity (optics)|opacity]], ''ρ''(''r'') is the matter density, ''L''(''r'') is the luminosity, and ''σ''<sub>''B''</sub> is the [[Stefan–Boltzmann constant]].<ref name=ryan_norton2010/> 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 zone]]s.<ref name=leblanc2010/>

This relation can be derived by integrating [[Fick's laws of diffusion#Fick's first law|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]]:
::<math>L = -4\pi\,r^2 D\frac{\partial u}{\partial r}</math>
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:
::<math>U = \frac{4}{c} \, \sigma_B \, T^4 </math>

Finally, as in the [[Diffusion#Elementary theory of diffusion coefficient in gases|elementary theory of diffusion coefficient in gases]], the diffusion coefficient ''D'' approximately satisfies:
::<math> D = \frac{1}{3}c\,\lambda </math>
where &lambda; is the photon [[mean free path]], and is the reciprocal of the opacity ''κ''.