Editing Radiative zone (section)

==Eddington stellar model==
[[Arthur Eddington|Eddington]] assumed the [[pressure]] ''P'' in a star is a combination of an [[ideal gas]] pressure and [[radiation pressure]], and that there is a constant ratio, &beta;, of the gas pressure to the total pressure.
Therefore, by the [[ideal gas law]]:
::<math>\beta P = k_B\frac{\rho}{\mu}T</math>
where ''k''<sub>''B''</sub> is [[Boltzmann constant]] and &mu; the mass of a single atom (actually, an ion since matter is ionized; usually a hydrogen ion, i.e. a proton).
While the radiation pressure satisfies:
:<math>1-\beta = \frac{P_\text{radiation}}{P} =\frac{u}{3P} =\frac{4\sigma_B}{3c} \frac{T^4}{P} </math>
so that ''T''<sup>4</sup> is proportional to ''P'' throughout the star.

This gives the [[polytrope|polytropic]] equation (with ''n''=3):<ref name="Pols2011" />
::<math>P = \left(\frac{3c k_B^4}{4\sigma_B\mu^4}\frac{1-\beta}{\beta^4}\right)^{1/3}\rho^{4/3}</math>

Using the [[hydrostatic equilibrium]] equation, the second equation becomes equivalent to:
::<math>-\frac{GM\rho}{r^2} = \frac{\text{d}P}{\text{d}r} = \frac{16\sigma_B}{3c(1-\beta)}T^3\frac{\text{d}T}{\text{d}r}</math>
For energy transmission by radiation only, we may use the equation for the temperature gradient (presented in the previous subsection) for the right-hand side and get
::<math>GM = \frac{\kappa L}{4\pi c (1-\beta)}</math>

Thus the Eddington [[Stellar model|model]] is a good approximation in the radiative zone as long as &kappa;''L''/''M'' is approximately constant, which is often the case.<ref name=Pols2011/>