Radiative zone

Matter in a radiative 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 radiative zone.

Therefore, by the ideal gas law: where kB is Boltzmann constant and μ the mass of a single atom (actually, an ion since matter is ionized; usually a hydrogen ion, i.e. a proton).

For a homogenic ideal gas, this is equivalent to: We can calculate the left-hand side by dividing the equation for the temperature gradient by the equation relating the pressure gradient to the gravity acceleration g: M(r) being the mass within the sphere of radius r, and is approximately the whole star mass for large enough r. This gives the following form of the Schwarzschild criterion for stability against convection:[4]: 64 Note that for non-homogenic gas this criterion should be replaced by the Ledoux criterion, because the density gradient now also depends on concentration gradients.

For a polytrope solution with n=3 (as in the Eddington stellar model for radiative zone), P is proportional to T4 and the left-hand side is constant and equals 1/4, smaller than the ideal monatomic gas approximation for the right-hand side giving

However, at a large enough radius, the opacity κ increases due to the decrease in temperature (by Kramers' opacity law), and possibly also due to a smaller degree of ionization in the lower shells of heavy elements ions.

[6] Additional situations in which this stability criterion is not met are: For main sequence stars—those stars that are generating energy through the thermonuclear fusion of hydrogen at the core, the presence and location of radiative regions depends on the star's mass.

Main sequence stars below about 0.3 solar masses are entirely convective, meaning they do not have a radiative zone.