usually a hydrogen ion, i.e. a proton). While the radiation pressure satisfies: so that T4 is proportional to P throughout the star. This gives the polytropic equation (with n=3): Using the hydrostatic equilibrium equation, the second equation becomes equivalent to: 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 Thus the Eddington model is a good approximation in the radiation zone as long as κL/M is approximately constant, which is often the case. Stability against convection The radiation zone is stable against formation of convection cells if the density gradient is high enough, so that an element moving upwards has its density lowered (due to adiabatic expansion) less than the drop in density of its surrounding, so that it will experience a net buoyancy force downwards. The criterion for this is: where P is the pressure, ρ the density and is the heat capacity ratio. 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: 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 radiation 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 . This explains the stability of the radiation zone against convection. 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. This leads to a violation of the stability criterion and to the creation of the convection zone; in the sun, opacity increases by more than a tenfold across the radiation zone, before the transition to the convection zone happens. Additional situations in which this stability criterion is not met are: Large values of , which