The Ionization Structure of Planetary Nebulae: I. Pure Hydrogen Nebulae

The problem is formulated in terms of the equations of radiative transfer, of ionization equilibrium and of the thermal balance. The intensity of ionizing radiation is |I_ν = I_νˢ + I_νᵈ| , where I νs is the attenuated intensity of stellar radiation and I νd the intensity of diffuse radiation produced in the nebula. In Approximation I it is assumed that there is no transfer problem for the diffuse radiation, emission and absorption occurring at the same place. The problem is then solved using a method due to Zanstra and de Jong. Assuming the star to radiate as a black body, numerical results are obtained for a wide range of star temperatures. In Approximation II the transfer equation for I νd is solved using the source function from Approximation I. For an isothermal plane parallel model it is found that the mean intensities J ν , as given by Approximations I and II, never differ by more than a few per cent.