Abstract
Because of the recent evidence that a planetary nebula does not completely absorb Lyman continuum radiation for a substantial part of its life, we have used a generalized discrete-ordinate method to obtain accurate numerical solutions to the ionization balance problem in pure hydrogen, plane-parallel model nebulae of various optical thicknesses. The effects of incomplete absorption, interior boundary conditions and non-Planckian stellar fluxes are examined. We find that the density of neutral hydrogen in the nebula increases by less than a factor of two as the optical thickness varies from 0.5 to ∞, and is insensitive to large deviations in the stellar flux from the Planckian distribution, if the total number of Lyman photons is constant. The radius of the Strömgren sphere differs by about 5 per cent for the two boundary conditions considered. The accuracies of two simple approximations are assessed, and conditions for their validity are obtained.
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