The radial distribution function in planetary nebulae

We have investigated the variation of planetary nebula number densities as a function of nebular radius, taking account of uncertainties arising from interstellar extinction. We find that the trend is composed of two components: one (a “spike” component) located at radii R < 0.035 pc, and the other (a “plateau” component) extending to larger radii. The plateau component appears to follow a Gaussian fall‐off law with scale radius R₀ = 0.28 pc. It is shown that this latter trend is not consistent with the assumption that larger shells are optically thin and density bounded. Rather, it seems likely thatmany of the larger sources have appreciable Lyman continuum optical depths and are ionization bounded. The deduced variation in N(R) then suggests that the velocities of the ionization fronts increase with radius. The nature of the spike component is less easy to fathom, and this may arise as a result of sharply lower ionization front velocities at radii R < 0.035 pc, or through contraction of the shells following a down‐turn in central star luminosities.