Molecular Hydrogen in the Ionized Region of Planetary Nebulae

This paper presents an analysis of the concentration of hydrogen molecules inside the ionized region of planetary nebulae (PNs). The equations corresponding to the ionization and chemical equilibria of H, H⁺, H^-, H₂, H, and H are coupled with the equations of ionization and thermal balance for a photoionized atomic gas. A total of 40 different reactions related to the formation or destruction of these species are included. The presence of dust is taken into account, since grains act as catalysts for the production of H₂ as well as shield the molecules against the stellar ionizing radiation. We analyze the effect of the stellar ionizing continuum as well as of the gas and grain properties on the calculated H₂ mass. It is shown that a significant concentration of H₂ can survive inside the ionized region of planetary nebulae, mostly in the inner region of the recombination zone. The total H₂ to total hydrogen mass ratio inside the ionized region increases with the central star temperature, and, depending on the PN physical conditions, it may be of the order of ~10^-6 or even higher. The increase of the recombination zone with stellar temperature can account for such correlation. This may explain why H₂ emission is more frequently observed in bipolar PNs (Gatley's rule), since this kind of object typically has hotter stars. Applying our results to the planetary nebula NGC 6720, we obtain an H₂ to hydrogen mass ratio similar to the value obtained from the observed H₂ line emission.