Molecular hydrogen emission is commonly observed in planetary nebulae. Images taken in infrared H2 emission lines show that at least part of the molecular emission is produced inside the ionised region. In the best-studied case, the Helix nebula, the
H2 emission is produced inside cometary knots (CKs), comet-shaped structures believed to be clumps of dense neutral gas embedded within the ionised gas. Most of the H2 emission of the CKs seems to be produced in a thin layer between the ionised diffuse gas and the neutral material of the knot, in a mini photodissociation region (PDR). However, PDR models published so far cannot fully explain all the characteristics of the H2 emission of the CKs. In this work, we use the photoionisation code textsc{Aangaba} to study the H2 emission of the CKs, particularly that produced in the interface H^+/H^0 of the knot, where a significant fraction of the H2 1-0S(1) emission seems to be produced. Our results show that the production of molecular hydrogen in such a region may explain several characteristics of the observed emission, particularly the high excitation temperature of the H2 infrared lines. We find that the temperature derived from H2 observations even of a single knot, will depend very strongly on the observed transitions, with much higher temperatures derived from excited levels. We also proposed that the separation between the H_alpha and NII peak emission observed in the images of CKs may be an effect of the distance of the knot from the star, since for knots farther from the central star the NII line is produced closer to the border of the CK than H_alpha.
The analysis and interpretation of the H2 line emission from planetary nebulae have been done in the literature assuming that the molecule survives only in regions where the hydrogen is neutral, as in photodissociation, neutral clumps or shocked regi
ons. However, there is strong observational and theoretical evidence that at least part of the H2 emission is produced inside the ionized region of such objects. The aim of the present work is to calculate and analyze the infrared line emission of H2 produced inside the ionized region of planetary nebulae using a one-dimensional photoionization code. The photoionization code Aangaba was improved in order to calculate the statistical population of the H2 energy levels and the intensity of the H2 infrared emission lines in physical conditions typical of planetary nebulae. A grid of models was obtained and the results are analyzed and compared with the observational data. We show that the contribution of the ionized region to the H2 line emission can be important, particularly in the case of nebulae with high temperature central stars. This result explains why H2 emission is more frequently observed in bipolar planetary nebulae (Gatleys rule), since this kind of object typically has hotter stars. Collisional excitation plays an important role on the population of the rovibrational levels of the electronic ground state of H2. Radiative mechanisms are also important, particularly for the upper vibrational levels. Formation pumping can have minor effects on the line intensities produced by de-excitation from very high rotational levels, especially in dense and dusty environments. We included the effect of the H2 on the thermal equilibrium of the gas, concluding that H2 only contributes to the thermal equilibrium in the case of a very high temperature of the central star or a high dust-to-gas ratio, mainly through collisional de-excitation.
