This paper presents an analysis of the concentration of the hydrogen molecule
inside the ionized region of planetary nebulae. The equations corresponding to
the ionization and chemical equilibria of H, H+, H-, H2, H2+, and H3+ are
coupled with the equations of ionization and thermal balance for a photoionized
atomic gas. Forty different reactions related to the formation or the
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 can be of the
order of 10^-6 or even higher. The increase of the recombination zone with the
stellar temperature can account for such correlation. This can explain why the
H2 emission is more frequently observed in bipolar planetary nebulae (Gatley's
rule), since this kind of object has typically hotter stars. Applying our
results for the planetary nebula NGC 6720, we obtain an H2 to hydrogen mass
ratio similar to the value obtained from the observed H2 line emission.Comment: 13 pages, 4 figures. Accepted for publication in Ap