Some empirical estimates of the H2 formation rate in photon-dominated regions

We combine recent ISO observations of the vibrational ground state lines of H-2 towards Photon-Dominated Regions (PDRs) with observations of vibrationally excited states made with ground - based telescopes in order to constrain the formation rate of H-2 on grain surfaces under the physical conditions in the layers responsible for H-2 emission. We briefly review the data available for five nearby PDRs. We use steady state PDR models in order to examine the sensitivity of different H-2 line ratios to the H-2 formation rate R-f. We show that the ratio of the 0-0 S(3) to the 1-0 S(1) line increases with R-f but that one requires independent estimates of the radiation field incident upon the PDR and the density in order to infer R-f from the H-2 line data. We confirm earlier work by Habart et al. (2003) on the OphWPDR which showed that an H-2 formation rate higher than the standard value of 3 x 10(-17) cm(3) s(-1) inferred from UV observations of diffuse clouds is needed to explain the observed H-2 excitation. From comparison of the ISO and ground-based data, we find that moderately excited PDRs such as Oph W, S140 and IC 63 require an H-2 formation rate of about five times the standard value whereas the data for PDRs with a higher incident radiation field such as NGC 2023 and the Orion Bar can be explained with the standard value of R-f. We compare also the H-2 1 - 0 S(1) line intensities with the emission in PAH features and find a rough scaling of the ratio of these quantities with the ratio of local density to radiation field. This suggests but does not prove that formation of H-2 on PAHs is important in PDRs. We also consider some empirical models of the H-2 formation process with the aim of explaining these results. Here we consider both formation on classical grains of size roughly 0.1 mum and on very small (similar to10 Angstrom) grains by either direct recombination from the gas phase (Eley - Rideal mechanism) or recombination of physisorbed H atoms with atoms in a chemisorbed site. We conclude that indirect chemisorption where a physisorbed H-atom scans the grain surface before recombining with a chemisorbed H-atom is most promising in PDRs. Moreover small grains which dominate the total grain surface and spend most of their time at relatively low (below 30 K for chi less than or equal to 3000) temperatures may be the most promising surface for forming H-2 in PDRs.