Some empirical estimates of the H₂formation 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 I-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 Oph W PDR 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 μm and on very small (∼ 10 A) 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 X < 3000) temperatures may be the most promising surface for forming H 2 in PDRs.