Isentropic thermal instability in atomic surface layers of photodissociation regions

Abstract: We consider the evolution of an isentropic thermal instability in the atomic zone of a photodissociation region (PDR). In this zone, gas heating and cooling are associated mainly with photoelectric emission from dust grains and fine-structure lines ([\ion{C}{ii}] 158, [\ion{O}{i}] 63, and [\ion{O}{i}] 146 {\micron}), respectively. The instability criterion has a multi-parametric dependence on the conditions of the interstellar medium. We found that instability occurs when the intensity of the incident far-ultraviolet field $G_0$ and gas density $n$ are high. For example, we have $3\times10^3<G_0<10^6$ and $4.5\times10^4<n<10^6$ {\cmc} at temperatures $360 <T<10^4$ K for typical carbon and oxygen abundances $\xi_{\rm C}=1.4\times10^{-4}$ and $\xi_{\rm O}=3.2\times10^{-4}$. The instability criterion depends on the relation between $\xi_{\rm C}$ and $\xi_{\rm O}$ abundances and line opacities. We also give examples of observed PDRs where instability could occur. For these PDRs, the characteristic perturbation growth time is $t_{\rm inst}\sim10^3$ -- $10^4$ yr and the distance characterizing the formation of secondary waves is $L\sim10^{-3}$ -- $5\times10^{-2}$ pc. For objects that are older than $t_{\rm inst}$ and have sizes of the atomic zone larger than $L$, we expect that instability influences the PDR structure significantly. The presence of multiple shock waves, turbulent velocities of several kilometers per second and inhomogeneities with higher density and temperature than the surrounding medium can characterize isentropic thermal instability in PDRs.