A Model for Nonlinear Photoexcitation of H_2 in Photon-Dominated Regions (PDRs)

We have recently analyzed the published ORFEUS II 1000-1200 Angstrom emission spectrum of H_2 in the PDR IC 63 and find that it cannot be understood on the basis of linear photoexcitation theory. To explain PDR VUV emission bands, we have developed a simple nonlinear H_2 photoexcitation model. In the model, a B0 III star is surrounded by an ionized hydrogen region (H II region), represented by a conventional Stromgren sphere of radius 1 pc. The latter is bounded by a cold, neutral, (H, H_2-containing) PDR cloud. The H II region efficiently converts all ionizing radiation from the star into Ly-alpha photons. As these photons start to propagate into the neutral region of the PDR, they are elastically scattered back into the H II region by H atoms. In principle, the Ly-alpha photon density should continually increase inside the Stromgren sphere until the emission rate of ionizing photons by the star becomes balanced by the outward diffusive flow of Ly-alpha photons through the PDR cloud. At this point, the Ly-alpha photon density existing within the PDR cloud would have become enhanced over the free-space value by roughly one hundred million times. However, to achieve the nonlinearities described below, one only requires Ly-alpha enhancements on the order of 10,000. The resulting high densities of Ly-alpha photons within the PDR induce a second crucial generic process to occur - inverse Raman scattering (IRS) at three 'primary' orthohydrogen frequencies (B9-0P1, B6-0P1, and B3-0R1) and at one 'primary' parahydrogen frequency (B3-0R0). An estimate shows that (for a Ly-alpha enhancement value of 10,000) the transition rates for these IRS processes are roughly one hundred times greater than those for the corresponding linear (i.e. spontaneous resonant Raman scattering) processes. Since the IRS transition rates also exceed the radiative decay rates of X-state levels by an order of magnitude, population buildup starts to occur in all four IRS terminal levels. Via spontaneous resonant Raman scattering, the Ly-alpha radiation redistributes this population into a number of other X-state quantum levels. A thin sheath of vibrationally excited molecules, roughly ten thousand kilometers in thickness, thus surrounds the Stromgren sphere, the thickness of the sheath being determined by the balance existing between the input fluxes of the 'primary' photons and loss due to radiative vibrational decay of the populated X-state quantum levels. From a number of the populated X-state vibrational levels, there exist strong upward transitions that are resonant with Ly-alpha radiation. The latter can thus pump stimulated Raman scattering (SRS) processes, with coherent Stokes-wave generation occuring in the IR on strong transitions to EF-state quantum levels. This coherent Stokes-wave generation would occur throughout the thin sheath, in directions that are tangential to it. The SRS processes would induce cascading sequences of two-photon emission steps to occur via parametric oscillation (PO) processes, generating additional light at IR and VUV frequencies and returning H_2 molecules to the vibrationally excited X-state quantum levels from which the SRS-PO processes originated. We show evidence that the observed IC 63 VUV emission bands result from such SRS-PO processes. We also show evidence that such SRS-PO processes are responsible for the Unidentified Infrared (Emission) Bands (UIBs), which are ubiquitously observed to be radiated from PDRs.