Structure of photodissociation fronts in star-forming regions revealed
  by observations of high-J CO emission lines with Herschel
  In bright photodissociation regions (PDRs) associated to massive star
formation, the presence of dense "clumps" that are immersed in a less dense
interclump medium is often proposed to explain the difficulty of models to
account for the observed gas emission in high-excitation lines. We aim at
presenting a comprehensive view of the modeling of the CO rotational ladder in
PDRs, including the high-J lines that trace warm molecular gas at PDR
interfaces. We observed the 12CO and 13CO ladders in two prototypical PDRs, the
Orion Bar and NGC 7023 NW using the instruments onboard Herschel. We also
considered line emission from key species in the gas cooling of PDRs (C+, O,
H2) and other tracers of PDR edges such as OH and CH+. All the intensities are
collected from Herschel observations, the literature and the Spitzer archive
and are analyzed using the Meudon PDR code. A grid of models was run to explore
the parameter space of only two parameters: thermal gas pressure and a global
scaling factor that corrects for approximations in the assumed geometry. We
conclude that the emission in the high-J CO lines, which were observed up to
Jup=23 in the Orion Bar (Jup=19 in NGC7023), can only originate from small
structures of typical thickness of a few 1e-3 pc and at high thermal pressures
(Pth~1e8 K cm-3). Compiling data from the literature, we found that the gas
thermal pressure increases with the intensity of the UV radiation field given
by G0, following a trend in line with recent simulations of the
photoevaporation of illuminated edges of molecular clouds. This relation can
help rationalising the analysis of high-J CO emission in massive star formation
and provides an observational constraint for models that study stellar feedback
on molecular clouds.
