Herschel PACS and SPIRE spectroscopy of the Photodissociation Regions
  associated with S 106 and IRAS 23133+6050
  Photodissociation regions (PDRs) contain a large fraction of all of the
interstellar matter in galaxies. Classical examples include the boundaries
between ionized regions and molecular clouds in regions of massive star
formation, marking the point where all of the photons energetic enough to
ionize hydrogen have been absorbed. In this paper we determine the physical
properties of the PDRs associated with the star forming regions IRAS 23133+6050
and S 106 and present them in the context of other Galactic PDRs associated
with massive star forming regions. We employ Herschel PACS and SPIRE
spectroscopic observations to construct a full 55-650 {\mu}m spectrum of each
object from which we measure the PDR cooling lines, other fine- structure
lines, CO lines and the total far-infrared flux. These measurements are then
compared to standard PDR models. Subsequently detailed numerical PDR models are
compared to these predictions, yielding additional insights into the dominant
thermal processes in the PDRs and their structures. We find that the PDRs of
each object are very similar, and can be characterized by a two-phase PDR model
with a very dense, highly UV irradiated phase (n $\sim$ 10^6 cm^(-3), G$_0$
$\sim$ 10^5) interspersed within a lower density, weaker radiation field phase
(n $\sim$ 10^4 cm^(-3), G$_0$ $\sim$ 10^4). We employed two different numerical
models to investigate the data, firstly we used RADEX models to fit the peak of
the $^{12}$CO ladder, which in conjunction with the properties derived yielded
a temperature of around 300 K. Subsequent numerical modeling with a full PDR
model revealed that the dense phase has a filling factor of around 0.6 in both
objects. The shape of the $^{12}$CO ladder was consistent with these components
with heating dominated by grain photoelectric heating. An extra excitation
component for the highest J lines (J > 20) is required for S 106.
