[CII] 158$\mu$m emission from Orion A. II. Photodissociation region
  physics
  The [CII] 158$\mu$m fine-structure line is the dominant cooling line of
moderate-density photodissociation regions (PDRs) illuminated by moderately
bright far-ultraviolet (FUV) radiation fields. We aim to understand the origin
of [CII] emission and its relation to other tracers of gas and dust in PDRs.
One focus is a study of the heating efficiency of interstellar gas as traced by
the [CII] line to test models of the photoelectric heating of neutral gas by
polycyclic aromatic hydrocarbon (PAH) molecules and very small grains. We make
use of a one-square-degree map of velocity-resolved [CII] line emission toward
the Orion Nebula complex, and split this out into the individual spatial
components, the expanding Veil Shell, the surface of OMC4, and the PDRs
associated with the compact HII region of M43 and the reflection nebula NGC
1977. We employed Herschel far-infrared photometric images to determine dust
properties. Moreover, we compared with Spitzer mid-infrared photometry to trace
hot dust and large molecules, and velocity-resolved IRAM 30m CO(2-1)
observations of the molecular gas. The [CII] intensity is tightly correlated
with PAH emission in the IRAC 8$\mu$m band and far-infrared emission from warm
dust. The correlation between [CII] and CO(2-1) is very different in the four
subregions and is very sensitive to the detailed geometry. Constant-density PDR
models are able to reproduce the observed [CII], CO(2-1), and integrated
far-infrared (FIR) intensities. We observe strong variations in the
photoelectric heating efficiency in the Veil Shell behind the Orion Bar and
these variations are seemingly not related to the spectral properties of the
PAHs. The [CII] emission from the Orion Nebula complex stems mainly from
moderately illuminated PDR surfaces. Future observations with the James Webb
Space Telescope can shine light on the PAH properties that may be linked to
these variations.
