[CII] 158 mu m line emission from Orion A I. A template for extragalactic studies?

Context. The [CII] 158 mu m fine-structure line is one of the dominant coolants of the neutral interstellar medium. It is hence one of the brightest far-infrared (FIR) emission lines and can be observed not only in star-forming regions throughout the Galaxy, but also in the diffuse interstellar medium and in distant galaxies. [CII] line emission has been suggested to be a powerful tracer of star formation.Aims. We aim to understand the origin of [CII] emission and its relation to other tracers of interstellar gas and dust. This includes a study of the heating efficiency of interstellar gas as traced by the [CII] line to test models of gas heating.Methods. We made use of a one-square-degree map of velocity-resolved [CII] line emission toward the Orion Nebula complex, including M 43 and NGC 1977. We employed Herschel FIR photometric images to determine dust properties. Moreover, we compared with H alpha emission from the ionized gas, Spitzer mid-infrared photometry to trace hot dust and large polycyclic aromatic hydrocarbons (PAHs), and velocity-resolved IRAM 30m CO(2-1) observations of the molecular gas.Results. The [CII] intensity is tightly correlated with PAH emission in the IRAC 8 mu m band and FIR emission from warm dust. However, the [CII] intensity depends less than linearly on the 8 mu m and FIR intensity, while 8 mu m and FIR intensities are approximately linearly correlated. The correlation between [CII] and CO(2-1) does not show a clear trend and is affected by the detailed geometry of the region. We find particularly low [CII]-over-FIR intensity ratios toward large columns of (warm and cold) dust, which suggest the interpretation of the [CII] deficit in terms of a FIR excess.Conclusions. In terms of the [CII] deficit, we find clear evidence in our data for the importance of [OI] 63 mu m emission in the photodissociation regions (PDRs) associated with the Huygens region. A smaller contribution is made by a decreased heating efficiency in regions of high UV