[CII] 158 {\mu}m self-absorption and optical depth effects
  Context. The [CII] 158 {\mu}m far-infrared (FIR) fine-structure line is one
of the most important cooling lines of the star-forming interstellar medium
(ISM). High spectral resolution observations have shown complex structures in
the line profiles of the [CII] emission. Aims. Our aim is to determine whether
the complex profiles observed in [^{12}CII] are due to individual velocity
components along the line-of-sight or to self-absorption based on a comparison
of the [^{12}CII] and isotopic [^{13}CII] line profiles. Methods. Deep
integrations with the SOFIA/upGREAT 7-pixel array receiver in M43,
Horsehead~PDR, Monoceros~R2, and M17~SW allow for the detection of optically
thin [^{13}CII] emission lines, along with the [^{12}CII] emission lines, with
a high signal-to-noise ratio. We first derived the [^{12}CII] optical depth and
the [CII] column density from a single component model. However, the complex
line profiles observed require a double layer model with an emitting background
and an absorbing foreground. A multi-component velocity fit allows us to derive
the physical conditions of the [CII] gas: column density and excitation
temperature. Results. We find moderate to high [^{12}CII] optical depths in all
four sources and self-absorption of [^{12}CII] in Mon R2 and M17 SW. The high
column density of the warm background emission corresponds to an equivalent Av
of up to 41 mag. The foreground absorption requires substantial column
densities of cold and dense [CII] gas, with an equivalent Av ranging up to
about 13 mag. Conclusions. The column density of the warm background material
requires multiple photon-dominated region (PDR) surfaces stacked along the line
of sight and in velocity. The substantial column density of dense and cold
foreground [CII] gas detected in absorption cannot be explained with any known
scenario and we can only speculate on its origins
