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(abridged) The ambiguous origin of [CII] 158um in the interstellar mediumcomplicates its use for diagnostics concerning the star-formation rate andphysical conditions in photodissociation regions (PDRs). We observed the giantHII region N11 in the Large Magellanic Cloud with SOFIA/GREAT in order toinvestigate the origin of [CII] to obtain the total H2 gas content, thefraction of CO-dark H2 gas, and the influence of environmental effects such asstellar feedback. We present an innovative spectral decomposition method thatallows statistical trends to be derived. The [CII] line is resolved in velocityand compared to HI and CO, using a Bayesian approach to decompose the profiles.A simple model accounting for collisions in the neutral atomic and moleculargas was used in order to derive the H2 column density traced by C+. The profileof [CII] most closely resembles that of CO, but the integrated [CII] line widthlies between that of CO and that of HI. Using various methods, we find that[CII] mostly originates from the neutral gas. We show that [CII] mostly tracesthe CO-dark H2 gas but there is evidence of a weak contribution from neutralatomic gas preferentially in the faintest components. Most of the molecular gasis CO-dark. The fraction of CO-dark H2 gas decreases with increasing CO columndensity, with a slope that seems to depend on the impinging radiation fieldfrom nearby massive stars. Finally we extend previous measurements of thephotoelectric-effect heating efficiency, which we find is constant acrossregions probed with Herschel, with [CII] and [OI] being the main coolants infaint and diffuse, and bright and compact regions, respectively, and with PAHemission tracing the CO-dark H2 gas heating where [CII] and [OI] emit. Ourstudy highlights the importance of velocity-resolved PDR diagnostics and higherspatial resolution for HI observations.

Physical conditions in the gas phases of the giant HII region LMC-N11: II. Origin of [CII] and fraction of CO-dark gas