%0 Journal Article %T Physical conditions in the gas phases of the giant H£¿II region LMC-N 11 - II. Origin of [C£¿II] and fraction of CO-dark gas %A A. Hughes %A D. Cormier %A F. Galliano %A F. L. Polles %A J. Braine %A M. A. Reque£¿a-Torres %A M. Chevance %A M. Galametz %A M.-Y. Lee %A N. Abel %A R. Indebetouw %A S. C. Madden %A S. Hony %A V. Lebouteiller %J - %D 2019 %R 10.1051/0004-6361/201936303 %X Context. The ambiguous origin of the [C£¿II] 158¦Ìm line in the interstellar medium complicates its use for diagnostics concerning the star-formation rate and physical conditions in photodissociation regions.Aims. We investigate the origin of [C£¿II] in order to measure the total molecular gas content, the fraction of CO-dark H2 gas, and how these parameters are impacted by environmental effects such as stellar feedback.Methods. We observed the giant H£¿II region N 11 in the Large Magellanic Cloud with SOFIA/GREAT. The [C£¿II] line is resolved in velocity and compared to H£¿I and CO, using a Bayesian approach to decompose the line profiles. A simple model accounting for collisions in the neutral atomic and molecular gas was used in order to derive the H2 column density traced by C+.Results. The profile of [C£¿II] most closely resembles that of CO, but the integrated [C£¿II] line width lies between that of CO and that of H£¿I. Using various methods, we find that [C£¿II] mostly originates from the neutral gas. We show that [C£¿II] mostly traces the CO-dark H2 gas but there is evidence of a weak contribution from neutral atomic gas preferentially in the faintest components (as opposed to components with low [C£¿II]/CO or low CO column density). Most of the molecular gas is CO-dark. The CO-dark H2 gas, whose density is typically a few 100s cm£¿3 and thermal pressure in the range 103.5£¿5 K cm£¿3, is not always in pressure equilibrium with the neutral atomic gas. The fraction of CO-dark H2 gas decreases with increasing CO column density, with a slope that seems to depend on the impinging radiation field from nearby massive stars. Finally we extend previous measurements of the photoelectric-effect heating efficiency, which we find is constant across regions probed with Herschel, with [C£¿II] and [O£¿I] being the main coolants in faint and diffuse, and bright and compact regions, respectively, and with polycyclic aromatic hydrocarbon emission tracing the CO-dark H2 gas heating where [C£¿II] and [O£¿I] emit.Conclusions. We present an innovative spectral decomposition method that allows statistical trends to be derived for the molecular gas content using CO, [C£¿II], and H£¿I profiles. Our study highlights the importance of velocity-resolved photodissociation region (PDR) diagnostics and higher spatial resolution for H£¿I observations as future steps %U https://www.aanda.org/articles/aa/full_html/2019/12/aa36303-19/aa36303-19.html