Context : The ambiguous origin of the [ C ii ] 158 \mu m 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 H _ { 2 } 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 H _ { 2 } 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 H _ { 2 } 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 H _ { 2 } gas , whose density is typically a few 100 s cm ^ { -3 } and thermal pressure in the range 10 ^ { 3.5 - 5 } K cm ^ { -3 } , is not always in pressure equilibrium with the neutral atomic gas .
The fraction of CO-dark H _ { 2 } 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 H _ { 2 } 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 .