Physical conditions in the gas phases of the giant HII region LMC-N11 unveiled by Herschel - I. Diffuse [CII] and [OIII] emission in LMC-N11B

(Abridged) The Magellanic Clouds provide a nearby laboratory for metal-poor dwarf galaxies. The low dust abundance enhances the penetration of UV photons into the interstellar medium (ISM), resulting in a relatively larger filling factor of the ionized gas. Furthermore, there is likely a hidden molecular gas reservoir probed by the [CII]157um line. We present Herschel/PACS maps in several tracers, [CII], [OI]63um,145um, [NII]122um, [NIII]57um, and [OIII]88um in the HII region N11B in the Large Magellanic Cloud. Halpha and [OIII]5007A images were used as complementary data to investigate the effect of dust extinction. Observations were interpreted with photoionization models to infer the gas conditions and estimate the ionized gas contribution to the [CII] emission. Photodissociation regions (PDRs) are probed through polycyclic aromatic hydrocarbons (PAHs). We first study the distribution and properties of the ionized gas. We then constrain the origin of [CII]157um by comparing to tracers of the low-excitation ionized gas and of PDRs. [OIII] is dominated by extended emission from the high-excitation diffuse ionized gas; it is the brightest far-infrared line, ~4 times brighter than [CII]. The extent of the [OIII] emission suggests that the medium is rather fragmented, allowing far-UV photons to permeate into the ISM to scales of >30pc. Furthermore, by comparing [CII] with [NII], we find that 95% of [CII] arises in PDRs, except toward the stellar cluster for which as much as 15% could arise in the ionized gas. We find a remarkable correlation between [CII]+[OI] and PAH emission, with [CII] dominating the cooling in diffuse PDRs and [OI] dominating in the densest PDRs. The combination of [CII] and [OI] provides a proxy for the total gas cooling in PDRs. Our results suggest that PAH emission describes better the PDR gas heating as compared to the total infrared emission.