We present a study of the infrared/submm emission of the LMC star forming complex N158-N159-N160. Combining observations from the Spitzer Space Telescope (3.6-70um), the Herschel Space Observatory (100-500um) and LABOCA (870um) allows us to work at the best angular resolution available now for an extragalactic source. We observe a remarkably good correlation between SPIRE and LABOCA emission and resolve the low surface brightnesses emission. We use the Spitzer and Herschel data to perform a resolved Spectral Energy Distribution (SED) modelling of the complex. Using MBB, we derive a global emissivity index beta_c of 1.47. If beta cold is fixed to 1.5, we find an average temperature of 27K. We also apply the Galliano et al. (2011) modelling technique (and amorphous carbon to model carbon dust) to derive maps of the star formation rate, the mean starlight intensity, the fraction of PAHs or the dust mass surface density of the region. We observe that the PAH fraction strongly decreases in the HII regions. This decrease coincides with peaks in the mean radiation field intensity map. The dust surface densities follow the FIR distribution, with a total dust mass of 2.1x10^4 Msolar (2.8 times less than when using graphite grains) in the resolved elements we model. We find a non-negligible amount of dust in the molecular cloud N159 South (showing no massive SF). We also investigate the drivers of the Herschel/PACS and SPIRE submm colours as well as the variations in the gas-to-dust mass ratio (G/D) and the XCO conversion factor in the region N159. We finally model individual regions to analyse variations in the SED shape across the complex and the 870um emission in more details. No measurable submm excess emission at 870um seems to be detected in these regions.
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