  Aims: In this paper, we perform detailed modelling of the Spitzer and
Herschel observations of the LMC, in order to: (i) systematically study the
uncertainties and biases affecting dust mass estimates; and to (ii) explore the
peculiar ISM properties of the LMC.
  Methods: To achieve these goals, we have modelled the spatially resolved SEDs
with two alternate grain compositions, to study the impact of different
submillimetre opacities on the dust mass. We have rigorously propagated the
observational errors (noise and calibration) through the entire fitting
process, in order to derive consistent parameter uncertainties.
  Results: First, we show that using the integrated SED leads to
underestimating the dust mass by ~50 % compared to the value obtained with
sufficient spatial resolution, for the region we studied. This might be the
case, in general, for unresolved galaxies. Second, we show that Milky Way type
grains produce higher gas-to-dust mass ratios than what seems possible
according to the element abundances in the LMC. A spatial analysis shows that
this dilemma is the result of an exceptional property: the grains of the LMC
have on average a larger intrinsic submm opacity (emissivity index beta~1.7 and
opacity kappa_abs(160 microns)=1.6 m2/kg) than those of the Galaxy. By studying
the spatial distribution of the gas-to-dust mass ratio, we are able to
constrain the fraction of unseen gas mass between ~10, and ~100 % and show that
it is not sufficient to explain the gas-to-dust mass ratio obtained with Milky
Way type grains. Finally, we confirm the detection of a 500 microns extended
emission excess with an average relative amplitude of ~15 %, varying up to 40
%. This excess anticorrelates well with the dust mass surface density. Although
we do not know the origin of this excess, we show that it is unlikely the
result of very cold dust, or CMB fluctuations.

Cosmology and Nongalactic Astrophysics;Astrophysics of Galaxies