  Spitzer and IRAS observations of the LMC suggest an excess of FIR emission
with respect to the gas surface density traced by 12CO and HI 21 cm emission
lines. This "FIR excess" is noticeable near molecular clouds in the LMC, and
has usually been interpreted as the presence of a self-shielded H2 component
not traced by CO molecular clouds' envelopes. Based on Herschel observations,
we examine the correlation between gas and dust at higher resolution than
previously achieved. We consider three additional causes for the FIR excess: X
factor, FIR dust emissivity, and gas-to-dust ratio variations between the
diffuse and dense phases of the ISM. We examine the structure of NT80 and NT71,
two molecular clouds detected in the NANTEN 12CO survey of the LMC. Dust
surface density maps are derived from the HERITAGE data. The gas phase is
traced by MAGMA 12CO and ATCA HI 21 cm observations of the LMC. The dust
emissivity, gas-to-dust ratio, and X factor required to match the dust and gas
surface densities are derived, and their correlations with the dust surface
density are examined. The dust surface density is spatially correlated with the
atomic and molecular gas phases. The dust temperature is consistently lower in
the dense phase of the ISM than in the diffuse phase. We confirm variations in
the ratio of FIR emission to gas surface density derived from HI and CO
observations. There is an excess of FIR emission, spatially correlated with
regions of intermediate HI and dust surface densities (Av = 1-2), and little or
no CO. While there is no significant trend in the dust emissivity or
gas-to-dust ratio with dust surface density, the X factor is enhanced at Av =
1-2. We conclude that H2 envelopes not traced by CO and X factor variations
close to the CO boundary are more likely to cause these deviations between FIR
emission and gas surface density than gas-to-dust ratio or emissivity
variations.
