Kinetic temperature of massive star-forming molecular clumps measured
  with formaldehyde IV. The ALMA view of N113 and N159W in the LMC
  We mapped the kinetic temperature structure of two massive star-forming
regions, N113 and N159W, in the Large Magellanic Cloud (LMC). We have used
$\sim$1\hbox{$\,.\!\!^{\prime\prime}$}6\,($\sim$0.4\,pc) resolution
measurements of the para-H$_2$CO\,$J_{\rm K_ aK_c}$\,=\,3$_{03}$--2$_{02}$,
3$_{22}$--2$_{21}$, and 3$_{21}$--2$_{20}$ transitions near 218.5\,GHz to
constrain RADEX non-LTE models of the physical conditions. The gas kinetic
temperatures derived from the para-H$_2$CO line ratios
3$_{22}$--2$_{21}$/3$_{03}$--2$_{02}$ and 3$_{21}$--2$_{20}$/3$_{03}$--2$_{02}$
range from 28 to 105\,K in N113 and 29 to 68\,K in N159W. Distributions of the
dense gas traced by para-H$_2$CO agree with those of the 1.3\,mm dust and
\emph{Spitzer}\,8.0\,$\mu$m emission, but do not significantly correlate with
the H$\alpha$ emission. The high kinetic temperatures ($T_{\rm
kin}$\,$\gtrsim$\,50\,K) of the dense gas traced by para-H$_2$CO appear to be
correlated with the embedded infrared sources inside the clouds and/or YSOs in
the N113 and N159W regions. The lower temperatures ($T_{\rm kin}$\,$<$\,50\,K)
are measured at the outskirts of the H$_2$CO-bearing distributions of both N113
and N159W. It seems that the kinetic temperatures of the dense gas traced by
para-H$_2$CO are weakly affected by the external sources of the H$\alpha$
emission. The non-thermal velocity dispersions of para-H$_2$CO are well
correlated with the gas kinetic temperatures in the N113 region, implying that
the higher kinetic temperature traced by para-H$_2$CO is related to turbulence
on a $\sim$0.4\,pc scale. The dense gas heating appears to be dominated by
internal star formation activity, radiation, and/or turbulence. It seems that
the mechanism heating the dense gas of the star-forming regions in the LMC is
consistent with that in Galactic massive star-forming regions located in the
Galactic plane.
