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In order to precisely determine temperature and density of molecular gas in the Large Magellanic Cloud, we made observations of optically thin $^{13}$CO($J=3-2$) transition by using the ASTE 10m telescope toward 9 peaks where $^{12}$CO($J=3-2$) clump s were previously detected with the same telescope. The molecular clumps include those in giant molecular cloud (GMC) Types I (with no signs of massive star formation), II (with HII regions only), and III (with HII regions and young star clusters). We detected $^{13}$CO($J=3-2$) emission toward all the peaks and found that their intensities are 3 -- 12 times lower than those of $^{12}$CO($J=3-2$). We determined the intensity ratios of $^{12}$CO($J=3-2$) to $^{13}$CO($J=3-2$), $R^{12/13}_{3-2}$, and $^{13}$CO($J=3-2$) to $^{13}$CO($J=1-0$), $R^{13}_{3-2/1-0}$, at 45$arcsec$ resolution. These ratios were used for radiative transfer calculations in order to estimate temperature and density of the clumps. The parameters of these clumps range kinetic temperature $Tmathrm{_{kin}}$ = 15 -- 200 K, and molecular hydrogen gas density $n(mathrm{H_2})$ = 8$times 10^2$ -- 7$times 10^3$ cm$^{-3}$. We confirmed that the higher density clumps show higher kinetic temperature and that the lower density clumps lower kinetic temperature at a better accuracy than in the previous work. The kinetic temperature and density increase generally from a Type I GMC to a Type III GMC. We interpret that this difference reflects an evolutionary trend of star formation in molecular clumps. The $R^{13}_{3-2/1-0}$ and kinetic temperature of the clumps are well correlated with H$alpha$ flux, suggesting that the heating of molecular gas $n(mathrm{H_2})$ = $10^3$ -- $10^4$ cm$^{-3}$ can be explained by stellar FUV photons.
We have carried out sub-mm 12CO(J=3-2) observations of 6 giant molecular clouds (GMCs) in the Large Magellanic Cloud (LMC) with the ASTE 10m sub-mm telescope at a spatial resolution of 5 pc and very high sensitivity. We have identified 32 molecular c lumps in the GMCs and revealed significant details of the warm and dense molecular gas with n(H2) $sim$ 10$^{3-5}$ cm$^{-3}$ and Tkin $sim$ 60 K. These data are combined with 12CO(J=1-0) and 13CO(J=1-0) results and compared with LVG calculations. We found that the ratio of 12CO(J=3-2) to 12CO(J=1-0) emission is sensitive to and is well correlated with the local Halpha flux. We interpret that differences of clump propeties represent an evolutionary sequence of GMCs in terms of density increase leading to star formation.Type I and II GMCs (starless GMCs and GMCs with HII regions only, respectively) are at the young phase of star formation where density does not yet become high enough to show active star formation and Type III GMCs (GMCs with HII regions and young star clusters) represents the later phase where the average density is increased and the GMCs are forming massive stars. The high kinetic temperature correlated with Halpha flux suggests that FUV heating is dominant in the molecular gas of the LMC.
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