We compare the CO J =(1-0) and HI emission in the Large Magellanic Cloud (LMC) in three dimensions, i.e. including a velocity axis in addition to the two spatial axes, with the aim of elucidating the physical connection between giant molecular clouds (GMCs) and their surrounding HI gas. The CO J =1-0 dataset is from the second NANTEN CO survey and the HI dataset is from the merged Australia Telescope Compact Array (ATCA) and Parkes Telescope surveys. The major findings of our analysis are: 1) GMCs are associated with an envelope of HI emission, 2) in GMCs [average CO intensity] is proportional to [average HI intensity]^[1.1+-0.1] and 3) the HI intensity tends to increase with the star formation activity within GMCs, from Type I to Type III. An analysis of the HI envelopes associated with GMCs shows that their average linewidth is 14 km s-1 and the mean density in the envelope is 10 cm-3. We argue that the HI envelopes are gravitationally bound by GMCs. These findings are consistent with a continual increase in the mass of GMCs via HI accretion at an accretion rate of 0.05 Msun/yr over a time scale of 10 Myr. The growth of GMCs is terminated via dissipative ionization and/or stellar-wind disruption in the final stage of GMC evolution.
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