  We present a ~ 1" (100 pc) resolution 12CO (3-2) map of the nearby
intermediate stage interacting galaxy pair NGC 4038/9 (the Antennae galaxies)
obtained with the Submillimeter Array. We find that half the CO (3-2) emission
originates in the overlap region where most of the tidally induced star
formation had been previously found in shorter wavelength images, with the rest
being centered on each of the nuclei. The gross distribution is consistent with
lower resolution single dish images, but we show for the first time the
detailed distribution of the warm and dense molecular gas across this galaxy
pair at resolutions comparable to the size of a typical giant molecular
complex. While we find that 58% (33/57) of the spatially resolved Giant
Molecular Associations (GMAs; a few x 100 pc) are located in the overlap
region, only \leqq 30% spatially coincides with the optically detected star
clusters, suggesting that the bulk of the CO (3-2) emission traces the regions
with very recent or near future star formation activity. The spatial
distribution of the CO (3-2)/CO (1-0) integrated brightness temperature ratios
mainly range between 0.3 and 0.8, which suggests that on average the CO (3-2)
line in the Antennae is not completely thermalized and similar to the average
values of nearby spirals. A higher ratio is seen in both nuclei and the
southern complexes in the overlap region. Higher radiation field associated
with intense star formation can account for the nucleus of NGC 4038 and the
overlap region, but the nuclear region of NGC 4039 show relatively little star
formation or AGN activities and cannot be easily explained. We show kinematical
evidence that the high line ratio in NGC 4039 is possibly caused by gas inflow
into the counter-rotating central disk.
