  We report high resolution 2" ~ 200 pc mappings of the central region of the
nearby barred spiral galaxy NGC 1365 in the CO(1--0) and CO(2--1) emission
lines. The 2--1/1--0 ratio of integrated intensities shows a large scatter
(0.15) with a median value of 0.67. We also calculate the ratio of velocity
dispersions and peak temperatures and find that in most cases the velocity
dispersion ratio is close to unity and thus the peak temperature ratio is
comparable to the integrated intensity ratio. This result indicates that both
CO(1--0) and CO(2--1) lines trace similar components of molecular gas, with
their integrated intensity (or peak temperature) ratios reflecting the gas
density and/or temperature. Similar to recent kpc scale studies, these ratios
show a positive correlation with a star formation rate indicator (here we use
an extinction-corrected H-alpha map), suggesting that molecular gas associated
with recent star formation is denser and/or warmer. We also find that some CO
spectra show two peaks owing to complicated kinematics, and such two components
likely trace molecular gas at different conditions. This result demonstrates
the importance of spectral fitting to measure integrated intensities and their
ratios more accurately.
