  We have used high resolution (~2.3") observations of the local (D = 46 Mpc)
luminous infrared galaxy Arp 299 to map out the physical properties of the
molecular gas which provides the fuel for its extreme star formation activity.
The 12CO J=3-2, 12CO J=2-1 and 13CO J=2-1 lines were observed with the
Submillimeter Array and the short spacings of the 12CO J=2-1 and J=3-2
observations have been recovered using James Clerk Maxwell Telescope single
dish observations. We use the radiative transfer code RADEX to estimate the
physical properties (density, column density and temperature) of the different
regions in this system. The RADEX solutions of the two galaxy nuclei, IC 694
and NGC 3690, are consistent with a wide range of gas components, from warm
moderately dense gas with T_{kin} > 30 K and n(H_{2}) ~ 0.3 - 3 x 10^{3}
cm^{-3} to cold dense gas with T_{kin} ~ 10-30 K and n(H_{2}) > 3 x 10^{3}
cm^{-3}. The overlap region is shown to have a better constrained solution with
T_{\rm{kin}}$ ~ 10-50 K and n(H_{2}) ~ 1-30 x 10^{3} cm^{-3}. We estimate the
gas masses and star formation rates of each region in order to derive molecular
gas depletion times. The depletion times of all regions (20-60 Myr) are found
to be about 2 orders of magnitude lower than those of normal spiral galaxies.
This rapid depletion time can probably be explained by a high fraction of dense
gas on kiloparsec scales in Arp 299. We estimate the CO-to-H_{2} factor,
\alpha_{co} to be 0.4 \pm 0.3 (3 x 10^{-4}/ x_{CO}) M_{sol} (K km s^{-1}
pc^{2})^{-1} for the overlap region. This value agrees well with values
determined previously for more advanced merger systems.
