We report ALMA Band 7 ( 350 GHz ) imaging at 0.4 - 0.6 ^ { \prime \prime } resolution and Band 9 ( 696 GHz ) at \sim 0.25 ^ { \prime \prime } resolution of the luminous IR galaxies Arp 220 and NGC 6240 .
The long wavelength dust continuum is used to estimate ISM masses for Arp 220 East , West and NGC 6240 of 1.9 , 4.2 and 1.6 \times 10 ^ { 9 } M _ { \odot } within radii of 69 , 65 and 190 pc .
The HCN emission was modeled to derive the emissivity distribution as a function of radius and the kinematics of each nuclear disk , yielding dynamical masses consistent with the masses and sizes derived from the dust emission .
In Arp 220 , the major dust and gas concentrations are at radii less than 50 pc in both counter-rotating nuclear disks .
The thickness of the disks in Arp 220 estimated from the velocity dispersion and rotation velocities are 10-20 pc and the mean gas densities are n _ { H _ { 2 } } \sim 10 ^ { 5 } cm ^ { -3 } at R < 50 pc .
We develop an analytic treatment for the molecular excitation ( including photon trapping ) , yielding volume densities for both the HCN and CS emission with n _ { H _ { 2 } } \sim 2 \times 10 ^ { 5 } cm ^ { -3 } .
The agreement of the mean density from the total mass and size with that required for excitation suggests that the volume is essentially filled with dense gas , i.e .
it is not cloudy or like swiss cheese .