We present new data obtained with the Submillimeter Array for a sample of fourteen nearby luminous and ultraluminous infrared galaxies .
The galaxies were selected to have distances D _ { L } < 200 Mpc and far-infrared luminosities \log L _ { FIR } > 11.4 .
The galaxies were observed with spatial resolutions of order 1 kpc in the CO J=3-2 , CO J=2-1 , ^ { 13 } CO J=2-1 , and HCO ^ { + } J=4-3 lines as well as the continuum at 880 \mu m and 1.3 mm .
We have combined our CO and continuum data to measure an average gas-to-dust mass ratio of 120 \pm 28 ( rms deviation 109 ) in the central regions of these galaxies , very similar to the value of 150 determined for the Milky Way .
This similarity is interesting given the more intense heating from the starburst and possibly accretion activity in the luminous infrared galaxies compared to the Milky Way .
We find that the peak H _ { 2 } surface density correlates with the far-infrared luminosity , which suggests that galaxies with higher gas surface densities inside the central kiloparsec have a higher star formation rate .
The lack of a significant correlation between total H _ { 2 } mass and far-infrared luminosity in our sample suggests that the increased star formation rate is due to the increased availability of molecular gas as fuel for star formation in the central regions .
In contrast to previous analyses by other authors , we do not find a significant correlation between central gas surface density and the star formation efficiency , as trace by the ratio of far-infrared luminosity to nuclear gas mass .
Our data show that it is the star formation rate , not the star formation efficiency , that increases with increasing central gas surface density in these galaxies .