We present the first statistical survey of the properties of the ^ { 12 } CO ( 1-0 ) and ^ { 12 } CO ( 3-2 ) line emission from the nuclei of a nearly complete subsample of 60 infrared ( IR ) luminous galaxies selected from SCUBA Local Universe Galaxy Survey ( SLUGS ) .
This subsample is flux limited at S _ { 60 \mu m } \geq 5.24 Jy with far-IR ( FIR ) luminosities mostly at L _ { FIR } > 10 ^ { 10 } L _ { \odot } .
We compare the emission line strengths of ^ { 12 } CO ( 1-0 ) and ( 3-2 ) transitions at a common resolution of 15 ^ { \prime \prime } .
The measured ^ { 12 } CO ( 3-2 ) to ( 1-0 ) line intensity ratios r _ { 31 } vary from 0.22 to 1.72 with a mean value of 0.66 for the sources observed , indicating a large spread of the degree of excitation of CO in the sample .
These CO data , together with a wide range of data at different wavelengths obtained from the literature , allow us to study the relationship between the CO excitation conditions and the physical properties of gas/dust and star formation in the central regions of galaxies .
Our analysis shows that there is a non-linear relation between CO and FIR luminosities , such that their ratio L _ { CO } / L _ { FIR } decreases linearly with increasing L _ { FIR } .
This behavior was found to be consistent with the Schmidt Law relating star formation rate to molecular gas content , with an index N = 1.4 \pm 0.3 .
We also find a possible dependence of the degree of CO gas excitation on the efficiency of star forming activity .
Using the large velocity gradient ( LVG ) approximation to model the observed data , we investigate the CO-to-H _ { 2 } conversion factor X for the SLUGS sample .
The results show that the mean value of X for the SLUGS sample is lower by a factor of 10 compared to the conventional value derived for the Galaxy , if we assume the abundance of CO relative to H _ { 2 } , Z _ { CO } = 10 ^ { -4 } .
For a subset of 12 galaxies with H I maps , we derive a mean total face-on surface density of H _ { 2 } +H I of about 42 M _ { \odot } pc ^ { -2 } within about 2 kpc of the nucleus .
This value is intermediate between that in galaxies like our own and those with strong star formation .