We study the global star formation law - the relation between the gas and star formation rate ( SFR ) in a sample of 130 local galaxies with infrared ( IR ) luminosities spanning over three orders of magnitude ( { 10 ^ { 9 } -10 ^ { 12 } L _ { \odot } } ) , which includes 91 normal spiral galaxies and 39 ( ultra ) luminous IR galaxies [ ( U ) LIRGs ] .
We derive their total ( atomic and molecular ) gas and dense molecular gas masses using newly available HI , CO and HCN data from the literature .
The SFR of galaxies is determined from total IR ( { 8 - 1000 ~ { } \mu m } ) and 1.4 GHz radio continuum ( RC ) luminosities .
The galaxy disk sizes are defined by the de-convolved elliptical Gaussian FWHM of the RC maps .
We derive the galaxy disk-averaged SFRs and various gas surface densities , and investigate their relationship .
We find that the galaxy disk-averaged surface densities of dense molecular gas mass has the tightest correlation with that of SFR ( scatter \sim 0.26 dex ) , and is linear in \log - \log space ( power-law slope of N = 1.03 \pm 0.02 ) across the full galaxy sample .
The correlation between the total gas and SFR surface densities for the full sample has a somewhat larger scatter ( \sim 0.48 dex ) , and is best fit by a power-law with slope 1.45 \pm 0.02 .
However , the slope changes from \sim 1 when only normal spirals are considered , to \sim 1.5 when more and more ( U ) LIRGs are included in the fitting .
When different CO-to- { H _ { 2 } } conversion factors are used to infer molecular gas masses for normal galaxies and ( U ) LIRGs , the bi-modal relations claimed recently in CO observations of high-redshift galaxies appear to also exist in local populations of star-forming galaxies .