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 Lsun), 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 um) 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 ~ 0.26 dex), and is linear in log-log space (power-law slope of N=1.03 +/- 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 (~ 0.48 dex), and is best fit by a power-law with slope 1.45 +/- 0.02. However, the slope changes from ~ 1 when only normal spirals are considered, to ~ 1.5 when more and more (U)LIRGs are included in the fitting. When different CO-to-H2 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.
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