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Description
We study the global star formation law --the relation between gas and star formation (SF) rates-- in a sample of 181 local galaxies with infrared (IR) luminosities spanning almost five orders of magnitude (10^7.8^-10^12.3^L_{sun}_), which includes 115 normal spiral galaxies and 66 (ultra)luminous IR galaxies ((U)LIRGs, L_IR_>>10^11^L_{sun}_). We derive their atomic, molecular gas, and dense molecular gas masses using newly available HI, CO, and HCN data from the literature, and SF rates are determined both from total IR (8-1000um) and 1.4GHz radio continuum (RC) luminosities. In order to derive the disk-averaged surface densities of gas and SF rates, we have taken a novel approach and used high-resolution RC observations to measure the radio sizes for all 181 galaxies. In our sample, we find that the surface density of dense molecular gas (as traced by HCN) has the tightest correlation with that of SF rates ({Sigma}_SFR_), and is linear in log-log space (power-law slope of N=1.01+/-0.02) across the full galaxy sample. The correlation between surface densities of molecular gas ({Sigma}_H_2__, traced by CO) and {Sigma}_SFR_ is sensitive to the adopted value of the CO-to-H_2_ conversion factor ({alpha}_CO_) used to infer molecular gas masses from CO luminosities. For a fixed Galactic value of {alpha}_CO_, a power law index of 1.14+/-0.02 is found. If instead we adopt values for {alpha}_CO_ of 4.6 and 0.8 for disk galaxies and (U)LIRGs, respectively, we find the two galaxy populations separate into two distinct {Sigma}_SFR_ versus {Sigma}_H_2__ relations. Finally, applying a continuously varying {alpha}_CO_ to our sample, we recover a single {Sigma}_SFR_-{Sigma}_H_2__ relation with slope of 1.60+/-0.03. The {Sigma}_SFR_ is a steeper function of total gas {Sigma}_gas_ (molecular gas with atomic gas) than that of molecular gas {Sigma}_H_2__, and are tighter among low-luminosity galaxies. We find no correlation between global surface densities of SFRs and atomic gas (HI).
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