The Global Star Formation Laws of Galaxies from a Radio Continuum Perspective

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}_⊙ }), which includes 115 normal spiral galaxies and 66 (ultra)luminous IR galaxies ((U)LIRGs, {{L}_IR}≥slant {{10}¹¹} {{L}_⊙ }). 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 (81000 μ m) and 1.4 GHz 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 (Σ_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 ({{{Σ }}_{{H2}}}, traced by CO) and Σ_SFR is sensitive to the adopted value of the CO-to-{{H}₂} conversion factor (α_CO) used to infer molecular gas masses from CO luminosities. For a fixed Galactic value of α_CO, a power law index of 1.14 ± 0.02 is found. If instead we adopt values for α_CO of 4.6 and 0.8 for disk galaxies and (U)LIRGs, respectively, we find the two galaxy populations separate into two distinct Σ_SFR versus {{{Σ }}_{{H2}}} relations. Finally, applying a continuously varying α_CO to our sample, we recover a single Σ_SFR-{{{Σ }}_{{H2}}} relation with slope of 1.60 ± 0.03. The Σ_SFR is a steeper function of total gas Σ_gas (molecular gas with atomic gas) than that of molecular gas {{{Σ }}_{{H2}}}, and are tighter among low-luminosity galaxies. We find no correlation between global surface densities of SFRs and atomic gas (H i).