Abstract 

   The global star formation (SF) law — the relation between star-forming gas and SF rate (SFR) — is reexamined in a large sample of 181 local star-forming galaxies with infrared luminosities (SFR) spanning almost five orders of

magnitude. The surface density of dense molecular gas (as traced by HCN) has the tightest and linear correlation with that of SFR. The ΣSFR is a steeper function of the total gas Σgas (molecular gas with atomic gas) than that of

molecular gas ΣH2. We further show that the SFR and a variety of dense gas tracers (e.g., HCN, CS, their high-J and high-J CO) are all linearly correlated for both the Galactic dense cores in our Milky Way and star-forming galaxies near and far. This has immediate implications on the modes of SF in galaxies because the dense cores are the sites of the active SF, and thus the basic units in contributing to the SF. The SFR should depend linearly upon the mass of dense molecular gas (the SF law!). These ground-based observations of last decade and recent Herschel results highlight what the ALMA is delivering on the studies of "SF laws" across large redshift ranges and on most SF scales.