STAR FORMATION LAWS in BOTH GALACTIC MASSIVE CLUMPS and EXTERNAL GALAXIES: EXTENSIVE STUDY with DUST CONINUUM, HCN (4-3), and CS (7-6)

We observed 146 Galactic clumps in HCN (4-3) and CS (7-6) with the Atacama Submillimeter Telescope Experiment 10 m telescope. A tight linear relationship between star formation rate and gas mass traced by dust continuum emission was found for both Galactic clumps and the high redshift (z > 1) star forming galaxies (SFGs), indicating a constant gas depletion time of similar to 100 Myr for molecular gas in both Galactic clumps and high z SFGs. However, low z galaxies do not follow this relation and seem to have a longer global gas depletion time. The correlations between total infrared luminosities (L-TIR) and molecular line luminosities (L-mol') of HCN (4-3) and CS (7-6) are tight and sublinear extending down to clumps with L-TIR similar to 10(3) L-circle dot. These correlations become linear when extended to external galaxies. A bimodal behavior in the L-TIR-L-mol' correlations was found for clumps with different dust temperature, luminosity-to-mass ratio, and sigma(line)/sigma(vir). Such bimodal behavior may be due to evolutionary effects. The slopes of L-TIR-L-mol' correlations become more shallow as clumps evolve. We compared our results with lower J transition lines in Wu et al. (2010). The correlations between clump masses and line luminosities are close to linear for low effective excitation density tracers but become sublinear for high effective excitation density tracers for clumps with L-TIR larger than L-TIR similar to 10(4.5) L-circle dot. High effective excitation density tracers cannot linearly trace the total clump masses, leading to a sublinear correlations for both M-clump-L-mol' and L-TIR-L-mol' relations.