Star formation laws in both Galactic massive clumps and external galaxies: An extensive study with dust continuum, 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 (ASTE) 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 ~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 LTIR~10^{3} L_sun. These correlations become linear when extended to external galaxies. A bimodal behavior in the LTIR--L'mol correlations was found for clumps with different dust temperature, luminosity-to-mass ratio, and sigmaline/sigmavir. Such bimodal behavior may be due to evolutionary effects. The slopes of LTIR--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 LTIR larger than LTIR~10^4.5 Lsun. High effective excitation density tracers cannot linearly trace the total clump masses, leading to a sublinear correlations for both Mclump-L'mol and LTIR-L'mol relations.