Dense molecular gas star formation law in Galactic clumps: an extensive survey of HCN (4-3) and CS (7-6) with the ASTE telescope

We observed 146 Galactic clumps in HCN (4-3) and CS (7-6) with the Atacama Submillimeter Telescope Experiment (ASTE) 10-m telescope. The star formation rates probed by total infrared luminosities (LTIR) are linearly correlated with clump masses (Mclump) for those clumps with LTIR larger than 10^3 Lsun, leading to a constant gas depletion time of ~107 Myr. The correlations between LTIR and molecular line luminosities (Lmol) of HCN (4-3) and CS (7-6) are tight and sublinear extending down to clumps with LTIR 10^3 Lsun. These correlations become linear when extended to external galaxies. A bimodal behavior in the LTIR-Lmol correlations was found for clumps with different dust temperature, luminosity-to-mass ratio, and sigma_line-to-sigma_vir ratio. Such bimodal behavior may be due to evolutionary effects. The slopes of LTIR-Lmol 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-Lmol and LTIR-Lmol relations.