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.
