The Properties of Massive, Dense, Clumps: Mapping Surveys of HCN and CS
  We have mapped over 50 massive, dense clumps with four dense gas tracers: HCN
J=1-0 and 3-2; and CS J=2-1 and 7-6 transitions. Spectral lines of optically
thin H^{13}CN 3-2 and C^{34}S 5-4 were also obtained towards the map centers.
These maps usually demonstrate single well-peaked distributions at our
resolution, even with higher J transitions. The size, virial mass, surface
density, and mean volume density within a well-defined angular size (FWHM) were
calculated from the contour maps for each transition. We found that transitions
with higher effective density usually trace the more compact, inner part of the
clumps but have larger linewidths, leading to an inverse linewidth-size
relation using different tracers. The mean surface densities are 0.29, 0.33,
0.78, 1.09 g cm^{-2} within FWHM contours of CS 2-1, HCN 1-0, HCN 3-2 and CS
7-6, respectively. We find no correlation of L_{IR} with surface density and a
possible inverse correlation with mean volume density, contrary to some
theoretical expectations. We see no evidence in the data for the relation
between L'_{mol} and mean density posited by modelers.
  The correlation between L'_{mol} and the virial mass is roughly linear for
each dense gas tracer. A nearly linear correlation was found between the
infrared luminosity and the line luminosity of all dense gas tracers for these
massive, dense clumps, with a lower cutoff in luminosity at L_{IR}=10^{4.5}
Lsun. The L_{IR}-L'_{HCN1-0} correlation agrees well with the one found in
galaxies. These correlations indicate a constant star formation rate per unit
mass from the scale of dense clumps to that of distant galaxies when the mass
is measured for dense gas. These results support the suggestion that starburst
galaxies may be understood as having a large fraction of gas in dense clumps.
