  We report single-dish multi-transition measurements of the 12^CO, HCN, and
HCO^+ molecular line emission as well as HNC J=1-0 and HNCO in the two
ultraluminous infra-red galaxies Arp220 and NGC6240. Using this new molecular
line inventory, in conjunction with existing data in the literature, we
compiled the most extensive molecular line data sets to date for such galaxies.
The many rotational transitions, with their different excitation requirements,
allow the study of the molecular gas over a wide range of different densities
and temperatures with significant redundancy, and thus allow good constraints
on the properties of the dense gas in these two systems. The mass (~(1-2) x
10^10 Msun) of dense gas (>10^5-6 cm^-3) found accounts for the bulk of their
molecular gas mass, and is consistent with most of their IR luminosities
powered by intense star bursts while self-regulated by O,B star cluster
radiative pressure onto the star-forming dense molecular gas. The highly
excited HCN transitions trace a gas phase ~(10-100)x denser than that of the
sub-thermally excited HCO^+ lines (for both galaxies). These two phases are
consistent with an underlying density-size power law found for Galactic GMCs
(but with a steeper exponent), with HCN lines tracing denser and more compact
regions than HCO^+. Whether this is true in IR-luminous, star forming galaxies
in general remains to be seen, and underlines the need for observations of
molecular transitions with high critical densities for a sample of bright
(U)LIRGs in the local Universe -- a task for which the HI-FI instrument on
board Herschel is ideally suited to do.
