  We fit the near-infrared to radio spectral energy distributions of 30
luminous and ultra-luminous infrared galaxies with pure starburst models or
models that include both starburst and AGN components to determine important
physical parameters for this population of objects. In particular we constrain
the optical depth towards the luminosity source, the star formation rate, the
star formation efficiency and the AGN fraction. We find that although about
half of our sample have best-fit models that include an AGN component, only 30%
have an AGN which accounts for more than 10% of the infrared luminosity,
whereas all have an energetically dominant starburst. Our derived AGN fractions
are generally in good agreement other measurements based in the mid-infrared
line ratios measured by Spitzer IRS, but lower than those derived from PAH
equivalent widths or the mid-infrared spectral slope. Our models determine the
mass of dense molecular gas via the extinction required to reproduce the SED.
Assuming that this mass is that traced by HCN, we reproduce the observed linear
relation between HCN and infrared luminosities found by Gao & Solomon. We also
find that the star formation efficiency, defined as the current star formation
rate per unit of dense molecular gas mass, is enhanced in the ULIRGs phase. If
the evolution of ULIRGs includes a phase in which an AGN contributes an
important fraction to the infrared luminosity, this phase should last an order
of magnitude less time than the starburst phase. Because the mass of dense
molecular gas which we derive is consistent with observations of the HCN
molecule,it should be possible to estimate the mass of dense, star-forming
molecular gas in such objects when molecular line data are not available.
