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.
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