2006ApJ...638..138W

We model the constraints set on the evolution of dusty starburst galaxies by the current deep extragalactic surveys performed in the far-infrared with Spitzer, and at radio wavelengths with the VLA. Our models fit the number counts in all the available spectral bands well and also provide a reasonably close match to the redshift distribution of the Spitzer detections. We find (1) dusty starburst galaxies with infrared burst phases triggered by galactic interactions at redshift z∼1-2 are good candidates to fit the Spitzer results at 24, 70, and 160 µm, assuming plausible strengths for the PAH features for the infrared luminous sources. An Arp 220-like spectral energy distribution (SED) for ultraluminous infrared galaxies (ULIRGs) of L_ir>10¹² L_☉and one like that of M82 for luminous infrared galaxies (LIRGs) of L_ir∼10¹¹-10¹² L_☉give a successful fit to the Spitzer 24 µm and ISOCAM 15 µm number counts at flux levels of S_ν<1 mJy. (2) The strong evolution of the number density of the ULIRGs from redshift z∼0 to ∼1 predicted by our models is consistent with the current deep 1.4 GHz radio surveys and accounts for the upturn in the 1.4 GHz differential counts at the submillijansky flux level. (3) Comparison with number counts at near-infrared bands, as well as the background measurements using DIRBE and 2MASS, shows that only a fraction of the stellar mass in the universe is included in our models of dusty starburst mergers at z∼1-2.