Modelling the evolution of dusty starburst galaxies in multi-band deep surveys

We model the constraints set on the evolution of dusty starburst galaxies by the current deep extragalactic surveys performed in the far-infrared with $\it Spitzer$, 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 $\it Spitzer$ detections. We find: 1.) dusty starburst galaxies with infrared burst phases triggered by galactic interactions at redshift $z \sim 1-2$ are good candidates to fit the $\it Spitzer$ results at $24\mu m$, $70 \mu m$ and $160 \mu m$, assuming plausible strengths for the PAH features for the infrared luminous sources. An Arp220-like spectral energy distribution (SED) for Ultraluminous Infrared Galaxies (ULIGs) of $L_{\rm ir}>10^{12} L_{\odot}$ and one like that of M82 for Luminous Infrared Galaxies (LIGs) of $L_{\rm ir}\sim 10^{11-12} L_{\odot}$ give a successful fit to the $\it Spitzer$ $24\mu m$ and $\rm ISOCAM 15\mu m$ number counts at flux levels of $S_{\nu}< 1 mJy$; 2.) the strong evolution of the number density of the ULIGs from redshift $z\sim 0$ to $\sim 1$ predicted by our models is consistent with the current deep $\rm 1.4 GHz$ radio surveys and accounts for the upturn in the $\rm 1.4 GHz$ differential counts at the sub-mJy flux level; and 3.) comparing 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 $z \sim 1 - 2$.