Radio wavelength constraints on the sources of the far-infrared background

The cosmic far-infrared background detected recently by the COBE-DIRBE team is presumably due, in large part, to the far-infrared (FIR) emission from all galaxies. We take the well-established correlation between FIR and radio luminosity for individual galaxies and apply it to the FIR background. we find that these sources make up about half of the extragalactic radio background, the other half being due to active galactic nuclei (AGNs). This is in agreement with other radio observations, which leads us to conclude that the FIR-radio correlation holds well for the very faint sources making up the FIR background and that the FIR background is indeed due to star formation activity (not AGNs or other possible sources). If these star-forming galaxies have a radio spectral index between 0.4 and 0.8 and make up 40%-60% of the extragalactic radio background, we find that they have redshifts between roughly 1 and 2, which is in agreement with recent estimates by Madau et al. of the redshift of peak star formation activity. We compare the observed extragalactic radio background to the integral over the log N- log S curve for star-forming radio sources and find that the slope of the curve must change significantly below about 1 mu Jy. At 1 mu Jy, the faint radio source counts predict about 25 sources per square arcminute, and these will cause the Space Infrared Telescope Facility to be confusion limited at 160 mu m.