Star forming galaxies exhibit a remarkable correlation between their radio and infrared (IR) fluxes covering over four decades of IR flux intensities (Helou, Soifer, & Rowan-Robinson 1985, and references therein). The correlation results from the fact that the radio and infrared fluxes are different manifestations of the physical processes associated with the lifecycle of the same stellar objects (Helou & Bicay 1993, Lisenfeld, Völk, & Xu 1996). Massive stars heat the dust in the interstellar medium, form H II regions, and after their explosive deaths accelerate particles to cosmic ray energies, processes that, respectively, give rise to the observed galactic thermal infrared, radio thermal and synchrotron emission. The correlation may not hold for active galactic nuclei (AGN), in which the radio emission is not associated with the life cycle of massive stars.
If the radio-IR correlation for individual star forming galaxies in the local universe holds for all redshifts, then their cumulative contributions to the cosmic radio and infrared backgrounds should be related. Haarsma & Partridge (1998, hereafter HP98) used this correlation to estimate the intensity of the cosmic radio background (CRB) that can be attributed to star-forming galaxies. At the time of their analysis only the CIB at wavelengths larger than ~ 120 µm was definitively detected by the Diffuse Infrared Background Experiment (DIRBE) and Far Infrared Spectrophotometer (FIRAS) instruments on board the Cosmic Background Explorer (COBE) satellite (Hauser et al. 1998, Fixsen et al. 1998). For simplicity, HP98 assumed that all the sources giving rise to the CIB release their energy instantaneously at redshift z = 1. With this simple assumption about the formation epoch of the CIB, most of its detected intensity is determined by the ~ 80 µm spectral luminosity density of galaxies at the assumed redshift of its creation. Adopting a linear relation, S(20 cm) S(80 µm), between the radio and IR fluxes from star-forming galaxies, HP98 derived their contribution to the 40 cm CRB intensity. To compare this CRB estimate to the observed Bridle (1967) datum point at 178 MHz, HP98 adopted a -0.7 power law spectrum for the radio sources. They derived a brightness temperature of Tcrb(178 MHz) 15 K, about half the value inferred from the observations. HP98 attributed the remaining CRB intensity to the contribution of AGN which do not contribute significantly to the CIB (Barger et al. 2001, Fadda et al. 2001).
In this paper we extend the analysis of HP98 to the more general case in which the cosmic star formation rate (CSFR) of the CIB sources is a general function of redshift. First, in Section 2, we briefly review the various presentations of the radio-IR correlation and rederive this correlation in terms of the galaxies' 8 - 1000 µm IR fluxes. Previous presentations expressed this correlation as a function of only the far-IR (FIR) fluxes, derived from the galaxies 60 and 100 µm detections by the Infrared Astronomy Satellite (IRAS). Such a correlation may systematically underestimate the radio flux from more luminous star forming galaxies in which an increasing fraction of the IR flux may be emitted in the shorter (12 and 25 µm) IRAS bands. We then explore the functional form of the radio-IR correlation. HP98 adopted a linear relation between the radio and IR fluxes, which may not be an accurate fit to the data. Significant deviations from linearity will require detailed knowledge of the evolution of the galaxies' IR luminosity function with redshift. However, we argue that the data are consistent with a linear relation over most of the range of the IR luminosities that contribute to the local IR luminosity density. In Section 3 we first derive the expressions for the CIB and CRB intensities produced by star-forming galaxies for a general power-law correlation between their radio and IR fluxes. We then derive a simple analytic expression relating these background intensities when their radio-IR correlation is linear. In Section 4 we apply these results to different cosmic star formation histories with their associated CIB intensity limits. A brief summary of our paper is presented in Section 5.