In this paper we derived an analytical expression for the correlation between the CIB and CRB intensities as a function of , the spectral index of the radio sources [see eq. (15)]. This correlation is summarized for select galaxy number counts and CIB models in Table 1. Several conclusions can be drawn from a simple examination of the table: (1) the minimal CSFR,defined by the lower envelope of the data, is definitely ruled out as a viable representation of the CSFR since it falls short of providing the observed intensity of the CIB. The maximal CSFR,defined by the upper envelope of the data, is consistent with the CIB and CRB limits only for values of 0.8; (2) the baseline model of Malkan & Stecker is barely consistent with the lower limit on the CIB intensity and consequently, for = 0.7, it requires AGN to contribute more than 70% of the 178 MHz background; (3) for = 0.9, all models, with the exception of those of Malkan & Stecker and Chary & Elbaz, predict CRB temperatures that are 2 above the observed value. The latter two models leave no room for a significant contribution of AGN to the CRB; (4) for values of 0.6-0.8, the calculated Tcrb / ICIB ratio is lower than the nominal observed ratios, suggesting that ~ 60 to 20% of the CRB at 178 MHz must arise from AGN, regardles of the radiative history of star-forming galaxies.
All conclusions listed above assume that the radio-IR correlation observed in the local universe can extended to galaxies at all redshifts. Future observations will provide a larger sample of galaxies with which to study the radio-IR correlation and place tighter limits on the CIB, advances that will lead to a better understanding of the relative contribution of star-forming galaxies and AGN to the CRB.
Acknowledgement: We thank Rick Arendt for useful discussions and his insightful comments on an earlier version of the manuscript. ED acknowledges NASA's Astrophysics Theory Program NRA 99-OSS-01 for support of this work. MB's summer student internship at NASA/GSFC was supported by the "Research Opportunities for Undergraduates in the Laboratory for Astronomy and Solar Physics" program.