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.