2011MNRAS.413..852G

We study the correlation between the γ-ray flux (F_γ), averaged over the first 11 months of the Fermi survey and integrated above 100 MeV, and the radio flux density (F_r at 20 GHz) of Fermi sources associated with a radio counterpart in the 20-GHz Australia Telescope Compact Array (AT20G) survey. Considering the blazars detected in both bands, the correlation is highly significant and has the form F_γ∝F^0.85±0.04_r, similar to BL Lacertae objects and flat-spectrum radio quasars. However, only a small fraction (∼1/15) of the AT20G radio sources with flat radio spectra are detected by Fermi. To understand if this correlation is real, we examine the selection effects introduced by the flux limits of both the radio and the γ-ray surveys, and the importance of variability of the γ-ray flux. After accounting for these effects, we find that the radio-γ-ray flux correlation is real, but its slope is steeper than the observed one, that is, F_γ∝F^δ_r with δ in the range 1.25-1.5. The observed F_γ-F_r correlation and the fraction of radio sources detected by Fermi are reproduced assuming a long-term γ-ray flux variability, following a lognormal probability distribution with standard deviation σ ≥ 0.5 (corresponding to F_γ varying by at least a factor of 3). Such a variability is compatible, even if not necessarily equal, with what is observed when comparing, for the sources in common, the EGRET and the Fermi γ-ray fluxes (even if the Fermi fluxes are averaged over ∼1 yr). Another indication of variability is the non-detection of 12 out of 66 EGRET blazars by Fermi, despite its higher sensitivity. We also study the strong linear correlation between the γ-ray and the radio luminosity of the 144 AT20G-Fermi associations with known redshift and show, through partial correlation analysis, that it is statistically robust. Two possible implications of these correlations are discussed: the contribution of blazars to the extragalactic γ-ray background and the prediction of blazars that might undergo extremely high states of γ-ray emission in the next few years.