The radio/gamma-ray connection in Fermi-blazars

We study the correlation between the gamma-ray flux F_g, averaged over the first 11 months of 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 AT20G survey. Considering the blazars detected in both bands, the correlation is highly significant and it is F_g~F_r^0.85+-0.04, similar for BL Lac and FSRQ sources. However, only a small fraction (~1/15) of the AT20G radio sources with flat radio spectrum, are detected by Fermi. To understand if this correlation is real, we examine the selection effects introduced by the flux limits of the radio and gamma-ray surveys, and the importance of variability of the gamma-ray flux. We find that the radio/gamma-ray flux correlation is real, but its slope is steeper than the observed one, i.e. F_g~F_r^delta with delta in the range 1.25-1.5. The observed F_g-F_r correlation and the fraction of radio sources detected by Fermi is reproduced assuming a long term gamma-ray flux variability following a log-normal probability distribution with standard deviation sigma>0.5 (corresponding to F_g varying by at least a factor 3). Such a variability is compatible with what observed when comparing, for the sources in common, the EGRET and the Fermi gamma-ray fluxes (even if the Fermi fluxes are averaged over ~1 year). 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 gamma-ray and the radio luminosity of the 144 AT20G-Fermi associations with known redshift and show that it is statistically robust. Two possible implications of these correlations are discussed: the contribution of blazars to the extragalactic gamma-ray background and the prediction of blazars that might undergo extremely high states of gamma-ray emission in the next years.