Time correlation between the radio and gamma-ray activity in blazars and the production site of the gamma-ray emission

In order to determine the location of the gamma-ray emission site in blazars, we investigate the time-domain relationship between their radio and gamma-ray emission. Light curves for the brightest detected blazars from the first 3 yr of the mission of the Fermi Gamma-ray Space Telescope are cross-correlated with 4 yr of 15 GHz observations from the Owens Valley Radio Observatory 40 m monitoring programme. The large sample and long light-curve duration enable us to carry out a statistically robust analysis of the significance of the cross-correlations, which is investigated using Monte Carlo simulations including the uneven sampling and noise properties of the light curves. Modelling the light curves as red noise processes with power-law power spectral densities, we find that only one of 41 sources with high-quality data in both bands shows correlations with significance larger than 3 sigma (AO 0235+164), with only two more larger than even 2.25 sigma (PKS 1502+106 and B2 2308+34). Additionally, we find correlated variability in Mrk 421 when including a strong flare that occurred in 2012 July-September. These results demonstrate very clearly the difficulty of measuring statistically robust multiwavelength correlations and the care needed when comparing light curves even when many years of data are used. This should be a caution. In all four sources, the radio variations lag the gamma-ray variations, suggesting that the gamma-ray emission originates upstream of the radio emission. Continuous simultaneous monitoring over a longer time period is required to obtain high significance levels in cross-correlations between gamma-ray and radio variability in most blazars.