Testing the inverse-Compton catastrophe scenario in the intra-day variable blazar S5 0716+71 III. Rapid and correlated flux density variability from radio to sub-mm bands

Aims. The BL Lac object S5 0716+71 was observed in a global multi-frequency campaign to search for rapid and correlated flux density variability and signatures of an inverse-Compton (IC) catastrophe during the states of extreme apparent brightness temperatures. Methods. The observing campaign involved simultaneous ground-based monitoring at radio to IR/optical wavelengths and was centered around a 500-ks pointing with the INTEGRAL satellite (November 10-17, 2003). Here, we present the combined analysis and results of the radio observations, covering the cm- to sub-mm bands. This facilitates a detailed study of the variability characteristics of an inter- to intra-day variable IDV source from cm- to the short mm-bands. We further aim to constrain the variability brightness temperatures (T-B) and Doppler factors (delta) comparing the radio-bands with the hard X-ray emission, as seen by INTEGRAL at 3-200 keV. Results. 0716+714 was in an exceptionally high state and different (slower) phase of short-term variability, when compared to the past, most likely due to a pronounced outburst shortly before the campaign. The flux density variability in the cm- to mm-bands is dominated by a similar to 4 day time scale amplitude increase of up to similar to 35%, systematically more pronounced towards shorter wavelengths. The cross-correlation analysis reveals systematic time-lags with the higher frequencies varying earlier, similar to canonical variability on longer time-scales. The increase of the variability amplitudes with frequency contradicts expectations from standard interstellar scintillation (ISS) and suggests a source-intrinsic origin for the observed inter- day variability. We find an inverted synchrotron spectrum peaking near 90 GHz, with the peak flux increasing during the first 4 days. The lower limits to TB derived from the inter- day variations exceed the 1012 K IC-limit by up to 3-4 orders of magnitude. Assuming relativistic boosting, our different estimates of d yield robust and self-consistent lower limits of delta >= 5-33 - in good agreement with delta(VLBI) obtained from VLBI studies and the IC-Doppler factors delta(IC) > 14-16 obtained from the INTEGRAL data. Conclusions. The non-detection of S5 0716+714 with INTEGRAL in this campaign excludes an excessively high X-ray flux associated with a simultaneous IC catastrophe. Since a strong contribution from ISS can be excluded, we conclude that relativistic Doppler boosting naturally explains the apparent violation of the theoretical limits. All derived Doppler factors are internally consistent, agree with the results from different observations and can be explained within the framework of standard synchrotron-self-Compton (SSC) jet models of AGN.