Testing the inverse-Compton catastrophe scenario in the intra-day variable blazar S5 0716+71: II. A search for intra-day variability at millimetre wavelengths with the IRAM 30 m telescope

We report on a densely time sampled polarimetric flux density monitoring of the BL Lac object S5 0716+71 at 86 GHz and 229 GHz with the IRAM 30 m telescope within a coordinated broad spectral band campaign, centred around an INTEGRAL observation during November 10 to 16, 2003. Our aim was to search for signatures of inverse-Compton catastrophes. At 86 GHz, making use of a new calibration strategy, we reach a relative rms accuracy of the flux density measurements of 1.2%. At this frequency, S5 0716+71 showed no intra-day variability, but showed remarkable inter-day variability with a flux density increase of 34% during the first four observing days, which can not be explained by source extrinsic causes. The 86 GHz linear polarization fraction of S5 0716+71 was unusually large 15.0+-1.8%. Inter-day variability in linear polarization at 86 GHz, with significance level >~95%; sigma_P/<P>=15% and sigma_chi=6 deg., was also observed. From the emission variations at the synchrotron turnover frequency (~86 GHz) we compute an apparent brightness temperature T_B,app>1.4x10^14K at a redshift of 0.3, which exceeds by two orders of magnitude the inverse-Compton limit. A relativistic correction for T_B,app with a Doppler factor delta > 7.8 brings the observed brightness temperature down to the inverse Compton limit. A more accurate lower limit of delta > 14.0, is obtained from the comparison of the 86 GHz synchrotron flux density and the upper limits for the synchrotron self-Compton flux density obtained from the INTEGRAL observations. The relativistic beaming of the emission by this high Doppler factor explains the non-detection of catastrophic inverse-Compton avalanches by INTEGRAL.