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. The source was observed with the IRAM 30 m telescope at Pico Veleta within a coordinated multi-frequency observing campaign, which was centred around a 500 ks INTEGRAL observation during November 10 to 16, 2003. The aim of this campaign was to search for signatures of inverse-Compton catastrophes through the observation of the broad-band variability of the source. At 86 GHz, 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 cannot be explained by source extrinsic causes. At this frequency, making use of a new calibration strategy, we reach a relative rms accuracy of the flux density measurements of 1.2%. Although the flux density variability at 229 GHz was consistent with that at 86 GHz, the larger measurement errors at 229 GHz do not allow us to detect, with high confidence, inter-day variations at this frequency. At 86 GHz, the 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}%; σ_P/< P>=15% and σ_χ=6°, was observed during the first four observing days. From the total flux density variations at the synchrotron turnover frequency (∼ 86 {GHz}) we compute an apparent brightness temperature T_{B}^{{app}} > 1.4 × {10}¹⁴ K 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 δ > 7.8 brings the observed brightness temperature down to the inverse Compton limit. A more accurate lower limit of δ > {{14.0}}, consistent with previous estimates from VLBI observations, 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.