The Millimeter-Radio Emission of BL Lacertae During Two γ-ray Outbursts

We present a study of the inexplicit connection between radio jet activity and gamma-ray emission of BL Lacertae (BL Lac; 2200+420). We analyze the long-term millimeter activity of BL Lac via interferometric observations with the Korean VLBI Network (KVN) obtained at 22, 43, 86, and 129 GHz simultaneously over three years (from January 2013 to March 2016); during this time, two gamma-ray outbursts (in November 2013 and March 2015) can be seen in gamma-ray light curves obtained from Fermi observations. The KVN radio core is optically thick at least up to 86 GHz; there is indication that it might be optically thin at higher frequencies. To first order, the radio light curves decay exponentially over the time span covered by our observations, with decay timescales of 411+/-85 days, 352+/-79 days, 310+/-57 days, and 283+/-55 days at 22, 43, 86, and 129 GHz, respectively. Assuming synchrotron cooling, a cooling time of around one year is consistent with magnetic field strengths B~2microT and electron Lorentz factors gamma~10,000. Taking into account that our formal measurement errors include intrinsic variability and thus over-estimate the statistical uncertainties, we find that the decay timescale tau scales with frequency nu like tau~nu^{-0.2}. This relation is much shallower than the one expected from opacity effects (core shift), but in agreement with the (sub-)mm radio core being a standing recollimation shock. We do not find convincing radio flux counterparts to the gamma$ray outbursts. The spectral evolution is consistent with the `generalized shock model' of Valtaoja et al. (1992). A temporary increase in the core opacity and the emergence of a knot around the time of the second gamma-ray event indicate that this gamma-ray outburst might be an `orphan' flare powered by the `ring of fire' mechanism.