The Millimeter-Radio Emission of BL Lacertae During Two gamma-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.
