Estimating the Jet Power of Mrk\,231 During the 2017-2018 Flare

Long-term 17.6~GHz radio monitoring of the broad absorption line quasar, Mrk\,231, detected a strong flare in late 2017. This triggered four epochs of Very Long Baseline Array (VLBA) observations from 8.4~GHz to 43~GHz over a 10-week period as well as an X-ray observation with NuSTAR. This was the third campaign of VLBA monitoring that we have obtained. The 43~GHz VLBA was degraded in all epochs with only 7 of 10 antennas available in three epochs and 8 in the first epoch. However, useful results were obtained due to a fortuitous capturing of a complete short 100~mJy flare at 17.6~GHz: growth and decay. This provided useful constraints on the physical model of the ejected plasma that were not available in previous campaigns. We consider four classes of models, discrete ejections (both protonic and positronic) and jetted (protonic and positronic). The most viable model is a "dissipative bright knot" in a faint background leptonic jet with an energy flux $\sim10^{43}$ ergs/sec. Inverse Compton scattering calculations (based on these models) in the ambient quasar photon field explains the lack of a detectable increase in X-ray luminosity measured by NuSTAR. We show that the core (the bright knot) moves towards a nearby secondary at $\approx 0.97$c. The background jet is much fainter. Evidently, the high frequency VLBA core does not represent the point of origin of blazar jets, in general, and optical depth "core shift" estimates of jet points of origin can be misleading.