tokens: from September 22. Additionally, in the image related to the observation from September 22, there is a radial polarization pattern across the Southern half of the core region. This suggests that the magnetic field B is roughly circular and centred on the brightness peak of the core, as one might expect from a helical field when one views it down the axis. This polarization pattern remained through 2016 March. The γ-ray LC from the Fermi -LAT and X-ray LC from the Swift -BAT do not show any obvious flux enhancement during the time of the radio flaring activity, although they show some activity (both BAT and LAT) about 40 d before the radio flare. During this time, there were no optical or VHE observations because of the Sun. Figure 4. A sequence of total (contours) and polarized (colour scale) intensity images of Mrk 421 at 43 GHz obtained with the VLBA. The image is convolved with an FWHM of 0.24 × 0.15 mas 2 along PA = −10°. The global total intensity peak is 329 mJy/beam, and the contours 0.35, 0.70, 1.4, etc. up to 89.6 per cent of the global intensity peak. The colour scale is the polarized intensity, and the black line segments within each image show the direction of the polarization electric vector, with the length of the segment being proportional to the polarized intensity values. The black vertical line indicates the position of the core. See Section 3.2 for details. The low polarization fraction at 43 GHz on 2015 August 1 implies that the magnetic field was very highly disordered in the core at this epoch. A radial polarization pattern, as measured at 43 GHz on 2015 September 22, can result from turbulent plasma flowing across a conical standing shock, as found in the simulations of Cawthorne, Jorstad Marscher ( 2013 ) and Marscher ( 2016 ). However, in such a scenario the linear polarization pattern is always present, since it is created by the partial ordering of the magnetic field by the shock front. Periods of polarization across the entire core should not be observed. An alternative picture ascribes the radial polarization pattern to the circular appearance of a magnetic field with a helical or toroidal geometry that is viewed within ∼0.2/Γ radians of the axis of the jet (Marscher et al. 2002 ), where Γ is the bulk Lorentz factor of the emitting plasma. In this case, the ratio of the observed polarization measured in the image, , to the value for a uniform magnetic field direction, , 6 implies that the helical field is superposed on a highly disordered field component that is ∼10 times stronger. If the helical field becomes disrupted by a current-driven kink instability, particle acceleration could cause a flare (Nalewajko 2017 ; Zhang et al. 2017 ; Alves, Zrake Fiuza 2018 ). The polarization pattern then becomes complex, with the possibility that the polarization becomes very low at some point (Dong, Zhang Giannios 2020 ). Such a flare would be expected to start at X-ray and VHE γ-ray energies upstream of the core, then
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