Interpreting the time variable RM observed in the core region of the TeV blazar Mrk 421

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In this work we interpret and discuss the time variable rotation measure (RM) found, for the first time over a 1-yr period, in the core region of a blazar. These results are based on a one-year, multi-frequency (15, 24, and 43 GHz) Very Long Baseline Array (VLBA) monitoring of the TeV blazar Markarian 421 (Mrk 421). We investigate the Faraday screen properties and its location with respect to the jet emitting region. Given that the 43 GHz radio core flux density and the RM time evolution suggest a similar trend, we explore the possible connection between the RM and the accretion rate. Among the various scenarios that we explore, the jet sheath is the most promising candidate for being the main source of Faraday rotation. During the one-year observing period the RM trend shows two sign reversals, which may be qualitatively interpreted within the context of the magnetic tower models. We invoke the presence of two nested helical magnetic fields in the relativistic jet with opposite helicities, whose relative contribution produce the observed RM values. The inner helical field has the poloidal component ($B_{\rm p}$) oriented in the observer's direction and produces a positive RM, while the outer helical field, with $B_{\rm p}$ in the opposite direction, produces a negative RM. We assume that the external helical field dominates the contribution to the observed RM, while the internal helical field dominates when a jet perturbation arises during the second observing epoch. Being the intrinsic polarization angle parallel to the jet axis, a pitch angle of the helical magnetic field $\phi\gtrsim 70^\circ$ is required. Additional scenarios are also considered to explain the observed RM sign reversals.