Very Long Baseline polarimetry and the gamma-ray connection in Markarian 421 during the broadband campaign in 2011

We analyzed data in polarized intensity obtained with the Very Long Baseline Array (VLBA) at twelve epochs (one observation per month from January to December 2011) at 15, 24, and 43 GHz. For the absolute orientation of the electric vector position angles (EVPA) we used the D-terms method. We also used gamma-ray data from the Fermi Large Area Telescope on weekly time bins throughout 2011. The source shows polarized emission, and its properties vary with time, frequency, and location along the jet. The core mean polarization fraction is generally between 1% and 2%, with a 4% peak at 43 GHz in March; the polarization angle is variable, mainly at 15 GHz, where it changes frequently, and less so at 43 GHz, where it oscillates in the range 114 - 173 deg. The jet polarization properties are more stable, with a fractional polarization of around 16% and a polarization angle nearly perpendicular to the jet axis. The average flux and photon index at gamma-ray energies are (17.7+-0.5)x10^8 ph cm^-2 s^-1 and the photon index is 1.77+-0.02. The gamma-ray light curve shows variability, with a main peak that appears to be associated with the peak in the core polarized emission at 43 GHz, as well as with the total intensity light curve. A discrete correlation function analysis yields a correlation coefficient of 0.54 at zero delay, with a significance level above 99.7%. We accurately determine the polarization properties of Mrk 421, both in the core and in the jet region. The radio and gamma-ray light curves are correlated. The observed EVPA variability at 15 GHz is partly due to opacity and partly to a variable Faraday rotation effect. To explain the residual variability of the intrinsic polarization angle and the low degree of polarization in the core region, we invoke a blend of variable cross-polarized subcomponents with different polarization properties within the beam.