The TeV blazar Markarian 421 at the highest spatial resolution

Context. High-resolution radio observations allow us to directly image the innermost region of active galactic nuclei. The Very Long Baseline Array (VLBA) data analyzed in this paper were obtained during a multiwavelength (MWL) campaign, carried out in 2011, from radio to very high energy gamma rays, on the TeV blazar Markarian 421 (Mrk 421). Aims. Our aim was to obtain information on the jet structure in Mrk 421 during the MWL campaign at the highest possible angular resolution and with high temporal frequency observations, in order to compare structural and flux density evolution with higher energy variations. Methods. We consider data obtained with the VLBA at 43 GHz through two sets of observations: one is part of a dedicated multi-frequency monitoring campaign, in which we observed Mrk 421 once a month from January to December 2011 at three frequencies; the other is extracted from the Boston University monitoring program, which observes 34 blazars at 43 GHz about once per month. We model-fit the data in the visibility plane, study the proper motion of jet components, the light curve, and the spectral index of the jet features. We compare the radio data with optical light curves obtained at the Steward Observatory, considering also the optical polarization information. Results. Mrk 421 has a bright nucleus and a one-sided jet extending towards the north-west for a few parsecs. The model-fits show that brightness distribution is well described using 6-7 circular Gaussian components, four of which are reliably identified at all epochs; all components are effectively stationary except for component D, at similar to 0.4 mas from the core, whose motion is, however, subluminal. Analysis of the light curve shows two different states, with the source being brighter and more variable in the first half of 2011 than in the second half. The highest flux density is reached in February. A comparison with the optical data reveals an increase of the V magnitude and of the fractional polarization simultaneous with the enhancement of the radio activity.