Magnetic field properties inside the jet of Mrk 421

Aims. We aim to probe the magnetic field geometry and particle acceleration mechanism in the relativistic jets of supermassive black holes.Methods. We conducted a polarimetry campaign from radio to X-ray wavelengths of the high-synchrotron-peak (HSP) blazar Mrk 421, including Imaging X-ray Polarimetry Explorer (IXPE) measurements from 2022 December 6-8. During the IXPE observation, we also monitored Mrk 421 using Swift-XRT and obtained a single observation with XMM-Newton to improve the X-ray spectral analysis. The time-averaged X-ray polarization was determined consistently using the event-by-event Stokes parameter analysis, spectropolarimetric fit, and maximum likelihood methods. We examined the polarization variability over both time and energy, the former via analysis of IXPE data obtained over a time span of 7 months.Results. We detected X-ray polarization of Mrk 421 with a degree of Pi(X) = 14 +/- 1% and an electric-vector position angle psi(X) = 107 +/- 3 degrees in the 2-8 keV band. From the time variability analysis, we find a significant episodic variation in psi(X). During the 7 months from the first IXPE pointing of Mrk 421 in 2022 May, psi(X) varied in the range 0 degrees to 180 degrees, while Pi(X) remained relatively constant within similar to 10-15%. Furthermore, a swing in psi(X) in 2022 June was accompanied by simultaneous spectral variations. The results of the multiwavelength polarimetry show that Pi(X) was generally similar to 2-3 times greater than Pi at longer wavelengths, while psi fluctuated. Additionally, based on radio, infrared, and optical polarimetry, we find that the rotation of psi occurred in the opposite direction with respect to the rotation of psi(X) and over longer timescales at similar epochs.Conclusions. The polarization behavior observed across multiple wavelengths is consistent with previous IXPE findings for HSP blazars. This result favors the energy-stratified shock model developed to explain variable emission in relativistic jets. We considered two versions of the model, one with linear and the other with radial stratification geometry, to explain the rotation of psi(X). The accompanying spectral variation during the psi(X) rotation can be explained by a fluctuation in the physical conditions, for example in the energy distribution of relativistic electrons. The opposite rotation direction of psi between the X-ray and longer wavelength polarization accentuates the conclusion that the X-ray emitting region is spatially separated from that at longer wavelengths. Moreover, we identify a highly polarized knot of radio emission moving down the parsec-scale jet during the episode of psi(X) rotation, although it is unclear whether there is any connection between the two events.