Magnetic Field Properties inside the Jet of Mrk 421: Multiwavelength Polarimetry Including the Imaging X-ray Polarimetry Explorer

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 on 2022 December 6-8. We detected X-ray polarization of Mrk 421 with a degree of $Π_{\rm X}$=14$\pm$1$\%$ and an electric-vector position angle $ψ_{\rm X}$=107$\pm$3$^{\circ}$ in the 2-8 keV band. From the time variability analysis, we find a significant episodic variation in $ψ_{\rm X}$. During 7 months from the first IXPE pointing of Mrk 421 in 2022 May, $ψ_{\rm X}$ varied across the range of 0$^{\circ}$ to 180$^{\circ}$, while $Π_{\rm X}$ maintained similar values within $\sim$10-15$\%$. Furthermore, a swing in $ψ_{\rm X}$ in 2022 June was accompanied by simultaneous spectral variations. The results of the multiwavelength polarimetry show that the X-ray polarization degree was generally $\sim$2-3 times greater than that at longer wavelengths, while the polarization angle fluctuated. Additionally, based on radio, infrared, and optical polarimetry, we find that rotation of $ψ$ occurred in the opposite direction with respect to the rotation of $ψ_{\rm X}$ over longer timescales at similar epochs. 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. The accompanying spectral variation during the $ψ_{\rm X}$ rotation can be explained by a fluctuation in the physical conditions, e.g., in the energy distribution of relativistic electrons. The opposite rotation direction of $ψ$ 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.