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Aims. We present the first multiwavelength study of Mrk 501 that contains simultaneous very-high-energy (VHE) γ-ray observations and X-ray polarization measurements from the Imaging X-ray Polarimetry Explorer (IXPE). Methods. We used radio-to-VHE data from a multiwavelength campaign carried out between March 1, 2022, and July 19, 2022 (MJD 59639 to MJD 59779). The observations were performed by MAGIC, Fermi-LAT, NuSTAR, Swift (XRT and UVOT), and several other instruments that cover the optical and radio bands to complement the IXPE pointings. We characterized the dynamics of the broadband emission around the X-ray polarization measurements through its multiband fractional variability and correlations, and compared changes observed in the polarization degree to changes seen in the broadband emission using a multi-zone leptonic scenario. Results. During the IXPE pointings, the VHE state is close to the average behavior, with a 0.2–1 TeV flux of 20%–50% of the emission of the Crab Nebula. Additionally, it shows low variability and a hint of correlation between VHE γ-rays and X-rays. Despite the average VHE activity, an extreme X-ray behavior is measured for the first two IXPE pointings, taken in March 2022 (MJD 59646 to 59648 and MJD 59665 to 59667), with a synchrotron peak frequency > 1 keV. For the third IXPE pointing, in July 2022 (MJD 59769 to 59772), the synchrotron peak shifts toward lower energies and the optical/X-ray polarization degrees drop. All three IXPE epochs show an atypically low Compton dominance in the γ-rays. The X-ray polarization is systematically higher than at lower energies, suggesting an energy stratification of the jet. While during the IXPE epochs the polarization angles in the X-ray, optical, and radio bands align well, we find a clear discrepancy in the optical and radio polarization angles in the middle of the campaign. Such results further support the hypothesis of an energy-stratified jet. We modeled broadband spectra taken simultaneous to the IXPE pointings, assuming a compact zone that dominates in the X-rays and the VHE band, and an extended zone stretching farther downstream in the jet that dominates the emission at lower energies. NuSTAR data allow us to precisely constrain the synchrotron peak and therefore the underlying electron distribution. The change between the different states observed in the three IXPE pointings can be explained by a change in the magnetization and/or the emission region size, which directly connects the shift in the synchrotron peak to lower energies with the drop in the polarization degree. [ABSTRACT FROM AUTHOR]

Aims. The BL Lac 1ES 2344+514 is known for temporary extreme properties characterised by a shift of the synchrotron spectral energy distribution (SED) peak energy νsynch, p above 1 keV. While those extreme states have only been observed during high flux levels thus far, additional multi-year observing campaigns are required to achieve a coherent picture. Here, we report the longest investigation of the source from radio to very high energy (VHE) performed so far, focussing on a systematic characterisation of the intermittent extreme states. Methods. We organised a monitoring campaign covering a 3-year period from 2019 to 2021. More than ten instruments participated in the observations in order to cover the emission from radio to VHE. In particular, sensitive X-ray measurements by XMM-Newton, NuSTAR, and AstroSat took place simultaneously with multi-hour MAGIC observations, providing an unprecedented constraint of the two SED components for this blazar. Results. While our results confirm that 1ES 2344+514 typically exhibits νsynch, p > 1 keV during elevated flux periods, we also find periods where the extreme state coincides with low flux activity. A strong spectral variability thus happens in the quiescent state, and is likely caused by an increase in the electron acceleration efficiency without a change in the electron injection luminosity. On the other hand, we also report a strong X-ray flare (among the brightest for 1ES 2344+514) without a significant shift of νsynch, p. During this particular flare, the X-ray spectrum is among the softest of the campaign. It unveils complexity in the spectral evolution, where the common harder-when-brighter trend observed in BL Lacs is violated. By combining Swift-XRT and Swift-UVOT measurements during a low and hard X-ray state, we find an excess of the UV flux with respect to an extrapolation of the X-ray spectrum to lower energies. This UV excess implies that at least two regions significantly contribute to the infrared/optical/ultraviolet/X-ray emission. Using the simultaneous MAGIC, XMM-Newton, NuSTAR, and AstroSat observations, we argue that a region possibly associated with the 10 GHz radio core may explain such an excess. Finally, we investigate a VHE flare, showing an absence of simultaneous variability in the 0.3−2 keV band. Using time-dependent leptonic modelling, we show that this behaviour, in contradiction to single-zone scenarios, can instead be explained by a two-component model. [ABSTRACT FROM AUTHOR]