Insights into the broad-band emission of the TeV blazar Mrk 501 during the first X-ray polarization measurements

We present the first multi-wavelength study of Mrk 501 including very-high-energy (VHE) gamma-ray observations simultaneous to X-ray polarization measurements from the Imaging X-ray Polarimetry Explorer (IXPE). We use radio-to-VHE data from a multi-wavelength campaign organized between 2022-03-01 and 2022-07-19. The observations were performed by MAGIC, Fermi-LAT, NuSTAR, Swift (XRT and UVOT), and several instruments covering the optical and radio bands. During the IXPE pointings, the VHE state is close to the average behavior with a 0.2-1 TeV flux of 20%-50% the emission of the Crab Nebula. Despite the average VHE activity, an extreme X-ray behavior is measured for the first two IXPE pointings in March 2022 with a synchrotron peak frequency >1 keV. For the third IXPE pointing in July 2022, the synchrotron peak shifts towards lower energies and the optical/X-ray polarization degrees drop. 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 angle 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. We model the broad-band spectra simultaneous to the IXPE pointings assuming a compact zone dominating in the X-rays and VHE, and an extended zone stretching further downstream the jet dominating 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 of magnetization and/or emission region size, which directly connects the shift of the synchrotron peak to lower energies with the drop in polarization degree.