Multifrequency polarimetry of High-Synchrotron Peaked blazars probes the shape of their jets

Abstract: Multifrequency polarimetry is emerging as a powerful probe of blazar jets, especially due to the advent of the Imaging X-ray Polarimetry Explorer (IXPE) space observatory. We study the polarization of High-Synchrotron Peaked (HSP) blazars, where both optical and X-ray emission can be attributed to synchrotron radiation from a population of non-thermal electrons. We adopt an axisymmetric stationary force-free jet model, where the electromagnetic fields are determined by the jet shape. When the jet is nearly parabolic, the X-ray polarization degree is $\Pi_{\rm X}\sim 15-50\%$, and the optical polarization degree is $\Pi_{\rm O}\sim 5-25\%$. The polarization degree is strongly chromatic, as $\Pi_{\rm X}/\Pi_{\rm O}\sim 2-9$. The chromaticity is due to the softening of the electron distribution at high energies, and is much stronger than for a uniform magnetic field. The Electric Vector Position Angle (EVPA) is aligned with the projection of the jet axis on the plane of the sky. These results compare very well with multifrequency polarimetric observations of HSP blazars. Instead, when the jet is nearly cylindrical, the polarization degree is large and weakly chromatic (we find $\Pi_{\rm X}\sim 70\%$ and $\Pi_{\rm O}\sim 60\%$, close to the expected values for a uniform magnetic field). The EVPA is perpendicular to the projection of the jet axis on the plane of the sky. Then, a cylindrical geometry is practically ruled out by current observations. The polarization degree and the EVPA may be less sensitive to the specific particle acceleration process (e.g.,~magnetic reconnection or shocks) than previously thought.