Probing dissipation mechanisms in BL Lac jets through X-ray polarimetry

The dissipation of energy flux in blazar jets plays a key role in the acceleration of relativistic particles. Two possibilities are commonly considered for the dissipation processes, magnetic reconnection -- possibly triggered by instabilities in magnetically-dominated jets -- , or shocks -- for weakly magnetized flows. We consider the polarimetric features expected for the two scenarios analyzing the results of state-of-the-art simulations. For the magnetic reconnection scenario we conclude, using results from global relativistic MHD simulations, that the emission likely occurs in turbulent regions with unstructured magnetic fields, although the simulations do not allow us to draw firm conclusions. On the other hand, with local particle-in-cell simulations we show that, for shocks with a magnetic field geometry suitable for particle acceleration, the self-generated magnetic field at the shock front is predominantly orthogonal to the shock normal and becomes quasi-parallel downstream. Based on this result we develop a simplified model to calculate the frequency-dependent degree of polarization, assuming that high-energy particles are injected at the shock and cool downstream. We apply our results to HBLs, blazars with the maximum of their synchrotron output at UV-soft X-ray energies. While in the optical band the predicted degree of polarization is low, in the X-ray emission it can ideally reach 50\%. The comparison between measurements in the optical and in the X-ray band (feasible with the planned {\it IXPE} satellite) are expected to provide valuable constraints on the dissipation and acceleration processes.