Kink-driven magnetic reconnection in relativistic jets: consequences for X-ray polarimetry of BL Lacs

We investigate with relativistic MHD simulations the dissipation physics of BL Lac jets, by studying the synchrotron polarization signatures of particles accelerated by the kink instability in a magnetically-dominated plasma column. The nonlinear stage of the kink instability generates current sheets, where particles can be efficiently accelerated via magnetic reconnection. We identify current sheets as regions where s = J d/B is above some predefined threshold (where B is the field strength, J the current density and d the grid scale), and assume that the particle injection efficiency scales as proportional to the square of the current. X-ray emitting particles have short cooling times, so they only probe the field geometry of their injection sites. In contrast, particles emitting in the optical band, which we follow self-consistently as they propagate away from their injection sites while cooling, sample a larger volume, and so they may be expected to produce different polarimetric signatures. We find that the degree of polarization is roughly the same between X-ray and optical bands, because even the optical-emitting particles do not travel far from the current sheet where they were injected, due to lack of sufficient kink-generated turbulence. The polarization angle shows a different temporal evolution between the two bands, due to the different regions probed by X-ray and optical emitting particles. In view of the upcoming IXPE satellite, our results can help constrain whether kink-induced reconnection (as opposed to shocks) can be the source of multi-wavelength emission from BL Lacs.