Signatures of Black Hole Spin and Plasma Acceleration in Jet Polarimetry

We study the polarization of black hole jets on scales of $10-10^3\,GM/c^2$ and show that large spatial swings in the polarization occur at three characteristic distances from the black hole: the radius where the counter-jet dims, the radius where the magnetic field becomes azimuthally dominated (the light cylinder), and the radius where the plasma reaches its terminal Lorentz factor. To demonstrate the existence of these swings, we derive a correspondence between axisymmetric magnetohydrodynamic outflows and their force-free limits, which allows us to analytically compute the plasma kinematics and magnetic field structure of collimated, general relativistic jets. We then use this method to ray trace polarized images of black hole jets with a wide range of physical parameters, focusing on roughly face-on jets like that of M87. We show that the location of the polarization swings is strongly tied to the location of the light cylinder and thus to the black hole's spin, illustrating a new method of measuring spin from polarized images of the jet. This signature of black hole spin should be observable by future interferometric arrays like the (Next Generation) Event Horizon Telescope, which will be able to resolve the polarized emission of the jet down to the near-horizon region at high dynamic range.