We investigate the polarization properties of Comptonized X-rays from relativistic jets in Active Galactic Nuclei (AGN) using Monte Carlo simulations. We consider three scenarios commonly proposed for the observed X-ray emission in AGN: Compton scattering of blackbody photons emitted from an accretion disk; scattering of cosmic microwave background (CMB) photons; and self-Comptonization of intrinsically polarized synchrotron photons emitted by jet electrons. Our simulations show that for Comptonization of disk and CMB photons, the degree of polarization of the scattered photons increases with the viewing inclination angle with respect to the jet axis. In both cases the maximum linear polarization is approximately 20%. In the case of synchrotron self-Comptonization (SSC), we find that the resulting X-ray polarization depends strongly on the seed synchrotron photon injection site, with typical fractional polarizations of approximately P = 10 - 20% when synchrotron emission is localized near the jet base, while P = 20 - 70% for the case of uniform emission throughout the jet. These results indicate that X-ray polarimetry may be capable of providing unique clues to identify the location of particle acceleration sites in relativistic jets. In particular, if synchrotron photons are emitted quasi-uniformly throughout a jet, then the observed degree of X-ray polarization may be sufficiently different for each of the competing X-ray emission mechanisms (synchrotron, SSC or external Comptonization) to determine which is the dominant process. However, X-ray polarimetry alone is unlikely to be able to distinguish between disk and CMB Comptonization.
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