  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.
