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Synchrotron radiation and Compton scattering are widely accepted as the mostlikely emission mechanisms of some astrophysical phenomena, such as gamma-raybursts (GRBs) and active galactic nuclei (AGNs). The measurement onpolarization of photons provides a useful tool to distinguish differentemission mechanisms and structures of the emission region. Based on thedifferential cross section of a polarized photon scattered by an unpolarizedelectron of any initial momentum, we derive analytical formula of polarizationfor beamed photons scattered by isotropic electrons with a power lawdistribution. Numerical calculations are carried out in four special cases:electrons at rest, Thomson limit, head-on collision and monochromaticelectrons. It is found that the maximum polarization can be as high as $100\%$for low energy photons, if the electrons are at rest. Although polarization ishighly suppressed due to the isotropic electrons, a maximum value of $\sim 10\%\-- 20\%$ can still be achieved. Compton scattering process can be used toexplain the polarization of GRB 041219A and GRB 100826A.

Gamma-ray burst polarization via Compton scattering process