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Relativistic electrons accelerated by both the first-order and thesecond-order Fermi accelerations in some synchrotron sources have a hybridshape of thermal and nonthermal energy distribution. This particle accelerationresult is supported by some recent numerical simulations. We calculate thesynchrotron polarization by applying this electron energy distribution. Thepolarization degrees in the cases of active galactic nucleus (AGN) jets andgamma-ray bursts (GRBs) are given as examples. The possible application for thepolarization study of Sgr A* is also mentioned. We finally suggest high-energypolarization measurements for these synchrotron sources to test our results.

Synchrotron Polarization of Relativistic Thermal Electrons