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Circular Polarization of Pulsar Wind Nebulae and the Cosmic-Ray Positron Excess

Recent observations by the PAMELA and AMS-02 telescopes have uncovered an anomalous rise in the positron fraction at energies above 10~GeV. One possible explanation for this excess is the production of primary electron/positron pairs through electromagnetic cascades in pulsar magnetospheres. This process results in a high multiplicity of electron/positron pairs within the wind-termination shock of pulsar wind nebula (PWN). A consequence of this scenario is that no circular polarization should be observed within PWN, since the contributions from electrons and positrons exactly cancel. Here we note that current radio instruments are capable of setting meaningful limits on the circular polarization of synchrotron radiation in PWNs, which observationally test the model for pulsar production of the local positron excess. The observation of a PWN with detectable circular polarization would cast strong doubt on pulsar interpretations of the positron excess, while observations setting strong limits on the circular polarization of PWN would lend credence to these models. Finally, we indicate which pulsar wind nebulae are likely to provide the best targets for observational tests of the AMS-02 excess.