Polarization of High Energy Emission from the Crab Pulsar: Model Prediction Versus Observation

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We discuss polarization characteristics of high-energy photons from pulsar magnetospheres. Polarization measurements play an important role to discriminate the various models that successfully explain observed spectra or light curves. As indicated by the outer gap model of Cheng et al. (2000), the Crab optical and soft -ray spectrum can be easily explained by the synchrotron radiation. We therefore study the polarization predicted by the synchrotron emission in the framework of the outer gap model and the two-pole caustic model (Dyks et al. 2004).We assume that the emitted photons are linearly polarized in the direction of particle acceleration, which is perpendicular to the magnetic field line, for which the rotating dipole field is used. Emission direction and Stokes parameters Q and U are appropriately treated with the effects of particle’s gyration and aberration. A radial-distance dependent emissivity (Cheng et al. 2000) is employed for the outer gap model and a constant one is assumed for the caustic model. We find that the minimum in the polarization degree is < 10% at the bridge phase for both models, and the maximum is 60% at outer wings of peaks for the outer gap model and 20% at trailing of peaks for the caustic model. These patterns are not similar to the Crab optical data, in which the minimum is at both peaks and the maximum is at the bridge phase. The computed position angle swing does not match with the data either.The curvature radiation model predicts too high a degree of polarization (Dyks et al. 2004) and no successful spectra have been achieved up to date. On the other hand, none of the models discussed above is able to reproduce the Crab optical polarization. To understand the Crab polarization, we may need a more realistic structure of the pulsar magnetosphere.

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