We investigate the changes in polarization position angle in radiation from
pulsar A around the eclipse in the Double Pulsar system PSR J0737-3039A/B at
the 20 cm and 50 cm wavelengths using the Parkes 64-m telescope. The changes
are ~2\sigma\ during and shortly after the eclipse at 20 cm but less
significant at 50 cm. We show that the changes in position angle during the
eclipse can be modelled by differential synchrotron absorption in the eclipse
regions. Position angle changes after the eclipse are interpreted as Faraday
rotation in the magnetotail of pulsar B. Implied charge densities are
consistent with the Goldreich-Julian density, suggesting that the particle
energies in the magnetotail are mildly relativistic.Comment: Accepted for publication in The Astrophysical Journal Letter