We present new 6 and 20 cm Very Large Array (VLA) observations of polarized continuum emission of roughly 0.5 square degrees of the Galactic center (GC) region. The 6 cm observations detect diffuse linearly-polarized emission throughout the region with a brightness of roughly 1 mJy per 15x10 beam. The Faraday rotation measure (RM) toward this polarized emission has structure on degree size scales and ranges from roughly +330 rad/m2 east of the dynamical center (Sgr A) to -880 rad/m2 west of the dynamical center. This RM structure is also seen toward several nonthermal radio filaments, which implies that they have a similar magnetic field orientation and constrains models for their origin. Modeling shows that the RM and its change with Galactic longitude are best explained by the high electron density and strong magnetic field of the GC region. Considering the emissivity of the GC plasma shows that while the absolute RM values are indirect measures of the GC magnetic field, the RM longitude structure directly traces the magnetic field in the central kiloparsec of the Galaxy. Combining this result with previous work reveals a larger RM structure covering the central ~2 degrees of the Galaxy. This RM structure is similar to that proposed by Novak and coworkers, but is shifted roughly 50 pc west of the dynamical center of the Galaxy. If this RM structure originates in the GC region, it shows that the GC magnetic field is organized on ~300 pc size scales. The pattern is consistent with a predominantly poloidal field geometry, pointing from south to north, that is perturbed by the motion of gas in the Galactic disk.
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