We present high-resolution (~ 35 au) ALMA Band 6 1.3 mm dust polarization observations of IRAS 16293. These observations spatially resolve the dust polarization across the two protostellar sources and toward the filamentary structures between them. The dust polarization and inferred magnetic field have complicated structures throughout the region. In particular, we find that the magnetic field is aligned parallel to three filamentary structures. We characterize the physical properties of the filamentary structure that bridges IRAS 16293A and IRAS 16293B and estimate a magnetic field strength of 23-78 mG using the Davis-Chandrasekhar-Fermi method. We construct a toy model for the bridge material assuming that the young stars dominate the mass and gravitational potential of the system. We find that the expected gas flow to each star is of comparable order to the Alfven speed, which suggests that the field may be regulating the gas flow. We also find that the bridging material should be depleted in ~ 1000 yr. If the bridge is part of the natal filament that formed the stars, then it must have accreted new material. Alternatively, the bridge could be a transient structure. Finally, we show that the 1.3 mm polarization morphology of the optically thick IRAS 16293B system is qualitatively similar to dust self-scattering. Based on similar polarization measurements at 6.9 mm, we propose that IRAS 16293B has produced a substantial population of large dust grains with sizes between 200 and 2000 um.
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