We have detected linear polarization in the 115 micron continuum radiation from the giant molecular cloud Sagittarius B2. We found polarization at nine positions in the dense cloud core, and at fifteen positions in the less-dense envelope. The polarization mechanism in the core is polarization due to absorption by magnetically aligned grains, and that in the envelope is polarized emission from magnetically aligned grains. The inferred magnetic field direction is roughly North-South everywhere, but with spatially smooth variations of up to 30 degrees. By considering our data together with Zeeman splitting observations we are able to set a conservative lower limit of 150 microGauss on the strength of the large-scale field in the envelope. If large-scale fields this strong are common in Galactic Center clouds, they could be detectable via large-beam Zeeman measurements. For positions in the envelope that are furthest from the core, the field is nearly parallel to the plane of the Galaxy. This is consistent with the idea of a globally azimuthal magnetic field in the Galactic Center neutral gas layer, which is expected if gravitational forces dominate magnetic forces.
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