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In order to study the in—uence and structure of the magnetic —eld in the early phases of low-mass star formation, we obtained polarization maps of three Bok globules at a wavelength of 850 km, using the Submillimeter Common-User Bolometer Array at the James Clerk Maxwell Telescope. We observed the following sources: CB 26, a globule with a nearly dispersed dense core containing a source with a circumstellar disk; CB 54, a deeply embedded young stellar cluster; and DC 253[1.6 (CG 30), a protostellar double core. We —nd strongly aligned polarization vectors in the case of CB 26 and DC 253[1.6, while the vector orientations in the case of CB 54 are more or less randomly distributed. The degree of polarization, amounting to several percent, was found to decrease toward the center in each source. In the case of CB 54 and DC 253[1.6, the degree of polarization similarly depends on the corresponding intensity. Assuming dichroic emission by aligned nonspherical grains as the polarization mechanism, where the magnetic —eld plays a role in the alignment process, we derive magnetic —eld strengths and structures from the observed polarization patterns. In the case of the double core DC 253[1.6, we discuss the correlation between the fragmentation process and the magnetic —eld direction.

Measurements of the Magnetic Field Geometry and Strength in Bok Globules