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Figure 3.16 (a) The dense core L63, mapped in the 1.3 cm line of NH3. (b) The core as mapped in 1.3 mm continuum radiation.

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Figure 3.16 (a) The dense core L63, mapped in the 1.3 cm line of NH3. (b) The core as mapped in 1.3 mm continuum radiation.

Figure 3.17 is an optical polarization map of the p Ophiuchi dark cloud complex. Here, the more filamentary density contours display the elongated substructure mentioned previously. The short line segments indicate the direction of the electric vector of the stellar radiation. Assuming the polarization is due to magnetically aligned grains, this direction is also that of the ambient magnetic field. Note that most of the mass of this complex, as well as the intense star formation activity, is contained in the L1688 cloud toward the lower right. In this region, there is no strong correspondence between the field direction and the cloud morphology. However, there is striking alignment in the lower-mass fragments L1709 and L1755 stretching to the northeast. Further south, this same field direction is preserved, creating a systematic offset from the orientation of the clouds L1729 and L1712.

A particularly well-studied object, with magnetic field measurements spanning a range of densities, is B1, a fragment some 3 pc in diameter within the Perseus dark cloud complex. Measurements in OH emission lines yield field strengths ranging from 10 |G in the more rarified outer portion of the cloud to 54 |G in a compact central region of diameter 0.2 pc. Since this latter region, which includes an embedded star, contains some 10 M& of cloud gas, the magnetic virial term M is about 1/3 the gravitational potential energy W. Such a fraction is consistent with the analysis of NH3 line profiles in typical dense cores, provided that the amplitude of the fluctuating field is comparable to that of the more uniform component.

One promising development in this field is the observation of polarized, submillimeter emission from heated dust grains. This technique allows us, at least in principle, to trace directly the field geometry within dense cores themselves. Curiously, the maps obtained thus far show a steep falloff in the degree of polarization toward the core center. It is unclear whether this trend is due to the magnetic field topology, or to altered properties of the grains themselves. In

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Figure 3.17 Dark clouds in the p Ophiuchi complex. The contours represent13C16O emission. The short line segments indicate the direction and degree of polarization of the electric field vector.

the case of B1, the polarization dips, but is nonzero, at each of several internal density clumps, including the one with the embedded star. The magnetic field vectors of the various clumps are not aligned.

3.3.4 Rotation

As cores collapse to form stars, field lines are pulled in, following the gas motion. The resulting buildup in magnetic pressure acts as an impediment to further collapse and alters the direction of the dynamical evolution. In a similar manner, any initial rotational motion in the core must increase through angular momentum conservation, ultimately creating a centrifugal barrier to collapse. It is therefore also important to search observationally for core rotation. Here the idea is to look for variation in the radial velocity Vr across the cloud face. As usual, we gauge Vr by the Doppler-induced shift in some spectral line. The majority of dense cores analyzed thus far indeed display the expected variation.

As one illustration, Figure 3.18 is an NH3 map of a dense core within L1251A, an elongated dark cloud at a distance of 200 pc. The filled squares superposed on the contour map of the 1.3 cm line have sizes proportional to the measured Vr at each position. A velocity gradient from left to right is clearly present. Its magnitude of 1.3 km s_1 pc_1, is typical of those observed, which range from the detection limit near 0.3 km s_1 pc_1 to a factor of ten higher. Tracer molecules other than NH3 yield similar figures. If every dense core were rotating as a solid body with its rotation axis perpendicular to the line of sight, the measured gradient would c

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