Return now to the case of a structure initially closer to force balance. Its evolution must embody certain key features. One is ambipolar diffusion. This drift of cloud matter across field lines sets the time scale for contraction, allowing gravity to compress the gas without excessive buildup of opposing magnetic forces. The inevitable result is that the function dM/d$B rises near the central axis ($B = 0), regardless of its initial form. This development proceeds until the cloud becomes gravitationally unstable, and it continues during the subsequent collapse. The actual form of dM/d$B at the point of marginal stability is hardly likely to be the illustrative one in equation (9.53). If the current numerical models were correct and dense cores become increasingly flatter structures, then equation (9.59) for thin slabs would apply. The sequence in Figure 10.3 indeed exhibits the onset of rapid, central contraction once dM/d$B at the center (which equals £c/Bc) approaches the limit in equation (9.59). The thin-slab approximation is not valid, however, for a more spherical or prolate configuration. Here, M > Mbe prior to collapse, so that equality of M and M$ does not mark the stability transition.
Another general result from theory is that the nature of the support against gravity varies in different regions of the cloud. Thermal pressure is strongest in the dense, central part, where the magnetic flux has diffusively leaked out. In the farthest reaches of the cloud, i. e., at distances greater than Amin in equation (10.23), Alfven-wave support is significant, while ordinary gas pressure is not. Also important here are tension and pressure from the static, ambient field. This static force must predominate throughout much of the intermediate region.
Finally, the collapse itself should proceed in an inside-out fashion, at least after the formation of the central protostar. The reason is that the force of gravity toward the star increases too steeply to be opposed by thermal pressure. Thus, as we have seen, the growth in stellar mass must be accompanied by a spreading of the infall region. This spreading sets into collapse that part of the cloud originally supported by pressure.
Figure 10.8 sketches a conception of dense core evolution that incorporates these three basic elements. Panel (a) depicts a region of relatively uniform gas and magnetic field, presumably the environment out of which the cores originate. Any incipient density enhancement, such as the one shown, attracts additional mass through its gravity. The incoming matter either diffuses across the field or else slides down it. Both types of motion occur. However, the gas will tend to accumulate along the field, i. e., in the direction where it meets the least resistance. Thus, it forms the elongated structure shown in panel (b). Meanwhile, the cross-field drift also distorts B, in the manner depicted. This distortion occurs through the collisional drag exerted on the gyrating ions and electrons by the inflowing neutral gas, and results in a buildup of magnetic tension.
As the central density grows, the field continues to pinch together until it reaches a configuration like the one sketched in panel (c). Here we are approaching a "split monopole" structure. The field lines diverge nearly radially from the center, but their direction reverses across the equatorial plane. Thus, the net flux through any surface enclosing the origin still vanishes, as required by V • B = 0. The split monopole has effectively divided the cloud into two types of regions. In the pinched columns above and below the center (labeled A and A! in the figure), the pull of gravity is counteracted almost entirely by the thermal pressure gradient. In the extended equatorial zone B, which wraps around the axis by azimuthal symmetry, magnetic tension and pressure take up this role, with the former increasing toward the origin. Finally, wave support dominates in the outermost regions, not depicted here.
In the course of time, the columns A and A' grow as mass settles from the more turbulent, wave-supported exterior. Rapid contraction, and ultimately collapse, begin once the linear extent of a column exceeds the Jeans length Aj, evaluated at the unperturbed density and temperature. As the protostellar mass grows, the zone of infall works its way out in the columns,
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