20 |iGy \25 pc/ \ 105 Me where we have crudely represented the cloud as a sphere of radius R in estimating M. The magnetic field strength in molecular clouds is currently obtained from the Zeeman splitting of either the 21 cm line of HI or of a cluster of lines near 18 cm from OH (see Chapter 6). Unfortunately, this technique has not yet provided results for either the clump or interclump gas in giant clouds. Our representative B-value in equation (3.18) comes from measurements in nearby dark clouds and is consistent with the somewhat lower values detected in the warm HI envelopes of giant complexes.
The numerical estimate of M/\W\ indicates that the magnetic field is important, but in precisely what sense? According to equation (3.3), the associated force acts on a fluid element in a direction orthogonal to B. Thus any self-gravitating cloud supported mainly by a well-ordered field can slide freely along field lines until it settles into a nearly planar configuration. Such flattening is not evident in the giant complexes, so we are forced to reject the hypothesis of a perfectly smooth internal field. Now the direction of B in the plane of the sky, but not its magnitude, can be ascertained from the optical polarization mentioned earlier. We saw in Chapter 2 how elongated grains lying perpendicular to the field polarize starlight through dichroic extinction. However, the observed E vectors in any local region are never perfectly aligned, but display significant scatter. This scatter indicates the presence of a random component to B, coexisting with the smooth background. The field distortion arises, at least in part, from magnetohydrodynamic (MHD) waves, also called hydromagnetic waves. As we will discuss in Chapter 9, these waves may provide the isotropic support preventing the cloud from flattening.
The final term to consider in equation (3.16) is the kinetic energy T. The bulk velocity within giant clouds stems mostly from the random motion of their clumps. Denoting by AV the mean value of this speed, we find
To obtain a representative AV, which we take to be the three-dimensional velocity dispersion, we have increased the Rosette line-of-sight dispersion of 2.3 km s_1 by a factor of %/3, as would be appropriate for a random, three-dimensional velocity field. Our numerical result for T/\W\ implies that the typical internal AV is close to the virial velocity Vvir, which we define as
Comparison with equation (3.14) shows that Vvir is the velocity of a parcel of gas that traverses the cloud over the free-fall time tff. In other words, it is the typical speed attained by matter under the influence of the cloud's internal gravitational field.
The actual velocity dispersion in any cloud can readily be determined by the broadening of some spectral line, generally one of CO. Figure 3.9 shows that, despite considerable scatter, AV roughly matches Vvir (or, equivalently, that T matches \W\) not only in our typical giant molecular cloud, but over a much wider range of sizes. In giant complexes, this approximate equality is consistent with the picture of a swarm of relatively small clumps, each one moving in the gravitational field created by the whole ensemble. The kinetic energy in clump motion is matched by that of the internal magnetic field, which also has a significant random component. Since energy can be exchanged between the matter and field through hydromagnetic waves, such equipartition is not too surprising. Nevertheless, there are as yet no quantitative, theoretical models of giant clouds, incorporating both the uniform and fluctuating field, that account naturally for this result.
Viewed as separate entities, the clumps within giant molecular clouds fall under the "individual dark cloud" category in Table 3.1. The largest clumps have masses of order 103 M0, but
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