C

Figure 3.2 Galactic distribution of giant molecular clouds interior to the solar position. Note the "zone of avoidance," where radial velocities are too small for accurate position determination.

Figure 3.2 Galactic distribution of giant molecular clouds interior to the solar position. Note the "zone of avoidance," where radial velocities are too small for accurate position determination.

Figure 3.1 is a representative 12C16O spectrum. The figure follows radio astronomical convention by plotting, instead of the specific intensity Iv, a proportional quantity known as the antenna temperature, TA; this quantity is defined precisely in Appendix C. Note also that the independent variable in Figure 3.1 is not the frequency v itself, but rather the "radial" gas velocity Vr along the line of sight. This is the velocity that would, through the Doppler effect, shift the line-center frequency va into v. Thus, Vr is given by c(va — v)/va. A positive Vr-value thus corresponds to a redshifted line (v < va).

The spectrum in Figure 3.1 shows a number of discrete peaks. Each of these represents an individual giant molecular cloud along the line of sight, which is here given in Galactic coordinates by l = 30° and b = 0° (i. e., in the disk plane). The radial velocity of each cloud reflects its particular Galactocentric orbital speed. This speed varies in a known way with distance from the Galactic center. By taking a large number of spectra, therefore, one can map the distribution of clouds over a wide area of the disk. Moreover, the integrated value of TA under each peak is a measure of the total cloud mass (see Chapter 6). Figure 3.2 displays the results of a cloud survey utilizing these tools. Here the observations are limited to Galactocentric radii comparable to or less than solar, and to very massive cloud complexes in excess of 105 Me. The "zone of avoidance" toward the Galactic center is the region where the line-of-sight component of the clouds' circular velocity is too small to yield a reliable distance. Notice how the alignment of clouds in two regions delineates fragments of spiral arms. 1

1 In some renderings of Galactic structure, the two local features shown in Figure 3.2 are pieces of a contiguous "Sagittarius-Cygnus arm." A second global structure, the Perseus arm, passes outside the solar position.

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Right Ascension a

Figure 3.3 The Rosette Molecular Cloud, as seen in the 2.6 mm line of 12C16O. The dashed contour indicates the boundary of the HI envelope.

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Right Ascension a

Figure 3.3 The Rosette Molecular Cloud, as seen in the 2.6 mm line of 12C16O. The dashed contour indicates the boundary of the HI envelope.

Figure 3.3 is a map in 12C16O of the Rosette Molecular Cloud. This well-studied giant complex is located in the Monoceros region at a distance of 1.5 kpc. It appears as the small shaded region in Figure 1.1, just to the left of the Orion Molecular Cloud and inside the Milky Way band. The cloud contains the Rosette Nebula, an HII region generated by a compact group of five O stars. As was the case for the Orion Nebula, the massive stars are themselves embedded within a more extended cluster of low-mass members. The location of this cluster, designated NGC 2244, is also indicated in Figure 3.3.

3.1.2 Internal Clumps

The Rosette Molecular Cloud has an elongated, clumpy appearance reminiscent of the Orion cloud (Figure 1.2). We must bear in mind that the 2.6 mm line of 12C16O is always optically thick in giant molecular clouds and so emanates only from their surface layers. To probe internal structure, one can utilize the analogous line from a rarer isotope, such as 13C16O. In this case, a photon from the deep interior has a smaller probability of absorption in the lower column density of 13C16O molecules. On the other hand, the received intensity is also less than for the main isotope, necessitating longer integration times at the telescope. Figure 3.4 is a 13C16O map of an interior portion of the Rosette cloud. Again we see that the emission presents a highly clumpy appearance. However, we can be certain that the peaks represent true internal density enhancements.

Any map is a two-dimensional projection onto the plane of the sky and therefore blends together structures that are physically distinct. As before, the radial velocity of the emitting gas can be effectively used as the third coordinate. The distribution of velocities is contained in the line spectrum at each sampled position, but it is cumbersome to display a two-dimensional array of all the spectra. Alternatively, one can take a linear slice through the full map and give the values of Iv (or rather TA(Vr)) only at points along that slice. Figure 3.5 shows the resulting position-velocity diagram for the cut at b = -1°75; this cut is indicated in Figure 3.4. The diagram shows, for example, that the clump seen near l = 207° 75 actually consists of two overlapping structures separated in velocity by about 5 km s-1.

There is an important difference between the velocity variation encountered in this highresolution scan and that displayed by the complexes as a whole, illustrated in Figure 3.1. In the latter case, the velocities of the giant molecular clouds correlate systematically with Galac-tocentric radius. In contrast, the clump velocities within a complex appear to be randomly dispersed about a mean value. For the Rosette Molecular Cloud, this mean is +13 km s-1, while the one-dimensional dispersion, i. e., the root-mean-square deviation, of the radial velocity is 2.3 km s-1. The simplest interpretation of this local dispersion is that the clumps represent a swarm of relatively high-density parcels that maintain their integrity as they move within the interior of the cloud complex.

By integrating the13C16O intensity within the borders of individual clumps, one can reliably determine the clump mass and the volume-averaged density. We will be detailing this technique in Chapter 6. In the Rosette cloud, where the typical clump radius is 1.5 pc, the average mass thus obtained is 250 Mq, corresponding to a hydrogen density nH = 550 cm-3. Since the mean density for the entire complex is only 60 cm-3, the clumps cannot occupy a large fraction of the volume.

Figure 3.6 shows the actual distribution of the clump mass M. Above a certain minimum, the number of clumps per unit mass, N, falls off as a power law:

where Na is a constant, and where Mmin « 30 Mq. The pure power-law dependence is indicated in the figure by a dashed line. Other giant molecular clouds yield a similar result. Interestingly, cloud surveys such as that displayed in Figure 3.2 also find this power law for the masses of complexes as a whole. Such universality suggests that giant clouds are built up by the agglomeration of many clumps which were already distributed in mass according to equation (3.1).

Returning to our Rosette example, the structure of the complex is further clarified by examining the visual extinction through the cloud gas. By multiplying Equations (2.16) and (2.46), we first obtain the generally useful result

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