Ai pc i

An object of size ¿therm, which also has U « |W|, is a more quiescent environment than larger dark clouds with their energetic internal waves. In fact, both the clumps within giant complexes and isolated dark clouds do contain distinguishable substructures of this dimension. These entities are the dense cores responsible for individual star formation.

Our surveys of Orion and Taurus-Auriga showed how these cores are found throughout the interiors of dark clouds (recall Figure 1.2). With densities exceeding 104 cm~3, such structures cannot be probed by the usual 12C16O or even 13C16O lines, which are both optically thick. Other species, such as NH3, 12C18O, and CS, emit radio lines that are optically thin and can be used both for discerning global properties and for spatial mapping. These observations, carried out since the early 1980s, show that the typical dense core comprises several solar masses of gas, and has a temperature near 10 K. Although a few individual cores within a dark cloud may be far more massive, the aggregate of all cores generally comprises less than 10 percent of the total gas supply.

The most extensive studies have been conducted using the 1.3 cm line of NH3. Figure 3.11 is a typical NH3 spectrum toward the center of the dense core L260, at a distance of 160 pc. The dashed curve is the profile expected from thermal motion alone, as calculated for the internal temperature of 9 K. (We will later see how such a figure is obtained.) Here, it is assumed that the probability of any line-of-sight velocity Vr is given by the Maxwell-Boltzmann distribution, so that the observed intensity varies as r,(K,«exp(-?l|Si2) (3*2)

where mNH3 is the mass of the ammonia molecule. (See Appendix E for a general discussion of line broadening.) Note that the root-mean-square value of Vr is (kBT/mNH3 )1/2; this is the one-dimensional dispersion for thermal motion.

The profile in equation (3.22) has a full-width half-maximum extent of


which has the value 0.15 km s^1 for L260. Figure 3.11 shows that the observed profile is actually broader than this. The additional broadening can be ascribed to a random field of turbulent velocities; the solid line is the calculated model result. The turbulent velocities in the model obey a Gaussian probability distribution like that in equation (3.22), but with an associated width denoted AVFWHM (turb). Since the two distributions are uncorrelated, the total profile width is

AVf2WHM (tot) = AVFWHM (therm) + AVF2WHM (turb) , (3.24)

Velocity Vr (km s-1)

Figure 3.11 Profile in the 1.3 mm line of NH3 of the dense core L260. The histogram represents the observed profile, while the dashed curve is a theoretical result assuming purely thermal motion. The heavy solid curve is the theoretical profile including a Gaussian distribution of turbulent speeds.

Velocity Vr (km s-1)

Figure 3.11 Profile in the 1.3 mm line of NH3 of the dense core L260. The histogram represents the observed profile, while the dashed curve is a theoretical result assuming purely thermal motion. The heavy solid curve is the theoretical profile including a Gaussian distribution of turbulent speeds.

as we show in Appendix E. In our example, we find that A VFWHM (turb) must be 0.11 km s~1 in order to reproduce the observed total width of 0.19 km s^1.

It is instructive to compare the spatial maps of a given core in a number of different lines. Figure 3.12 is a composite map of L1489, a dense core containing an infrared point source, as indicated. Shown are the half-maximum intensity contours in NH3 (the 1.3 cm line), CS (at 3.0 mm), and 12C18O (at 2.7 mm). The observed lines are excited into emission by collisions with ambient hydrogen molecules. The fact that different molecular transitions require different threshold hydrogen densities for excitation accounts in part for the systematic widening of the maps. Thus, the 1.3 cm line from NH3 has a higher threshold than the line from 12C18O and therefore samples a compact, interior region. Smaller regions are less turbulent, according to equation (3.21), so that we can also understand the relatively low value of the nonthermal NH3 line width.

However, there are complications to this picture. The CS line has an even larger critical hydrogen density than NH3. Yet Figure 3.12 shows its map extending farther out. A plausible explanation is that the CS molecules stick to dust grains at the highest ambient densities. Then the observed central intensity would be lowered, and the radial falloff in flux made more shallow. The half-maximum contour thus moves outward, as seen. Another puzzle is the offset of all the maps in Figure 3.12 from the embedded star. The latter would naturally be expected to form at the density peak. This offset is seen in other cases but not well understood.

The presence of pointlike infrared sources in cores such as L1489 is, of course, the most direct evidence that these structures indeed form stars. The IRAS satellite found such embedded stars in about half the dense cores in Taurus-Auriga and p Ophiuchi that had been previously identified through molecular lines. While some of these sources have optical counterparts, an

*iras 04016 + 2610

Figure 3.12 Composite map of the dense core L1489 in the lines of NH3, CS, and 12C18O. Each contour corresponds to the intensity at half its peak value. Note the offset position of the embedded infrared source.

equal number do not. Finally, most of the optically invisible stars within cores are associated with outflows, as detected in CO. These important findings tell us, first, that dense cores exist for a substantial time prior to forming stars. Second, since optically invisible stars are presumably the youngest, outflow generation occurs extremely early in stellar evolution. Third, a dense core does not suddenly vanish after forming a star, but gradually dissipates as the object inside ages.

From an observational perspective, there are no outstanding differences between the dense cores lacking infrared sources and those containing young stars. Both types, for example, have visual extinctions that range from about 5 to 15 mag.3 On the other hand, the sample having deeply embedded, optically invisible stars includes some cores with significantly higher NH3 line widths, as illustrated in Figure 3.13. Since the difference in the measured gas temperature between cores with and without stars is negligible, the larger widths must be due to turbulent motion. It is tempting to associate the higher level of turbulence with the molecular outflows created by the youngest stars. As we will see in Chapter 13, turbulence is indeed an integral feature of outflows, but a more convincing link to the observed line widths needs to be made.

3.3.2 Intrinsic Shapes

Let us now turn to the more detailed properties of dense cores, beginning with their shapes. Here the type of composite map shown in Figure 3.12 represents the best data available. For the commonly used NH3 line at 1.3 cm, the beam diameter with a 40-meter telescope is 80", or 0.05 pc at the distance of Taurus-Auriga. The corresponding figure is 0.01 pc for the 3.0 mm line of CS. Thus, the current resolution of single-dish (as opposed to interferometric) observations is modest for NH3, but adequate at shorter wavelengths for discerning gross spatial features.

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