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numbers of O and B-star members, as established through both spectroscopy and proper motion. Notice that over half the systems have no O stars, which are rare objects indeed. Note finally that the relatively small association designated Trumpler 10 is not depicted in the spatial map, as it lies in front of the larger Vela OB2.

Returning to Figure 4.14, the shaded, open structure surrounding the solar position is Gould's Belt. This huge ring of bright stars and gas, up to 700 pc in diameter, links a number of the closest associations. Near its center lies the Cassiopeia-Taurus (Cas-Tau) system. Containing no stars brighter than MV = -5 and extending over some 200 pc, this diffuse grouping stands out from the background field only by virtue of the similar and parallel proper motions of its members. The entire Taurus-Auriga cloud complex lies within its borders, as does the small and possibly bound system a Persei listed in Table 4.2. The Cas-Tau association appears to represent the largely dispersed remnant from an earlier epoch of massive star formation. Other systems in such an advanced state of disintegration must exist throughout the Galaxy, but are currently impossible to find outside the solar neighborhood.

4.3.2 Expansion

The more compact associations strung out along Gould's Belt have velocities indicating a general expansion from the Cas-Tau region. The best-studied such system is that of Scorpius-Centaurus (Sco-Cen). With a maximum size that rivals Cas-Tau, this association consists of a sequence of three, spatially discrete subgroups (Figure 4.15). At one end lie the embedded stars of the p Ophiuchi molecular clouds. The Lupus T association and its molecular complex are just inside the border of the middle (Upper Centaurus-Lupus) subgroup, as shown in the figure. Neither cloud region is forming O stars, but the p Ophiuchi complex in particular has clearly been disturbed by such activity nearby. In Figure 3.17, the change in both the cloud morphology and the pattern of polarization vectors near L1688 suggest compression from the Upper Scorpius subgroup to its right. This impression is reinforced by 21 cm data revealing a

Upper Scorpius

Upper

Centaurus-Lupus

Upper Scorpius

Upper

Centaurus-Lupus

Galactic Longitude I

Figure 4.15 Subgroups within the Sco-Cen OB association. Shown are the prominent stars, as well as the molecular clouds in p Ophiuchi and Lupus.

Galactic Longitude I

Figure 4.15 Subgroups within the Sco-Cen OB association. Shown are the prominent stars, as well as the molecular clouds in p Ophiuchi and Lupus.

shell of atomic hydrogen centered on the massive stars in Upper Scorpius and impinging on the p Ophiuchi clouds.

From the dashed boundaries shown in Figure 4.15, it is apparent that the three optically visible subgroups within Sco-Cen have differing sizes and hence ages. That is, these groups are separated both spatially and temporally. It is natural to suppose that all three originated in a giant molecular complex, of which the p Ophiuchi and Lupus clouds are the sole remains. The pattern of subgroup ages then corresponds to the order in which various high-density regions of the parent complex underwent gravitational collapse. Thus, the first subgroup to form massive stars was Upper Centaurus-Lupus, followed by Lower Centaurus-Crux, and then Upper Scorpius.

To quantify matters and obtain actual ages, one may utilize the expansion velocities of individual stars. Tracing their motion backwards in time leads to a unique configuration for which the stellar density is highest. The corresponding time then gives the age of the subgroup in question. In practice, both radial velocities and proper motions of the expected magnitude (a few km s^1) are difficult to obtain. Within Sco-Cen, accurate proper motions are available in Upper Scorpius, while radial velocities here are too small for detection. Figure 4.16 depicts the proper motion vectors, as well as the inferred initial configuration, which has an associated age of 4 x 106 yr. The longest dimension of this configuration is about 45 pc, in good agreement with present-day giant cloud complexes. Note that all the velocities shown are those relative to the mean proper motion of the subgroup; the latter reflects the global expansion of Gould's Belt mentioned previously.

4.3.3 Main-Sequence Turnoff

An independent check on this kinematic method comes from another clock- the HR diagram. As was the case for the low-mass T associations, the distribution of stars in the diagram constitutes a record of star formation history, but now supplies complementary information. Fig-

Right Ascension a

Figure 4.16 Reconstructing the initial configuration of the Upper Scorpius subgroup. (a) Proper motion vectors of prominent stars. (b) Most compact structure leading to the present configuration.

Right Ascension a

Figure 4.16 Reconstructing the initial configuration of the Upper Scorpius subgroup. (a) Proper motion vectors of prominent stars. (b) Most compact structure leading to the present configuration.

ure 4.17 displays the HR diagram for the Upper Scorpius subgroup. While the intermediate-mass stars fall along the main sequence, higher-mass members begin to deviate from it, and the most massive stars are absent altogether. This main-sequence turnoff reflects the age of the system. The deviation occurs at a mass of about 30 Me, which translates into a main-sequence lifetime of 5 x 106 yr. The Upper Scorpius region must have begun producing stars at least that far back in the past. Stars of significantly greater mass formed then or earlier would have finished burning hydrogen by now and migrated out of the diagram, thus accounting for the present truncation of the main sequence. As illustrated in Figure 4.17, we may conveniently read off the system age (in the foregoing sense) by matching the empirical turnoff with the set of theoretical post-main-sequence isochrones, i. e., the loci of constant evolutionary time for stars of various mass. Here, t = 0 corresponds to the initiation of hydrogen fusion on the ZAMS.

These considerations will naturally remind the reader of our previous discussion of the main-sequence turnon in T associations. Both features of the HR diagram are age indicators, but their conceptual difference is noteworthy. The turnon point singles out the oldest pre-main-sequence stars in the association, i.e., it indicates when the formation of relatively low-mass objects began. Conversely, the turnoff identifies the youngest post-main-sequence members and thus tells us when the last high-mass stars were born. In a region currently devoid of molecular gas, this latter time marks the end of the star formation process. Quite generally, the turnon "age" should always exceed that given by the turnoff, with their difference being a measure of the total duration of star formation activity.

Because of the statistics of stellar masses, not all forming groups exhibit both turnon and turnoff points. Pure T associations like Lupus or Taurus-Auriga simply lack the high-mass component that would include a turnoff. With regard to OB associations, however, numerous surveys support the view that regions harboring massive stars invariably contain many more

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