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Figure 4.20 HR diagrams of four open clusters, arranged by age. For each system, both the ZAMS (dashed curve) and the best-fit isochrone (solid curve) are also displayed.

4.4.2 Evolution in the HR Diagram

As before, the HR diagram is a powerful tool for gauging the evolutionary status of any observed system. The vexing incompleteness problem that plagues more embedded T and OB associations is here greatly diminished. In addition, the age span of open clusters is such that both main-sequence turnoffs and turnons may be observed, sometimes within a single cluster. Figure 4.20 is a composite of four diagrams, in order of increasing age. The values of L* and Teff were derived in all cases from photometric observations at visual and near-infrared wavelengths, after applying a global extinction correction for each cluster. In addition to the ZAMS, the figure also includes the theoretical post-main-sequence isochrones that best fit the high-mass turnoff in each case.

Our youngest example (Figure 4.20a) is NGC 4755, or "Herschel's Jewel Box," a rich system of several hundred members. Located in the Southern Crux constellation, its distance of 2.1 kpc is too great for adequate study of the fainter objects, which undoubtedly contain an admixture of interlopers from the field. Even within the brighter population, the HR diagram shows considerable scatter, most of which stems from patchy extinction contaminating the luminosity estimates. Nevertheless, the stellar distribution displays, in addition to the turnoff, a clear departure from the ZAMS at low masses, below about log Teff =3.9. From Table 1.1, this temperature corresponds to a mass of 2 Mq. Such a star has a pre-main-sequence contraction time of 8 x 106 yr. The post-main-sequence isochrone in the figure has the similar associated age of 1 x 107 yr.

Systems this young containing massive stars are not uncommon and some may actually be OB associations rather than open clusters. Most often, classification is a matter of historical accident. The difference, however, is a true physical one, since it involves the eventual fate of the system. Will it quickly disperse, or will it remain gravitationally bound for an extended period? In principle, the answer may be obtained empirically, through accurate measurement of the stars' spatial velocities.

The advantages of proximity are evident for the Pleiades (Figure 4.20b), which lies only 130 pc away. Here, the scatter in the HR diagram is much less than for NGC 4755, and the low-mass portion of the 800 or so known members is better sampled. The very brightest of these, familiar in the Northern sky as the Seven Sisters, are part of a central core of stars within an extended halo, some 4° (i. e., 10 pc) in radius. The haze seen in optical photographs attests to the presence of interstellar matter, but the extinction is modest, with AV = 0.12 mag. In the HR diagram, the turnoff from the main sequence is clear. The displayed isochrone corresponds to an age of 1 x 108 yr. The main-sequence turnon is less apparent, but a careful examination confirms its presence near L* =0.1 Lq. As in our previous example, there is rough agreement between the turnon and turnoff ages, but the measurements are still too inexact to warrant further assessment of their difference.

One difficulty in obtaining more precise turnon ages is that even the empirical ZAMS is not known to great accuracy at the lowest luminosities. As we have seen, a crucial building block in this enterprise is the Hyades, whose diagram we display as Figure 4.20c. Spectroscopic analysis reveals that the metallicity in the Hyades is higher than that of other nearby clusters by a factor of about 1.5. This difference is enough to shift the Hyades main sequence slightly toward lower temperatures, and a proper compensation is necessary in constructing the fiducial ZAMS. As for the evolutionary status of the cluster itself, its nuclear age of 6 x 108 yr is relatively secure, and implies that the main sequence is populated only up to 2 Mq. Correspondingly, the turnon is now lowered to about 0.1 Mq, or a luminosity of 1 x 10~3 Lq. This point lies well below the observational cutoff present in the Figure.

Figure 4.20d depicts NGC 752, one of a handful of open clusters significantly older than the Hyades. At a distance of 400 pc, this sparsely populated system has fewer than a hundred observed members. Its advanced evolutionary state is apparent from the absence of all high- and intermediate-mass stars. At the turnoff age, estimated to be 2 x 109 yr, stars of 1.5 Mq are just completing main-sequence hydrogen fusion. There are undoubtedly additional cluster members below the 0.8 Mq minimum mass shown here. Only those of less than 0.09 Mq, however, are still in their pre-main-sequence phase.

An interesting feature in the HR diagram of NGC 752 is the clump of stars above and to the right of the main sequence. An analogous, but smaller, group is also visible in the Hyades. Evolutionary calculations show these stars to be red giants undergoing core helium burning. Finally, we see that the diagram again displays considerable scatter about the ZAMS, despite the fact that the cluster is at a high Galactic latitude and suffers little extinction. One plausible source for this scatter is the presence of unresolved binaries, which can raise the apparent luminosity if their mass ratios are close to unity.

4.4.3 Mass Segregation

Returning to the Pleiades, the central concentration of its brightest and most massive members is a phenomenon we have encountered before. We recall the deeply embedded clusters of L1630 in Orion, with their luminous cores of O and B stars (Figure 1.2), or the buildup of stars surrounding the massive object in S106 (Plate 2). Within the more exposed NGC 2264 cluster, careful mapping of the stellar density reveals two concentrations - one surrounding S Mon and another associated with a star that is again the most massive in its local region. In principle, more refined observations of mass segregation should be possible for open clusters, but less than two dozen systems have so far been examined in sufficient detail. For most of these, the average stellar mass drops steadily from the center outwards.

Since mass segregation is present to some extent in the very youngest systems, it is evidently part of the star formation process itself. Thus, the salient question, which we shall explore later, is not how the most massive objects find their way to the densest regions, but why they form there in the first place. Having said this, it is also true that open clusters are old enough that the process of dynamical relaxation can further promote the settling of massive stars toward their centers.

To understand dynamical relaxation, consider a hypothetical cluster of 1000 stars, with a total mass of 500 Mq and diameter of 5 pc. The typical velocity of a cluster member is given by the virial value in equation (3.20), and is about 1 km s~\ if we assume that no gas remains in the system. The crossing time over which the star can traverse most of the cluster is therefore 5 x 106 yr. During each such passage, the stellar orbit is determined mainly by the smoothly varying gravitational force arising from the system as a whole. However, each interaction with an individual field star produces an additional tug, and many such tugs change the orbit completely. The system gradually relaxes toward a state independent of initial conditions, one in which the total available energy is apportioned roughly equally among the members.

Under the new conditions, the least massive stars have the highest velocities and therefore fill out the largest volume. Conversely, the high-mass members tend to crowd toward the middle. For our sample cluster, theory predicts that such a state prevails within about 15 crossing times, where the precise figure depends on the stellar mass spectrum. Thus, the relaxation time is roughly 7 x 107 yr, too long for embedded systems but within the range for open clusters. One might expect, from this argument, that older clusters would exhibit a steeper outward falloff in the average mass of their members, but no such effect is evident in the data at hand.

4.4.4 Destruction by Giant Clouds

The centrally peaked appearance of open clusters is strong, though not conclusive, evidence that they are gravitationally bound. This is not to say they they remain intact for all time. Dynamical relaxation gradually inflates a halo of lighter stars, some of which actually escape. Such "evaporation," however, typically requires 100 crossing times to deplete an isolated system. Why, then, do so few observed clusters survive to even 109 yr? Clearly, some external process is at work that destroys them more efficiently.

There is little direct observational evidence bearing on this question, but theory suggests that the main culprit is encounters with giant molecular clouds. The rate of such encounters is low-about one for each rotation of the cluster about the Galaxy- but the cloud mass is so huge that the effect can be devastating. Both molecular clouds and clusters have similar random motions within the Galactic disk. Their typical relative velocity exceeds a cluster's internal velocity dispersion by about an order of magnitude. During an encounter, the cloud effectively imparts a brief impulse to each star, in a manner somewhat akin to dynamical relaxation. In this case, however, there is a net energy gain by the cluster as a whole.

The additional energy arises from the tidal component of the gravitational interaction. Stars that are closest to the passing cloud respond most strongly, causing the stellar system to stretch along the line joining the centers of mass. Incidentally, the same effect, but arising from the general Galactic field, strips stars from the cluster halos and truncates their radii to about 10 pc in the solar neighborhood. Often only a single encounter with a giant molecular cloud is sufficient to disrupt a cluster entirely. If not, the cumulative tidal stretching from several such encounters does the job. It is ironic, then, that the very structures giving rise to all young clusters appear responsible for their ultimate demise.

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