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3. Ecological Reaction Networks

With binary stars having locked up the bulk of the energy content of a typical globular cluster, we cannot afford to neglect the transformations in binary properties that take place in the course of normal stellar evolution. The reason is that stellar encounters do not have a monopoly on changing the energy and angular momentum of binaries; isolated binaries, too, have plenty of ways of changing their appearance in complicated ways (for a fascinating account of an ensemble simulation of these processes, see the contribution by Onno Pols in these proceedings).

Even a partial list of some of the processes involved in isolated binary evolution gives an idea of the complexity of the physics, such as there are: tidal capture, magnetic breaking, gravitational radiation, run-away mass transfer, and common envelope evolution. Take into account the manifold perturbations and disruptions that can occur when passing stars or binaries thicken the plot, and you see what we are up against. Clearly, the feed-back mechanisms between stellar dynamics and stellar evolution in globular clusters play a major role in the evolution of the cluster as a whole. The term `ecology', used by Douglas Heggie in his recent `news and views' article in Nature (Heggie 1992), indeed captures the essence of this interplay.

Blue Stragglers

In those clusters that have a relatively low central star density, as well as in the outer areas of all clusters, blue stragglers can be formed by mass overflow from an evolving star in a tight binary to the (initially) less massive star (Pols, this volume). In addition, physical collisions between initially unrelated single stars must produce blue stragglers as well, in the denser cluster cores, as was first realized by Hills &Day (1976). Furthermore, encounters between single stars and binaries are even more efficient in inducing physical collisions between stars, as was pointed out by Hut &Verbunt (1983), Hoffer (1983) and Leonard (1989).

More detailed estimates by Krolik (1983), Krolik, Meiksin &Joss (1984), and Hut &Inagaki (1985) confirmed the fact that many thousands of stellar collisions must have taken place throughout the history of our globular cluster system. The feedback of these merger remnants on the dynamical evolution of the cluster itself was first taken into account by Lee &Ostriker (1986) and Lee (1987).

Unfortunately, the present state of cluster modeling still does not allow us to make significant improvements over the order-of-magnitude estimates in the papers quoted above. As discussed by Hut et al. (1992), Fokker-Planck models have two intrinsic handicaps that make them unsuitable for a quantitative modeling of the evolution of a blue straggler population. First, they are not set up to deal with the separate evolution of internal and external degrees of freedom of the binaries that play an important role in the formation and evolution of blue stragglers.

The second problem stems from an introduction of a mass spectrum, as well as a distinction between stars of different radii, such as dwarfs, main-sequence stars, and giants. The root of the problem here is that a Fokker-Planck approach does not follow individual stars, but rather distribution functions. When the number of independent parameters characterizing the distribution functions becomes too large, there will be less than one star left in a typical cell in parameter space - something that clearly invalidates the statistical hypothesis on which the Fokker-Planck approach is based.

The only solution seems to be to drop the statistical assumption, and to revert to a star-by-star modeling of a globular cluster, through direct -body calculations. Unfortunately, such calculations are extremely expensive.

Next: 4. The Hardware Up: No Title Previous: 2. Gravitational Fusion

Thu Feb 24 00:52:57 EST 1994