Halfway between the study of individual stars (by now a relatively well-under-stood area) and that of galactic nuclei (still not very well understood) lies the study of star clusters. If we could not reach a detailed understanding of the basic structure and evolution of galactic and globular clusters, a quantitative modeling of active galactic nuclei would be even more remote.
With this motivation, it is rewarding to focus our attention on the densest and richest clusters available near our galaxy, the globular clusters, and especially their central areas where close encounters and even physical collisions between stars are not infrequent. Some of these encounters can produce exotic objects such as X-ray binaries and millisecond pulsars, but most encounters will involve garden-variety main-sequence stars. Judging from the numbers of exotic objects, as well as from back-of-the-envelope estimates, globular clusters must have formed a stage for thousands of stellar collisions, as first shown by Hills &Day (1976). What did these collisions produce?
When two main-sequence stars collide in a low-velocity-dispersion environment provided by a globular cluster, very little mass can escape, since the specific kinetic energy at infinity is typically three orders of magnitude smaller than the escape energy at the surface of a star. Therefore, the merger remnant will consist of a simple addition of the masses of the two stars, albeit in a rather excited stage at first. After the initial oscillations have damped out on a dynamical time scale, and the thermal excess has been radiated away on a thermal time scale, the resultant star is expected to resume a rather normal appearance.
Depending on the details of the collision and the prior evolutionary state of the stars, the merger product may have an excess rotation and unusual abundances (Hills &Day 1976, Benz &Hills 1987, Bailyn 1992), but by and large we will find ourselves simply with an overweight star, possibly of a type we don't expect to encounter any more at the present evolutionary state of the cluster - in this case we will have produced a blue straggler.
Star-by-Star Modeling of Star Clusters
To summarize: if want to probe the collisional history of dense stellar systems, and if we want to obtain optimal statistics, we should look for the products of collisions between ordinary stars. They come in two varieties. Those merger remnants that are less massive than the main sequence turn-off are buried in the HR diagram like needles in a hay stack. But those that are more massive do stand out as `blue stragglers' - that is, if we can resolve the region of interest down to the level of the main sequence. Now that this is possible, with the Hubble Space Telescope in even the densest cluster cores, it is time to roll up our sleeves and get serious with our modeling efforts.
Not that we have not been serious so far. The evolution of star clusters has approached a state of maturity comparable to that of stellar evolution three decades ago. We have begun to understand the physics driving core collapse and post-collapse evolution, and we are on the brink of building detailed models necessary for comparisons with observations. Since we have just published an extensive review of recent modeling efforts (Hut et al. 1992, section 3), we can limit ourselves to a brief summary-style review in §,3. From onwards, the paper is presented as a preview.
Another reason to look at the future, rather than the past, is that our present modeling efforts are simply not yet capable to meet the challenges posed by the state-of-the art observations. As discussed by Hut et al., Fokker-Planck simulations cannot handle binaries adequately, while -body methods still lack the necessary computational speed. In fact, at present three barriers still separate us from the goal of reaching parity with observational advances, as discussed below in §§4-6. What is most exciting, and what forms the central theme of this preview, is that we now have a firm time table for scaling these barriers, namely during the next one or two years.
Rolling up our sleeves is literally an appropriate expression for theorists who want to follow the evolution of globular clusters. Since we need a Teraflops-month to do so, we can either wait till the next millennium when that type of compute has become affordable, or we can build our own star-cluster machine. Fortunately, some enthusiastic astronomers in Tokyo have started to do just that, and are expected to produce the necessary cycles in one or two years, as will be discussed in §4.
However, speed alone won't do, and we also need to extend our present software, to be able to handle the extreme problems of disparate length scales and time scales (by relative factors of up to ). Current efforts in that directions are described in §5.
Handling point masses, although a good start towards globular cluster modeling, by itself will not enable meaningful comparisons with observations. We really need to take into account the intricate interplay between stellar evolution and stellar dynamics. A review of the general problem is given in §3, and a preview of our current modeling efforts is presented in §6.
With proper speed, integration algorithms, and stellar evolution recipes all in hand, a year or so from now, we will have to sort out the processes of interests from among the terabytes of data generated in star-by-star cluster simulations. This is the topic of §7. §8 sums up.
Before reviewing and previewing the various cluster evolution modeling efforts, we first summarize in §2 the physical principles underlying our understanding of the dynamics of dense star clusters, and in §3 their application to globular clusters.