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Globular Cluster Dynamics: the importance of close binaries in a real N-body system

Since the time of Newton, the N-body problem has been a fertile ground for physical insight. One of the most interesting N-body systems is a globular cluster, a gravitationally bound system of about a million or so stars, of which there are about 150 in our Milky Way. It is a general property of self-gravitating systems that they are unstable against collapse without some source of internal energy. Stars solve this problem by undergoing nuclear fusion in their cores; they burn lighter elements into heavier ones and, in so doing, tap into the rest-mass energy of their constituent atoms to provide the necessary power to support themselves. Globular clusters, in a sense, can “burn” stars (44); a cluster taps into the potential energy of binary systems to provide the means of stabilization against collapse (29). Globular clusters are fairly weakly bound systems, with escape velocities from their cores of only tens of km/s. Even a modest population of binaries contains a potential reservoir of gravitational binding energy that easily exceeds the kinetic energy of all single stars in the cluster.

Encounters between cluster members -- whether they be between two single stars, a single star and a binary, two binaries, or even more exotic scenarios -- are the means through which this reservoir is tapped. As an example, in an encounter between a binary system and a single star, one possible outcome of this three-body interaction is the “hardening” of the original binary, in which the two members of the binary are brought into a closer orbit. The negative gravitational potential energy of the original binary becomes more negative, imparting positive energy to the cluster. In this sense, a sort of stabilization can be achieved. As the core of a globular cluster begins to contract, the stellar density becomes higher, increasing the rate of encounters. This results in the liberation of potential energy from binaries, thus postponing deep core collapse of the cluster. Another consequence of this process is the “evaporation” of stars from the outer reaches of a cluster; in fact, the ultimate fate of all globular clusters is to eventually dissipate themselves (28). The situation is extremely complicated (after all, the gravitational N-body problem for N>2 is one of the oldest unsolved problems in physics), but this is the general picture.

Close binaries are thus of critical importance to the evolution of a globular cluster. However, they have been rather elusive before the Chandra era. Early optical surveys failed to reveal any binaries (33). Some of the first evidence for at least a small population of close binaries came from the X-ray satellites of the 1970s (e.g., Uhuru, OSO-7, SAS-3), which discovered eight bright X-ray sources in as many globular clusters (30). This discovery led to a flurry of renewed theoretical interest in globular clusters and the dynamical interactions within them (41,11,35,42,52,107,21). The theoretical work has steadily progressed, with ever more sophisticated numerical simulations being attempted1. The observational side has recently undergone another major advance, again via X-rays, and I have played a significant role in this.

One of my main contributions to this field has been to lead a large international collaboration to search for close binaries in globular clusters with the Chandra X-ray Observatory, Hubble Space Telescope, and ground-based facilities. My colleagues and I have received Chandra observations of 16 globular clusters to date (totaling 750 ksec) and HST observations of 11 (totaling 45 orbits), and I recently won a Chandra Large Project that will survey an additional 25 globular custers. The thrust of these proposals is that many classes of close binary systems (e.g., cataclysmic variables, quiescent low-mass X-ray binaries, chromospherically active main-sequence binaries, and millisecond pulsars) are observable as low-luminosity (around 1030 - 1033 erg/s) X-ray sources. Given the extreme crowding in the inner regions of globular clusters, previous X-ray satellites were unable to fully resolve this population. Whereas the former best X-ray imaging satellite ROSAT might find zero to a few X-ray sources in a cluster (110), Chandra is finding dozens to over a hundred such sources per cluster (1,31,85,84,36,37,2,32). Complementary HST observations and millisecond pulsar searches allow for the classification of the Chandra sources.

I have analyzed all of the Chandra data from our observations, as well as all publicly available Chandra observations of globular clusters. When I first did this in a systematic way three years ago (86), I noticed that the number of X-ray sources (a heterogenous mix of quiescent low-mass X-ray binaries, cataclysmic variables, active main-sequence binaries, and millisecond pulsars) in about a dozen clusters (which was all that had been observed to that point) did not scale well with the mass of the clusters. In fact, it scaled much better with a dynamical quantity, the stellar encounter frequency. This was direct evidence that the majority of these close binaries was actually formed dynamically in the cluster through encounters. Not only is this confirmation of the important role of binaries in a globular cluster, but it also provides a directly observable measure of the internal dynamics of a globular cluster. This was a major breakthrough.

Recently, Piet Hut and I further refined this by exploring the role of dynamics on specific subpopulations of the globular cluster X-ray sources. In the past few years and based on numerous HST identifications, we have learned that we can roughly separate the quiescent low-mass X-ray binaries from the cataclysmic variables based solely on the X-ray properties. As Piet and I showed (75), the quiescent low-mass X-ray binaries and the cataclysmic variables show a markedly different dependance on the encounter frequency. We also showed, for the first time, that the cataclysmic variables are overabundant in globular clusters, which means that the majority of them are formed dynamically. It had long been suspected that cataclysmic variables would be overabundant in globular clusters (15,45), but optical surveys had failed to find them (101). This remained something of a mystery until Chandra began finding dozens per cluster and Piet and I conclusively demonstrated their overabundance.

These are some of the highlights of the Chandra era, and the outlook for future major advances is quite good. Over two dozen globular clusters have been observed deeply by Chandra, but only a few have had the corresponding HST images analyzed for secure classification of the X-ray sources. When a substantial number of clusters have their populations classified, a more detailed and thorough analysis of the subpopulations will be possible. In addition, the above-mentioned survey of another 25 clusters will give us direct knowledge of over 90% of the total low-mass X-ray binary population in globular clusters. This will allow us to accurately determine the factors contributing to their formation in globular clusters as well as estimate their density in the field.

Beyond isolating and studying these dynamically formed populations, our analyses of Chandra and optical observations (both HST and ground-based) of NGC6121 (1) and NGC288 (56) have shown that the lowest luminosity X-ray sources -- the magnetically active binaries -- are likely descendants of primordial binaries. I have recently received a set of deep Chandra observations (totaling 100 ksec) of NGC6121 which will delve to the lowest X-ray luminosities yet in a globular cluster. These deep observations will uncover $\sim$90% of the magnetically active binaries. This will constitute the first nearly complete and well-defined sample of primordial binaries in a globular cluster.

As the observation side continues to rapidly progress, and the theoretical side matures to the point of undertaking full globular cluster simulations, we will continue to unlock the mysteries of these objects. It is interesting to note how globular clusters have had something important to say in so many areas of astrophysics: they were the first indication that the center of our Galaxy was located in the direction of Sagittarius (40); they were testbeds for the theory of stellar evolution (43,97,96); and they have constrained the age of the universe (57). In addition, globular clusters have held an allure for many of the best minds in the history of astrophysics; Jeans (51,50), Eddington (16,17), Chandrasekhar (5,6), Spitzer (105,104,103), Hénon (38,39), Lynden-Bell (62,61), Ostriker (73), and many others have made seminal contributions to the field. Globular clusters present a unique environment and a rich set of problems, and they allow us to observe and study (and eventually model) the behavior of stars in dense environments. As such, understanding globular cluster dynamics will continue to be important in other areas of astrophysics. For example, it will be a vital step on the road to understanding the even denser stellar populations in the vicinities of super-massive black holes in galactic nuclei.