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Astron. Astrophys. 328, 130-142 (1997)

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1. Introduction

In dense stellar systems, such as open and globular clusters and galactic nuclei, encounters between individual stars and binaries can affect the dynamical evolution of the system as a whole on a time scale comparable to, or even shorter than, a Hubble time. In order to reach a detailed theoretical understanding of such systems, the following three steps are necessary.

First, we need to understand the basic mechanism of the dynamical evolution, in the limit of a point-mass approximation for the stars. Second, effects of dynamical encounters on the internal evolution of single stars and binaries has to be taken into account. Third, we have to model the feedback of these internal changes onto the dynamical evolution of the whole system. Let us briefly review each step.

Great progress has been made with the first step, modeling the dynamical evolution of point-mass systems. In the seventies, the processes of core collapse and mass segregation were studied with the use of various types of Fokker-Planck approximations. In the eighties, these simulations were extended successfully beyond core collapse, and various studies were made of the phenomenon of gravothermal oscillations, ubiquitous in the post-collapse phase. Of these models a few even include mass loss due to the evolution of the stars (Chernoff & Weinberg 1990). In the nineties, we are finally beginning to switch over from Fokker-Planck approximations to much more detailed and realistic N -body simulations. In 1995, the construction of the GRAPE-4, a special-purpose machine with Teraflops speed, has made a [FORMULA] -body simulation feasible, providing the first direct evidence of gravothermal oscillations (Makino 1996a, b). Extending these simulations to the full realm of globular clusters ([FORMULA]) will require Petaflops speed, something that could be realized by future special-purpose machines in the GRAPE series by as early as the year 2000.

While the point-mass approximation provides a good qualitative guide for the construction of dynamical models of dense stellar systems, this approximation quickly breaks down when we require quantitatively accurate results. The second step attempts to model the effects of close encounters. A number of different investigations have estimated the rate at which physical collisions have taken place, under various circumstances (Hills & Day 1976, Verbunt & Meylan 1988, Di Stefano & Rappaport 1992 and Davies & Benz 1995). However, little progress has been made so far in following the changes induced in the stellar population, beyond enumerating the number of mergers. In the simulations presented below, collisions are modeled in an evolving population of single stars in a high-density stellar environment. Paper II in this series will extent our treatment to follow the induced changes in binary systems, both on the level of changes in orbital parameters as well as in the internal structure of the stars.

However, such investigations are only a start, and cannot lead to a quantitative modeling of dense stellar systems, since they are not yet self-consistent. What is needed in addition is a treatment of the feedback mechanism, from the changes in single stars and binaries back to the overall dynamics of the system. This third step is being pioneered for open clusters by Aarseth (1996). The current series of papers aims to provide self-consistent models of this type, by coupling relatively crude stellar evolution recipes, documented and tested in papers I and II, to a fully dynamical N -body system.

This paper is organized as follows. Our approach to the study of the ecology of star clusters is summarized in somewhat more detail in Sect. 2. The next section, Sect. 3, describes our simulation techniques, and the various approximations involved. In Sect. 4, we present the result of a simulation starting a single model, with a minimum of free parameters. The results of a more realistic core model run are presented in Sect. 5. Sect. 6 sums up.

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© European Southern Observatory (ESO) 1997

Online publication: March 24, 1998