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0. Preface

This whole volume is dedicated to a detailed study of Plummer's model. We could have called it `Plummer for dummies,' because the explanations and derivations given here are far more extensive than is usually the case in text books. Even so, the prefered type of `dummies' are those that are happy to learn about Abel integral equations and stuff like that.

We present all results in such an easy-going style, that you don't even need pen and paper to follow the argument. The main reason for this approach is that we want to be realistic in presenting the discussion as a dialogue. Whereas text books often state that `it can be easily seen that', in practice it may well take quite a while, and a number of pages of paper, before the reader finally has seen what was supposed to be easy. In contrast, when two people talk in front of a blackboard, or bend over a note pad, they don't follow such a clinical approach. They are more likely to write things out in long-hand, and that is exactly what our main characters do in this volume.

The main purpose for treating Plummer's model with such respect is that it forms a convenient example for showing how to construct models in phase space. Building a structure in six dimensions, rather than three, is something that you have to get used to. By the time you are really experienced doing so, it is easy to forget how counter-intuitive it probably looked, the first time you gave it a try. Our approach here is to present much of the theoretical argumentation that goes into model building not in an abstract way, but rather with the concrete example of Plummer's model, and specifically with the even more concrete question: here is a computer screen, and here is the keyboard, now sit down and create a star cluster.

It is this hands-on approach that Alice and Bob continue to pursue, as they have done in all previous volumes. In future volumes, they will no doubt come back to construct King models, as well as anisotropic and multi-mass generalizations. They will be able to move along much faster in those cases, having mastered the main principles while juggling Plummer's model. We hope you will enjoy the beauty and elegance of what is the most venerable star cluster model, with a history spanning now more than 120 years.

0.1. Acknowledgments

Besides thanking our home institutes, the Institute for Advanced Study in Princeton and the University of Tokyo, we want to convey our special gratitude to the Yukawa Institute of Theoretical Physics in Kyoto, where this volume was written, during a visit in June 2004, made possible by the kind invitations to both of us by Professor Masao Ninomiya.

We thank Shawn Slavin, Jason Underdown and Marcel Zemp for their comments on the manuscript.

Piet Hut and Jun Makino

Kyoto, July 2004
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