Numerical Experiments

To the best of my knowledge, the phrase ”Numerical Experiments” was coined by Michel Hénon himself in 1966, or as he called it ”Experiences Numérique” [6]. His idea was that one can study stellar systems within the context of a laboratory where all the parameters are known. Moreover, the effect of varying the parameters can be measured directly. This point of view conveniently ignores the role of chaos in non-linear systems but the principle still applies in a statistical sense. Bearing in mind the primitive state of the subject at the time, the new concept was very perceptive and is now taken for granted. Given my own long association with the N -body problem, it therefore makes a fitting theme for these brief comments on related contributions which were mainly made during his early career. I first met Michel in 1964 during the IAU Symposium No. 25 in Thessaloniki which also happened to be my first international meeting. In those early days, the number of people interested in performing direct N -body calculations was quite small so it was natural that we established close contact for the future. This contact was strengthened further by attending stellar dynamical conferences in Besancon (1966) and Paris (1968). Another notable event was that Michel was the first person to give a seminar at the brand new Institute of Theoretical Astronomy in the spring of 1967 (renamed IoA from 1972). On a personal level, I spent a few weeks at Nice Observatory around 1973 where I enjoyed fruitful discussions with Michel which resulted in a joint paper. I also came to appreciate his understanding of numerical errors. Thus in his opinion, the 1966 Bulirsch–Stoer method for numerical integration achieved the maximum accuracy that can be attained on a given computer. I also remember well his novel system for extracting specific references from a card index. The Ph.D. thesis of Michel Hénon [2] has played a major role for understanding the gravitational N -body problem as well as star cluster evolution. A key point here is that clusters evolve in response to energy generation at the centre. This novel idea anticipated the importance of binaries which was eventually clarified a decade later. In the proposed homology model, the evolution is towards infinite central density where the energy is accumulated by a small number of stars. To maintain energy conservation, about one-third of the energy is carried away by escaping stars. It is quite appropriate that an English translation of the two fundamental papers should now be available 50 years later