Activities in 1991-1992

From the Report for Academic Year 1991-1992
of the Institute for Advanced Study

PIET HUT has made contributions to a number of different areas in stellar dynamics, from the three-body problem and the evolution of star clusters to the structure of the dark matter in the Universe. In addition, he has continued his interdisciplinary collaborations in the areas of computer science and geology. In the former field, he is involved in a project to develop faster hardware and software for astrophysical simulations. In the latter, he is studying the dynamics of multiple cometary impacts, and their geological and paleontological consequences.

Prof. Hut has completed a long-term study of the three-body problem, including a definitive analytical treatment of the various approximation techniques for three-body gravitational scattering, in collaboration with Douglas Heggie from Edinburgh University. Other aspects of the three-body problem which they studied were the various four-dimensional regularization techniques which avoid the Kepler singularities in three-dimensional close encounters. Finally, the process of double star formation, through the net effect of two-body and three-body encounters, was analyzed in a thermodynamic treatment in collaboration with Jeremy Goodman from Princeton University.

The evolution of star clusters still yields new and fundamental results, as exemplified by another collaboration of Hut with Goodman and Heggie. This yielded the time scale for exponential growth in such systems, as being a fraction of the crossing time, independent of the number N of stars, apart from a very weak log log N dependence. Other basic new results were two forms of stability analysis: one of a self-gravitating isothermal sphere, in collaboration with Jun Makino from Tokyo University; the other a study of mass segregation in two-component star systems, both in a microcanonical and in a canonical ensemble, in collaboration with Yueming Xu, a postdoctoral member at the IAS.

On the more applied side, Prof. Hut gathered several observers and theorists together in a small meeting on the topic of double stars in globular clusters. This resulted in a comprehensive review paper on that topic, covering various types of optical, X-ray, and radio observations, as well as direct-integration, Fokker-Planck, and Monte-Carlo simulations. Also, together with George Djorgovski from the California Institute of Technology, Prof. Hut determined the average rates of core collapse and evaporation for the ensemble of galactic globular clusters.

In separate investigations, Prof. Hut put limits on the amount and type of dark matter present in two astrophysical systems: on massive black holes in the area around the center of our galaxy (with Martin Rees, a visitor from Cambridge University); and on elementary particles in the halos of star clusters (with Heggie and Kim Griest, a visitor from Berkeley).