Trillion-Body Problem: Galaxies
The number of stars in a galaxy typically lies between a billion (for the smallest dwarf galaxies) and a trillion (for more normal galaxies). With such large numbers of stars, the interactions between individual stars are almost negligible compared to the interactions between a star and the gravitational field produced by the combined effects of all the stars in a galaxy. In other words, two-body relaxation effects are negligible, even on time scales compared to the Hubble time, a measure for the age of the Universe, slightly more than ten billion years.
As a result, simulations of the stellar dynamics of galaxies do not have to follow the histories of individual stars. Rather, it suffices to follow the trajectories of a limited number of mass points that sample the overall gravitational field. Close encounters between such sampling points do not have any special meaning; in fact, the potential of those points are `softened' precisely to avoid any artifical strong deflections. A consequence is that we can use approximate methods such as the tree code to estimate the gravitational potential of galaxies in simulations.
In the eighties, advanced in both hardware and software developments made it feasible to study the encounters between two galaxies in detail, to determine under which circumstances the two galaxies would merge, and what the properties of the merger remnants would be. Here are the results of some of our studies in this area:
- Collisions Between Galaxies: The Cyber 205 as an Astrophysical Laboratory, by Barnes, J. & Hut, P., 1988, in Science at The John von Neuman National Supercomputer Center, Annual Research Report Fiscal Year 1987, Princeton: Consortium for Scientific Computing, ed. G. Cook, pp. 27-32.
- Galaxy-Galaxy-Scattering: Head-on Encounters between Isotropic Equal Mass Plummer Models, by Teuben P. & Hut, P., 1988, Science on the ETA10: The Friendly User Program, Princeton: Consortium for Scientific Computing, ed. G. Cook, pp. 67-69.
- Collisions of Spherical Galaxies, by Makino J. & Hut, P., 1988, in Science on the ETA10: The Friendly User Program, Princeton: Consortium for Scientific Computing, ed. G. Cook, pp. 33-43.
- Head-on Collisions Between Plummer Models, by Peter Teuben & Hut, P., 1990, in Dynamics and interactions of galaxies, in Proceedings of the International Conference, Heidelberg, ed. R. Wielen (Berlin: Springer), pp. 227-228.
- Merger Rate of Equal-Mass Spherical Galaxies, by Makino, J. & Hut, P., 1997 Astrophys. J. 481, 83-94.
Here are a few papers I have co-authored, adressing the question of dark matter on various scales, from galactic to cosmic (dark matter is a term to describe matter that is detected solely through its gravitational effects, without so far any discernible detection optically or otherwise).
- Can a Neutrino-dominated Universe be Rejected? by Hut, P. & White, S.D.M., 1984, Nature 310, 637-640.
- The Maximum Mass of the Objects that Constitute the Unseen Disk Material, by Bahcall, J.N., Hut, P. & Tremaine, S.D., 1985, Astrophys. J. 290, 15-20.
- Constraints on Massive Black Holes as Dark Matter Candidates, by Hut, P. & Rees, M., 1992, Mon. Not. R. astr. Soc. 259, 27P-30P.