Exact General Solutions to Extraordinary N-body Problems

We solve the N-body problems in which the total potential energy is any function of the mass-weighted root-mean-square radius of the system of N point masses. The fundamental breathing mode of such systems vibrates non-linearly for ever. If the potential is supplemented by any function that scales as the inverse square of the radius there is still no damping of the fundamental breathing mode. For such systems a remarkable new statistical equilibrium is found for the other coordinates and momenta, which persists even as the radius changes continually.Comment: 15 pages, LaTeX. Accepted for publication in Proc. Roy. Soc.

Relaxation to a Perpetually Pulsating Equilibrium

Paper in honour of Freeman Dyson on the occasion of his 80th birthday. Normal N-body systems relax to equilibrium distributions in which classical kinetic energy components are 1/2 kT, but, when inter-particle forces are an inverse cubic repulsion together with a linear (simple harmonic) attraction, the system pulsates for ever. In spite of this pulsation in scale, r(t), other degrees of freedom relax to an ever-changing Maxwellian distribution. With a new time, tau, defined so that r^2d/dt =d/d tau it is shown that the remaining degrees of freedom evolve with an unchanging reduced Hamiltonian. The distribution predicted by equilibrium statistical mechanics applied to the reduced Hamiltonian is an ever-pulsating Maxwellian in which the temperature pulsates like r^-2. Numerical simulation with 1000 particles demonstrate a rapid relaxation to this pulsating equilibrium.Comment: 9 pages including 4 figure

From Quasars to Extraordinary N-body Problems

We outline reasoning that led to the current theory of quasars and look at George Contopoulos's place in the long history of the N-body problem. Following Newton we find new exactly soluble N-body problems with multibody forces and give a strange eternally pulsating system that in its other degrees of freedom reaches statistical equilibrium.Comment: 13 pages, LaTeX with 1 postscript figure included. To appear in Proceedings of New York Academy of Sciences, 13th Florida Workshop in Nonlinear Astronomy and Physic

The Structure of the Outer Halo of the Galaxy and its Relationship to Nearby Large-Scale Structure

We present evidence to support an earlier indication that the Galaxy is embedded in an extended, highly inclined, triaxial halo outlined by the spatial distribution of companion galaxies to the Milky Way. Signatures of this spatial distribution are seen in 1) the angular variation of the radial-velocity dispersion of the companion galaxies, 2) the spatial distribution of the M~31 sub-group of galaxies, 3) the spatial distribution of the isolated, mainly dwarf irregular, galaxies of the Local Group, 4) the velocity anisotropy quadrupole of a sub-group of high-velocity clouds, and 5) the spatial distribution of galaxies in the Coma-Sculptor cloud. Tidal effects of M~31 and surrounding galaxies on the Galaxy are not strong enough to have affected the observed structure. We conclude that this distribution is a reflection of initial conditions. A simple galaxy formation scenario is proposed which ties together the results found here with those of Holmberg (1969) and Zaritsky et al. (1997) on the peculiar distribution of satellites around a large sample of spiral galaxies.Comment: Accepted for publication in the Astron J., March 2000, 12 pages with 1 figur

Gravothermal Catastrophe, an Example

This work discusses gravothermal catastrophe in astrophysical systems and provides an analytic collapse solution which exhibits many of the catastrophe properties. The system collapses into a trapped surface with outgoing energy radiated to a future boundary, and provides an example of catastrophic collapse.Comment: To appear in Phys. Rev.

The Relativistically Spinning Charged Sphere

When the equatorial spin velocity, $v$, of a charged conducting sphere approaches $c$, the Lorentz force causes a remarkable rearrangement of the total charge $q$. Charge of that sign is confined to a narrow equatorial belt at latitudes $b \leqslant \sqrt{3} (1 - v^2/c^2)^{{1/2}}$ while charge of the opposite sign occupies most of the sphere's surface. The change in field structure is shown to be a growing contribution of the `magic' electromagnetic field of the charged Kerr-Newman black hole with Newton's G set to zero. The total charge within the narrow equatorial belt grows as $(1-v^2/c^2)^{-{1/4}}$ and tends to infinity as $v$ approaches $c$. The electromagnetic field, Poynting vector, field angular momentum and field energy are calculated for these configurations. Gyromagnetic ratio, g-factor and electromagnetic mass are illustrated in terms of a 19th Century electron model. Classical models with no spin had the small classical electron radius $e^2/mc^2\sim$ a hundredth of the Compton wavelength, but models with spin take that larger size but are so relativistically concentrated to the equator that most of their mass is electromagnetic. The method of images at inverse points of the sphere is shown to extend to charges at points with imaginary co-ordinates.Comment: 15 pages, 1figur

Are Complex A and the Orphan Stream related?

We consider the possibility that the Galactic neutral hydrogen stream Complex A and the stellar Orphan stream are related, and use this hypothesis to determine possible distances to Complex A and the Orphan stream, and line-of-sight velocities for the latter. The method presented uses our current knowledge of the projected positions of the streams, as well as line-of-sight velocities for Complex A, and we show that a solution exists in which the two streams share the same orbit. If Complex A and the Orphan stream are on this orbit, our calculations suggest the Orphan stream to be at an average distance of 20 kpc, with heliocentric radial velocities of approximately -110 km/s. Complex A would be ahead of the Orphan stream in the same wrap of the orbit, with an average distance of 10 kpc, which is consistent with the distance constraints determined through interstellar absorption line techniques.Comment: 4 pages, 2 figures; typos corrected, fig 2 and numerical predictions updated; accepted for publication in MNRAS Letter