NONLINEAR DYNAMICS IN GALAXIES AND EXO-SOLAR PLANETARY SYSTEMS



The Sixteenth Annual Workshop on Nonlinear Astronomy and Physics is scheduled to take place on the University of Florida campus in Gainesville, Florida on Thursday 15 February through Saturday 17 February 2001.

The objective of the workshop is to bring together for three days experts from galactic dynamics, solar system dynamics, and applied mathematics to discuss problems and recent progress which has been made in applying the technology of nonlinear dynamics to problems relevant to galactic astronomy and exo-solar planetary systems. The principal focus is on interdisciplinary interactions between astronomers in different areas who are, in many respects, addressing problems that require similar tools and methodologies.

We aim typically for a small workshop, with a total of some fifteen to twenty speakers, each giving talks of order 30 - 40 minutes in length, thereby providing an environment conducive for extensive one-on-one exchanges. Our particular hope is to stimulate interactions between individuals in diverse fields addressing problems which, despite obvious differences, share significant commonalities.

The workshop is supported in part by the Department of Astronomy, Department of Physics, and College of Liberal Arts and Sciences at the University of Florida. We have also received a modest grant from the National Science Foundation to help support the participation of graduate students and young postdocs from other institutions. Students and/or postdocs interested in such support should contact:

kandrup@astro.ufl.edu.

There will be six regular sessions, two each on Thursday, Friday, and Saturday, in the mornings and afternoons. There will also be an informal reception/poster session where students and postdocs can present their work.
The following material is extracted from our successful NSF grant proposal:

Motivation

The objective of the workshop is to bring together for three days selected experts from galactic dynamics, solar system dynamics, and applied mathematics to discuss problems and recent progress which has been made in applying the technology of nonlinear dynamics to problems relevant to galactic astronomy and exo-solar planetary systems. The principal focus is on interdisciplinary interactions between astronomers in different areas who are, in many respects, addressing problems that require similar tools and methodologies. The workshop is funded primarily by the Departments of Astronomy and of Physics, the College of Liberal Arts and Sciences, and the Office of Research, Technology, and Graduate Education at the University of Florida.

Introduction

Cross-disciplinary research in Astronomy and Physics has become increasingly intense and productive over the past decade. It is evident from numerous examples that developments in one field can proceed more quickly when infomation is made available about parallel developments in other fields. This occurs not only by exchange of methods and techniques but also from conceptual refinement resulting from different perspectives applied to similar problems. One of the most effective means for stimulating such exchanges is to assemble expert representatives from several different fields for discussions of broadly defined topics in which there have been recent developments. The 2001 Florida Workshop in Nonlinear Astronomy and Physics, to be held on 15 - 17 February at the University of Florida, will assemble a collection of theorists from the fields of galactic dyanmics, solar system dynamics, and applied mathematics to discuss various topics involving applications of nonlinear dynamics to problems in galactic astronomy and exo-solar planetary systems.

Now is a particularly appropriate time for such a workshop. Over the past several years, observations provided both by the Hubble Space Telescope and ground-based telescopes have provided compelling evidence that many galaxies are genuinely three-dimensional, i.e., neither spherical nor axisymmetric, that they typically have a central density cusp, and that the center of the galaxy often contains a supermassive black hole. However, succesfully modeling cuspy triaxial galaxies requires new techniques which necessitate a more sophisticated understanding of nonlinear dynamics than is the case for axisymmetric systems without a central cusp. The past several years have also witnessed the discovery of numerous planets around other stars as well as increasingly detailed images of protoplanetary discs. Synthesising these observations with an improved understanding of planetesimals and other debris from the formation of our own Solar System could lead to the first clear picture of how planetary systems form and evolve.

Until recently, much of the theoretical work in both these areas has been almost completely numerical, with the aim of modeling specific astronomical objects. However, the success of these efforts would suggest that the time has come to assess this work so as to better understand the specific dynamical features which are responsible for what is actually observed. Although protoplanetary systems and galaxies are very different sorts of objects, the dynamical issues that arise exhibit striking similarities. In both cases, one is concerned with resonance phenomena and tidal interactions in a complex phase space associated with a system which is nearly, but not completely, Hamiltonian.

The Workshop

The main purpose of this workshop, the sixteenth in a series of annual Workshops in Nonlinear Astronomy and Physics held at the University of Florida, is to acquaint the participants with developments in neighbouring areas. Our past experience is that the Florida Workshops are very conducive to such cross-fertilization: in particular, many collaborations have developed from interactions during the first fifteen workshops. The Workshop will focus on four basic themes:

New theoretical tools and techniques

Some of these are primarily computational, e.g., the development of improved, more efficient integration schemes which, combined with recent advances in hardware, allow one to perform computations that were almost inconceivable a decade ago. In particular, it is now possible to solve both the N-body problem and partial differential equation using symplectic integration schemes similar to those which have been developed by accelerator dynamicists over the past decade. However, the past few years have also seen significant advances in the tools available to dynamicists interested in understanding and quantifying transport phenomena in a complex phase space, including, e.g., spectral techniques and short time Lyapunov exponents

Resonance Phenomena

Resonance phenomena clearly play a major role in both galaxies and protplanetary systems. In the context of galactic astronomy, it has been recognised recently that resonances can play a crucial role in phenomena as different as the origins of spiral structure and warps in galactic discs; the dynamical evolution of globular clusters and satellite objects in and near our Galaxy; and tidal interactions between different galaxies situated in a dense cluster environment. It also appears likely that resonance overlap will trigger large amounts of chaos in the centers of realistic triaxial galaxies which may preclude the possibility of their achieving a true equilibrium. Resonance overlap clearly accounts for the origin of the Kirkwood gaps in the asteroid belt and is the driving mechanism that results in the transfer of meteorites from the asteroid belt to the Earth. Resonance overlap also has a pivotal role in the orbital evolution of comets in the Kuiper belt, although this is less well understood.

Transport Theory in Chaotic Phase Spaces

Phase space transport undoubtedly plays an important role in both galaxies and planetary systems. Planetary systems exhibit a systematic secular evolution as planetesimals and other smaller objects drift through a complex phase space. A correct interpretation of the asteroid belt and the Kuiper belt as fossil relics of the early Solar System requires that one account for this evolution, so that one can translate what is currently observed into useful information about what the Solar System was like more than four billion years ago. Our own Solar System is the best example of a well-observed, dynamically evolved disk system and may be our best guide to understanding the dynamical evolution of protoplanetary disks in general. Phase space transport is likely to prove a crucial ingredient in the formation and dissipation of bars and other transitory structures in galaxies, particularly near corotation and the Lindblad resonances and, in cuspy triaxial galaxies, could be associated with systematic changes in shape that can in principle be inferred from the Sloan Digital Sky Survey and other similar projects.

Low Level Perturbations

Comparatively low amplitude perturbations, often associated with dissipation, can play an important role in the evolution of both galaxies and protoplanetary systems. For example, comparatively weak forces associated with Poynting-Robertson light drag and even the Yarkovsky effect may have had a profound effect on the dynamical evolution of dust and other small bodies in our own Solar System and in other, exo-solar systems. Galaxies situated in a dense cluster are continually subjected to near-random forces and torques associated with neighbouring objects which imply that they are never in a true equilibrium; and, at least for cuspy triaxial galaxies, it is likely that the existence of discrete substructures like globular clusters and giant molecular clouds can have a significant effect.

The workshop will explore the themes described above, but the meeting will be defined by the participants and will follow directions generated by their presentations and discussions.


Confirmed Speakers

Courtlandt Bohn, Fermilab:
Chaotic-Mixing Time Scales in Charged-Particle Beams and Galaxies

Philip Boyland, University of Florida:
How does topology influence Hamiltonian dynamics?

Robert Buchler, University of Florida

George Contopoulos, University of Athens:
Order and Chaos in Self-Consistent Galactic Models

Chris Hunter, Florida State University:
Spectral analysis of orbits via discrete Fourier transforms

Henry Kandrup, University of Florida:
Noise, graininess, and phase space diffusion in the N-body problem

Richard Lovelace, Cornell University:
Hamiltonians for Accretion Disk Modes
Poynting Outflows and Jets from Accretion Disks

Daniel Pfenniger, Observatoire de Geneve:
The highly non-linear dynamics of interstellar matter

Renu Malhotra, University of Arizona:
Resonance sweeping phenomena in the solar system

Andrea Milani, University of Pisa:
Stable chaos and diffusion in the asteroid main belt

Ji Qiang, Los Alamos National Laboratory:
Self-Consistent Modeling of Coulomb Collisions

Edward Spiegel, Columbia University:

Glen Stewart, University of Colorado:
Negative Energy Modes and the Nonlinear Evolution of Planetary Rings



ORGANISERS:
Henry E. Kandrup: kandrup@astro.ufl.edu
Stanley D. Dermott: dermott@astro.ufl.edu
J. Robert Buchler: buchler@phys.ufl.edu