Workshop title: Modeling Dense Stellar Systems 

Organizers:

Douglas Heggie, School of Mathematics, University of Edinburgh
Steve McMillan, Department of Physics, Drexel University
Simon Portegies Zwart, Sterrewacht Leiden, Leiden University
Alison Sills, Department of Physics and Astronomy, McMaster University

Overview: 

The three-body problem has exercised the best mathematicians since the
time of Newton, leading to a stream of research which culminated in
the ground-breaking work of Poincare and the subsequent explosion of
research in low-dimensional dynamical systems.  At the other extreme,
the mathematical problems posed by systems with huge numbers of
particles were tackled in the parallel stream of research into
statistical mechanics, pioneered by Maxwell, Boltzmann, and many
others.  Somewhere in between lies the million-body problem: too large
to be treated by low-dimensional methods, and too small to be treated
statistically.  Yet systems in this range of size are ubiquitous.

Clusters of stars can be found throughout our Milky Way and other
galaxies. Ranging in size from hundreds to about a million stars, the
stars in these self-gravitating groups are all thought to have formed
at the same time. These systems are the birthplaces of stars and
planetary systems, and form the building blocks of galaxies. In dense
stellar systems, both long-range and short-range gravitational
encounters between stars have an important impact on the overall
evolution of the cluster. These encounters can also modify the
constitutent stellar populations, creating exotic objects such as
X-ray emitting neutron star binaries or possibly intermediate-mass
black holes.

The main challenge of modeling these systems comes from the many order
of magnitude of both length and time that must simultaneously be
followed computationally. Gravity is a long-range force, so the
contributions of all stars in the cluster must be included in each
calculation. At the other extreme, a binary star system can have a
separation which is 8 orders of magnitude smaller than the cluster
radius. We would like to follow these systems for the age of the
universe, about 12 billion years, but a strong encounter between two
stars can dramatically change their trajectories within a day or a
week. Dense stellar systems are also the ultimate "multi-physics"
problem, where we should include gravity (Newtonian and general
relativity), gas dynamics, radiative processes, stellar and binary
star evolution, nucleosynthesis, and chemical reactions in the
interstellar medium.

How do we address these challenges? From the perspective of applied
mathematics and physics, much work has been done to understand
techniques such as orbit regularization (Levi-Civita 1918,
Kustaanheimo & Stiefel 1965), adaptive resolution in both time and
space (Greengard et al. 1988, Leimkhler 2002), and understanding the
interations between different kinds of physical systems. From the
perspective of computer science, the N-body gravitational community
has long been involved in designing and implementing the computing
necessary to solve some of these problems.  The special-purpose GRAPE
hardware (Makino & Taiji, 1998) first emerged in 1989 and led the
field until the early 2000's. It has recently been superceded by both
GPU and SIMD programmable systems, combined with MPI parallelization
of the "front-end" computing
(http://www.khalisi.com/phdthesis/nb6manual.html).

A decade ago, a small group of researchers from astrophysics,
mathematics, and computer science came together to create the MODEST
collaboration (see http://www.manybody.org/modest). This loose-knit,
informal group changes fluidly in size and scope over the years, but
is anchored by the commitment of all its members to a collaborative,
cross-disciplinary approach to MOdelling DEnse STellar systems. The
meetings of this group range from small workshops and schools to
formal conferences, depending on the circumstances and the wishes of
the various meeting organizers. The proposed workshop will return
MODEST to its roots of a small, informal workshop at which issues are
discussed in depth between researchers with a variety of backgrounds
and expertise.

REFERENCES: 

Greengard L. et al 1988, SIAM J. Sci. Stat. Comput. 9, 669
Kustaanheimo P & Stiefel E (1965), J. Reine Angew. Math., 218, 204
Leimkuhler, B (2002) Applied Num. Math., 48, 175
Levi-Civita T. (1918) Acta Math., 42, 99
Makino J., Taiji M., 1998, Scientific Simulations with Special-Purpose
Computers - The GRAPE Systems (Wiley: Chichester)


Objectives, relevance, importance, and timeliness:

The early evolution of dense stellar systems is an open and important
topic. There is a phase between the giant molecular cloud and the
(gas-less) star cluster that is currently unknown and largely
unexplored. We know observationally that most stars form in clusters,
but the transition between gas-rich star forming regions and gas-free
clusters has not been observed in much detail. On the theoretical
side, almost all dynamical simulations of star clusters begin with a
gas-free cluster in equilibrium. In the last few years, with the
advent of faster computers and more sophisticated codes, theorists
have been investigating star formation in clustered environments, the
early dynamical relaxation of young clusters, and the implications of
the presence of gas on, for example, the mass functions in clusters,
the presence of free-floating planets & brown dwarfs, and the creation
of massive stars and intermediate mass black holes. This is a field
with many avenues for advancement.

The complex interplay among many physical processes makes dense
stellar systems important but difficult targets for both theoretical
modeling and high-resolution observations.  Great progress has been
made in recent years, with binary dynamics, realistic external fields,
central black holes, and stellar and binary evolution now routinely
incorporated into large-scale simulations, and powerful hardware (in
the form of GPU and GRAPE systems) has become available to vastly
speed up these calculations. In particular, the GRAPE-DR project at
the University of Tokyo is nearing completion, and recently ranked
top as the most energy-efficient supercomputer, with a rating of 815
Mflops/W. The AMUSE project (Astrophysical MUltipurpose Software
Environment; see http:\\amusecode.org) is a comprehensive environment
for modeling dense stellar systems, including multiphysics/legacy
codes and flexible interfaces to integrate existing software (written
in many languages) within this unifying environment. They have just
announced their first release. At the same time, a wealth of new
observational data has become available, and more can be expected to
emerge in the near future (including international ground-based and
space missions such as GAIA, LAMOST, LOFAR, etc.).

The dynamics of dense stellar systems are driven by a wide variety of
tightly coupled physical phenomena. Understanding these phenomena
requires similarly close coordination among researchers working in
these fields. The purpose of this workshop is to bring together
experts (physicists and mathematicians) in theoretical and computer
modeling of dense star clusters, and interested experts in computer
hardware and software design.  Our goal is to inspire new models and
simulation techniques, to define new joint projects likely to advance
these collaborations, and to make progress in confronting detailed
models with high-resolution observations. Understanding the kinds of
algorithms that will be used in the next 5-10 years is crucial to
determing what kind of hardware we design. Looking forward, we see
that software is starting to follow telescopes into the realm of team
projects. Collaboration between users and creators of software and
hardware, and training of individuals who are both users and creators,
will be crucial to allow us to fully understand these important
components of the universe.