Astrophysical N-Body Simulations of Star ClustersTeam: 68 School: Los Alamos High Area of Science: Physics and Mathematics
Interim: Problem Statement:
Questions about star clusters are central to understanding many problems in astronomy and cosmology [1,2]. We are working to simulate the formation and evolution of small star clusters using a direct N-body method [3,4] to model their gravitational interactions. Last year for the SuperComputing Challenge, our team developed an N-body code and simulations of the solar system using a small number of bodies. This year we are extending our analysis of the solar system to model star clusters using a few thousand bodies.
Problem Solution:
We are working on computational models using Newtonian mechanics and the Universal Law of Gravitation. Each star (or body) is modeled as a point mass with a prescribed initial position and velocity [5]. A leapfrog numerical method [6,7] is being used to integrate the equations of motion based on Euclidean geometry and Newton’s Universal Law of Gravitation. All simulations are being performed with codes written in C [8]. For the star cluster simulations, a random number generator is being used to specify all initial data. The simulations are being run on both Mac and PC platforms with both Apple and Microsoft operating systems.
Progress to Date:
We have successfully simulated several basic problems in Newtonian mechanics using a leapfrog integrator. We have solved linear spring-mass problems with one and two masses, and nonlinear aerodynamic drag problems in one- and two-dimensions. In the mechanics simulations, the basic physical properties were studied. For example, in the drag problems a body was dropped from a fixed height and the time of flight was computed as well as the terminal velocity and impact position. These problems were studied to understand how the leapfrog integrator works and how to validate the numerical results. The mechanics problems have also helped us to develop coding techniques for N-body star cluster problem.
Preliminary simulations have been run for N-body problems with a few thousand bodies using the leapfrog scheme. Calculations with up to 4000 bodies have been run. A single multi-day simulation has been run with approximately 2200 bodies. We are currently working to specify the physical constants and length and time scales needed for a realistic model of a star cluster. We are also experimenting with random number generators to compute the required initial data for a star cluster simulation. All star cluster simulations are run in three spatial dimensions.
Expected Results:
We are planning to redo our model of the solar system to develop a variable step-size leapfrog integrator. After completing simulations of the solar system, we plan to run numerical experiments on small star clusters modeled with 1000 to 3000 bodies. It is expected that a practical limit to the number of bodies will be less than 3000 bodies based on the wall-clock time (~ a few days) required to complete a simulation. Our key expectation from this work is to apply the N-body codes to perform numerical experiments to improve our understanding of the gravitational mechanics of the universe.
References:
1. Binney, J. and Merrifield, M., Galactic Astronomy, Princeton University
Press, 1998.
2. Binney, J. and Tremaine, S., Galactic Dynamics, Second Edition, Princeton University Press, 2008.
3. Aarseth, S. J., Gravitational N-Body Simulations, Cambridge University Press, 2003.
4. Aarseth, S. J., Tout, C. A., and Mardling, R. A. (Editors), The Cambridge N-Body Lectures, Springer-Verlag, 2008.
5. Heggie, D., and Hut, Piet, The Gravitational Million-Body Problem, Cambridge University Press, 2003.
6. Wikipedia Article: en.wikipedia.org/wiki/Leapfrog_integration.
7. Hut, P., Makino, J., and McMillan, S., “Building a Better Leapfrog,” The Astrophysical Journal, Vol. 443, 1995.
8. Kernighan, B. W. and Ritchie, D. M., The C Programming Language, 2nd Edition, Prentice Hall, 1988.
Team Members: Samuel Baty
Peter Armijo
Sponsoring Teacher: Lee Goodwin Mail the entire Team |
