# high performance computing on graphics processing units: hgpu.org

## Computer Simulation of Dark Matter Effects on Galaxy Rotation

Cole Kendrick
Los Alamos Middle School
Los Alamos Middle School, 2011

@article{mexico2011computer,

title={Computer Simulation of Dark Matter Effects on Galaxy Rotation},

author={Mexico, N. and Challenge, S. and Kendrick, C. and Kendrick, B.},

year={2011}

}

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The main goal of this project is to develop a computer program to model the rotation of a galaxy including dark matter. The computer program will be used to answer these questions: (1) How does dark matter affect rotational curves in galaxies; (2) how accurately can this be modeled; (3) what will happen when the dark matter and galaxy masses are changed; and (4) How well can this method work for different galaxies. The computer program was built-up over time. The first step was writing a computer program using Python to model a mass attached to a spring. This model was extended to twodimensions and then to a solar system model with both sun and interplanetary gravity interactions. Finally, the galaxy program was constructed using C by adding hundreds of "stars" to my solar system model in place of the planets and replacing the sun’s mass with a large central galaxy "core" mass. Dark matter is implemented in this model by treating it as an additional large mass point located at the center of the galaxy. Newton’s laws of motion were solved using a velocity Verlet method. The forces due to gravity were computed using two different methods: (1) nearest neighbor, a method that decreases calculation time by drawing a circle around each star and seeing whether a star is inside or not. Only the force due to gravity between the star and its neighbors will be computed (with the exception of the central mass); and (2) N-body, a method that computes the gravitational force between the current star and every other star in the galaxy and the central mass. The N-body approach is very slow. Both methods gave the essentially the same results but nearest neighbor is much faster and capable of using more stars. Five different calculations were run for the Andromeda galaxy. Nearest neighbor with dark matter, without dark matter, and less dark matter using 4400 stars, and N-body with and without dark matter using 520 stars. Two other galaxies NGC 2403 and NGC 3198 were also modeled using 4400 stars with dark matter. From these simulations I was able to successfully match the experimental data measured for Andromeda, NGC 2403 and 3198. My results show that dark matter is needed to maintain a stable galaxy. Dark matter also causes the galaxy to rotate much faster so that the rotational velocity remains constant out to the edge of the galaxy. These "flat" rotational curves are experimentally observed for nearly all spiral galaxie.
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