Optimal choice of the softening length and time step in <Emphasis Type="Italic">N</Emphasis>-body simulations |
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| Authors: | S A Rodionov N Ya Sotnikova |
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| Institution: | (1) Sobolev Astronomical Institute, St. Petersburg State University, Universitetskii pr. 28, Petrodvorets, St. Petersburg, 198904, Russia |
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| Abstract: | A criterion for the choice of optimal softening length ε for the potential and the choice of time step dt for N-body simulations of a collisionless stellar system is analyzed. Plummer and Hernquist spheres are used as models to analyze how changes in various parameters of an initially equilibrium stable model depend on ε and dt. These dependences are used to derive a criterion for choosing ε and dt. The resulting criterion is compared to Merritt’s criterion for choosing the softening length, which is based on minimizing the mean irregular force acting on a particle with unit mass. Our criterion for choosing ε and dt indicate that ε must be a factor of 1.5–2 smaller than the mean distance between particles in the densest regions to be resolved. The time step must always be adjusted to the chosen ε (the particle must, on average, travel a distance smaller than 0.5 ε during one time step). An algorithm for solving N-body problems with adaptive variations of the softening length is discussed in connection with the task of choosing ε, but is found not to be promising. |
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