A numerical algorithm for dissipative Keplerian particle discs |
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| Authors: | M D Melita & M M Woolfson |
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| Institution: | Physics Department, University of York, Heslington, York YO1 5DD |
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| Abstract: | We present a numerical algorithm designed to study the evolution of a distribution of solid particles orbiting around the Sun that could be applied to similar systems in which f c ≤ Ω/2π, where f c is the frequency of collisions, and Ω is the orbital angular speed. A number of sample particles are used to represent the whole system. Binary collisions are treated in a novel way using a Monte Carlo method that works as follows. Orbits are locally sampled to compute the velocity dispersion. Then the velocity vectors of the sample particles are modified according to random collisions with virtual particles which have velocities taken from a normal distribution computed using the previously found local velocity dispersion. The energy and momentum taken up by the virtual particles are redistributed among the neighbours of the sample particle undergoing the collision, so that conservation laws are satisfied. Simulations using this model give an estimation of the final distribution of inclinations and the associated evolutionary time-scale. |
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| Keywords: | methods: numerical Solar system: formation |
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