Nonbaryonic dark matter, specifically weakly interacting massive particles (WIMPs) can become bound within the Solar System due to three-body interactions with Jupiter and the Sun. Numerical simulation and analytical methods were used to determine a time-averaged cross section for the capture process. This cross section of bound particles as found by simulated two-dimensional WIMP trajectories, along with the partial flux of WIMPs based on a Maxwell-Boltzmann velocity distribution, can be used as a step towards understanding the current dearth of WIMP detection by finding the WIMPs' rate of capture. As an intermediary step,a two-dimensional toy Solar System was considered. For the two-dimensional simulation, this rate of capture is found to be R = ERjvjC, with Rj the radius of Jupiter's orbit, vj the orbital velocity of Jupiter, p, the dark matter density at the location of the Solar System, m, WIMP mass, and thc dimensionless constant C determined to be, C = 2.2942 x lop5. Similar methods were used in a three-dimensional simulation, which resulted in a rate of capture of R = ER?u,C, with the dimensionless constant C, determined to be, C = 2.3806 x lou6. The phase space distribution of captured WIMPs was also determined through numerical simulation. The rate of capture is one part of the calculation to determine the steady state distribution of bound dark matter particles in the Solar System.
Kennedy, Allison, "Rate of Gravitational Capture of Dark Matter Particles" (2011). Physics and Astronomy Honors Projects. Paper 12.
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