Evolution of the Ring of Gravitating Bodies with and Without the Central Body and Properties of Their Chaotic Behavior

Authors: A.V. Melkikh, E.A. Melkikh, V.A. Kozhevnikov

The time dependence of distribution function for the system composed of material points having circular orbits at initial moment of time with and without massive central body is obtained. As a result of chaotization of orbits, a part of material points evaporates (acquires positive total energy). Dependence of the fraction of evaporated material points on the width of the disk, their mass and initial distance to the central body is obtained. Wherein, the maximum fraction of evaporated particles for the case with central body is equal to 0.4. Initial stage of evaporation of a ring of particles with a central body is a subdiffusion with the dependence of the mean square bias on time =Kαt^α, where α = 0.27. For the case without a central body, the fraction of evaporated particles is obtained as a function of the number of particles in the ring and virial ratios. The dependence of the fraction of particle pairs leaving the system on the number of particles in the ring is obtained. The average fraction of pairs for the virial ratio K = -U turned out to be 0.2. Power spectra characterizing the evaporation of particles, approximated by a power-law dependence on frequency, are obtained.

Comments: 35 Pages.

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[v1] 2018-06-27 23:19:02

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