Semistochastic orbits in a triaxial potential

Abstract

view Abstract Citations (79) References (4) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Semistochastic orbits in a triaxial potential Goodman, J. ; Schwarzschild, M. Abstract The numerical investigation of stellar orbits in a specific triaxial potential, which was previously described, has been extended. The local stability has been tested for box orbits for one representative energy. Of these box orbits, 27% were found to be unstable. The stationary points of the unstable orbits fall in an area mostly near the minor axis but also extending to the intermediate axis. This situation is related to the characteristics of the special periodic orbits along the principal axes. The orbit along the major axis is stable, the one along the minor axis is unstable, and the one along the intermediate axis is unstable in one out of two independent perturbation directions. These results, which can be interpreted in terms of resonances between an orbit and its perturbations, may extend to a wider class of triaxial nonharmonic potentials. Seven box orbits-three stable ones and four unstable ones-were further investigated by integrating each orbit over a full Hubble time and recording the velocity vector each time the orbit crossed through a small cell at the center of the figure. For each stable orbit the velocities for all central crossings were identical within the numerical uncertainty, except for an eightfold multiplicity with the same reflection symmetries as the potential. This reemphasizes that the majority of orbits in the chosen potential have three effective integrals. On the other hand, for each unstable orbit the velocities for central crossings scatter around a mean value. However, the scatter is much less than one expects for a truly stochastic orbit. Each of the four unstable orbits visited only a small subregion of the total velocity domain visited by all unstable box orbits of the same energy. Accordingly these orbits are here referred to as semi stochastic rather than truly stochastic. The cause of this semistochasticity is not understood. To test whether the gross features of semistochastic orbits are more sensitive to perturbations than those of orbits with three effective integrals, three box orbits one stable and two unstable-were rerun with the application of perturbations at regular intervals. The perturbation strength varied between runs from the low level expected from stellar encounters to much stronger levels. Though strong perturbations increased the velocity dispersion for central crossings, the semi stochastic orbits proved no more sensitive than the stable one. It is concluded that in the specific case investigated no truly stochastic orbits exist and that, for the purpose of constructing numerical self-consistent equilibrium configurations, the semistochastic orbits may be considered in much the same way as regular orbits with three effective integrals. if the absence of truly stochastic orbits should prove to be a general phenomenon for potentials relevant to galaxies, the variety of equilibrium figures for galaxies should be larger than otherwise might be expected. Publication: The Astrophysical Journal Pub Date: May 1981 DOI: 10.1086/158885 Bibcode: 1981ApJ...245.1087G Keywords: Dynamic Stability; Mathematical Models; Orbit Perturbation; Orbital Mechanics; Stellar Motions; Encounters; Hubble Diagram; Self Consistent Fields; Stochastic Processes; Astrophysics full text sources ADS |