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This paper summarises an investigation of chaos in a toy potential which mimics much of the behaviour observed for the more realistic triaxial generalisations of the Dehnen potentials, which have been used to model cuspy triaxial galaxies both with and without a supermassive black hole. The potential is the sum of an anisotropic harmonic oscillator potential, V_o=(1/2)*(a^{2}x^{2}+b^{2}y^{2}+c^{2}z^{2}), and a spherical Plummer potential, V_o=-M_{BH}/(r^{2}+e^{2})^{1/2} with r^{2}=x^{2}+y^{2}+z^{2}. Attention focuses on three issues related to the properties of ensembles of chaotic orbits which impact on chaotic mixing and the possibility of constructing self-consistent equilibria: (1) What fraction of the orbits are chaotic? (2) How sensitive are the chaotic orbits, i.e., how large are their largest (short time) Lyapunov exponents? (3) To what extent is the motion of chaotic orbits impeded by Arnold webs, i.e.,, how `sticky are the chaotic orbits? These questions are explored as functions of the axis ratio a:b:c, black hole mass M_BH, softening length e, and energy E with the aims of understanding how the manifestations of chaos depend on the shape of the system and why the black hole generates chaos. The simplicity of the model makes it amenable to a perturbative analysis. That it mimics the behaviour of more complicated potentials suggests that much of this behaviour should be generic.
This talk provides a progress report on an extended collaboration which has aimed to address two basic questions, namely: Should one expect to see cuspy, triaxial galaxies in nature? And can one construct realistic cuspy, triaxial equilibrium models
Cuspy shadow was first reported for hairy rotating black holes, whose metrics deviate significantly from the Kerr one. The non-smooth edge of the shadow is attributed to a transition between different branches of unstable but bounded orbits, known as
This paper investigates chaos and chaotic phase mixing in triaxial Dehnen potentials which have been proposed to describe realistic ellipticals. Earlier work is extended by exploring the effects of (1) variable axis ratios, (2) `graininess associated
We have constructed realistic, self-consistent models of triaxial elliptical galaxies embedded in triaxial dark matter halos. Self-consistent solutions by means of the standard orbital superposition technique introduced by Schwarzschild were found in
Galaxies that contain bulges appear to contain central black holes whose masses correlate with the velocity dispersion of the bulge. We show that no corresponding relationship applies in the pure disk galaxy M33. Three-integral dynamical models fit H