Self-consistent triaxial de Zeeuw-Carollo models

¹ Department of Physics and Institute of Astronomy, National Tsing-Hua University, Hsin-Chu 30013, Taiwan e-mail: [pthakur;jiang]@phys.nthu.edu.tw
² Division of Science Education, Pusan National University, Busan 609-735, Korea e-mail: [mdas;hbann]@pusan.ac.kr
³ School of Studies in Physics, Pt. Ravishankar Shukla University, Raipur 492 010, India e-mail: ircrsu@sancharnet.in

Received: 6 May 2004
Accepted: 10 September 2007

Abstract

We use the standard method of Schwarzschild to construct self-consistent solutions for the triaxial de Zeeuw & Carollo (1996) models with central density cusps. ZC96 models are triaxial generalizations of spherical γ-models of Dehnen whose densities vary as near the center and r^-4 at large radii and hence, possess a central density core for and cusps for . We consider four triaxial models from ZC96, two prolate triaxials: with and 1.5, and two oblate triaxials: with and 1.5. We compute 4500 orbits in each model for time periods of . We find that a large fraction of the orbits in each model are stochastic by means of their nonzero Liapunov exponents. The stochastic orbits in each model can sustain regular shapes for ~ or longer, which suggests that they diffuse slowly through their allowed phase-space. With the exception of the oblate triaxial models with , our attempts to construct self-consistent solutions employing only the regular orbits fail for the remaining three models. However, the self-consistent solutions are found to exist for all models when the stochastic and regular orbits are treated in the same way because the mixing-time, ~, is shorter than the integration time, . Moreover, the “fully-mixed” solutions can also be constructed for all models when the stochastic orbits are fully mixed at 15 lowest energy shells. Thus, we conclude that the self-consistent solutions exist for our selected prolate and oblate triaxial models with and 1.5.