EDP Sciences
Free access
Volume 475, Number 3, December I 2007
Page(s) 821 - 825
Section Extragalactic astronomy
DOI http://dx.doi.org/10.1051/0004-6361:20041236

A&A 475, 821-825 (2007)
DOI: 10.1051/0004-6361:20041236

Self-consistent triaxial de Zeeuw-Carollo models

Parijat Thakur1, Ing-Guey Jiang1, M. Das2, D. K. Chakraborty3, and H. B. Ann2

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 )

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 $\gamma$-models of Dehnen whose densities vary as $r^{-\gamma}$ near the center and r-4 at large radii and hence, possess a central density core for $\gamma=0$ and cusps for $\gamma > 0$. We consider four triaxial models from ZC96, two prolate triaxials: (p, q) = (0.65, 0.60) with $\gamma = 1.0$ and 1.5, and two oblate triaxials: (p, q) = (0.95, 0.60) with $\gamma = 1.0$ and 1.5. We compute 4500 orbits in each model for time periods of $10^{5} T_{\rm D}$. 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 ~ $10^{3} T_{\rm D}$ or longer, which suggests that they diffuse slowly through their allowed phase-space. With the exception of the oblate triaxial models with $\gamma = 1.0$, 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, ~ $10^{4} T_{\rm D}$, is shorter than the integration time, $10^{5} T_{\rm D}$. 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 $\gamma = 1.0$ and 1.5.

Key words: galaxies: kinematics and dynamics -- galaxies: structure -- methods: numerical

© ESO 2007