自洽的三轴de Zeeuw-Carollo模型
Self-consistent triaxial de Zeeuw-Carollo Models
摘要：
本文利用Schwarzschild方法构造了具有中心密度尖点的三轴de Zeeuw & Alberlo（1996）模型的自洽解。ZC 96模型是球形$γ$ -Dehnen模型的三轴概括，其密度在中心附近变化为$r^{-γ}$，在大半径处变化为$r^{-4}$，因此，具有$γ=0$的中心密度核心和$γ> 0$的尖点。我们考虑ZC 96的四个三轴模型，两个长轴三轴：$(p, q) = (0.65, 0.60)$与$γ= 1.0$和1.5，和两个扁轴三轴：$(p, q) = (0.95, 0.60)$与$γ= 1.0$和1.5。我们计算4500轨道在每个模型的时间周期为$10^{5} T_{D}$。我们发现，在每个模型中的大部分轨道是随机的非零的李雅普诺夫指数。在每个模型中的随机轨道可以维持规则的形状为$\sim 10^{3} T_{D}$或更长的时间，这表明他们通过其允许的相空间缓慢扩散。除了具有$γ=1.0$的扁圆三轴模型外，我们试图只使用规则轨道来构造自洽解的尝试对于其余三个模型都失败了。然而，自洽的解决方案被发现存在的随机和规则的轨道以相同的方式处理时，所有的模型，因为混合时间，$\sim10^{4} T_{D}$，是短于积分时间，$10^{5} T_{D}$。此外，当随机轨道在15个最低能量壳层处完全混合时，也可以构造所有模型的"完全混合“解。因此，我们得出结论，自洽的解决方案存在于我们所选择的长轴和扁三轴模型与$γ= 1.0$和1.5。
英文摘要：
We use the usual method of Schwarzschild to construct self-consistent solutions for the triaxial de Zeeuw & Carollo (1996) models with central density cusps. ZC96 models are triaxial generalisations of spherical $γ$-models of Dehnen whose densities vary as $r^{-γ}$ near the center and $r^{-4}$ at large radii and hence, possess a central density core for $γ=0$ and cusps for $γ> 0$. We consider four triaxial models from ZC96, two prolate triaxials: $(p, q) = (0.65, 0.60)$ with $γ= 1.0$ and 1.5, and two oblate triaxials: $(p, q) = (0.95, 0.60)$ with $γ= 1.0$ and 1.5. We compute 4500 orbits in each model for time periods of $10^{5} T_{D}$. 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 $\sim 10^{3} T_{D}$ or longer, which suggests that they diffuse slowly through their allowed phase-space. Except for the oblate triaxial models with $γ=1.0$, 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, $\sim10^{4} T_{D}$, is shorter than the integration time, $10^{5} T_{D}$. 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 $γ= 1.0$ and 1.5.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
