We present a detailed analysis of the behavior of the triaxial Schwarzschild orbit superposition method near the axisymmetric limit. Orbit superposition modeling is the primary method used to determine dynamical masses of supermassive black holes (M _BH) in nearby galaxies; however, prior studies have reported conflicting results when comparing the outcome from axisymmetric orbit codes with that from a triaxial orbit code in the axisymmetric limit. We show that in order to achieve (oblate) axisymmetry in a triaxial code, care needs to be taken to axisymmetrize the short-axis tube orbits and to exclude both the long-axis tube and box orbits from the orbit library. Using up to 12 Gauss–Hermite moments of the line-of-sight velocity distributions as constraints, we demonstrate the effects of orbit types on the best-fit M _BH in orbit modeling of the massive elliptical galaxy NGC 1453 reported in Liepold et al. In addition, we verify the efficacy of our updated code on a mock galaxy data set. We identify a subset of slowly precessing quasi-planar orbits for which the typical integration times can be insufficient to fully capture the equilibrium orbital behavior in both axisymmetric and triaxial systems with central black holes. Further investigation is needed for a more reliable treatment of these orbits.

我们详细分析了轴对称极限附近的三轴 Schwarzschild 轨道叠加方法的行为。轨道叠加建模是用于确定超大质量黑洞（M _BH) 在附近的星系；然而，在将轴对称轨道代码的结果与轴对称极限中的三轴轨道代码的结果进行比较时，先前的研究报告了相互矛盾的结果。我们表明，为了在三轴代码中实现（扁圆）轴对称，需要注意对短轴管轨道进行轴对称，并从轨道库中排除长轴管和盒轨道。使用多达 12 个视线速度分布的高斯-厄米矩作为约束，我们证明了轨道类型对最佳拟合M _{BH 的影响}在 Liepold 等人报道的大质量椭圆星系 NGC 1453 的轨道建模中。此外，我们在模拟星系数据集上验证了我们更新的代码的有效性。我们确定了一个缓慢进动的准平面轨道的子集，对于这些轨道，典型的积分时间可能不足以完全捕获具有中心黑洞的轴对称和三轴系统中的平衡轨道行为。需要进一步研究以更可靠地处理这些轨道。