恒星系统质量分布的约束：离散速度数据集的史瓦西模型
Constraining the Mass Profiles of Stellar Systems: Schwarzschild Modeling of Discrete Velocity Datasets
摘要：
我们提出了一个新的史瓦西轨道叠加代码，旨在模拟离散数据集组成的动力学系统中的单个运动示踪剂的速度。这构成了先前实现的扩展，其只能以速度分布（的时刻）的形式处理连续数据，从而避免由于数据分箱而导致的潜在重要信息损失。此外，代码可以处理可用速度分量的任何组合，即，只有视线速度，只有自行，或两者的组合。它还可以处理离散和连续数据的组合。该代码找到分布函数（DF，运动E，Lz和I3的三个积分的函数），最好地再现了给定轴对称引力势中的运动学和光度观测。完全数值方法确保DF f（E，Lz，I3）的形式具有相当大的自由度。这允许对轨道结构进行非常一般的建模，从而避免了对轨道各向同性程度的限制性假设。我们描述了离散代码的实现，并提出了一系列的测试其性能的基础上，从一个已知的DF生成的模拟数据集的建模。我们发现，离散史瓦西代码恢复原始的轨道结构，M/L比，和倾斜的输入数据集令人满意的精度，量化的各种统计。代码将是有价值的，例如，用于模拟银河系球状星团中的恒星运动，以及邻近星系中单个恒星、行星状星云或球状星团的恒星运动。这可以为这些系统的总质量分布提供新的线索，特别是中心黑洞和暗物质晕。
英文摘要：
(ABRIDGED) We present a new Schwarzschild orbit-superposition code designed to model discrete datasets composed of velocities of individual kinematic tracers in a dynamical system. This constitutes an extension of previous implementations that can only address continuous data in the form of (the moments of) velocity distributions, thus avoiding potentially important losses of information due to data binning. Furthermore, the code can handle any combination of available velocity components, i.e., only line-of-sight velocities, only proper motions, or a combination of both. It can also handle a combination of discrete and continuous data. The code finds the distribution function (DF, a function of the three integrals of motion E, Lz, and I3) that best reproduces the available kinematic and photometric observations in a given axisymmetric gravitational potential. The fully numerical approach ensures considerable freedom on the form of the DF f(E,Lz,I3). This allows a very general modeling of the orbital structure, thus avoiding restrictive assumptions about the degree of (an)isotropy of the orbits. We describe the implementation of the discrete code and present a series of tests of its performance based on the modeling of simulated datasets generated from a known DF. We find that the discrete Schwarzschild code recovers the original orbital structure, M/L ratios, and inclination of the input datasets to satisfactory accuracy, as quantified by various statistics. The code will be valuable, e.g., for modeling stellar motions in Galactic globular clusters, and those of individual stars, planetary nebulae, or globular clusters in nearby galaxies. This can shed new light on the total mass distributions of these systems, with central black holes and dark matter halos being of particular interest.
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