离散的、不完全的恒星运动学的轨道叠加模型：对银河系中心的应用
Orbit-superposition models of discrete, incomplete stellar kinematics: application to the Galactic centre
摘要：
我们提出了一种方法来拟合轨道叠加模型的离散恒星系统的运动学时，可用的恒星样本已被过滤的一个已知的选择函数。拟合方法可以应用于任何模型，其中分布函数表示为具有未知权重的基元素的线性叠加。作为一个例子，我们将其应用到弗里茨等人。银河系核心星团最内部区域的运动学。假设球对称，我们的模型适合一个质量为$M_\bullet=(3.76\pm0.22)\times10^6\,M_\odot$的黑洞，周围有一个扩展的质量$M_\star=(6.57\pm0.54)\times10^6\,M_\odot$在4 pc。在1 pc内，最佳拟合质量模型具有近似的幂律密度尖点$ρ\propto r^{-γ}$和$γ=1.3\pm0.3$。我们进行了广泛的调查，我们的建模假设可能会偏见这些估计：$M_\bullet$是最强大的参数和$γ$最少。在内部，最佳拟合模型具有广泛的各向同性轨道分布，除了偏向0.1和0.3秒差距之间的圆形轨道。
英文摘要：
We present a method for fitting orbit-superposition models to the kinematics of discrete stellar systems when the available stellar sample has been filtered by a known selection function. The fitting method can be applied to any model in which the distribution function is represented as a linear superposition of basis elements with unknown weights. As an example, we apply it to Fritz et al.'s kinematics of the innermost regions of the Milky Way's nuclear stellar cluster. Assuming spherical symmetry, our models fit a black hole of mass $M_\bullet=(3.76\pm0.22)\times10^6\,M_\odot$, surrounded by an extended mass $M_\star=(6.57\pm0.54)\times10^6\,M_\odot$ within 4 pc. Within 1 pc the best-fitting mass models have an approximate power-law density cusp $ρ\propto r^{-γ}$ with $γ=1.3\pm0.3$. We carry out an extensive investigation of how our modelling assumptions might bias these estimates: $M_\bullet$ is the most robust parameter and $γ$ the least. Internally the best-fitting models have broadly isotropic orbit distributions, apart from a bias towards circular orbits between 0.1 and 0.3 parsec.
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