轨道PDF：从稳态示踪剂对引力势的一般推论
The orbital PDF: general inference of the gravitational potential from steady-state tracers
摘要：
我们发展了两种一般的方法来推断一个系统的引力势使用稳态示踪剂，即，具有与时间无关的相空间分布的示踪剂。结合相空间连续性方程，时间独立性意味着一个通用的轨道概率密度函数（oPDF）$\mathrm{d} P(λ|{\rm orbit})\propto \mathrm{d} t$，其中$λ$是粒子沿轨道的坐标。oPDF等价于Jeans定理，并且是稳态示踪剂的大多数动力学建模背后的关键物理成分。在球形势的情况下，我们开发了一个似然估计，适合分析潜力的系统，和一个非参数的方法（“相位标记”），重建的潜在的配置文件，都假设只有oPDF。该方法不涉及任何额外的假设示踪剂分布函数，并可以应用于任何任意分布的轨道示踪剂，与可能的扩展到非球形的潜力。在暗物质晕中稳态示踪剂的蒙特卡罗样本上对该方法进行了测试，以表明它们是无偏的和有效的。实现我们方法的完整文档\textsc{C/Python}代码可以在GitHub存储库中免费获得，该存储库链接自\url{http://icc.dur.ac.uk/data/#oPDF}。
英文摘要：
We develop two general methods to infer the gravitational potential of a system using steady-state tracers, i.e., tracers with a time-independent phase-space distribution. Combined with the phase-space continuity equation, the time independence implies a universal Orbital Probability Density Function (oPDF) $\mathrm{d} P(λ|{\rm orbit})\propto \mathrm{d} t$, where $λ$ is the coordinate of the particle along the orbit. The oPDF is equivalent to Jeans theorem, and is the key physical ingredient behind most dynamical modelling of steady-state tracers. In the case of a spherical potential, we develop a likelihood estimator that fits analytical potentials to the system, and a non-parametric method ("phase-mark") that reconstructs the potential profile, both assuming only the oPDF. The methods involve no extra assumptions about the tracer distribution function and can be applied to tracers with any arbitrary distribution of orbits, with possible extension to non-spherical potentials. The methods are tested on Monte Carlo samples of steady-state tracers in dark matter haloes to show that they are unbiased as well as efficient. A fully documented \textsc{C/Python} code implementing our method is freely available at a GitHub repository linked from \url{http://icc.dur.ac.uk/data/#oPDF}.
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