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arXiv 1908.02336astro-ph.GAastro-ph.COhep-ph
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action空间小尺度成团的引力势：对Gaia DR2的应用

Gravitational Potential from small-scale clustering in action space: Application to Gaia DR2

Tianyi. Yang, Supranta Sarma Boruah, Niayesh. Afshordi

备注：
21 pages, 14 figures (4 appendices). Accepted by MNRAS. Figure 1 is updated. Comments are welcomed
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摘要：

天文学中大多数使用恒星或气体运动学的质量测量都依赖于通常难以验证的平衡假设。相反，我们开发了一种新的想法，使用动作空间中的聚类，作为潜在的引力势的探测器：正确的势应该最大化动作空间中的小规模聚类。我们提供了一个第一性原理推导的可能性使用两点关联函数在行动空间，并测试它对模拟的恒星流。然后将该方法应用于盖亚第二次数据发布中，测量了暗物质晕剖面的径向力分数$f_h$和对数斜率$α$。我们研究了距离银河系中心9-11 kpc和11.5-15 kpc的恒星，分别发现了$(f_h,α)= (0.391\pm 0.009, 1.835\pm 0.092) $和$(0.351\pm 0.012,1.687\pm 0.079)$。我们还确认，最大化似然函数的参数集对应于动作空间中的最聚类。银河系势的最佳拟合圆速度曲线与过去的测量结果一致（尽管它比以前使用脉泽或球状星团的方法低$\sim$ 5-10\%）。我们的工作提供了一个完整的统计功率，在于完整的相空间信息，减轻了需要{ \it特设}假设，如维里平衡，圆周运动，或蒸汽发现算法。

英文摘要：

Most measurements of mass in Astronomy that use kinematics of stars or gas rely on assumptions of equilibrium that are often hard to verify. Instead, we develop a novel idea that uses the clustering in action space, as a probe of underlying gravitational potential: the correct potential should maximize small-scale clustering in the action space. We provide a first-principle derivation of likelihood using the two-point correlation function in action space, and test it against simulations of stellar streams. We then apply this method to the 2nd data release of Gaia, and use it to measure the radial force fraction $f_h$ and logarithmic slope $α$ of dark matter halo profile. We investigate stars within 9-11 kpc and 11.5-15 kpc from Galactic centre, and find $(f_h,α)= (0.391\pm 0.009, 1.835\pm 0.092) $ and $(0.351\pm 0.012,1.687\pm 0.079)$, respectively. We also confirm that the set of parameters that maximize the likelihood function do correspond to the most clustering in the action space. The best-fit circular velocity curve for Milky Way potential is consistent with past measurements (although it is $\sim$ 5-10\% lower than previous methods that use masers or globular clusters). Our work provides a clear demonstration of the full statistical power that lies in the full phase space information, relieving the need for {\it ad hoc} assumptions such as virial equilibrium, circular motion, or steam-finding algorithms.

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