如何打破球形恒星系统中的密度各向异性简并
How to break the density-anisotropy degeneracy in spherical stellar systems
摘要：
我们提出了一个新的非参数的Jeans代码，GravSphere，恢复的密度$ρ(r)$和速度各向异性$β(r)$的球形恒星系统，假设它们是在一个稳定的状态。使用一个大的模拟数据套件，我们证实，只有视线速度数据，GravSphere提供了一个很好的估计密度在投影恒星半质量半径，$ρ(R_{1/2})$，但不能测量$ρ(r)$或$β(r)$，即使有10,000跟踪星。然后，我们测试三种流行的方法来打破这种$ρ-β$简并性：使用不同的$R_{1/2}$多个人口，使用高阶“维里形状参数”（VSP），并包括适当的运动数据。我们发现，两个群体在其各自的$R_{1/2}$之间提供了极好的$ρ(r)$恢复。然而，即使使用全部$\sim 7,000$示踪剂，我们也不能很好地约束两个群体中的$β(r)$。相比之下，使用具有更高阶VSP的1000个示踪剂，我们能够在范围$0.5 < r/R_{1/2} < 2$上测量$ρ(r)$并且广泛地约束$β(r)$。包括所有恒星的自行数据提供了更好的性能，$ρ$和$β$在$0.25 < r/R_{1/2} < 4$范围内得到了很好的测量。最后，我们测试GravSphere上的三轴模拟星系，具有典型的合并残余物，$[1:0.8:0.6]$的轴比。在这种情况下，GravSphere可能会稍微有偏差。然而，我们发现，当这种情况发生时，数据拟合不佳，使我们能够检测到这种偏离球面对称的情况。
英文摘要：
We present a new non-parametric Jeans code, GravSphere, that recovers the density $ρ(r)$ and velocity anisotropy $β(r)$ of spherical stellar systems, assuming only that they are in a steady-state. Using a large suite of mock data, we confirm that with only line-of-sight velocity data, GravSphere provides a good estimate of the density at the projected stellar half mass radius, $ρ(R_{1/2})$, but is not able to measure $ρ(r)$ or $β(r)$, even with 10,000 tracer stars. We then test three popular methods for breaking this $ρ-β$ degeneracy: using multiple populations with different $R_{1/2}$; using higher order `Virial Shape Parameters' (VSPs); and including proper motion data. We find that two populations provide an excellent recovery of $ρ(r)$ in-between their respective $R_{1/2}$. However, even with a total of $\sim 7,000$ tracers, we are not able to well-constrain $β(r)$ for either population. By contrast, using 1000 tracers with higher order VSPs we are able to measure $ρ(r)$ over the range $0.5 < r/R_{1/2} < 2$ and broadly constrain $β(r)$. Including proper motion data for all stars gives an even better performance, with $ρ$ and $β$ well-measured over the range $0.25 < r/R_{1/2} < 4$. Finally, we test GravSphere on a triaxial mock galaxy that has axis ratios typical of a merger remnant, $[1:0.8:0.6]$. In this case, GravSphere can become slightly biased. However, we find that when this occurs the data are poorly fit, allowing us to detect when such departures from spherical symmetry become problematic.
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