标题： 打破Beta：球状系统的质量建模方法比较 显示英文标题

标题： Breaking Beta: A comparison of mass modelling methods for spherical systems

摘要： 我们对一组公开可用的球状恒星系统的模拟数据应用了四种不同的质量建模方法。 我们专注于通过视线速度数据，或者结合自行数据，来恢复密度和速度各向异性随半径的变化情况。 所有方法在各向同性和切向各向异性模拟数据上表现良好，在半径范围 0.25 < R/Rhalf < 4 内（Rhalf 为半光半径），能够将密度和速度各向异性恢复到其 95% 置信区间内。 然而，径向各向异性模拟数据更具挑战性。 对于仅使用视线速度数据的情况，只有那些利用速度分布函数形状信息的方法能够打破密度剖面与速度各向异性之间的退化，从而获得两者均无偏估计。 这种形状信息可以通过直接拟合全局相空间分布函数、使用高阶“维里形状参数”，或者假设局部高斯速度分布函数但沿视线方向自洽投影而获得。 加入自行数据后，进一步提高了性能，并且在这种情况下，所有方法都能很好地恢复径向密度和速度各向异性剖面。 显示英文摘要

摘要： We apply four different mass modelling methods to a suite of publicly available mock data for spherical stellar systems. We focus on the recovery of the density and velocity anisotropy as a function of radius, using either line-of-sight velocity data only, or adding proper motion data. All methods perform well on isotropic and tangentially anisotropic mock data, recovering the density and velocity anisotropy within their 95% confidence intervals over the radial range 0.25 < R/Rhalf < 4, where Rhalf is the half light radius. However, radially-anisotropic mocks are more challenging. For line-of-sight data alone, only methods that use information about the shape of the velocity distribution function are able to break the degeneracy between the density profile and the velocity anisotropy to obtain an unbiased estimate of both. This shape information can be obtained through directly fitting a global phase space distribution function, by using higher order 'Virial Shape Parameters', or by assuming a Gaussian velocity distribution function locally, but projecting it self-consistently along the line of sight. Including proper motion data yields further improvements, and in this case, all methods give a good recovery of both the radial density and velocity anisotropy profiles.