已知速度各向异性球系的运动学反投影和质量反演
Kinematic deprojection and mass inversion of spherical systems of known velocity anisotropy
摘要：
传统上，质量/速度各向异性简并（MAD）固有的球形，静止，非流动的Jeans方程已被处理通过假设一个质量分布和拟合模型所观察到的运动学数据。在这里，被认为是相反的方法：各向异性运动投影方程被倒置为已知的任意各向异性，以产生空间径向速度色散分布的各向异性和各向同性的动态压力的径向分布的积分方面。然后，通过Jeans方程，质量分布导出的可观测量的双重积分。对于几种简单的各向异性模型（各向同性、径向、圆形、一般常数、Osipkov-Merritt、Mamon-Lokas和Diemand-Moore-Stadel），给出了解投影和质量反演的单积分公式。这些各向异性模型的NFW模型的质量反演测试产生准确的结果，在完美的观测数据的情况下，通常优于70%（在5例中的4例）准确的质量分布的采样误差预期从目前的观测数据的星系团。对于径向各向异性轻度增加的NFW模型，质量被发现是不敏感的7个尺度半径和3个尺度半径的各向异性半径采用的各向异性配置文件。这种各向异性质量反演方法是一个有用的补充工具，分析质量和各向异性的球形系统的配置文件。当示踪剂的各向异性与其密度的斜率成线性关系时，它提供了在准球形系统如球状星团、圆形矮椭球星系和椭圆星系以及星系团和星系团中提升MAD的实用方法。
英文摘要：
Traditionally, the mass / velocity anisotropy degeneracy (MAD) inherent in the spherical, stationary, non-streaming Jeans equation has been handled by assuming a mass profile and fitting models to the observed kinematical data. Here, the opposite approach is considered: the equation of anisotropic kinematic projection is inverted for known arbitrary anisotropy to yield the space radial velocity dispersion profile in terms of an integral involving the radial profiles of anisotropy and isotropic dynamical pressure. Then, through the Jeans equation, the mass profile is derived in terms of double integrals of observable quantities. Single integral formulas for both deprojection and mass inversion are provided for several simple anisotropy models (isotropic, radial, circular, general constant, Osipkov-Merritt, Mamon-Lokas and Diemand-Moore-Stadel). Tests of the mass inversion on NFW models with these anisotropy models yield accurate results in the case of perfect observational data, and typically better than 70% (in 4 cases out of 5) accurate mass profiles for the sampling errors expected from current observational data on clusters of galaxies. For the NFW model with mildly increasing radial anisotropy, the mass is found to be insensitive to the adopted anisotropy profile at 7 scale radii and to the adopted anisotropy radius at 3 scale radii. This anisotropic mass inversion method is a useful complementary tool to analyze the mass and anisotropy profiles of spherical systems. It provides the practical means to lift the MAD in quasi-spherical systems such as globular clusters, round dwarf spheroidal and elliptical galaxies, as well as groups and clusters of galaxies, when the anisotropy of the tracer is expected to be linearly related to the slope of its density.
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