We present the theoretical framework to efficiently solve the Jeans equations for multicomponent axisymmetric stellar systems, focusing on the scaling of all quantities entering them. The models may include an arbitrary number of stellar distributions, a dark matter halo, and a central supermassive black hole; each stellar distribution is implicitly described by a two- or three-integral distribution function, and the stellar components can have different structural (density profile, flattening, mass, scale length), dynamical (rotation, velocity dispersion anisotropy), and population (age, metallicity, initial mass function, mass-to-light ratio) properties. In order to determine the ordered rotational velocity and the azimuthal velocity dispersion fields of each component, we introduce a decomposition that can be used when the commonly adopted Satoh decomposition cannot be applied. The scheme developed is particularly suitable for a numerical implementation; we describe its realization within our code JASMINE2, optimized to maximally exploit the scalings allowed by the Poisson and the Jeans equations, also in the post-processing procedures. As applications, we illustrate the building of three multicomponent galaxy models with two distinct stellar populations, a central black hole, and a dark matter halo; we also study the solution of the Jeans equations for an exponential thick disc, and for its multicomponent representation as the superposition of three Miyamoto–Nagai discs. A useful general formula for the numerical evaluation of the gravitational potential of factorized thick discs is finally given.

中文翻译：

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具有多个恒星群的轴对称星系的牛仔裤模型

我们提出了有效求解多分量轴对称恒星系统的 Jeans 方程的理论框架，重点关注输入它们的所有量的缩放。这些模型可能包括任意数量的恒星分布、暗物质晕和中心超大质量黑洞；每个恒星分布由二或三积分分布函数隐含地描述，恒星成分可以具有不同的结构（密度分布、扁平化、质量、尺度长度）、动力学（旋转、速度色散各向异性）和种群（年龄，金属丰度，初始质量函数，质光比）属性。为了确定各分量的有序旋转速度和方位速度色散场，我们引入了一种分解，可以在不能应用常用的 Satoh 分解时使用。开发的方案特别适用于数值实现；我们在我们的代码 JASMINE2 中描述了它的实现，经过优化以最大限度地利用 Poisson 和 Jeans 方程所允许的缩放，也在后处理过程中。作为应用，我们展示了三个多分量星系模型的构建，其中包含两个不同的恒星群、一个中心黑洞和一个暗物质晕；我们还研究了指数厚圆盘的 Jeans 方程的解，并将其多分量表示为三个 Miyamoto-Nagai 圆盘的叠加。最后给出了一个有用的通用公式，用于数值评估分解后的厚圆盘的引力势。