标题： 一种用于模拟星系的有效正电势-密度对展开方法 显示英文标题

标题： An efficient positive potential-density pair expansion for modelling galaxies

摘要： 我们提出了一种新的正电势-密度对展开方法，用于模拟星系，该方法基于Miyamoto-Nagai（MN）盘。 通过使用三组这样的盘，每组盘沿每个对称轴对齐，我们能够重建一系列对应的电势，这些电势对应于从指数盘到具有不同三轴性的三维幂律模型的密度分布（因此简称为“扭曲”模型）。 通过允许每个盘的尺度长度参数为负数，我们提高了展开方法的效率。 我们证明，在尺度长度和高度参数的适当先验条件下，这些“MNn盘”只有一个负密度极小值。 这使我们能够通过要求全局最小处的总密度为正来确保全局正性。 我们发现，在密度重建精度优于10%的情况下，我们可以用4个MNn盘表示径向和垂直方向的指数盘，覆盖$0.1-10$个尺度长度/高度，用4个MNn盘表示NFW分布，覆盖$0.1-10$个尺度长度，以及用每个对称轴3个MNn盘表示扭曲的三轴NFW分布。 我们的展开方法高效、完全解析，并且非常适合从盘到椭球体再现星系的密度分布和引力势。 显示英文摘要

摘要： We present a novel positive potential-density pair expansion for modelling galaxies, based on the Miyamoto-Nagai (MN) disc. By using three sets of such discs, each one of them aligned along each symmetry axis, we are able to reconstruct a broad range of potentials that correspond to density profiles from exponential discs to 3D power law models with varying triaxiality (henceforth simply "twisted" models). We increase the efficiency of our expansion by allowing the scale length parameter of each disc to be negative. We show that, for suitable priors on the scale length and height parameters, these "MNn discs" have just one negative density minimum. This allows us to ensure global positivity by demanding that the total density at the global minimum is positive. We find that at better than 10\% accuracy in our density reconstruction, we can represent a radial and vertical exponential disc over $0.1-10$ scale lengths/heights with 4 MNn discs, an NFW profile over $0.1-10$ scale lengths with 4 MNn discs, and a twisted triaxial NFW profile with 3 MNn discs per symmetry axis. Our expansion is efficient, fully analytic, and well-suited to reproducing the density distribution and gravitational potential of galaxies from discs to ellipsoids.