论文标题
宇宙结构从数学角度1。暗物质光环质量密度曲线
Cosmic structures from a mathematical perspective 1. Dark matter halo mass density profiles
论文作者
论文摘要
几十年来，相同无碰撞颗粒的合奏团体的单个自我磨损结构的形状一直是难以捉摸的。特别是，尚未发现诸如Navarro-frenk-white或Einasto概况之类的质量密度曲线的原因很适合模拟和基于观察的暗物质光环。鉴于三维，球形对称的幂律概率密度分布以在上述合奏中定位单个粒子，我们以最可能和最不可能的关节集合配置得出了幂律索引的约束方程。我们发现，任何暗物质光环都可以分为三个区域：一个核心，一个中间部分和郊区零件到边界半径$ r_ \ mathrm {max} $。核心的幂律指数取决于核心内部粒子分布的平均半径。中间区域在无限多个颗粒的极限下变为等温。 The slope of the mass density profile far from the centre is determined by the choice of $r_\mathrm{max}$ with respect to the outmost halo particle, such that two typical limiting cases arise that explain the $r^{-3}$-slope for galaxy-cluster outskirts and the $r^{-4}$-slope for galactic outskirts.因此，我们从一般的角度成功地得出了共同拟合函数的质量密度曲线。这些结果还允许为尖式核心问题找到一个简单的解释，并将光环描述与其动力学分开。
The shapes of individual self-gravitating structures of an ensemble of identical, collisionless particles have remained elusive for decades. In particular, a reason why mass density profiles like the Navarro-Frenk-White or the Einasto profile are good fits to simulation- and observation-based dark matter halos has not been found. Given the class of three dimensional, spherically symmetric power-law probability density distributions to locate individual particles in the ensemble mentioned above, we derive the constraining equation for the power-law index for the most and least likely joint ensemble configurations. We find that any dark matter halo can be partitioned into three regions: a core, an intermediate part, and an outskirts part up to boundary radius $r_\mathrm{max}$. The power-law index of the core is determined by the mean radius of the particle distribution within the core. The intermediate region becomes isothermal in the limit of infinitely many particles. The slope of the mass density profile far from the centre is determined by the choice of $r_\mathrm{max}$ with respect to the outmost halo particle, such that two typical limiting cases arise that explain the $r^{-3}$-slope for galaxy-cluster outskirts and the $r^{-4}$-slope for galactic outskirts. Hence, we succeed in deriving the mass density profiles of common fitting functions from a general viewpoint. These results also allow to find a simple explanation for the cusp-core-problem and to separate the halo description from its dynamics.
