[论文解读] Inverse energy cascade in self-gravitating collisionless dark matter flow and effects of halo shape

Zhijie Xu, Xu|arXiv (Cornell University)|Oct 26, 2021

Stellar, planetary, and galactic studies被引用 4

一句话总结

本文提出，在自引力、无碰撞的暗物质流中，反向能量级联将动能从较小尺度传递至较大尺度，其持续机制是大尺度向小尺度的直接势能级联。该过程由持续的质量吸积和星系晕结构演化驱动，星系晕随时间逐渐趋向球形，且主要由相干的径向与旋转运动而非仅形状变化所促成。

ABSTRACT

Halo-mediated mass and energy cascades are key to understand dark matter flow. Both cascades origin from the mass exchange between halo and out-of-halo sub-systems. Kinetic energy can be from the motion of halos and particle motion in halos. Similarly, potential energy can be due to the inter- and intra-halo interactions. Intra-halo virial equilibrium is established much faster than inter-halo. Change of energy of entire system comes from virilization in halos. At statistically steady state, continuous mass exchange is required to sustain growth of total halo mass $M_h\propto a^{1/2}$ and energy $E\propto a^{3/2}$, where $a$ is scale factor. Inverse cascade is identified for kinetic energy that is transferred from the smallest scale to large mass scales. This is sustained by the direct cascade of potential energy from large to small scale. Both energies have a scale- and time-independent flux in propagation range that is proportional to mass flux. Energy cascade is mostly facilitated by mass cascade, which can be quantitatively described by mass accretion of typical halos. Halo radial, angular momentum, and angular velocity are modelled and inverse cascade is identified for the coherent radial and rotational motion in halos. In turbulence, vortex stretching (shape changing) along its axis of spin enables energy cascade from large to small length scales. However, change in halo shape is not the dominant mechanism for energy cascade as the moment of inertial gained from shape changing is less than 2 times. Large halos exhibit preference for prolateness over oblateness and most halos have spin axis perpendicular to major axis. Since mass cascade is local in mass space, halo shape evolves continuously in mass space with halos formed by incrementally inheriting structure from progenitor halos. A unique evolution path of halos is found that gradually approaches sphere with increasing size.

研究动机与目标

• 理解自引力、无碰撞暗物质流中能量与质量级联的驱动机制。
• 研究星系晕形状如何影响能量级联动力学，并探讨致密化在能量传递中的作用。
• 解释在统计稳态下星系晕质量（M_h ∝ a^{1/2}）与能量（E ∝ a^{3/2}）所呈现的观测标度律。
• 确定在暗物质星系晕中，形状变化还是质量吸积在能量级联过程中占主导地位。
• 对星系晕角动量、径向运动与自转轴取向进行建模，以识别维系反向级联的相干流动结构。

提出的方法

• 将星系晕质量吸积建模为质量空间中的局部过程，星系晕逐步继承前体结构。
• 以尺度因子 a 作为时间变量，描述总星系晕质量与能量的演化，假设为稳态增长。
• 分析动能与势能领域的能量通量，识别动能中的反向级联与势能中的直接级联。
• 通过主转动惯量的变化量化星系晕形状的作用，评估形状形变是否对能量传递有显著贡献。
• 在星系晕中模拟相干的径向与旋转运动，以识别实现反向能量级联的条件。
• 应用统计力学与流体动力学类比于暗物质流，将星系晕视为自引力、无碰撞系统。

实验结果

研究问题

• RQ1 是什么驱动了自引力、无碰撞暗物质流中的反向能量级联？其如何随时间持续维持？
• RQ2 星系晕形状变化（如拉长或扁平）相较于质量吸积，对能量级联效率的影响如何？
• RQ3 致密化过程以及星系晕与晕外子系统之间的质量交换，在维持能量与质量增长中起到何种作用？
• RQ4 为何大质量星系晕更倾向于呈现拉长形状？自转轴与主轴对齐如何影响能量级联？
• RQ5 能量级联通量在多大程度上与尺度和时间无关？其与系统中质量通量的关系如何？

主要发现

• 反向能量级联将动能从较小尺度传递至较大尺度，其持续机制是大尺度向小尺度的直接势能级联。
• 动能与势能领域中的能量通量在传播范围内具有尺度与时间不变性，且与质量通量成正比。
• 星系晕质量增长符合 M_h ∝ a^{1/2}，能量增长符合 E ∝ a^{3/2}，与统计稳态及持续质量吸积一致。
• 星系晕形状演化在质量空间中是连续的，随着质量增大，星系晕逐渐趋于球对称。
• 由形状变化获得的转动惯量增加不足两倍，表明形状形变并非能量级联的主导机制。
• 大多数星系晕的自转轴垂直于其主轴，且大质量星系晕表现出对拉长构型的偏好，而非扁平构型。