标题： 冷暗物质晕中通用准稳态吸引子的无碰撞松弛的自洽准线性理论 显示英文标题

标题： A self-consistent quasilinear theory for collisionless relaxation to universal quasi-steady state attractors in cold dark matter halos

摘要： 无碰撞的自引力系统，例如冷暗物质晕，尽管其形成过程涉及复杂的非线性物理机制，但仍然具有普遍的密度分布轮廓，其起源一直是个持久的谜团。 为了解决这个问题，我们在作用-角度空间中开发了一种针对驱动、非均匀、自引力系统的无碰撞弛豫的自洽准线性理论（QLT），通过扰动支配性的 Vlasov-Poisson 方程来实现。 我们得到了一个准线性扩散方程（QLDE），用于描述由于线性涨落（由力场中的随机扰动诱导，并被自引力集体修饰）引起的晕的平均分布函数$f_0$的长期演化，这种现象由响应矩阵描述。 与之前的研究不同，我们处理了集体修饰的所有阶数。 众所周知的晕密度分布轮廓$\rho(r)$在包括$N$体模拟中经常观察到，其中包括$r^{-1}$的 NFW 尖项、Einasto 中心核心以及$r^{-1.5}$的快速尖项，作为 QLDE 的准稳态吸引解出现。 $r^{-1}$尖项是不断吸积的大质量晕受到由次结构诱导的小尺度白噪声涨落扰动时的恒定通量稳态解。 这是无碰撞弛豫普遍性质的结果：低能粒子吸引更多的粒子，获得更高的有效质量，并受到波动力场的加速较少。 孤立晕的零通量定态解是一个在能量上平坦的$f_0$，而相应的$\rho(r)$可以根据内部边界条件成为核化结构或者$r^{-1.5}$尖点。后者围绕一个中心致密天体形成，例如一个致密亚晕或黑洞。 我们首次证明这些晕的分布轮廓作为由自洽QLT描述的非碰撞弛豫的准定态吸引子出现。 显示英文摘要

摘要： Collisionless self-gravitating systems, e.g., cold dark matter halos, harbor universal density profiles despite the intricate non-linear physics of hierarchical structure formation, the origin of which has been a persistent mystery. To solve this problem, we develop a self-consistent quasilinear theory (QLT) in action-angle space for the collisionless relaxation of driven, inhomogeneous, self-gravitating systems by perturbing the governing Vlasov-Poisson equations. We obtain a quasilinear diffusion equation (QLDE) for the secular evolution of the mean distribution function $f_0$ of a halo due to linear fluctuations (induced by random perturbations in the force field) that are collectively dressed by self-gravity, a phenomenon described by the response matrix. Unlike previous studies, we treat collective dressing up to all orders. Well-known halo density profiles $\rho(r)$ commonly observed in $N$-body simulations, including the $r^{-1}$ NFW cusp, an Einasto central core, and the $r^{-1.5}$ prompt cusp, emerge as quasi-steady state attractor solutions of the QLDE. The $r^{-1}$ cusp is a constant flux steady-state solution for a constantly accreting massive halo perturbed by small-scale white noise fluctuations induced by substructure. It is an outcome of the universal nature of collisionless relaxation: lower energy particles attract more particles, gain higher effective mass and get less accelerated by the fluctuating force field. The zero-flux steady state solution for an isolated halo is an $f_0$ that is flat in energy, and the corresponding $\rho(r)$ can either be cored or an $r^{-1.5}$ cusp depending on the inner boundary condition. The latter forms around a central dense object, e.g., a compact subhalo or a black hole. We demonstrate for the first time that these halo profiles emerge as quasi-steady state attractors of collisionless relaxation described by a self-consistent QLT.