一维空间的引力坍缩
Gravitational Collapse in One Dimension
摘要：
我们从非平衡初始条件模拟了一维引力无碰撞系统的演化，类似于导致三维暗物质晕形成的条件。在三维晕形成的情况下，我们发现，最初冷，几乎均匀的粒子分布崩溃，接近最终的平衡态与普遍的密度分布。在小半径处，该吸引子在密度上表现出幂律行为，ρ（x）\propto |x| ^（-γ_crit），γ_crit \simeq 0.47，比先前建议的值γ = 1/2略浅但明显更浅。这种状态从初始条件通过相混合和剧烈弛豫的过程发展。这个过程保持了粒子的能量等级。通过温暖的初始条件，我们说明了一个交叉，从这个幂律的最终状态，最终状态包含一个均匀的核心。我们进一步证明了非均匀但冷的幂律初始条件，初始指数γ_i> γ_crit，不会向吸引子演化，而是到达一个在轮廓内部保持其原始幂律行为的最终状态，表明最终状态的分叉是初始指数的函数。我们的研究结果依赖于高保真事件驱动的模拟技术。
英文摘要：
We simulate the evolution of one-dimensional gravitating collisionless systems from non- equilibrium initial conditions, similar to the conditions that lead to the formation of dark- matter halos in three dimensions. As in the case of 3D halo formation we find that initially cold, nearly homogeneous particle distributions collapse to approach a final equilibrium state with a universal density profile. At small radii, this attractor exhibits a power-law behavior in density, ρ(x) \propto |x|^(-γ_crit), γ_crit \simeq 0.47, slightly but significantly shallower than the value γ = 1/2 suggested previously. This state develops from the initial conditions through a process of phase mixing and violent relaxation. This process preserves the energy ranks of particles. By warming the initial conditions, we illustrate a cross-over from this power-law final state to a final state containing a homogeneous core. We further show that inhomogeneous but cold power-law initial conditions, with initial exponent γ_i > γ_crit, do not evolve toward the attractor but reach a final state that retains their original power-law behavior in the interior of the profile, indicating a bifurcation in the final state as a function of the initial exponent. Our results rely on a high-fidelity event-driven simulation technique.
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