[论文解读] On the evolution of shape in N-body simulations

Ch. Theis, Rainer Spurzem|arXiv (Cornell University)|Oct 1, 1998

Stellar, planetary, and galactic studies被引用 4

一句话总结

本文利用专用的GRAPE和HARP计算机，研究了冷、无耗散N体系统的形状演化，揭示了三个不同阶段：快速坍缩引发径向轨道不稳定性与最大三轴性，随后经历剧烈弛豫和两体弛豫，使系统趋向轴对称性，最终趋向球对称性。关键发现是，当正确考虑软化参数时，长期形状弛豫 timescale 与两体弛豫 timescale 非常吻合，且核心振荡被识别为剧烈弛豫的驱动机制。

ABSTRACT

A database on shape evolution of direct N-body models formed out of cold, dissipationless collapse is generated using GRAPE and HARP special purpose computers. Such models are important to understand the formation of elliptical galaxies. Three dynamically distinct phases of shape evolution were found, first a fast dynamical collapse which gives rise to the radial orbit instability (ROI) and generates at its end the maximal triaxiality of the system. Subsequently, two phases of violent and two-body shape relaxation occur, which drive the system first towards axisymmetry, finally to spherical symmetry (the final state, however, is still much more concentrated than the initial model). In a sequence of models the influence of numerical and physical parameters, like particle number, softening, initial virial ratio, timestep choice, different N-body codes, are examined. We find that an improper combination of softening and particle number can produce erroneous results. Selected models were evolved on the secular timescale until they became spherically symmetric again. The secular shape relaxation time scale is shown to agree very well with the two-body relaxation time, if softening is properly taken into account for the latter. Finally, we argue, that the intermediate phase of violent shape relaxation after collapse is induced by strong core oscillations in the centre, which cause potential fluctuations, dampening out the triaxiality.

研究动机与目标

• 理解与椭圆星系形成相关的冷、无耗散N体系统中形状的动力学演化。
• 识别从三轴性向球对称性演化过程中形状弛豫的物理机制。
• 评估数值参数（如粒子数、软化长度和时间步长）对形状演化模拟精度与可靠性的影。
• 验证在正确软化条件下，长期形状弛豫 timescale 与两体弛豫 timescale 之间的关联。

提出的方法

• 利用GRAPE和HARP专用计算硬件进行模拟，以高精度建模冷、无耗散坍缩过程。
• 构建了一个包含不同粒子数、软化长度、初始维里比和时间步长选择的N体模型数据库。
• 采用多种N体代码以检验不同实现方式下的结果一致性与数值鲁棒性。
• 通过主轴比和三轴性度量随时间的变化来追踪形状演化。
• 在正确软化修正下计算两体弛豫 timescale，并与观测到的长期形状弛豫 timescale 进行比较。
• 分析核心振荡与势能涨落，以识别其在剧烈形状弛豫中的作用。

实验结果

研究问题

• RQ1 冷、无耗散N体系统的形状演化中是否存在明显的动力学阶段？
• RQ2 核心振荡与势能涨落如何在坍缩后促进剧烈形状弛豫？
• RQ3 软化长度与粒子数等数值参数在多大程度上影响形状演化模拟的准确性？
• RQ4 当软化参数被正确考虑时，长期形状弛豫 timescale 是否与两体弛豫 timescale 一致？
• RQ5 这些系统中从三轴性向球对称性转变的成因是什么？

主要发现

• 识别出形状演化的三个明显阶段：快速动力学坍缩导致径向轨道不稳定性与最大三轴性，随后经历剧烈弛豫与两体弛豫阶段。
• 系统从三轴性演化为轴对称性，最终趋向球对称性，但最终状态的集中度仍显著高于初始模型。
• 软化与粒子数的不适当组合可能导致N体模拟中出现错误结果。
• 当软化在计算中被正确包含时，长期形状弛豫 timescale 与两体弛豫 timescale 非常吻合。
• 剧烈形状弛豫的中间阶段由强烈的中心振荡引起，这些振荡引发势能涨落，从而抑制三轴性。
• 核心振荡被识别为坍缩后触发剧烈弛豫的主要物理机制。