论文标题
美元
$l=1$: Weinberg's weakly damped mode in an $N$-body model of a spherical stellar system
论文作者
论文摘要
在无碰撞动力学的意义上，分布函数是能量的降低，并且取决于其他不变的函数，在该系统中，球形恒星系统（例如King模型）是稳定的。但是温伯格通过巧妙地应用线性稳定性的矩阵方法表明，它们可能几乎是不稳定的，它具有{\ sl弱}的振动模式。他还通过赋予其扰动解决方案产生的初始条件来赋予它在$ n $ body模型中的存在。在本文中，我们为国王$ W_0 = 5 $型号的$ n $ body模拟中存在相同模式提供了证据，其中最初的条件是由国王分配功能的通常的蒙特卡洛采样生成的。结果表明，密度中心的振荡与系统结构的变化相关，使半径约为1个病毒半径，但反读带有超出该半径的变化。尽管振荡似乎不断重新激发（大概是通过粒子的运动）通过计算电源光谱显示的，但温伯格对该时期的估计值（严格来说，$2π$除以特征征的真实部分）位于范围内。但是，功率谱在较短的时间（约5个交叉时间）中显示出另一个非常突出的特征。
Spherical stellar systems such as King models, in which the distribution function is a decreasing function of energy and depends on no other invariant, are stable in the sense of collisionless dynamics. But Weinberg showed, by a clever application of the matrix method of linear stability, that they may be nearly unstable, in the sense of possessing {\sl weakly} damped modes of oscillation. He also demonstrated the presence of such a mode in an $N$-body model by endowing it with initial conditions generated from his perturbative solution. In the present paper we provide evidence for the presence of this same mode in $N$-body simulations of the King $W_0 = 5$ model, in which the initial conditions are generated by the usual Monte Carlo sampling of the King distribution function. It is shown that the oscillation of the density centre correlates with variations in the structure of the system out to a radius of about 1 virial radius, but anticorrelates with variations beyond that radius. Though the oscillations appear to be continually reexcited (presumably by the motions of the particles) we show by calculation of power spectra that Weinberg's estimate of the period (strictly, $2π$ divided by the real part of the eigenfrequency) lies within the range where the power is largest. In addition, however, the power spectrum displays another very prominent feature at shorter periods, around 5 crossing times.
