The general consensus in the N-body community is that statistical results of an ensemble of collisional N-body simulations are accurate, even though individual simulations are not. A way to test this hypothesis is to make a direct comparison of an ensemble of solutions obtained by conventional methods with an ensemble of true solutions. In order to make this possible, we wrote an N-body code called Brutus, that uses arbitrary-precision arithmetic. In combination with the Bulirsch-Stoer method, Brutus is able to obtain converged solutions, which are true up to a specified number of digits. We perform simulations of democratic 3-body systems, where after a sequence of resonances and ejections, a final configuration is reached consisting of a permanent binary and an escaping star. We do this with conventional double-precision methods, and with Brutus; both have the same set of initial conditions and initial realisations. The ensemble of solutions from the conventional simulations is compared directly to that of the converged simulations, both as an ensemble and on an individual basis to determine the distribution of the errors. We find that on average at least half of the conventional simulations diverge from the converged solution, such that the two solutions are microscopically incomparable. For the solutions which have not diverged significantly, we observe that if the integrator has a bias in energy and angular momentum, this propagates to a bias in the statistical properties of the binaries. In the case when the conventional solution has diverged onto an entirely different trajectory in phase-space, we find that the errors are centred around zero and symmetric; the error due to divergence is unbiased, as long as the time-step parameter, $\eta\le2^{-5}$ and when simulations which violate energy conservation by more than 10% are excluded. For resonant 3-body interactions, we conclude that the statistical results of an ensemble of conventional solutions are indeed accurate.

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关于N体模拟的可靠性

N体社区中的普遍共识是，即使单个模拟都不是一样，碰撞N体模拟集合的统计结果也是准确的。检验该假设的一种方法是将通过常规方法获得的解的集合与真实解的集合进行直接比较。为了使之成为可能，我们编写了一个名为Brutus的N体代码，该代码使用任意精度算术。结合Bulirsch-Stoer方法，Brutus能够获得收敛的解，直到指定数量的数字都适用。我们对民主的3体系统进行仿真，在经历了一系列的共振和弹射之后，最终结构由永久双星和逃逸星组成。我们使用常规的双精度方法以及Brutus来执行此操作。两者具有相同的初始条件和初始实现。可以将常规仿真中的解决方案集合与融合仿真中的集合直接比较，既可以作为集合，也可以在单独的基础上确定误差分布。我们发现，平均而言，至少有一半的常规模拟与收敛解有所不同，因此这两种解决方案在微观上是无法比拟的。对于没有明显差异的解，我们观察到，如果积分器在能量和角动量上存在偏差，则该偏差会传播为二进制的统计性质上的偏差。当传统解决方案在相空间上偏离到完全不同的轨迹时，我们发现误差集中在零附近且对称。只要将时间步长参数$ \ eta \ le2 ^ {-5} $以及违反节能量超过10％的模拟排除在外，由于发散引起的误差就不会受到偏见。对于共振的三体相互作用，我们得出的结论是，一组常规解决方案的统计结果确实是准确的。