On the reliability of N-body simulations
On the reliability of N-body simulations
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论N体模拟的可靠性
DOI：
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发表时间：
2014
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通讯作者：
S. P. Portegies Zwart
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作者：
Tjarda Boekholt;S. P. Portegies Zwart
在N体社区的普遍共识是，碰撞N体模拟的集合的统计结果是准确的，即使个别模拟是不准确的。检验这一假设的一种方法是将传统方法得到的解的集合与真解的集合进行直接比较。为了实现这一点，我们编写了一个名为Brutus的N体代码，它使用了任意精度的算术。结合Bulirsch-Stoer方法，Brutus能够获得收敛的解决方案，这是真正的到指定的digits.We数字的数字。我们进行民主的3-体系统的模拟，其中经过一系列的共振和喷射，最终的配置是由一个永久的二进制和逃逸的星星达到。我们用传统的双精度方法和Brutus来做这件事;两者都有相同的初始条件和初始实现。从传统的模拟合奏的解决方案进行比较，直接收敛的模拟，无论是作为合奏和个人的基础上，以确定分布的错误。我们发现，平均至少有一半的传统模拟发散收敛的解决方案，使这两个解决方案是微观上不可比的。对于没有显着发散的解决方案，我们观察到，如果积分器有一个偏置的能量和角动量，这传播到一个偏置的二进制的统计特性。当传统解在相空间中发散到一个完全不同的轨迹上时，我们发现误差以零为中心，并且是对称的;只要时间步长参数η≤2−5$etale2^{-5}$，并且排除违反能量守恒超过10%的模拟，发散引起的误差是无偏的。对于共振三体相互作用，我们的结论是，传统的解决方案的合奏的统计结果确实是准确的。
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, η≤2−5$etale2^{-5}$ 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.