Fundamental Discreteness Limitations of Cosmological N-Body Clustering Simulations
Fundamental Discreteness Limitations of Cosmological N-Body Clustering Simulations
复制标题
宇宙学 N 体聚类模拟的基本离散性限制
DOI：
10.1086/305450
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发表时间：
1997
期刊：
影响因子：
--
通讯作者：
Y. Suto
中科院分区：
文献类型：
--
作者：
Randall J. Splinter;A. Melott;S. Shandarin;Y. Suto
基本的物理考虑和过去的测试表明，在宇宙学集群研究中广泛使用的N体方法可能存在离散性误差问题。当与流体力学程序结合时，这可能会导致精度问题。因此，我们研究了离散性和二体散射对具有“真实”宇宙初始条件的N体模拟的一些影响。我们使用与1283粒子网格(PM)计算的初始条件相同的粒子子集作为各种粒子-粒子-粒子网格(P3M)的初始条件，并运行树代码。P3M和TREE代码运行中的力软化长度和粒子数是不同的，并将结果与PM运行的结果进行了比较。特别是，我们研究了质量分辨率(或相当于平均粒子间分离)的影响，因为大多数“高分辨率”代码只有引力的高分辨率，而不是质量的高分辨率。我们展示了各种统计指标的演变。在力分辨率保持不变的情况下，相位不敏感的两点统计量P(K)和ξ(R)受粒子数的影响，并且在具有相似参数和相同初始条件的不同N体代码中是不同的。相敏统计数据显示出更大的差异。结果收敛于最低质量分辨率代码的平均粒子间分离尺度。随着加入更多的粒子，但力分辨率的绝对尺度保持不变，P3M和树运行彼此以及与具有相同初始条件的PM运行的一致性越来越强，这表明时间积分正在收敛。然而，它们并不特别收敛于将幂定律波动延续到小范围的PM运行。这表明高粒子密度对于正确的时间演化是必要的，因为许多不同的结果并不都是正确的。我们的结果显示了小尺度初始功率的存在或不存在的影响，这表明省略它是丢失波长的共标的相当大的误差来源，这可以通过加入高粒子密度来解决。由于这些代码在低于平均移动粒子间距离的尺度上从来不能很好地吻合，我们认为没有理由使用这些尺度上的结果来做出宇宙学中的定量预测。一些量的取值范围为50%，但其他一些量，如高密度区域的质量，可能会相差3倍或更多。我们的结果对星系晕密度、早期天体如类星体吸收云等应用具有很强的指导意义。
Fundamental physical considerations and past tests suggest that there may be a problem with discreteness error in N-body methods widely used in cosmological clustering studies. This could cause problems with accuracy when coupled to hydrodynamics codes. We therefore investigate some of the effects that discreteness and two-body scattering may have on N-body simulations with "realistic" cosmological initial conditions. We use an identical subset of particles from the initial conditions for a 1283 particle-mesh (PM) calculation as the initial conditions for a variety of particle-particle-particle mesh (P3M) and tree code runs. The force softening length and particle number in the P3M and tree code runs are varied, and results are compared with those of the PM run. In particular, we investigate the effect of mass resolution (or equivalently the mean interparticle separation) since most "high-resolution" codes only have high resolution in gravitational force, not in mass. We show the evolution of a wide variety of statistical measures. The phase-insensitive two-point statistics, P(k) and ξ(R), are affected by the number of particles when the force resolution is held constant and differ in different N-body codes with similar parameters and the same initial conditions. Phase-sensitive statistics show greater differences. Results converge at the mean interparticle separation scale of the lowest mass-resolution code. As more particles are added but the absolute scale of the force resolution is held constant, the P3M and the tree runs agree more and more strongly with each other and with the PM run that had the same initial conditions, suggesting that the time integration is converging. However, they do not particularly converge to a PM run that continued the power-law fluctuations to small scales. This suggests high particle density is necessary for correct time evolution, since many different results cannot all be correct. Our results showing the effect of the presence or absence of small-scale initial power suggest that leaving it out is a considerable source of error on comoving scales of the missing wavelengths, which can be resolved by putting in a high particle density. Since the codes never agree well on scales below the mean comoving interparticle separation, we find little justification to use results on these scales to make quantitative predictions in cosmology. The range of values found for some quantities spans 50%, but others, such as the amount of mass in high-density regions, can be off by a factor of 3 or more. Our results have strong implications for applications such as the density of galaxy halos, early generation objects such as QSO absorber clouds, etc.