自相互作用暗物质模拟的收敛性测试
Convergence Tests of Self-Interacting Dark Matter Simulations
AI总结：
本研究针对自相互作用暗物质核坍缩N体模拟的数值误差问题，用Arepo程序测试不同参数下的收敛性，发现分辨率、时间步长等参数对结果有显著影响，为SIDM模拟的参数选择提供了参考。
摘要：
自相互作用暗物质（Self-interacting dark matter, SIDM）理论预言，暗物质晕会经历核坍缩——这是一种晕的内部区域密度快速升高、尺寸快速缩小的过程。当模拟参数选择不当时，用于研究该过程的N体模拟可能会出现数值误差。冷暗物质（cold dark matter, CDM）的最优模拟参数选择已得到充分研究，但在纳入自相互作用的情况下，人们对此仍缺乏深入理解。为开展可靠的N体模拟并准确建立核坍缩模型，我们必须了解潜在的数值误差、诊断方法，以及需选择哪些参数来降低误差。我们使用\texttt{Arepo} N体程序，针对一系列晕浓度和SIDM截面下的核坍缩SIDM晕开展收敛性测试，量化了与质量分辨率、时间步长和引力软化长度相关的潜在数值问题。我们的测试发现，模拟粒子数少于$10^5$的晕（这一分辨率通常是N体模拟中的子晕无法达到的）会受到显著的离散噪声影响，导致坍缩速率出现波动和极端离群值。在我们最低的$N=10^4$粒子分辨率下，坍缩时间的波动幅度可高达20\%。在这种低分辨率下，我们还发现坍缩时间存在偏差，且会出现少量极端离群值。此外，我们发现，运行时间远超宇宙年龄的模拟（这类模拟曾在以往研究中被用于校准SIDM引力热流体模型）对时间步长具有敏感性，而这种敏感性在较短时间的模拟或仅使用CDM的模拟中并不存在。我们的研究表明，对某些晕质量和SIDM模型能给出收敛结果的模拟参数选择，对其他情况不一定能得到收敛结果。
英文摘要：
Self-interacting dark matter (SIDM) theory predicts that dark matter halos experience core-collapse, a process where the halo's inner region rapidly increases in density and decreases in size. The N-body simulations used to study this process can suffer from numerical errors when simulation parameters are selected incorrectly. Optimal choices for simulation parameters are well studied for cold dark matter (CDM), but are not deeply understood when self-interactions are included. In order to perform reliable N-body simulations and model core-collapse accurately we must understand the potential numerical errors, how to diagnose them, and what parameter selections must be made to reduce them. We use the \texttt{Arepo} N-body code to perform convergence tests of core-collapsing SIDM halos across a range of halo concentrations and SIDM cross-sections, and quantify potential numerical issues related to mass resolution, timestep size, and gravitational softening length. Our tests discover that halos with fewer than $10^5$ simulation particles, a resolution typically not met by subhalos in N-body simulations, suffer from significant discreteness noise that leads to variation and extreme outliers in the collapse rate. At our lowest resolution of $N=10^4$ particles, this collapse time variation can reach as high as 20\%. At this low resolution we also find a bias in collapse times and a small number of extreme outliers. Additionally, we find that simulations which run far beyond the age of the Universe, which have been used to calibrate SIDM gravothermal fluid models in previous work, have a sensitivity to the timestep size that is not present in shorter simulations or simulations using only CDM. Our work shows that choices of simulation parameters that yield converged results for some halo masses and SIDM models do not necessarily yield convergence for others.
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