在局部模拟中缩小重力湍流收敛的差距
Closing the gap to convergence of gravitoturbulence in local simulations
摘要：
目的。我们的目标是找到一个收敛的冷却限制碎片在自引力磁盘。这对于行星、褐矮星或恒星的形成以及黑洞的成长尤其有趣。在研究极限的同时，我们希望给出一个明确的收敛状态的判据。方法.我们运行二维shearingsheet模拟与流体动力学软件包Fosite在高分辨率。从而改变分辨率和限制器。随后，我们调查的光谱的重要物理量的长度尺度发生碎裂。为了避免在高分辨率的提示碎片，我们开始这些模拟与一个充分发展的gravitoturbulent状态在较低的分辨率。结果我们显示出接近收敛的结果与临界冷却时间尺度$t_{\mathrm{crit}} \sim 10\,Ω^{-1}$的碎片。我们可以通过在压力标度高度附近和以下的长度标度上研究相关物理变量的谱来回溯这一主张。我们认为，如果抵消量在这些临界长度尺度上变化太大，无论是通过改变分辨率还是数值方法，都不能期望得到良好的结果。碎裂行为与相关光谱的比较表明，模拟行为相似，如果光谱收敛到自引力导致不稳定的长度尺度。用不同的数值设置得到的结果中的可观察到的偏差仅限于这些临界长度尺度以下的尺度。
英文摘要：
Aims. Our goal is to find a converged cooling limit for fragmentation in self-gravitating disks. This is especially interesting for the formation of planets, brown dwarfs or stars and the growth of black holes. While investigating the limit, we want to give a clear criterion for the state of convergence. Methods. We run two-dimensional shearingsheet simulations with the hydrodynamic package Fosite at high resolutions. Thereby resolution and limiters are altered. Subsequently, we investigate the spectra of important physical quantities at the length scales where fragmentation occurs. In order to avoid prompt fragmentation at high resolutions we start these simulations with a fully developed gravitoturbulent state obtained at a lower resolution. Results. We show nearly converged results for fragmentation with a critical cooling timescale $t_{\mathrm{crit}} \sim 10\,Ω^{-1}$ . We can backtrace this claim by investigating the spectra of relevant physical variables at length scales around and below the pressure scale height. We argue that well behaved results cannot be expected if counteracting quantities are varying too much on these critical length scales, either by change of resolution or numerical method. A comparison of fragmentation behaviour with the related spectra reveals that simulations behave similar, if the spectra are converged to the length scales where self-gravity leads to instabilities. Observable deviations in the results obtained with different numerical setup are confined to scales below these critical length scales.
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