On the convergence of the critical cooling timescale for the fragmentation of self-gravitating discs
On the convergence of the critical cooling timescale for the fragmentation of self-gravitating discs
复制标题
自引力圆盘破碎临界冷却时间尺度的收敛
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
M. Bate
中科院分区：
文献类型：
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作者：
F. Meru;M. Bate
我们使用光滑粒子流体动力学（SPH）代码和基于网格的流体动力学代码FARGO对引力不稳定盘进行模拟，以理解Meru & Bate（2011 a）报告的先前非收敛结果。我们得到的证据表明，收敛与增加分辨率发生与SPH和FARGO，在这两种情况下，我们发现，临界冷却时间尺度比以前认为的要大。我们表明，SPH具有一阶收敛速度，而FARGO收敛与二阶速度。我们发现，临界冷却时间尺度的收敛碎裂在很大程度上取决于在SPH和FARGO采用的数值粘度。对于SPH，颗粒速度分散也可能起作用。我们表明，减少从数值粘性耗散导致较大的值的临界冷却时间在给定的分辨率。对于SPH，我们发现，由于数值粘性的耗散的效果是有点大于以前被赞赏。特别地，我们发现在SPH人工粘性（beta_{SPH}）中使用二次项太低似乎会导致引力不稳定盘中的过度耗散，这可能会影响任何敏感地依赖于热力学的结果，例如盘碎裂。我们表明，这两个代码收敛到临界冷却时标的值，β_{crit} > 20（γ =5/3的比热比），甚至可能大到β_{crit}约30。这比大多数以前的研究发现的大约大3-5倍。这相当于一个圆盘在不发生α_{GI，crit}碎裂的情况下所能承受的最大重力应力约为0.013-0.02，这比文献中通常使用的值要小得多。因此，自引力盘比过去大多数研究得出的结论更容易破碎。
We carry out simulations of gravitationally unstable discs using a Smoothed Particle Hydrodynamics (SPH) code and a grid-based hydrodynamics code, FARGO, to understand the previous non-convergent results reported by Meru & Bate (2011a). We obtain evidence that convergence with increasing resolution occurs with both SPH and FARGO and in both cases we find that the critical cooling timescale is larger than previously thought. We show that SPH has a first-order convergence rate while FARGO converges with a second-order rate. We show that the convergence of the critical cooling timescale for fragmentation depends largely on the numerical viscosity employed in both SPH and FARGO. With SPH, particle velocity dispersion may also play a role. We show that reducing the dissipation from the numerical viscosity leads to larger values of the critical cooling time at a given resolution. For SPH, we find that the effect of the dissipation due to the numerical viscosity is somewhat larger than had previously been appreciated. In particular, we show that using a quadratic term in the SPH artificial viscosity (beta_{SPH}) that is too low appears to lead to excess dissipation in gravitationally unstable discs, which may affect any results that sensitively depend on the thermodynamics, such as disc fragmentation. We show that the two codes converge to values of the critical cooling timescale, beta_{crit} > 20 (for a ratio of specific heats of gamma=5/3), and perhaps even as large as beta_{crit} approx 30. These are approximately 3-5 times larger than has been found by most previous studies. This is equivalent to a maximum gravitational stress that a disc can withstand without fragmenting of alpha_{GI,crit} approx 0.013-0.02, which is much smaller than the values typically used in the literature. It is therefore easier for self-gravitating discs to fragment than has been concluded from most past studies.