Dust settling in magnetorotationally driven turbulent discs – I. Numerical methods and evidence for a vigorous streaming instability
Dust settling in magnetorotationally driven turbulent discs – I. Numerical methods and evidence for a vigorous streaming instability
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磁旋转驱动的湍流盘中的灰尘沉降 - I. 剧烈流动不稳定性的数值方法和证据
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发表时间：
2008
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通讯作者：
Sean A. Brittain
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作者：
D. Balsara;D. Tilley;T. Rettig;Sean A. Brittain
在本文中，我们使用计算天体物理学的黎曼代码来研究垂直分层原恒星吸积盘中特定径向位置处尘埃颗粒与气体的真实分布的相互作用。该圆盘被建模为具有最小质量太阳星云的密度和温度，并且此处报告了半径为 0.3 和 10 天文单位的剪切盒模拟。通过磁旋转不稳定性（MRI）将圆盘驱动至完全发展的湍流。模拟跨越了圆盘中平面的三个气体尺度高度。我们发现，即使灰尘沉积到吸积盘的中平面，包含标准尘气比也不会对 MRI 产生任何显着影响。各种尺寸的灰尘的密度分布在圆盘中平面的两个刻度高度内达到高斯分布。当考虑大的球形尘埃颗粒时，这些高斯分布的垂直尺度高度与尘埃半径的平方根的倒数成正比。这一结果与理论预期一致。
在我们的一项模拟中，最大的两个尘埃家族显示出强烈的沉降到吸积盘中平面的趋势。大的灰尘往往会组织成细长的高密度团块。这些团块的动态被证明与流动不稳定性一致。一旦形成，流动不稳定就会非常剧烈和持久。每股高密度灰尘流均显示出降低的均方根速度色散。流内的速度方向也相对于平均剪切力对齐，这进一步证明我们正在目睹流的不稳定性。溪流交汇处形成了最密集的大尘埃团。
我们还表明，参与流动不稳定性的灰尘的平均自由程和碰撞时间相对于平均自由程和碰撞时间减少了几乎两个数量级。颗粒之间的均方根速度也需要降至最低阈值以下，以便颗粒粘附，并且我们表明，10 au 模拟中的少量大灰尘应该具有颗粒聚结的倾向。我们的模拟结果可能对那些模拟原恒星盘光谱能量分布的人以及那些模拟尘埃凝结和生长的人有用。
In this paper, we have used the riemann code for computational astrophysics to study the interaction of a realistic distribution of dust grains with gas at specific radial locations in a vertically stratified protostellar accretion disc. The disc was modelled to have the density and temperature of a minimum mass solar nebula, and shearing box simulations at radii of 0.3 and 10 au are reported here. The disc was driven to a fully developed turbulence via the magnetorotational instability (MRI). The simulations span three gas scaleheights about the disc's midplane. We find that the inclusion of standard dust-to-gas ratios does not have any significant effect on the MRI even when the dust sediments to the midplane of the accretion disc. The density distribution of the dust of all sizes reached a Gaussian profile within two scaleheights of the disc's midplane. The vertical scaleheights of these Gaussian profiles are shown to be proportional to the reciprocal of the square root of the dust radius when large spherical dust grains are considered. This result is consistent with theoretical expectation.
The largest two families of dust in one of our simulations show a strong tendency to settle to the midplane of the accretion disc. The large dust tends to organize itself into elongated clumps of high density. The dynamics of these clumps is shown to be consistent with a streaming instability. The streaming instability is seen to be very vigorous and persistent once it forms. Each stream of high-density dust displays a reduced rms velocity dispersion. The velocity directions within the streams are also aligned relative to the mean shear, providing further evidence that we are witnessing a streaming instability. The densest clumpings of large dust are shown to form where the streams intersect.
We have also shown that the mean free path and collision time for dust that participates in the streaming instability are reduced by almost two orders of magnitude relative to the average mean free paths and collision times. The rms velocities between the grains also need to fall below a minimum threshold in order for the grains to stick and we show that a small amount of the large dust in our 10 au simulation should have a propensity for grain coalescence. The results of our simulations are likely to be useful for those who model spectral energy distributions of protostellar discs and also for those who model dust coagulation and growth.