On the dynamics of planetesimals embedded in turbulent protoplanetary discs Dynamics of planetesimals in turbulent discs
On the dynamics of planetesimals embedded in turbulent protoplanetary discs Dynamics of planetesimals in turbulent discs
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嵌入在湍流原行星盘中的星子动力学 湍流盘中的星子动力学
DOI：
10.1111/j.1365-2966.2010.17327.x
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发表时间：
2010
影响因子：
4.8
通讯作者：
Nelson R
中科院分区：
文献类型：
--
作者：
Nelson R
原行星盘中的角动量输运和吸积通常被认为是由磁旋不稳定性（MRI）中的磁流体动力学（MHD）湍流驱动的。嵌入在这些圆盘中的固体（尘埃颗粒、巨石、星子和行星）的动力学可能会受到湍流的强烈影响，因此行星系统的形成路径部分取决于湍流的强度和空间分布。我们研究了星子的动力学，半径在1米到10公里之间，嵌入湍流原行星盘，使用三维MHD模拟。由于湍流盘的作用，星子受到气体阻力和随机引力的作用。在本研究中，我们使用并比较了局部剪切箱模拟和全局模型的结果。这项工作的主要目的是检查：嵌入的星子的速度色散的增长和可能的饱和，作为它们的大小和圆盘参数的函数；星子的径向迁移和扩散速率；剪切箱模拟结果与整体模拟结果吻合的条件。当使用尺寸为4hx16hx2的剪切盒（h为局部尺度高度）时，我们发现局部和全局模拟之间有很好的一致性。由于螺旋密度波的激发和传播，得到的密度波动幅度对箱体尺寸很敏感。这影响了星子所经历的随机强迫。与随机强迫有关的相关时间也发现是箱形尺寸和纵横比的函数。得到的平衡径向速度色散σ(vr)取决于星子的半径Rp。当σ(vr) = 50 m时，σ(vr)达到最小值，σ(vr)为20 m s−1。较小的天体与气体紧密耦合，而thrp = 1 m的巨石达到了与气体湍流速度相似的σ(vr)值（~ 100 m s−1）。在我们的模拟中，大于100米的天体没有达到σ(vr)的平衡值，但在所有模型中，我们发现尺寸为1和10公里的星子的速度色散快速增长，使得σ(vr)≥160 m s - 1，在距离中心恒星5 au的距离运行1200次后。这些数值太大，无法允许星子的失控增长，相互碰撞将导致灾难性的破坏。当物体的温度为1 m时，可以观察到气体阻力引起的径向迁移，并且受湍流的影响不大。较大的天体在其半长轴上进行随机游走，导致径向扩散通过圆盘。对于我们的基准圆盘模型，我们估计在一个位于5au的星子群中，典型的星子在圆盘寿命为5myr时，在一个距离为2.5 au的地方会发生径向扩散。这种量级的径向扩散似乎与太阳系的约束条件不一致。我们的模型表明，原行星盘中充分发展的磁流体动力学（MHD）湍流将对嵌入的星子产生破坏性影响。传统的星子吸积模型需要相对低水平的湍流才能运行，这与原行星盘中死区的存在是一致的。
Angular momentum transport and accretion in protoplanetary discs are generally believed to be driven by magnetohydrodynamics (MHD) turbulenceviathe magnetorotational instability (MRI). The dynamics of solid bodies embedded in such discs (dust grains, boulders, planetesimals and planets) may be strongly affected by the turbulence, such that the formation pathways for planetary systems are determined in part by the strength and spatial distribution of the turbulent flow.We examine the dynamics of planetesimals, with radii between 1 m and 10 km, embedded in turbulent protoplanetary discs, using 3D MHD simulations. The planetesimals experience gas drag and stochastic gravitational forces due to the turbulent disc. We use, and compare the results from, local shearing box simulations and global models in this study.The main aims of this work are to examine: the growth, and possible saturation, of the velocity dispersion of embedded planetesimals as a function of their size and disc parameters; the rate of radial migration and diffusion of planetesimals; the conditions under which the results from shearing box and global simulations agree.We find good agreement between local and global simulations when shearing boxes of dimension 4H× 16H× 2Hare used (Hbeing the local scaleheight). The magnitude of the density fluctuations obtained is sensitive to the box size, due to the excitation and propagation of spiral density waves. This affects the stochastic forcing experienced by planetesimals. The correlation time associated with the stochastic forcing is also found to be a function of the box size and aspect ratio.The equilibrium radial velocity dispersion, σ(vr), obtained depends on the radii,Rp, of the planetesimals. Bodies withRp= 50 m achieve the smallest value with σ(vr) ≃ 20 m s−1. Smaller bodies are tightly coupled to the gas, and boulders withRp= 1 m attain a value of σ(vr) similar to the turbulent velocity of the gas (∼100 m s−1). Equilibrium values of σ(vr) for bodies larger than 100 m are not achieved in our simulations, but in all models we find rapid growth of the velocity dispersion for planetesimals of size 1 and 10 km, such that σ(vr) ≥ 160 m s−1after a run time of 1200 orbits at a distance of 5 au from the central star. These values are too large to allow for the runaway growth of planetesimals, and mutual collisions would lead to catastrophic disruption. Radial migration due to gas drag is observed for bodies withRp≃ 1 m, and is only modestly affected by the turbulence. Larger bodies undergo a random walk in their semimajor axes, leading to radial diffusion through the disc. For our fiducial disc model, we estimate that radial diffusion across a distance of ≃2.5 au would occur for typical planetesimals in a swarm located at 5 au over a disc lifetime of 5 Myr. Radial diffusion of this magnitude appears to be inconsistent with Solar system constraints.Our models show that fully developed magnetohydrodynamics (MHD) turbulence in protoplanetary discs would have a destructive effect on embedded planetesimals. Relatively low levels of turbulence are required for traditional models of planetesimal accretion to operate, this being consistent with the existence of a dead zone in protoplanetary discs.