标题： 原磁盘中动态尘埃和冷却率的垂直剪切不稳定性流体动力学模拟 显示英文标题

标题： Hydrodynamical simulations of the vertical shear instability with dynamic dust and cooling rates in protoplanetary disks

摘要： 湍流在原行星盘中影响尘埃演化和星子形成。垂直剪切不稳定性（VSI）是外盘区域候选湍流驱动机制之一。由于VSI需要快速气体冷却，盘中的尘埃颗粒可以影响甚至控制由VSI驱动的湍流。然而，由VSI驱动的湍流具有强烈的垂直运动，导致垂直方向上的尘埃扩散。因此，尚不清楚湍流结构和尘埃分布是如何形成的。我们的目标是澄清在与湍流扩散尘埃相关的冷却速率演变下，VSI是否能够实现准稳态的尘埃分布。我们还阐明了尘埃粒径和尘埃-气体质量比对平衡态实现和持续性的依赖关系。我们进行了轴对称盘的全球二维流体动力学模拟，以研究VSI如何驱动湍流并维持尘埃沉降与扩散之间的平衡。这些模拟考虑了尘埃分布、冷却速率和湍流之间的动态相互作用。我们发现，VSI混合、尘埃沉降和局部冷却达到平衡，形成一个无量纲垂直混合系数约为10^{-3}的厚尘埃层。VSI维持这种状态的能力也取决于尘埃粒径和尘埃-气体质量比。较大的颗粒或较低的质量比会削弱湍流，导致尘埃沉降。平衡态存在的条件与Fukuhara & Okuzumi（2024）提出的半解析模型的预测一致。我们的结果表明，高效的湍流尘埃混合和高效的冷却可以同时发生。它们还暗示，在由VSI主导的盘中，湍流强度水平因颗粒大小而异。这表明，原行星盘中尘埃增长的效率可能取决于VSI。 显示英文摘要

摘要： Turbulence in protoplanetary disks affects dust evolution and planetesimal formation. The vertical shear instability (VSI) is one of the candidate turbulence-driving mechanisms in the outer disk region. Since the VSI requires rapid gas cooling, dust grains in disks can influence and potentially control VSI-driven turbulence. However, VSI-driven turbulence has strong vertical motion, causing vertical dust diffusion. As a result, it remains unclear how turbulent structures and dust distributions form. We aim to clarify whether the VSI can achieve a quasi-steady dust profile under cooling rate evolution associated with turbulently diffusing dust. We also elucidate the dependence of the dust size and dust-to-gas mass ratio on the realization and persistence of the equilibrium state. We perform global two-dimensional hydrodynamical simulations of an axisymmetric disk to investigate how the VSI drives turbulence and maintains a balance between dust settling and diffusion. These simulations account for the dynamic interplay between dust distribution, cooling rates, and turbulence. We find that VSI mixing, dust settling, and local cooling reach an equilibrium, forming a thick dust layer with a dimensionless vertical mixing coefficient of approximately 10^{-3}. The ability of the VSI to sustain this state also depends on the dust size and dust-to-gas mass ratio. Larger grains or lower mass ratios weaken turbulence, leading to dust settling. The condition of equilibrium state existence is consistent with the prediction of the semi-analytic model presented by Fukuhara & Okuzumi (2024). Our results indicate that efficient turbulent dust mixing and efficient cooling can occur simultaneously. They also imply that turbulence in VSI-dominated disks has different intensity levels depending on the grain size. This suggests that the efficiency of dust growth can depend on the VSI in protoplanetary disks.