冷却诱导的开普勒涡旋衰变
Cooling-Induced Vortex Decay in Keplerian Disks
摘要：
在原行星盘中，流体动力学不稳定性，如罗斯贝波不稳定性，很容易产生涡旋。然而，在亚毫米连续观测中，大尺度的不对称性指示尘埃捕获涡旋是不常见的。一种可能的解释是，涡旋的寿命很短。在本文中，我们探讨了辐射冷却如何导致涡旋衰变。开普勒圆盘中的椭圆涡经历绝热加热和冷却循环。辐射冷却改变了这些循环，并产生斜压性，改变了涡旋的位涡。我们表明，净效应是典型的自旋下降，或衰减，亚绝热径向分层的旋涡。我们进行了一系列的二维剪切盒模拟，改变气体冷却（或弛豫）时间，$t_{\rm cool}$，和初始涡强度。我们测量了涡旋衰变半衰期$t_{\rm half}$，发现它可以通过时标比$t_{\rm cool}/t_{\rm turn}$粗略预测，其中$t_{\rm turn}$是涡旋周转时间。在等温（$t_{\rm cool}\ll t_{\rm turn}$）和绝热（$t_{\rm cool}\gg t_{\rm turn}$）极限下衰减都很慢;当$t_{\rm cool}\sim0.1\,t_{\rm turn}$（其中$t_{\rm half}$与$\sim300$轨道一样短）时衰减最快。在通常发现盘环的数十天文单位处，$t_{\rm turn}$可能比$t_{\rm cool}$长得多，可能将涡旋置于快速衰变状态。
英文摘要：
Vortices are readily produced by hydrodynamical instabilities, such as the Rossby wave instability, in protoplanetary disks. However, large-scale asymmetries indicative of dust-trapping vortices are uncommon in sub-millimeter continuum observations. One possible explanation is that vortices have short lifetimes. In this paper, we explore how radiative cooling can lead to vortex decay. Elliptical vortices in Keplerian disks go through adiabatic heating and cooling cycles. Radiative cooling modifies these cycles and generates baroclinicity that changes the potential vorticity of the vortex. We show that the net effect is typically a spin down, or decay, of the vortex for a sub-adiabatic radial stratification. We perform a series of two-dimensional shearing box simulations, varying the gas cooling (or relaxation) time, $t_{\rm cool}$, and initial vortex strength. We measure the vortex decay half-life, $t_{\rm half}$, and find that it can be roughly predicted by the timescale ratio $t_{\rm cool}/t_{\rm turn}$, where $t_{\rm turn}$ is the vortex turnaround time. Decay is slow in both the isothermal ($t_{\rm cool}\ll t_{\rm turn}$) and adiabatic ($t_{\rm cool}\gg t_{\rm turn}$) limits; it is fastest when $t_{\rm cool}\sim0.1\,t_{\rm turn}$, where $t_{\rm half}$ is as short as $\sim300$ orbits. At tens of au where disk rings are typically found, $t_{\rm turn}$ is likely much longer than $t_{\rm cool}$, potentially placing vortices in the fast decay regime.
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