标题： 罗斯比波不稳定性在开普勒吸积盘中 显示英文标题

标题： Rossby Wave Instability of Keplerian Accretion Disks

摘要： 我们发现在存在关键函数${\cal L}(r) \equiv {\cal F}(r) S^{2/\Gamma}(r)$的径向剖面局部最大值时，薄的非磁化开普勒盘中会出现非轴对称罗斯比波的线性不稳定性，其中${\cal F}^{-1} = \hat {\bf z}\cdot ({\bf \nabla}\times {\bf v}) /\Sigma$是位涡度，$S = P/\Sigma^\Gamma$是熵，$\Sigma$是表面质量密度，$P$是垂直积分压力，以及$\Gamma$是绝热指数。我们详细考虑了盘熵剖面$S(r)$存在局部最大值的特殊情况。 这个最大值如果其高度与宽度比${\rm max}(S)/\Delta r$大于一个阈值，则会将其附近的波困住。 由此熵变化得到的压强梯度为波的增长提供恢复力。 我们表明，被束缚的波有助于向外传输角动量。 产生熵变化的一种可能方式是当吸积盘从可忽略的质量和温度开始，因此熵可忽略。 当质量通过潮汐扭矩、磁扭矩或罗氏瓣溢出而逐渐积累时，热量的限制将在盘的外边界处导致一个熵的最大值。 由此不稳定性可能产生的非线性发展包括罗斯比涡旋的形成和螺旋激波的形成。 从流体动力学模拟中尚需确定的是，罗斯比波包（或涡旋）在径向向内传播时是否“保持在一起”。 显示英文摘要

摘要： We find a linear instability of non-axisymmetric Rossby waves in a thin non-magnetized Keplerian disk when there is a local maximum in the radial profile of a key function ${\cal L}(r) \equiv {\cal F}(r) S^{2/\Gamma}(r)$, where ${\cal F}^{-1} = \hat {\bf z}\cdot ({\bf \nabla}\times {\bf v}) /\Sigma$ is the potential vorticity, $S = P/\Sigma^\Gamma$ is the entropy, $\Sigma$ is the surface mass density, $P$ is the vertically integrated pressure, and $\Gamma$ is the adiabatic index. We consider in detail the special case where there is a local maximum in the disk entropy profile $S(r)$. This maximum acts to trap the waves in its vicinity if its height to width ratio ${\rm max}(S)/\Delta r$ is larger than a threshold value. The pressure gradient derived from this entropy variation provides the restoring force for the wave growth. We show that the trapped waves act to transport angular momentum outward. A plausible way to produce an entropy variation is when an accretion disk is starting from negligible mass and temperature, therefore negligible entropy. As mass accumulates by either tidal torquing, magnetic torquing, or Roche-lobe overflow, confinement of heat will lead to an entropy maximum at the outer boundary of the disk. Possible nonlinear developments from this instability include the formation of Rossby vortices and the formation of spiral shocks. What remains to be determined from hydrodynamic simulations is whether or not Rossby wave packets (or vortices) ``hold together'' as they propagate radially inward.