论文标题
磁性旋转磁盘的线性稳定性分析，欧姆耗散和双极扩散
Linear Stability Analysis of a Magnetic Rotating Disk with Ohmic Dissipation and Ambipolar Diffusion
论文作者
论文摘要
我们对弱离子化的等温，旋转，磁性，自我磨碎的表的稳定性进行线性分析。磁场和旋转轴垂直于纸张。我们包括对热压，重力，旋转和磁性（压力和张力）力以及两个非理想的磁性水力动力学（MHD）效应（欧姆消散和歧义性耗散和歧义性扩散）的自洽处理，这些效果对它们对旋转纸张类似旋转纸的云型云或脉冲的重力不稳定性的影响进行了处理。我们的结果表明，始终有一个首选的长度尺度和相关的最小时间尺度，用于重力不稳定性。我们调查了问题的依赖性问题的依赖性：最初的归一化质量与频率比$μ_0$，旋转toomre参数$ q $，无尺寸的无尺寸欧姆扩散性$ \tildeη_ {\ rm od，0} $，以及无维度碰撞的时间碰撞时间$ \tildeτ_ {\ rm {ni，0}} $，这是对双极扩散性的度量。 $ \tildeη_ {\ rm od，0} $的结果是，在质量（$μ_0\ gtrsim 1 $）方面发生了最大的首选不稳定长度，在质量上类似于$ \ tilde tilde tilde tilde tilde tilde tilde tilde _ {\ rm {\ rm {ni {ni} $ ni vent partitive of $ \ tilde tilde anditiant of partive。旋转的添加导致了广义的Toomre标准（包括磁依赖性）和修改的长度尺度和时间尺度，以进行崩溃。当还包括非理想的MHD效应时，Toomre Criterion恢复为流体动力值。我们将结果应用于早期嵌入阶段的Protostellar磁盘性能，发现首选的不稳定性尺度可以显着超过热（牛仔裤）尺度，并且峰优选的片段化质量可能为$ \ sim 10-90 \ m _ {\ rm jup jup} $。
We perform a linear analysis of the stability of isothermal, rotating, magnetic, self-gravitating sheets that are weakly ionized. The magnetic field and rotation axis are perpendicular to the sheet. We include a self-consistent treatment of thermal pressure, gravitational, rotational, and magnetic (pressure and tension) forces together with two nonideal magnetohydrodynamic (MHD) effects (Ohmic dissipation and ambipolar diffusion) that are treated together for their influence on the properties of gravitational instability for a rotating sheet-like cloud or disk. Our results show that there is always a preferred length scale and associated minimum timescale for gravitational instability. We investigate their dependence on important dimensionless free parameters of the problem: the initial normalized mass-to-flux ratio $μ_0$, the rotational Toomre parameter $Q$, the dimensionless Ohmic diffusivity $\tildeη_{\rm OD,0}$, and the dimensionless neutral-ion collision time $\tildeτ_{\rm{ni,0}}$ that is a measure of the ambipolar diffusivity. One consequence of $\tildeη_{\rm OD,0}$ is that there is a maximum preferred lengthscale of instability that occurs in the transcritical ($μ_0 \gtrsim 1$) regime, qualitatively similar to the effect of $\tildeτ_{\rm{ni,0}}$, but with quantitative differences. The addition of rotation leads to a generalized Toomre criterion (that includes a magnetic dependence) and modified lengthscales and timescales for collapse. When nonideal MHD effects are also included, the Toomre criterion reverts back to the hydrodynamic value. We apply our results to protostellar disk properties in the early embedded phase and find that the preferred scale of instability can significantly exceed the thermal (Jeans) scale and the peak preferred fragmentation mass is likely to be $\sim 10- 90 \ M_{\rm Jup}$.
