arXiv 2203.047922022-03-09astro-ph.EP

原行星盘中尘埃沉降的爆炸不稳定性

Explosive instability of dust settling in a protoplanetary disc

V. V. Zhuravlev

备注：: 19 pages, 5 figures, accepted for publication in MNRAS
DOI：: 10.1093/mnras/stac678

摘要：

结果表明，尘埃沉降到圆盘中面时，圆盘中的气尘扰动表现出流动尘埃波（SDW）与两个惯性波（IW）之间的非线性三波共振相互作用。在本文所考虑的特殊情况下，波数为$k^\bullet = 2κ/ (g_z t_s)$的SDW（其中$κ$、$g_z$和$t_s$分别是周转频率、垂直重力加速度和粒子停止时间）与波数较低的两个IW（$k^\prime$和$k^{\prime\prime}$）相互作用，使得$k^\prime < k_{\rm DSI} < k^{\prime\prime} < k^\bullet$，其中$k_{\rm DSI} = κ/ (g_z t_s)$是与先前发现的线性尘埃沉降不稳定性相关的SDW和IW之间的线性共振的波数。这个问题在小粉尘分数的限制下得到了解析解决。考虑到尘埃对气体的动力学反作用，${\bf k}^\bullet$、${\bf k}^\prime$和${\bf k}^{\prime\prime}$变得稍微不共线，并且波的相互作用导致它们的振幅同时爆炸性增长。这种增长可以用波与波之间能量的保守交换来解释。所有三个波的振幅都在增长，因为负能量SDW将其能量转移到正能量IW。初始主导波的无量纲振幅与爆发时间的乘积可以小于圆盘中的开普勒时间。结果表明，一般情况下，一种炸药类型的三波共振存在于很宽的波数范围内$0 < k^\bullet \leq 2κ/ (g_z t_s)$。气体-尘埃混合物的爆炸性不稳定性可能会促进尘埃的聚集和随后在年轻的原行星盘中形成星子。

英文摘要：

It is shown that gas-dust perturbations in a disc with dust settling to the disc midplane exhibit the non-linear three-wave resonant interactions between streaming dust wave (SDW) and two inertial waves (IW). In the particular case considered in this paper, SDW at the wavenumber $k^\bullet = 2κ/ (g_z t_s)$, where $κ$, $g_z$ and $t_s$ are, respectively, epicyclic frequency, vertical gravitational acceleration and particle's stopping time, interacts with two IW at the lower wavenumbers $k^\prime$ and $k^{\prime\prime}$ such that $k^\prime < k_{\rm DSI} < k^{\prime\prime} < k^\bullet$, where $k_{\rm DSI} = κ/ (g_z t_s)$ is the wavenumber of the linear resonance between SDW and IW associated with the previously discovered linear dust settling instability. The problem is solved analytically in the limit of the small dust fraction. As soon as the dynamical dust back reaction on gas is taken into account, ${\bf k}^\bullet$, ${\bf k}^\prime$ and ${\bf k}^{\prime\prime}$ become slightly non-collinear and the emerging interaction of waves leads to simultaneous explosive growth of their amplitudes. This growth is explained by the conservative exchange with energy between the waves. The amplitudes of all three waves grow because the negative energy SDW transfers its energy to the positive energy IW. The product of the dimensionless amplitude of initially dominant wave and the time of explosion can be less than Keplerian time in a disc. It is shown that, generally, the three-wave resonance of an explosive type exists in a wide range of wavenumbers $0 < k^\bullet \leq 2κ/ (g_z t_s)$. An explosive instability of gas-dust mixture may facilitate the dust clumping and the subsequent formation of planetesimals in young protoplanetary discs.

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