论文标题
在原月光下沉降的灰尘的爆炸性不稳定
Explosive instability of dust settling in a protoplanetary disc
论文作者
论文摘要
结果表明，灰尘沉淀到圆盘中平面的圆盘中的气盘扰动表现出非线性的三波谐振相互作用（SDW）和两个惯性波（IW）。在本文中考虑的特殊情况下，SDW处于aveNumber $ k^\ bullet =2κ/（g_z t_s）$，其中$κ$，$ g_z $和$ t_s $分别是epicyclic频率，垂直引力加速度和粒子的停止时间，在下$ k^$ k^$ k^$ k^$ k^$ k^$ k^$ k^$ k^$ k^$ k^$^prement a^; $k^\prime < k_{\rm DSI} < k^{\prime\prime} < k^\bullet$, 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.该问题以小尘埃分解的极限进行分析解决。 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.这种增长是通过波浪之间的能量的保守交换来解释的。所有三个波的幅度都会增长，因为负能量SDW将其能量转移到正能IW上。最初主导波和爆炸时间的无量纲幅度的乘积可能比圆盘中的开普勒时间小。结果表明，通常，爆炸性类型的三波共振存在于广泛的波数中$ 0 <k^\ bullet \ lex \ leq2κ/（g_z t_s）$。气盘混合物的爆炸性不稳定可能有助于粉尘块，随后在年轻的原球圆盘中形成行星。
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.
