Spiral-driven accretion in protoplanetary discs - II Self-similar solutions
Spiral-driven accretion in protoplanetary discs - II Self-similar solutions
复制标题
原行星盘中的螺旋驱动吸积 - II 自相似解
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
S. Fromang
中科院分区：
文献类型：
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作者：
P. Hennebelle;G. Lesur;S. Fromang
吸积盘在宇宙中无处不在，了解这些物体的角动量和质量是如何径向传输的是一个关键问题。在这里，我们研究了非线性螺旋模式在流体动力和非自引力吸积盘中所起的作用，假设外部干扰（如落入盘上）可能触发它们。为此，我们计算了描述螺旋波在其中传播的圆盘的自相似解。这样的解决方案提出了我们仔细分析的冲击和临界声音点。对于所有允许的温度和几个螺旋冲击，我们计算了波的结构。特别地，我们推断出螺旋形状的角度，它对圆盘施加的应力以及相关的质量通量和角动量作为温度的函数。我们用无量纲参数量化了角动量输运率。对于我们考虑的最厚的圆盘（对应于$h/r$的值约为1/3），我们发现$alpha$的值高达$0.1$，并且随着温度$T$缩放，使得$alpha propto T^{3/2} propto (h/r)^3$。螺旋角随温度的变化为$arctan(r/h)$。这些解的存在表明，发生在圆盘外边界的扰动，例如由落入运动引起的扰动，可以传播到圆盘内部深处，因此即使考虑小半径也不应被忽视。
Accretion discs are ubiquitous in the universe and it is a crucial issue to understand how angular momentum and mass are being radially transported in these objects. Here, we study the role played by non-linear spiral patterns within hydrodynamical and non self-gravitating accretion disc assuming that external disturbances such as infall onto the disc may trigger them. To do so, we computed self-similar solutions that describe discs in which a spiral wave propagates. Such solutions present both shocks and critical sonic points that we carefully analyze. For all allowed temperatures and for several spiral shocks, we calculated the wave structure. In particular we inferred the angle of the spiral patern, the stress it exerts on the disc as well as the associated flux of mass and angular momentum as a function of temperature. We quantified the rate of angular momentum transport by means of the dimensionless $alpha$ parameter. For the thickest disc we considered (corresponding to $h/r$ values of about 1/3), we found values of $alpha$ as high as $0.1$, and scaling with the temperature $T$ such that $alpha propto T^{3/2} propto (h/r)^3$. The spiral angle scales with the temperature as $arctan(r/h)$. The existence of these solutions suggests that perturbations occurring at disc outer boundaries, such as for example perturbations due to infall motions, can propagate deep inside the disc and therefore should not be ignored, even when considering small radii.