旋转对失速圆柱激波稳定性的影响及其对核塌缩超新星的影响
Effect of Rotation on the Stability of a Stalled Cylindrical Shock and its Consequences for Core-Collapse Supernovae
摘要：
为了更好地理解坍缩核中含有角动量的超新星爆炸，利用微扰分析方法，在一个简单的玩具模型中研究了旋转对稳定吸积激波（SASI）不稳定性的影响.为了简单起见，选择圆柱形几何形状。即使当离心力很小，旋转可以有很强的影响，通过增加的螺旋模式的增长率在同一方向旋转的稳定流的非轴对称模式。反向旋转螺旋模式受到显着阻尼，而轴对称模式几乎不受旋转的影响。螺旋模的增长率与流体的角动量比成近似线性关系。基本单臂螺旋模式（m=1）有利于小的旋转速率，而更强的旋转速率有利于模式m=2。高次谐波的WKB分析表明，与螺旋模式相关的对流声学循环的效率受到旋转的强烈影响，与低频模式相同，而纯声学循环是稳定的。这些结果表明，旋转核心坍缩超新星中SASI的线性相位自然选择了与流动方向相同的螺旋模式，正如Blondin & Mezzacappa（2007）的3D数值模拟所观察到的那样。这强调了在得出爆炸机制和脉冲星反冲的结论之前，需要一个旋转核心坍缩的3D方法。
英文摘要：
A perturbative analysis is used to investigate the effect of rotation on the instability of a steady accretion shock (SASI) in a simple toy-model, in view of better understanding supernova explosions in which the collapsing core contains angular momentum. A cylindrical geometry is chosen for the sake of simplicity. Even when the centrifugal force is very small, rotation can have a strong effect on the non axisymmetric modes of SASI by increasing the growth rate of the spiral modes rotating in the same direction as the steady flow. Counter-rotating spiral modes are significantly damped, while axisymmetric modes are hardly affected by rotation. The growth rates of spiral modes have a nearly linear dependence on the specific angular momentum of the flow. The fundamental one-armed spiral mode (m=1) is favoured for small rotation rates, whereas stronger rotation rates favour the mode m=2. A WKB analysis of higher harmonics indicates that the efficiency of the advective-acoustic cycles associated to spiral modes is strongly affected by rotation in the same manner as low frequency modes, whereas the purely acoustic cycles are stable. These results suggest that the linear phase of SASI in rotating core-collapse supernovae naturally selects a spiral mode rotating in the same direction of the flow, as observed in the 3D numerical simulations of Blondin & Mezzacappa (2007). This emphasizes the need for a 3D approach of rotating core-collapse, before conclusions on the explosion mechanisms and pulsar kicks can be drawn.
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