Modulation and symmetry changes in stellar dynamos
Modulation and symmetry changes in stellar dynamos
复制标题
恒星发电机的调制和对称性变化
DOI：
10.1046/j.1365-8711.1998.01572.x
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发表时间：
1998
影响因子：
4.8
通讯作者：
N. Weiss
中科院分区：
文献类型：
--
作者：
E. Knobloch;S. Tobias;N. Weiss
恒星发电机是由非线性偏微分方程（PDE），承认解决方案与偶极，四极或混合对称（即不同的宇称）。这些偏微分方程具有描述磁周期的周期解，数值研究揭示了两种不同类型的调制。对于类型1的调制，存在奇偶性变化而没有幅度的显著变化，而对于类型2，存在幅度变化而没有奇偶性的显著变化。在像太阳这样的恒星中，周期性的磁场活动被对应于2型调制的大极小值打断。虽然太阳的磁场已经维持了近300年的偶极对称性，但在蒙德极小期结束时有一个显着的宇称变化。我们推断，太阳场可能已经翻转从偶极到四极极性（和背部）后，在过去的深极小，并可能在未来再次这样做。其他恒星，具有不同的质量或旋转速率，可能会表现出偶极，四极或混合宇称的周期活动。这种行为的起源可以通过将PDE结果与适当的低阶常微分方程（ODE）系统的解相关联来理解。类型1调制在四阶系统中再现，而类型2调制在三阶系统中发生。在这里，我们构建了一个新的六阶系统，描述了这两种类型的调制，并澄清了破坏和调制活动之间的相互作用。这些非线性常微分方程的解决方案重现了偏微分方程的定性行为，包括翻转极性后，一个长期的大极小。因此，我们可以确信，这些行为模式是稳健的，并将适用于与太阳相似的恒星。
Stellar dynamos are governed by non-linear partial differential equations (PDEs) which admit solutions with dipole, quadrupole or mixed symmetry (i.e. with different parities). These PDEs possess periodic solutions that describe magnetic cycles, and numerical studies reveal two different types of modulation. For modulations of Type 1 there are parity changes without significant changes of amplitude, while for Type 2 there are amplitude changes without significant changes in parity. In stars like the Sun, cyclic magnetic activity is interrupted by grand minima that correspond to Type 2 modulation. Although the Sun’s magnetic field has maintained dipole symmetry for almost 300 yr, there was a significant parity change at the end of the Maunder Minimum. We infer that the solar field may have flipped from dipole to quadrupole polarity (and back) after deep minima in the past and may do so again in the future. Other stars, with different masses or rotation rates, may exhibit cyclic activity with dipole, quadrupole or mixed parity. The origins of such behaviour can be understood by relating the PDE results to solutions of appropriate low-order systems of ordinary differential equations (ODEs). Type 1 modulation is reproduced in a fourth-order system while Type 2 modulation occurs in a third-order system. Here we construct a new sixth-order system that describes both types of modulation and clarifies the interactions between symmetry-breaking and modulation of activity. Solutions of these non-linear ODEs reproduce the qualitative behaviour found for the PDEs, including flipping of polarity after a prolonged grand minimum. Thus we can be confident that these patterns of behaviour are robust, and will apply to stars that are similar to the Sun.