From Planetary to Stellar Dynamos - An investigation of the origin and the variability of stellar magnetic fields by direct numerical simulations

大多数低质量恒星都有磁场。恒星磁场可能在它们的场拓扑、它们的场强和它们的时间依赖性方面有很大的不同。低质量恒星和行星的磁场是由其内部导电流体(或气体)运动产生的电流维持的。因此，恒星磁场的巨大变异性很可能与恒星内部结构和内部动力学的差异有关。反之亦然，在几乎所有的演化状态中，磁场都会对恒星动力学和恒星演化产生重大影响。这项拟议的工作将有助于解释恒星磁场的起源和巨大的多样性。发电机问题的复杂性以及广泛的空间和时间尺度使其在很长一段时间内不可能进行直接的数值处理。直到最近，不断增加的计算机能力才使全球直接的发电机数值模拟成为可能，特别是对地球发电机而言。这些模型描述了对流驱动的、导电的和不可压缩的流体(地球外核的液态铁)与磁场的复杂相互作用。然而，对于恒星发电机来说，不可压缩流体的简化假设不再有效，气体是可压缩的。最近开发的一个数值发电机程序考虑了可压缩性。我们将在众所周知的不可压缩模拟结果的指导下，开展可压缩发电机模拟的系统参数研究。通过这种方式，我们打算指出并解释可压缩和不可压缩模型在磁场几何、场强、时间依赖性、场产生机制以及差异旋转的强度和模式方面的系统差异。与这些观测结果的进一步比较将突出可压缩效应的相关性，并将提供对恒星发电机工作原理的洞察。

Most low-mass stars possess a magnetic field. Stellar magnetic fields may differ a lot in their field topology, their field strength and their time dependence. Magnetic fields of low-mass stars and planets are maintained by currents resulting from the motion of a conducting fluid (or gas) in their interiors. Thus, the huge variability of stellar magnetic fields is most probably related to differences in the internal structure and interior dynamics of stars. Vice versa, magnetic fields have a major influence on stellar dynamics and stellar evolution in almost all evolutionary states. The proposed work will contribute to an explanation for the origin and the huge variety of stellar magnetic fields. The complexity of the dynamo problem together with a vast range of spatial and temporal scales rendered its direct numerical treatment impossible for long time. Only recently, increasing computer power made global, direct numerical dynamo simulations feasible, in particular for the geodynamo. These models describe the complicated interaction of a convection-driven, conducting and incompressible fluid (liquid iron in the Earth’s outer core) with a magnetic field. However, for stellar dynamos the simplifying assumption of an incompressible fluid is no longer valid, gas is compressible.A recently developed numerical dynamo code takes compressibility into account. We will carry out a systematic parameter study of compressible dynamo simulations guided by well-known results from incompressible modelling. In this way we intend to point out and to explain systematic differences between compressible and incompressible models with respect to the geometry of magnetic fields, the field strength, the time dependence, the mechanism of field generation and the strength and the pattern of differential rotation. A further comparison with observations along these lines will highlight the relevance of compressible effects and will offer insight into the working of stellar dynamos.