通过直接数值模拟评估太阳半球磁旋度偏置的Σ效应模型
Evaluating the $Σ$-effect Model of the Solar Hemispherical Helicity Bias via Direct Numerical Simulations
AI总结：
通过直接数值模拟研究太阳半球磁旋度偏置的Σ效应模型，发现其与磁旋度演变无明显关联，引发对模型实际效用的质疑。
摘要：
太阳半球磁旋度规则（SHHR）是用来表示在太阳表面活跃区域的磁旋度代理中观察到的偏置。SHHR指出，在北半球活跃区域主要观察到负磁旋度，而在南半球则主要为正。Longcope等人1998年的Σ效应模型是解释SHHR最被引用的模型之一。在该模型中，磁结构通过湍流对流中所经历的动能旋度产生偏置，后者由于恒星的旋转影响而具有手性。原始论文为受参数化螺旋湍流影响的薄磁通管的动力学建立了优雅的数学模型。在此，我们尝试利用完全非线性、三维、笛卡尔域的模拟，对孤立的有限横截面、扭曲磁通结构在旋转、超射、湍流可压缩对流中上升的情况进行研究。我们寻找湍流动能旋度内容与结构演变磁旋度之间的相关性证据。我们发现这种关系的证据很少，甚至没有明显的半球依赖性。尽管这些模拟离对概念的完美表示还很远，但这项工作引发了关于Σ效应在现实中的潜在有效性问题的许多疑问。
英文摘要：
The Solar Hemispherical Helicity Rule(s) (SHHR) is a term used to represent a bias observed in proxies for the magnetic helicity in active regions at the solar surface. The SHHR states that predominantly negative magnetic helicity is observed in active regions in the northern hemisphere, whereas predominantly positive is found in the southern. The $Σ$-effect model of \cite{longcope1998flux} is one of the most cited models for the explanation of the SHHR. In this model, the magnetic structures derive the bias in their magnetic helicity from the kinetic helicity of the turbulent convection through which they travel, where the latter is handed owing to the rotational influence of the star. The original paper built an elegant mathematical model for the dynamics of thin flux tubes influenced by parameterized helical turbulence. Here, we attempt to explore the conceptual ideas of this original simplified model using fully-nonlinear, three-dimensional, Cartesian-domain simulations of isolated, finite cross-sectional, twisted magnetic flux structures rising though rotating, overshooting, turbulent compressible convection. We look for evidence of a correlation between the kinetic helicity content of the turbulence and the evolving magnetic helicity of the structures. We find little evidence of such a relationship, and do not even find any clear hemispheric dependence. Although these simulations are far from a perfect representation of the ideas, this work raises many questions about the potential efficacy of the $Σ$-effect in reality.
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