ABSTRACT Recent numerical work in helioseismology has shown that a periodically varying subsurface magnetic field leads to a fanning of the f-mode, which emerges from a density jump at the surface. In an attempt to model a more realistic situation, we now modulate this periodic variation with an envelope, giving thus more emphasis on localised bipolar magnetic structures in the middle of the domain. Some notable findings are: (i) compared to the purely hydrodynamic case, the strength of the f-mode is significantly larger at high horizontal wavenumbers k, but the fanning is weaker for the localised subsurface magnetic field concentrations investigated here than the periodic ones studied earlier; (ii) when the strength of the magnetic field is enhanced at a fixed depth below the surface, the fanning of the f-mode in the diagram increases proportionally in such a way that the normalised f-mode strengths remain nearly the same in different such cases; (iii) the unstable Bloch modes reported previously in case of harmonically varying magnetic fields are now completely absent when more realistic localised magnetic field concentrations are imposed beneath the surface, thus suggesting that the Bloch modes are unlikely to be supported during most phases of the solar cycle; (iv) the f-mode strength appears to depend also on the depth of magnetic field concentrations such that it shows a relative decrement when the maximum of the magnetic field is moved to a deeper layer. We argue that detections of f-mode perturbations such as those being explored here could be effective tracers of solar magnetic fields below the photosphere before these are directly detectable as visible manifestations in terms of active regions or sunspots.

中文翻译：

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来自局部双极地下磁场的 f 模式强化

摘要 日震学最近的数值研究表明，周期性变化的地下磁场会导致 f 模式的扇形，这是从地表的密度跳跃中出现的。为了模拟更现实的情况，我们现在用包络调制这种周期性变化，因此更加强调域中间的局部双极磁结构。一些值得注意的发现是：(i) 与纯流体动力学情况相比，f 模式的强度在高水平波数 k 时明显更大，但此处研究的局部地下磁场集中的扇形比研究的周期性更弱更早；(ii) 当磁场强度在地表以下固定深度增强时，图中 f 模式的扇形按比例增加，使得归一化 f 模式强度在不同的此类情况下几乎保持相同；(iii) 当更真实的局部磁场集中被强加在地表之下时，先前在谐波变化磁场的情况下报告的不稳定 Bloch 模式现在完全不存在，因此表明在太阳的大多数阶段不太可能支持 Bloch 模式循环; (iv) f 模式强度似乎也取决于磁场集中的深度，因此当磁场的最大值移动到更深的层时，它显示出相对减少。