Magnetic fields in red giant stars remain a poorly understood topic, particularly in what concerns their intensity in regions far below the surface. In this work, we propose that gravity-dominated mixed modes of high absolute radial order and low angular degree can be used to probe the magnetic field in their radiative cores. Using two poloidal, axisymmetric configurations for the field in the core and the classical perturbative approach, we derive an analytical expression for the magnetic frequency splitting of these oscillation modes. Considering three distinct red giant models, with masses of 1.3\(M_\odot\), 1.6\(M_\odot\) and 2.0\(M_\odot\), we find that a field strength of $10^5$ G is necessary in the core of these stars to induce a frequency splitting of the order of a $\mu$Hz in dipole and quadrupole oscillation modes. Moreover, taking into account observational limits, we estimate that magnetic fields in the cores of red giants that do not present observable magnetic splittings cannot exceed $10^4$ G. Given the general absence of observable splittings in the oscillation spectra of these stars, and assuming that present mode suppression mechanisms are not biased towards certain azimuthal orders and retain all peaks in each multiplet, our results lead us to conclude that internal fields with the considered configurations and strengths above $10^4$ G are not prevalent in red giants.

中文翻译：

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红巨星非径向振荡中的核心磁场印记

红巨星中的磁场仍然是一个鲜为人知的话题，特别是关于它们在远低于地表区域的强度的问题。在这项工作中，我们建议可以使用高绝对径向阶和低角度的重力主导混合模式来探测其辐射核心中的磁场。使用核心场的两个极向轴对称配置和经典微扰方法，我们推导出这些振荡模式的磁频率分裂的解析表达式。考虑三个不同的红巨星模型，质量分别为 1.3\(M_\odot\)、1.6\(M_\odot\) 和 2.0\(M_\odot\)，我们发现 $10^5$ G 的场强是在这些恒星的核心中，必须在偶极子和四极子振荡模式中引起 $\mu$Hz 量级的频率分裂。而且，