Fluctuation dynamos are thought to play an essential role in magnetized galaxy evolution, saturating within $\sim0.01~$Gyr and thus potentially acting as seeds for large-scale dynamos. However, unambiguous observational confirmation of the fluctuation dynamo action in a galactic environment is still missing. This is because, in spiral galaxies, it is difficult to differentiate between small-scale magnetic fields generated by a fluctuation dynamo and those due to the tangling of the large-scale field. We propose that observations of magnetic fields in elliptical galaxies would directly probe the fluctuation dynamo action. This is motivated by the fact that in ellipticals, due to their lack of significant rotation, the conventional large-scale dynamo is absent and the fluctuation dynamo is responsible for controlling the magnetic field strength and structure. By considering turbulence injected by Type Ia supernova explosions and possible magnetic field amplification by cooling flows, we estimate expected magnetic field strengths of $0.2~-~1 \,\mu{\rm G}$ in quiescent elliptical galaxies. We use a semi-analytic model of galaxy formation to estimate the distribution and redshift evolution of field strengths, tentatively finding a decrease in magnetic field strength with decreasing redshift. We analyse a sample of radio sources that exhibit the Laing-Garrington (LG) effect (radio polarization asymmetry in jets) and infer magnetic field strengths between $0.14~-~1.33 \,\mu{\rm G}$ for a uniform thermal electron density and between $1.36~-~6.21\,\mu{\rm G}$ for the thermal electron density following the King profile. We examine observational techniques for measuring the magnetic field saturation state in elliptical galaxies, focusing on Faraday RM grids, the LG effect, synchrotron emission, and gravitational lensing, finding appealing prospects for future empirical analysis.

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椭圆星系中的磁场：波动发电机作用的观测探测器

波动发电机被认为在磁化星系演化中起着至关重要的作用，在 $\sim0.01~$Gyr 内饱和，因此可能充当大型发电机的种子。然而，仍然缺少对银河环境中波动发电机作用的明确观测确认。这是因为，在旋涡星系中，很难区分由涨落发电机产生的小尺度磁场和由大尺度磁场缠结引起的磁场。我们建议对椭圆星系中的磁场进行观测将直接探测波动发电机的作用。这是因为在椭圆机中，由于它们没有明显的旋转，没有传统的大型发电机，波动发电机负责控制磁场强度和结构。通过考虑 Ia 型超新星爆炸注入的湍流和冷却流可能导致的磁场放大，我们估计静态椭圆星系中的预期磁场强度为 $0.2~-~1 \,\mu{\rm G}$。我们使用星系形成的半解析模型来估计场强的分布和红移演化，初步发现磁场强度随着红移的减小而减小。我们分析了表现出 Laing-Garrington (LG) 效应（射流中的无线电极化不对称性）的无线电源样本，并推断均匀热电子的磁场强度在 $0.14~-~1.33 \,\mu{\rm G}$ 之间密度在 $1.36~-~6.21\ 之间，\mu{\rm G}$ 用于遵循 King 轮廓的热电子密度。我们研究了测量椭圆星系磁场饱和状态的观测技术，重点关注法拉第 RM 网格、LG 效应、同步加速器发射和引力透镜，为未来的实证分析寻找有吸引力的前景。