It is known that stellar differential rotation can be detected by analyzing the Fourier transform of spectral line profiles, since the ratio of the 1st- and 2nd-zero frequencies is a useful indicator. This approach essentially relies on the conventional formulation that the observed flux profile is expressible as a convolution of the rotational broadning function and the intrinsic profile, which implicitly assumes that the local intensity profile does not change over disk. Although this postulation is unrealistic in the strict sense, how the result is affected by this approximation is still unclear. In order to examine this problem, profiles of several lines (showing different center-limb variations) were simulated using a model atmosphere corresponding to a mid-F dwarf by integrating intensity profiles for various combinations of vsini (rot. velocity), alpha (diff. degree), and i (inc. angle), and their Fourier transforms were computed to check whether zeros are detected at the predicted positions or not. For this comparison purpose, a large grid of standard rotational broadening functions and their transforms/zeros were also calculated. It turned out that the situation criticaly depends on vsini: In case of vsini>~20km/s where rotational broadening is predominant over other line broadening velocities (typically several km/s), the 1st/2nd zeros of the transform are confirmed almost at the expected positions. In contrast, deviations begin to appear as vsini is lowered, and the zero features of the transform are totally different from the expectation at vsini as low as ~10km/s, which means that the classical formulation is no more valid. Accordingly, while the zero-frequency approach is safely applicable to studying differential rotation in the former broader-line case, it would be difficult to practice for the latter sharp-line case.

中文翻译：

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基于谱线轮廓傅里叶变换的恒星微分旋转检测

众所周知，可以通过分析谱线轮廓的傅立叶变换来检测恒星的微分旋转，因为第 1 和第 2 零频率的比率是一个有用的指标。这种方法基本上依赖于常规公式，即观察到的通量分布可表示为旋转展宽函数和固有分布的卷积，这隐含地假设局部强度分布不会随盘变化。虽然这个假设在严格意义上是不切实际的，但是这个近似值如何影响结果仍然不清楚。为了研究这个问题，通过整合 vsini (rot. 1) 的各种组合的强度剖面，使用对应于中 F 矮矮星的模型大气模拟了几条线的剖面（显示不同的中心肢体变化）。速度）、alpha（差异度数）和 i（增量角），计算它们的傅立叶变换以检查是否在预测位置检测到零点。为了这个比较目的，还计算了标准旋转展宽函数的大网格及其变换/零点。事实证明，情况关键取决于 vsini：在 vsini>~20km/s 的情况下，其中旋转加宽比其他线加宽速度（通常几公里/秒）占主导地位，变换的第一个/第二个零点几乎在预期的位置。相比之下，随着 vsini 的降低，偏差开始出现，并且变换的零特征与 vsini 低至~10km/s 的预期完全不同，这意味着经典公式不再有效。因此，