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It is known that stellar differential rotation can be detected by analyzingthe Fourier transform of spectral line profiles, since the ratio of the 1st-and 2nd-zero frequencies is a useful indicator. This approach essentiallyrelies on the conventional formulation that the observed flux profile isexpressible as a convolution of the rotational broadning function and theintrinsic profile, which implicitly assumes that the local intensity profiledoes not change over disk. Although this postulation is unrealistic in thestrict sense, how the result is affected by this approximation is stillunclear. In order to examine this problem, profiles of several lines (showingdifferent center-limb variations) were simulated using a model atmospherecorresponding to a mid-F dwarf by integrating intensity profiles for variouscombinations of vsini (rot. velocity), alpha (diff. degree), and i (inc.angle), and their Fourier transforms were computed to check whether zeros aredetected at the predicted positions or not. For this comparison purpose, alarge grid of standard rotational broadening functions and theirtransforms/zeros were also calculated. It turned out that the situationcriticaly depends on vsini: In case of vsini>~20km/s where rotationalbroadening is predominant over other line broadening velocities (typicallyseveral km/s), the 1st/2nd zeros of the transform are confirmed almost at theexpected positions. In contrast, deviations begin to appear as vsini islowered, and the zero features of the transform are totally different from theexpectation at vsini as low as ~10km/s, which means that the classicalformulation is no more valid. Accordingly, while the zero-frequency approach issafely applicable to studying differential rotation in the former broader-linecase, it would be difficult to practice for the latter sharp-line case.

On the detection of stellar differential rotation based on the Fourier transform of spectral line profiles