  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.
