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

TL;DR

This study investigates the reliability of using Fourier transform zero ratios of spectral lines to detect stellar differential rotation, revealing limitations at low rotational velocities due to assumptions in the traditional method.

Contribution

The paper critically examines the classical Fourier transform method for detecting stellar differential rotation, highlighting its validity range and limitations at low vsini values.

Findings

Reliable for vsini >~20 km/s where rotational broadening dominates

Deviations occur at vsini around 10 km/s, invalidating classical assumptions

Classical zero-frequency approach is limited to broader-line stars

Abstract

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.