On the feasibility of the detection of differential rotation in stellar absorption profiles

Stellar differential rotation invokes subtle effects on line absorption profiles which can be best studied in the Fourier domain. Detailed calculations of the behavior of Fourier transformed profiles with respect to varying differential rotation, limb darkening and inclination angles are presented. The zero positions of the Fourier transform are found to be very good tracers of differential rotation. The ratio of the first two zero positions sigma(2)/sigma(1) can be easily measured and is a reliable parameter to deduce the amount of differential rotation. It is shown that solar-like differential rotation (equatorial regions have larger angular velocity then polar regions) has an unambigious signature in the Fourier domain and that in certain cases it can easily be distinguished from limb darkening effects. A simple procedure is given allowing the determination of the amount of differential rotation by the knowledge of the first two zero positions of a line profile's Fourier transform alone (i.e., without the need for thorough atmospheric modelling), under the assumption of a linear limb darkening law with a limb darkening coefficient of epsilon=0.6.