Rotational splittings for slow to moderate rotators: Latitudinal dependency or higher order effects in Ω?

Abstract: Information about the rotation rate is contained in the low frequency part of power spectra, where signatures of nonuniform surface rotation are expected, as well as in the frequency splittings induced by the internal rotation rate. We wish to figure out whether the differences between the seismic rotation period as determined by a mean rotational splitting, and the rotation period measured from the low frequency peak in the Fourier spectrum (observed for some of CoRoT's targets) can provide constraints on the rotation profile. For uniform moderate rotators,perturbative corrections to second and third order in terms of the rotation angular velocity \Omega, may mimic differential rotation. We apply our perturbation method to evaluate mode frequencies accurate up to \Omega^3 for uniform rotation. Effects of latitudinal dependence are calculated in the linear approximation. In \beta Cephei pulsators models, third order effects become comparable to that of a horizontal shear similar to the solar one at rotation rates well below the breakup values. We show how a clean signature of the latitudinal shear may be extracted. Our models of two CoRoT target HD 181906 and HD 181420, represent lower main sequence objects. These are slow rotators and nonlinear effects in splittings are accordingly small. We use data on one low frequency peak and one splitting of a dipolar mode to constrain the rotation profile in HD 181420 and HD 181906. The relative influence of the two effects strongly depends on the type of the oscillation modes in the star and on the magnitude of the rotation rate. Given mean rotational splitting and the frequency of a spot signature, it is possible to distinguish between the two hypothesis, and in the case of differential rotation in latitude, we propose a method to determine the type of rotation profile and a range of values for the shear.