Gravity modes in rapidly rotating stars Limits of perturbative methods

Context. CoRoT and Kepler missions are now providing high-quality asteroseismic data for a large number of stars. Among intermediate-mass and massive stars, fast rotators are common objects. Taking the rotation effects into account is needed to correctly understand, identify, and interpret the observed oscillation frequencies of these stars. A classical approach is to consider the rotation as a perturbation. Aims. In this paper, we focus on gravity modes, such as those occurring in gamma Doradus, slowly pulsating B (SPB), or Be stars. We aim to define the suitability of perturbative methods. Methods. With the two-dimensional oscillation program (TOP), we performed complete computations of gravity modes - including the Coriolis force, the centrifugal distortion, and compressible effects - in 2D distorted polytropic models of stars. We started with the modes l = 1, n = 1-14, and l = 2-3, n = 1-5, 16-20 of a nonrotating star, and followed these modes by increasing the rotation rate up to 70% of the break-up rotation rate. We then derived perturbative coefficients and determined the domains of validity of the perturbative methods. Results. Second-order perturbative methods are suited to computing low-order, low-degree mode frequencies up to rotation speeds similar to 100 km s(-1) for typical gamma Dor stars or similar to 150 km s(-1) for B stars. The domains of validity can be extended by a few tens of km s(-1) thanks to the third-order terms. For higher order modes, the domains of validity are noticeably reduced. Moreover, perturbative methods are inefficient for modes with frequencies lower than the Coriolis frequency 2 Omega. We interpret this failure as a consequence of a modification in the shape of the resonant cavity that is not taken into account in the perturbative approach.