Effects of the Coriolis force on high-order g modes in γ Doradus stars

γ Doradus stars pulsate with high-order gravity modes having typical frequencies which can be comparable to or higher than their rotation frequencies. Therefore, rotation has a non-negligible effect on their oscillation properties. To explore the rotation–pulsation coupling in γ Dor stars, we perform a non-adiabatic study including the traditional approximation of rotation on a grid of spherical stellar models covering the mass range 1.4 < M* < 2.1 M⊙. This approximation allows us to treat the effect of the Coriolis force on the frequencies and the stability of high-order g modes. The effect of the Coriolis force depends on the kind of mode considered (prograde sectoral or not) and increases with their periods. As a consequence, we first find that the period spacing between modes is no longer periodically oscillating around a constant value. Secondly, we show that the frequency gap (5–15 cycles day−1) arising from stable modes between γ Dor-type high-order g modes and δ Scuti-type modes can be easily filled by g-mode frequencies shifted to higher values by the rotation. Thirdly, we analyse the combined effect of diffusive mixing and the Coriolis force on the period spacings. And finally, we predict a slight broadening of the γ Dor instability strip.