Top: sign of as a function of R_o and Λ_E for non-axisymmetric retrograde (m = 1) and prograde (m =  −1) waves. The MHD traditional approximation applies in the orange region where |ν_M;m| < 1 and ; in this case, waves are regular and propagate at all latitudes. In the other case (|ν_M;m| ≥ 1 and ), the MHD traditional approximation does not apply and waves are trapped in an equatorial belt (θ ∈ [θ_c;m,π − θ_c;m]), where θ_c;m is the critical latitude given in Eq. (21) and plotted in Fig. 4. The external white region at the top-left corner in each case corresponds to the domain where , the wave is therefore completely vertically trapped there. Middle: same for m = 2 and m =  −2. Bottom: corresponding wave families extending the classification by Dintrans et al. (1999) (see text) to the hydromagnetic case.