Top: ν_M as a function of ν_s and Λ_E for non-axisymmetric retrograde (m = 1) and prograde (m = −1) waves. The surfaces such that  |ν_M|  = 1 are given by the thick black lines and the iso-ν_M lines for  |ν_M|  < 1 and  |ν_M|  > 1 are given by the red and the blue lines. The big external white region in the top-right corner in each case corresponds to the domain where , the wave being thus vertically trapped there. The MHD TA applies when  |ν_M|  < 1 and (red lines). In the other case (blue and black lines, i.e.  | ν_M |  ≥ 1 and ), it does not apply due to the singularity at the critical latitude (θ_c) given in Eq. (88) and plotted in Fig. (7). Bottom: same for m = 2 and m = −2.