Top: θ_c as a function of ν_s and Λ_E for non-axisymmetric retrograde (m = 1) and prograde (m = −1) waves. As in Fig. (6), the large white top-right corner region corresponds to the domain where and where the waves are trapped in the vertical direction. In the white region at the left, the MHD TA applies (i.e.  |ν_M|  < 1 and ) and there is no critical latitude. Finally, the blue θ_c-iso lines correspond to the regime where the TA does not apply (i.e.  |ν_M|  ≥ 1 and ). Middle: same for m = 2 and m = −2. Bottom: cartoon for the wave propagation region: traditional elliptic waves are regular for every latitude and live in the whole sphere (E), while hyperbolic ones are trapped in the equatorial belt where θ ∈ [θ_c,π − θ_c] (H).