Impact of the radial profile of B_r on the mode frequencies. We considered fields with radial extensions of σ_B = 0.0015 R_★ (red lines), 0.002 R_★ (green lines), and 0.003 R_★ (blue lines) and a constant field (black lines). Left: radial profile of B_r. Middle: profile of the parameter a(r) in the g-mode cavity for the mode closest to ν_max (Eq. (12)). Right: profile of λ(r) deduced from the interpolation of the a(λ) relation for the same mode (see text). We show the departure from the value λ = 2 corresponding to the perturbative approach.