Third-order term in the frequency expansion σ₃ε³ as a function of the polytropic index n, for the sectoral r modes ℓ = m = 3 and several radial orders k. The corresponding frequency term in the incompressible case, which has only ℓ = m, k = 0 solutions, is given by a blue dotted line (see text). The frequency is given in pHz, using the relevant solar quantities, and is displayed in symmetric log scaling, with linear scaling between ±6 pHz. The quantity τ_⊙ is our unit of time and corresponds to the Sun’s dynamical time scale.