Main quantities entering in the eigenvalue problem defined by Eq. (12). (a) Normalized solar differential rotation rate δ(θ) at different radii, inferred from helioseismology and averaged over 1996 to 2018 (the shaded area covers ±3σ), with respect to the Carrington rotation rate, Ω_ref = Ω_Carr. The solid curves show the N = 30 fits to the solar rotation rates. The dashed curve shows the N = 2 fit to the solar surface rotation rate, i.e., Ω₀ + Ω₂cos²θ with Ω₀/2π = 452 nHz and Ω₂/2π = −114 nHz. (b) The function ζ defined by Eq. (9) is plotted for each of the three cases of panel (a). For r = R_⊙ and N = 30, the function reaches a minimum at ζ(θ = 0)≈ − 22 (not shown on the plot). The oscillations at the surface are due to the m = 0 zonal flows (also known as torsional oscillations). The horizontal dashed-black line shows , where β = 2Ω_ref/r, which plays the role of ζ in the equatorial β plane (see Eq. (17) in Gizon et al. 2020).