Validity of analytical prescriptions. Top: dimensionless ratios B_r/B_ϕ versus , for the dynamo simulations shown in Petitdemange et al. (2023) and for our additional highly stratified model. B_r and B_ϕ are determined by averaging the energy of the m = 0 poloidal and toroidal magnetic fields over space and time (at steady state). Here ß = 1.8 is a fitting coefficient. The empty symbols denote simulations in only weakly supercritical regimes (as quantified arbitrarily here by Re/Re_c ≤ 5/3). Because the flow regime remains close to the onset of instability, the relevance of diffusionless scaling is subject to caution. Bottom: scaling of the dimensionless magnetic torque with Spruit’s diffusionless prediction in Eq. (19) (black line). The data include the simulations shown in Petitdemange et al. (2023) and an additional highly stratified model with Ra = 10¹⁰.