Red: Variation of $s_{\mathrm{env}}^{\ast }$ in the hydrodynamic differentially rotating case with respect to the amount of differential rotation. Blue: MHD bi-layer Alfvén frequency case with respect to the core Lehnert number. The considered core Lehnert numbers translate to mid-core magnetic fields range from 0.5 to 5 MG in the fz model, and 0.25 to 2.5 MG in the im model. The horizontal thin lines represent the value of s_env^* expected for each of the models in the magnetostrophic regime. In the im model, a mid-core equatorial magnetic field in the magnetostrophic regime of 1.63 MG, corresponding to Le_core = 5.6 × 10⁻², would shift the dip to s_env^* = 8.41 in a solid-body rotating magnetic model. This is the same effect as a differential rotation of α_rot = 0.951 in the differentially rotating hydrodynamic model.