Inverse of the velocity of the torsional Alfvén wave as a function of radius. The enclosed area by the curves corresponds to the crossing time. From top to bottom, results for n_Brad = +1.0, +0.0, and −1.0, with B_pole = 1 kG are shown. The density distributions are based on the 3 M_⊙ model. Each panel includes 11 lines corresponding to different fractional main-sequence ages of 0.0, 0.1, …, 1.0, with the color of the lines changing from red to blue. Filled circles represent a change in radius.