Angular velocity, Ω (red lines), and strength of the ϕ-component of the magnetic field, B_ϕ (blue lines), for ten different times during the evolution of a 1.5 M_⊙ main-sequence stellar model, illustrating the propagation of torsional Alfvén waves in the stellar interior. Here, the Ω effect and the Maxwell stress are taken into account, but the η effect is not. The x-axis for the left panels, showing times up to 8 × 10⁸ s, is the Lagrangian mass coordinate, the right panels, depicting later times, use the radius coordinate. On the y-axis, The logarithm of Ω divided by Ω_min (or log B_ϕ, min/B_ϕ, min) is plotted with the normalization values of Ω_min = 1 × 10⁻⁶ rad s⁻¹ and B_ϕ, min = 1 × 10³ G. Prograde rotation and positive B-field polarity are plotted in the upper half of the panels, retrograde rotation and negative polarity are plotted in the lower half. Small structure with −Ω_min <  Ω <  Ω_min and −B_ϕ, min <  B_ϕ <  B_ϕ, min is omitted from this plot. The black dashed and black dotted lines show the positions of the wavefronts, r_f, which are estimated by Eq. (45). Arrows indicate the direction of the wave propagation.