Comparison of time evolutions of four MRI-active PPDs with . The four cases are (i) strong DW + Σ-dependent torque (red); (ii) strong DW + zero-torque (green); (iii) weak DW + zero-torque (purple); and (iv) no DW (black), summarized in Table 1. Top: radial profiles of temperatures, T, at t = 0 (dotted lines), 10⁵ (dashed lines), and 10⁶ (solid lines) years. We note that the initial temperatures of the four cases are almost the same and that the red and green solid lines at t = 10⁶ yr overlap at T = T_req (Eq. (27)). Bottom: radial profiles of surface densities, Σ, at t = 0 (dotted lines), 10⁵ (long dashed lines), 10⁶ (solid lines), and 10⁷ (short dashed lines) years. We note that the radial range of the top panel is more zoomed-in than the radial range of the bottom panel.