Angular velocity Ω, Ω − κ/2 curves, and v_ϕ from 1.5 to 5 Gyr in 0.5 Gyr steps, with increasing line transparency for earlier times. The profile at 5 Gyr is displayed as a thick solid line. In the insets, i denotes initial stars, n denotes new stars, g denotes the gas component, and t indicates the total stellar component. The bar pattern speed Ω_b at 5 Gyr is marked as a dashed horizontal line. The bar pattern speeds are 35.8, 42.3, and 48.7 km s⁻¹ kpc⁻¹, and remain nearly constant in our models (Fig. A.2); the corotation radii (R_CR where Ω_b = Ω_t) are 4.4, 3.9, and 3.6 kpc for models r1c14b00, r1c14b05, and r1c14b10, respectively. The time evolution of the ILRs as a function of bar pattern speed is shown in Fig. A.4 and compared to the nuclear ring region (see also Fig. 11 for the radial profiles of mean rotation).