Bar strength, pattern speed, and length variation for Au18 with time. Top panel: pattern speed as estimated from the phase of the m = 2 Fourier mode (right axis – blue), the m = 2 Fourier mode (bar strength) of the surface density, and the m = 1 Fourier mode (dashed red line) as a function of lookback time. Middle panel: various measures of bar length as a function of lookback time (see text). Bottom panel: variation in ℛ as a function of time using different estimates for the bar length.