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tokens: time variations appear for all radii, with typical amplitude changes in η R / η max of ∼0.2, except for the innermost radial bin. The thick solid grey curve indicates the mean bar half-length variations (black curve from Fig. 5 ), showing a very good agreement with the amplitude fluctuations. Note that as the bar decreases in length, so does its amplitude. Very similar time variations appear for all radii, with typical amplitude changes in η R / η max of ∼0.2, except for the innermost radius considered. The thick solid grey curve in Fig. 7 represents the mean bar half-length variations (black curve from Fig. 5 ), which can be seen to agree very well with the amplitude fluctuations, including the short and long periods. The fluctuations seen in the bar amplitude at fixed radii (Fig. 7 ) are more similar to the bar length time variations than the η max , which can vary with radius (see Fig. A6 ). This can generally be seen for Model2 as well in Fig. 8 . One key difference between the two simulations is the fact that for Model1 all radii peak at nearly the same time, while in Model2, they are delayed with the lowest radius of 3 kpc always peaking last. Such a pattern suggests a spiral arm contribution. Indeed, we established in Section 3.4 that the Model2 bar true length is about 3 kpc; therefore, the region examined in Fig. 8 lies at or outside the true bar, yet in the regime where our three measurement methods detect a bar. The solid grey curve in Fig. 7 shows the bar length time variations, seen to follow the overall trend in η R / η max , in best agreement with the two outermost radii. Figure 8. As Fig. 7 , but for Model2. The solid grey thick curve indicates the mean bar half-length variations (black curve from Fig. 6 ), showing an overall good agreement with the amplitude fluctuations. Since the true bar length is ∼3 kpc, the outermost three radial bins for which η R was estimated correspond to the spiral arms, as evident from the systematic time offset among different curves. 4.4 Bar pattern speed We estimated the instantaneous bar pattern speed using the modified TW method by Sanders et al. ( 2019 ), who applied it to both MW data and N -body simulations. The top left-hand panel of Fig. 9 shows the configuration we used to measure Ω p , over the stellar density of Model1. As done by Sanders et al. ( 2019 ), we assumed a bar angle of 33°, a Galactic latitude range | b | 5°, and a solar Galactocentric distance of R 0 = 8.12 kpc. The rotation is clockwise. Estimates are done in bins of Galactic longitude dl = 2° in the radial range indicated by the two arches centred on the Sun (at distances of 4.12 and 8.12 kpc), which is sitting at ( x, y ) = (8.12, 0). The straight black line over the bar has a half-length of 3.2 kpc, which corresponds to l ∼ 17° for our bar angle. The bar angle is kept the same at each time output. The white circles show the bar time-median CR, 4:1 OLR, and 2:1 OLR at R CR = 3.25, R 4: 1OLR = 4.2, and R 2: 1OLR =