Recent Developments in Galactic Dynamics

Kinematic Clues to Bar Evolution for Galaxies in the Local Universe: Why the Fastest Rotating Bars are Rotating Most Slowly

“…We plot in Figure 3 the distribution of the rotational parameter (left panel) and the relative bar pattern speed (right panel). The histogram of the relative bar corotation clearly shows that the rotational parameter is somewhat larger than unity, within uncertainties, as theoretically predicted by Contopoulos (1980), who studied the response of a bar to the barred perturbations of density, deriving the result that the bar corotation resonance must occur Note. The mean values, and their standard deviations, of the corotation to the bar length ratio for earlier, intermediate, and later type of galaxies are given in the three central columns.…”

“…It is important to emphasize that the designation "fast" ("slow") rotator bar does not mean that the bar is rotating with a high (low) angular speed; this classification is based only on the value of the rotation parameter, . Contopoulos (1980) studied how a galaxy responds to the barred perturbations of density, and he concluded that the bar corotation should be found close to the end of the bar, and in principle, the value of the rotational parameter should be quite close to but larger than 1. This general conclusion has since been supported in diverse publications, both theoretical and observational (Athanassoula 1992;Valenzuela & Klypin 2003;Rautiainen et al 2008;Buta & Zhang 2009;Font et al 2014a;Aguerri et al 2015).…”

“…They took the ratio, , of the corotation radius to the bar length as an index of whether a bar could be characterized as fast or slow. Starting from the theoretical argument by Contopoulos (1980), showing that  should be close to and a little greater than unity, Debattista and Sellwood proposed that bars in the range 1<  < 1.4, (i.e., where corotation is not far from the end of the bar) should be considered fast, because dynamical braking would move corotation progressively farther out compared to the bar length. The authors noted that to use this as a test for dynamical braking was, at that time, made difficult by the rather small numbers of measurements of the pattern speed, and pointed to the Tremaine-Weinberg (Tremaine & Weinberg 1984) method as a preferred option for this.…”

Constraints from Dynamical Friction on the Dark Matter Content of Barred Galaxies

“…a B More precisely, is the distance from the center to the D L Lagrange point on the bar major axis where the gravitational attraction balances the centripetal acceleration in the frame rotating with the bar. Theoretical arguments (Contopoulos 1980) require R [ 1, and there is a prejudice that (see Sellwood & Wilkinson 1993 for a review). R Z 1 We describe bars for which 1 ¹ R ¹ 1.4 (i.e., those for which corotation is not far beyond the barÏs end) as fast.…”

Dynamics of Disks and Warps

“…As the period lengthens, the proliferation of orbit families causes a precipitous decrease in the stable regions around each parent and chaotic behavior ensues (Chirikov 1979). The onset of chaos near CR led Contopoulos (1980) to expect the density of a selfconsistent bar to drop steeply near the major axis Lagrange points, leading to the rule that the length of a bar is limited by CR. This rule predicts that the parameter (Elmegreen 1996) …”