No Arabic abstract
Based on a high quality $N$-body simulation of a double bar galaxy model, we investigate the evolution of the bar properties, including their size, strength and instantaneous pattern speed derived by using three distinct methods: the Fourier, Jacobi integral, and moment of inertia methods. The interaction of the two bars, which rotate at distinct speeds, primarily affects the size, strength and pattern speed of the inner bar. When the two bars are perpendicular to each other, the size and the pattern speed of the inner bar decrease and its strength increases. The emergence of a strong Fourier $m=1$ mode increases the oscillation amplitude of the size, strength and pattern speed of the inner bar. On the other hand, the characteristics of the outer bar are substantially influenced by its adjacent spiral structure. When the spiral structure disappears, the size of the outer bar increases and its strength and pattern speed decrease. Consequently, the ratio of the pattern speed of the outer bar with respect to the inner bar is not constant and increases with time. Overall, the double bar and disk system displays substantial high frequency semi-chaotic fluctuations of the pattern strengths and speeds both in space and time, superposed on the slow secular evolution, which invalidates the assumption that the actions of individual stars should be well conserved in barred galaxies, such as the Milky Way.
We aim at investigating the formation process of weak bars by measuring their properties in a sample of 29 nearby SAB galaxies, spanning a wide range of morphological types and luminosities. The sample galaxies were selected to have an intermediate inclination, a bar at an intermediate angle between the disc minor and major axes, and an undisturbed morphology and kinematics to allow the direct measurement of the bar pattern speed. Combining our analysis with previous studies, we compared the properties of weak and strong bars. We measured the bar radius and strength from the r-band images available in SDSS and bar pattern speed and corotation radius from the stellar kinematics obtained by CALIFA. We derived the bar rotation rate as the ratio between the corotation and bar radii. Thirteen out of 29 galaxies, which were morphologically classified as SABs from a visual inspection, do not actually host a bar component or their central elongated component is not in rigid rotation. We successfully derived the bar pattern speed in 16 objects. Two of them host an ultrafast bar. Using the bar strength to differentiate weak and strong bars, we found that the SABs host shorter bars with smaller corotation radii than their strongly barred counterparts. Weak and strong bars have similar bar pattern speeds and rotation rates, which are all consistent with being fast. We did not observe any difference between the bulge prominence in SAB and SB galaxies, whereas nearly all the weak bars reside in the disc inner parts, contrary to strong bars. We ruled out that the bar weakening is only related to the bulge prominence and that the formation of weak bars is triggered by the tidal interaction with a companion. Our observational results suggest that weak bars may be evolved systems exchanging less angular momentum with other galactic components than strong bars.
In the manifold theory of spiral structure in barred galaxies, the usual assumption is that the spirals rotate with the same pattern speed as the bar. Here we generalize the manifold theory under the assumption that the spirals rotate with different pattern speed than the bar. More generally, we consider the case when one or more modes, represented by the potentials V_2, V_3, ldots, co-exist in the galactic disc in addition to the bars mode V_{bar}, but rotate with pattern speeds Omega_2, Omega_3, ldots incommensurable between themselves and with Omega_{bar}. Through a perturbative treatment (assuming that V_2,V_3... are small with respect to V_{bar}) we then show that the unstable Lagrangian points L_1, L_2 of the pure bar model (V_{bar},Omega_{bar}) are `continued in the full model as periodic orbits, when we have one extra pattern speed different from Omega_{bar}, or as epicyclic `Lissajous-like unstable orbits, when we have more than one extra pattern speeds. As an example we compute the generalized orbits GL_1, GL_2 and their manifolds in a Milky-way like model with bar and spiral pattern speeds assumed different. We find that the manifolds produce a time-varying morphology consisting of segments of spirals or `pseudorings. These structures are repeated after a period equal to half the relative period of the imposed spirals with respect to the bar. Along one period, the manifold-induced time-varying structures are found to continuously support at least some part of the imposed spirals, except at short intervals around those times at which the relative phase of the imposed spirals with respect to the bar becomes equal to pmpi/2. A connection of these effects to the phenomenon of recurrent spirals is discussed.
The effective potential neighboring the corotation resonance region in barred galaxies is shown to be strongly time-dependent in any rotating frame because of the competition of nearby perturbations of similar strengths with differing rotation speeds. Contrary to the generally adopted assumption, that in the bar rotating frame the corotation region should possess four stationary equilibrium points (Lagrange points), with high quality N-body simulations we localize the instantaneous equilibrium points and find that they circulate or oscillate broadly in azimuth with respect to the pattern speeds of the inner or outer perturbations. This implies that at the particle level the Jacobi integral is not well conserved around the corotation radius. That is, angular momentum exchanges decouple from energy exchanges, enhancing the chaotic diffusion of stars through the corotation region.
A brief review is given of different methods used to determine the pattern speeds of the Galactic bar and spiral arms. The Galactic bar rotates rapidly, with corotation about halfway between the Galactic center and the Sun, and outer Lindblad resonance not far from the solar orbit, R0. The Galactic spiral arms currently rotate with a distinctly slower pattern speed, such that corotation is just outside R0. Both structures therefore seem dynamically decoupled.
More than 10% of the barred galaxies with a direct measurement of the bar pattern speed host an ultrafast bar. These bars extend beyond the corotation radius and challenge our understanding of the orbital structure of barred galaxies. Most of them are found in spiral galaxies, rather than in lenticular ones. We analysed the properties of the ultrafast bars detected in the CALIFA Survey to investigate whether they are an artefact resulting from an overestimation of the bar radius and/or an underestimation of the corotation radius or a new class of bars, whose orbital structure has not yet been understood. We revised the available measurements of the bar radius based on ellipse fitting and Fourier analysis and of the bar pattern speed from the Tremaine-Weinberg method. In addition, we measured the bar radius from the analysis of the maps tracing the transverse-to-radial force ratio, which we obtained from the deprojected i-band images of the galaxies retrieved from the SDSS Survey. We found that nearly all the sample galaxies are spirals with an inner ring or pseudo-ring circling the bar and/or strong spiral arms, which hamper the measurement of the bar radius from the ellipse fitting and Fourier analysis. According to these methods, the bar ends overlap the ring or the spiral arms making the adopted bar radius unreliable. On the contrary, the bar radius from the ratio maps are shorter than the corotation radius. This is in agreement with the theoretical predictions and findings of numerical simulations about the extension and stability of the stellar orbits supporting the bars. We conclude that ultrafast bars are no longer observed when the correct measurement of the bar radius is adopted. Deriving the bar radius in galaxies with rings and strong spiral arms is not straightforward and a solid measurement method based on both photometric and kinematic data is still missing.