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Register a new userDynamically possible pattern speeds of double bars
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Authors
Witold Maciejewski
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The method to study oscillating potentials of double bars, based on invariant loops, is introduced here in a new way, intended to be more intelligible. Using this method, I show how the orbital structure of a double-barred galaxy (nested bars) changes with the variation of nuclear bars pattern speed. Not all pattern speeds are allowed when the inner bar rotates in the same direction as the outer bar. Below certain minimum pattern speed orbital support for the inner bar abruptly disappears, while high values of this speed lead to loops that are increasingly round. For values between these two extremes, loops supporting the inner bar extend further out as its pattern speed decreases, and they become more eccentric and pulsate more. These findings do not apply to counter-rotating inner bars.
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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.
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 present surface photometry and stellar kinematics of NGC 2950, which is a nearby and undisturbed SB0 galaxy hosting two nested stellar bars. We use the Tremaine-Weinberg method to measure the pattern speed of the primary bar. This also permits us to establish directly and for the first time that the two nested bars are rotating with different pattern speeds, and in particular that the rotation frequency of the secondary bar is higher than that of the primary one.
Using N-body simulations we study the formation and evolution of tidally induced bars in disky galaxies in clusters. Our progenitor is a massive, late-type galaxy similar to the Milky Way, composed of an exponential disk and an NFW dark matter halo. We place the galaxy on four different orbits in a Virgo-like cluster and evolve it for 10 Gyr. As a reference case we also evolve the same model in isolation. Tidally induced bars form on all orbits soon after the first pericenter passage and survive until the end of the evolution. They appear earlier, are stronger, longer and have lower pattern speeds for tighter orbits. Only for the tightest orbit the properties of the bar are controlled by the orientation of the tidal torque from the cluster at pericenters. The mechanism behind the formation of the bars is the angular momentum transfer from the galaxy stellar component to its halo. All bars undergo extended periods of buckling instability that occur earlier and lead to more pronounced boxy/peanut shapes when the tidal forces are stronger. Using all simulation outputs of galaxies at different evolutionary stages we construct a toy model of the galaxy population in the cluster and measure the average bar strength and bar fraction as a function of clustercentric radius. Both are found to be mildly decreasing functions of radius. We conclude that tidal forces can trigger bar formation in cluster cores, but not in the outskirts, and thus cause larger concentrations of barred galaxies towards cluster center.
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