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Register a new userOrbits in corotating and counterrotating double bars
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Authors
Witold Maciejewski
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The backbone of double bars is made out of double-frequency orbits, and loops, their maps, indicate the bars extent, morphology and dynamics.
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Bars in galaxies are mainly supported by particles trapped around stable periodic orbits. These orbits represent oscillatory motion with only one frequency, which is the bar driving frequency, and miss free oscillations. We show that a similar situation takes place in double bars: particles get trapped around parent orbits, which in this case represent oscillatory motion with two frequencies of driving by the two bars, and which also lack free oscillations. Thus the parent orbits, which constitute the backbone of an oscillating potential of two independently rotating bars, are the double-frequency orbits. These orbits do not close in any reference frame, but they map onto loops, first introduced by Maciejewski & Sparke (1997). Trajectories trapped around the parent double-frequency orbit map onto a set of points confined within a ring surrounding the loop.
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.
We report on our attempts to achieve a nearly steady-state gas flow in hydrodynamical simulations of doubly barred galaxies. After exploring the parameter space, we construct two models, for which we evaluate the photometric and the kinematic integrals, present in the Tremaine-Weinberg method, in search of observational signatures of two rotating patterns. We show that such signatures are often present, but a direct fit to data points is likely to return incorrect pattern speeds. However, for a particular distribution of the tracer, presented here, the values of the pattern speeds can be retrieved reliably even with the direct fit.
We show that stable double-frequency orbits form the backbone of double bars, because they trap around themselves regular orbits, as stable closed periodic orbits do in single bars, and in both cases the trapped orbits occupy similar volume of phase-space. We perform a global search for such stable double-frequency orbits in a model of double bars by constructing maps of trajectories with initial conditions well sampled over the available phase-space. We use the width of a ring sufficient to enclose a given map as the indicator of how tightly the trajectory is trapped around a double-frequency orbit. We construct histograms of these ring widths in order to determine the fraction of phase-space occupied by ordered motions. We build 22 further models of double bars, and we construct histograms showing the fraction of the phase-space occupied by regular orbits in each model. Our models indicate that resonant coupling between the bars may not be the dominant factor reducing chaos in the system.
We present hydrodynamical models for Corotating Interaction Regions, which were used by Lobel (2007) to model the Discrete Absorption Components in HD 64760. We also discuss our failure to model the rotational modulations seen in the same star.
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