We present a new method that derives both velocity components in the equatorial plane of a barred stellar disc from the observed line-of-sight velocity, assuming geometry of a thin disc. The method can be applied to large departures from circular mot
ion, and does not require multipole decomposition. It is based on assumptions that the bar is close to steady-state (i.e. does not evolve fast), and that both morphology and kinematics are symmetrical with respect to the major axis of the bar. We derive the equations used in the method, and analyze the effect of observational errors on the inferred velocity fields. We show that this method produces meaningful results via a simple toy model. We also apply the method on integral-field data of NGC 936, for which we recover both velocity components in the disc. Knowing both velocity components in the disc, i.e. the non-observable transverse velocity in addition to the line-of-sight velocity, puts additional constraints on dynamical models and allows for new ways of determining parameters that are crucial in characterizing galaxies.
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) change
s 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 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.
The backbone of double bars is made out of double-frequency orbits, and loops, their maps, indicate the bars extent, morphology and dynamics.
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 integra
ls, 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.
In central regions of non-axisymmetric galaxies high-resolution hydrodynamical simulations indicate spiral shocks, which are capable of transporting gas inwards. The efficiency of transport is lower at smaller radii, therefore instead of all gas drop
ping onto the galactic centre, a roughly uniform distribution of high-density gas develops in the gaseous nuclear spiral downstream from the shock, and the shear in gas is very low there. These are excellent conditions for star formation. This mechanism is likely to contribute to the process of (pseudo-) bulge formation.
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 situat
ion 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.
