Resumen de Application of dynamical system methods to galactic dynamics: from warps to double bars
Most galaxies have a warped shape when they are seen from an edge-on point of view. In this work we apply dynamical system methods to find an explanation of this phenomenon that agrees with its abundance among galaxies, its persistence in time and the angular size of observed warps. Starting from a simple, but realistic, 3D galaxy model formed by a bar and a flat disc, we study the effect produced by a small misalignment between the angular momentum of the system and its angular velocity. To this end, a precession model is developed and considered, assuming that the bar behaves like a rigid body. In order to study the behaviour of the rigid body, we solve its Euler equations. We study the resulting solution in a precessing reference system, selected in such a way to make the angular momentum and angular velocity of the body time independent. After checking that the periodic orbits inside the bar keep being the skeleton of the inner system, even after inflicting a precession to the potential, we compute the invariant manifolds of the unstable periodic orbits departing from the equilibrium points at the ends of the bar to get evidence of their warped shapes. As is well known, from previous studies with 2D galaxy models, the invariant manifolds associated with these periodic orbits drive the arms and rings of barred galaxies and constitute the skeleton of these building blocks. Now, looking at them from an edge-on viewpoint, we find that these manifolds present warped shapes such as those recognized in observations with a close concordance in angles. In addition, test particle simulations have been performed to determine how the stars are affected by the applied precession, confirming in this way the theoretical results obtained. Once the behaviour of the precessing model is known, we develop the model with a more complex potential, including a spherical halo, in order to study the influence of each parameter that gives shape to the potential and to determine the effect of the halo in the formation of galaxy warps. We have observed that the presence of the halo helps to increase the resulting warp angle. The theory of invariant manifolds is also applied to the study of the existence of galaxies with four spiral arms, such as ESO 566-24 and possibly the Milky Way. A double-barred galaxy model is tested as a plausible explanation of the formation of four spiral arms in a galaxy. This is checked through the method of invariant manifolds in various double-barred systems, not restricting ourselves to the Milky Way. We find that the double-barred model is not sufficient by itself to give rise to the shape of four spiral arms as observed, and we suggest possible refinements of the galaxy model in order to better match the experimental observations. The most promising of these model refinements is to consider the galaxy as a non-autonomous system, with two bars which are rotating with different pattern speeds. Dealing with non-autonomous systems leads to the study of their dynamics by means of Lagrange Coherent Structures (LCS). This is a recent, still developing theory, in which the LCS behave analogously to the invariant manifolds in autonomous systems, organizing the evolution of the flow. We have developed our own code for the computation of LCS, which can be applied to parametrized surfaces in systems of any dimension. To establish the comparison between LCS and invariant manifolds, we apply both methods to the pendulum problem, in its autonomous and non-autonomous versions. After this, we compute the LCS for our galaxy model formed by a disc and bar, without precession. We demonstrate that the LCS show the same behaviour as the stable invariant manifolds, and that they exhibit more information in a wide region of the space.
