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MerceRomero - 15 Jan 2009
Here we consider the analytic potential to describe the Galactic bar and the axisymmetric component as in Pichardo et al. The procedure followed here to compute the invariant manifolds is described in detailed in
Paper I, and applied for several bar potentials in
Paper II. Briefly, we locate the equilibrium points on the galactic plane, we study their linear stability. We then concentrate on the two saddle points, L1 and L2, located at the ends of the bar. In all the plots shown in the papers and here, the system corotates with the bar, so the bar is fixed along the x-axis. We compute the family of periodic orbits around the eqilibrium points and for each periodic orbit (i.e., for each energy - Jacobi constant), we compute the invariant manifolds associated to the periodic orbit. In "easy words", invariant manifolds are asymptotic orbits that depart/tend to the periodic orbit and drive the motion of the particles around them. They are like flux tubes. They do not depart in any direction but in the two related to the saddle behaviour of the equilibrium point. So stars will follow orbits linked to these manifolds.
We first analyzed what parameters of the model have an influence in the outer part of the Galaxy by computing the effective potential along the x-axis. Here we found that only the Bar mass and its pattern speed show different curves in the outer parts. So the next step is creating a grid where in the x-axis we decrease the pattern speed and in the y-axis we increase the Bar mass, the rest of the parameters are fixed as in the standard model in B. Pichardo's thesis. For each model, we perform the study described above and the result is in the figure attached below, plot2d.ps. Similar plots can be found in Paper II for three other bar models.
The coding for the colours is the following: black for spirals, orange for rR1 pseudorings, green for rR1 rings and magenta for rings that maybe considered as single circular outer rings. There is a different trend in this figure compared to the figures in Paper II. So here I'd like to study in detail these models and check what happens there.
The next step is performing the same study when we consider only the axisymmetric part and the spiral and the third step is considering the axisymmetric + bar + spiral, i.e. the total potential.