-- 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, plot2dbar.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. The red lines delineate the locus of the spiral arms. There is a different trend in this figure compared to the figures in Paper III . So here I'd like to study in detail these models and check what happens there.

In the next step I proceeded the same way as with the bar potential. Here I consider the potential resulting from the superposition of the axisymmetric component and the spiral arms. I analysed each component of the model to check which one has an effect to the outer parts of the galaxy and, again, the spiral mass and its pattern speed are the two parameters with a major influence. I make families of models by fixing the rest of the parameters and varying "alfa2b" and "omegs" within a range of values. For each model, I compute the invariant manifolds and I plot the resulting morphology in a 2D grid. Analogously to that of the bar potential, I decrease on the x-axis the spiral pattern speed from left to right and, in the y-axis I decrease the spiral mass from top to bottom. The results are in the file: plot2dsp.ps, attached below. Again, the locus of the spiral is plotted in red lines. There are some models, were self-consistency is achieved.

The next step is performing the same study when we consider the axisymmetric + bar + spiral, i.e. the total potential, with the bar and spirals rotating at the same pattern speed.

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I Attachment History Action Size Date Who Comment
Postscriptps plot2dbar.ps r1 manage 2311.2 K 2009-02-27 - 11:17 MerceRomero 2D grid varying the pattern speed and the Bar mass
Postscriptps plot2dsp.ps r1 manage 2309.7 K 2009-02-27 - 11:19 MerceRomero 2D grid varying the pattern speed and the Spiral mass
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Topic revision: r4 - 2009-02-27 - MerceRomero
 
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