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 Orbits in Realistic Galaxy Potentials



We know that galaxies are made up of stars and gas, but what determines how these move within a galaxy, are the orbits.

Stable orbits can be thought of as the building blocks of galaxies, because they trap stars and gas around them, giving rise to the complex morphological features we observe in galaxies.

There are different types of orbits which make up galaxies, but here we will focus on periodic orbits found in barred, rotating galaxies. The orbits shown here, have all been calculated in potentials taken directly from images of either real, or simulated, galaxies.

Some nomenclature for those who are not familiar with it :

  • Stable periodic orbits : a periodic orbit is an orbit which closes up upon its self. Periodic orbits trap around them regular non-closed orbits.

In the images below, we plot some periodic orbits in a realistic potential of a galaxy. In these images the bar is along the x axis, and has a semi-major axis of about 7 kpc.

We see, in the Figure titled "x1 orbits", some periodic orbits of the so called x1 family. These orbits are elongated along the bars major axis, and "support" the bar. They are 2:1 orbits, which means that they close up upon themselves after one rotation around the centre, and two radial oscillations.

In the second figure, titled "x2 and x3 orbits", we plot some periodic orbits from the x2 and x3 families. These are elongated perpendicular to the bar and are confined to the inner parts. In the third figure title "x4 orbits" we plot some periodic orbits of the x4 family, which are nearly circular retrograde orbits (that is to say, they rotate opposite to the direction in which the galaxy is rotating)

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x1 orbits in a realistic barred galaxy potential. The bar is given by the solid black elongated line.
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x2 and x3 orbits. These are perpendicular to the bar, which is along the x-axis, and as we can see, they are confined to the central parts of the galaxy.
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x4 orbits in a realistic barred galaxy potential. The bar is along the x-axis. These orbits are retrograde (they turn around the galaxy in the opposite sense to the rotation of the bar)
  • Stable orbits : a stable orbit is that which, when another orbit has initial conditions in its vicinity, it will tend to stay (for infinite time) around the original orbit.

Stable periodic orbits trap around them regular non-closed orbits. This meas that an orbit that starts near (near in phase-space, i.e. in velocity and in position) to a stable periodic orbit, will tend to stay in its vicinity for infinite time. Below, in black, we show an example of a stable periodic parent orbit in our realistic potential of a galaxy. Below that, in the four panels shown, we show some examples of trapped orbits. We show non-closed orbits starting in the vicinity of a stable periodic orbit of the x1 family, which stay in its vicinity for infinite time. From top left to bottom right, the orbit is less and less tightly trapped around the parent orbit. This means that its initial conditions, are further away (in phase space) from the initial conditions of the parent orbit.

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Stable periodic orbit
A stable periodic x1 orbit.
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Trapped orbits
A sequence of trapped orbits (red) around a stable periodic orbit (solid black line). From top left to bottom right, the trapped orbit is less and less tightly bound around the stable periodic orbit.

Typically, stable periodic orbits have been used to study galaxies and their various morphological features, since they are thought to contribute most to shaping the morphology of the galaxy, by trapping stars around them. It is well known that certain types of periodic orbits sustain features such as the bar, whose backbone is made up of mainly the x1 family.

Periodic orbits in barred galaxies also affect the flow of gas in galaxies, as was shown in Athanassoula 1992a and 1992b. In that work, analytic models of barred galaxies were used to study the effect that changing periodic orbits will have on the flow of gas in the galaxy. We see in the two figures below, how the orbits obtained in our realistic potentials (lower figure) are very similar to those obtained by Athanassoula 1992a (upper figure), which thus re-confirms the accuracy of the results obtained in that work.

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x1 orbits from Athanassoula 1992
The image shows x1 orbits calculated in an analytic barred potential. In this case the bar is elongated along the y-axis and is shown by the dotted black line.
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Some x1 orbits calculated in a realistic galaxy potential. The bar is given by the solid black line, and it is elongated along the y-axis.


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