(From "Outer dynamics and escapes in barred galaxies" Contopoulos and Patsis 2006, MNRAS in press)

We study the dynamics of the outer parts of barred galaxies (beyond corotation). In this region there are several islands of stability around stable periodic orbits and chaotic orbits that eventually escape from the galaxy. We study the forms of the orbits (periodic and nonperiodic) and the intersections of the orbits by a surface of section $(x,\dot{x})$, i.e. $y=0$, for fixed values of the Jacobi constant. The structure of phase space is characterized by the {\em rotation curve}, i.e. the rotation number of successive orbits with initial conditions along the x-axis. The nonescaping orbits have initial conditions inside a ``last KAM torus''. The escaping orbits either have a positive energy from the beginning, or they change their energy at irregular intervals of time, acquiring finally positive energy that leads to escape. The successive consequents (intersections) of such an orbit are along ``bell-type curves'' (one curve for each value of the energy). On the surface of section we see also almost rectilinear ``rays'' that are the images of the x-axis (i.e. $\dot{x}=y=0$). The lower parts of these rays represent escaping orbits. These escapes are much faster than the escapes produced by encounters of stars among themselves. We considered two models of galactic type and various values of the Jacobi constant. These models have the same basic behaviour as regards the nonescaping and escaping orbits. This is an indication that these phenomena are characteristic of the outer parts of generic rotating galaxies.

The Figure shows the net of islands that prevents orbits from escaping. Colors are used in order to distinguish islands of stability or hyperbolic points belonging to the same orbit (see text).

From Patsis 2005, MNRAS 358,305

We investigate the morphological relation between the orbits of the central family of periodic orbits (x1 family) and the bar itself using models of test particles moving in a barred potential. We show that different bar morphologies may have as a backbone the same set of x1 periodic orbits. We point out that by populating initially axisymmetric stellar discs exponentially with test particles in circular, or almost circular motion, we may end up with a response bar which reveals a shape different in crucial details from that of the individual stable x1 orbits. For example, a bar model in which the x1 orbits are pure ellipses may have a much more complicated response morphology. This depends on the particular invariant curves around x1, which are populated in each model.

From Kaufmann and Patsis 2005, ApJ 624,693

Kaufmann and Patsis (2005) presented evidence that in two-dimensional models with sufficiently large bar axial ratios (a/c>~6), stable orbits having propeller shapes play the dominant role. In our models this propeller family is in fact a distant relative of the x1 family. There are also intermediate cases in which both families are important. The dominance of one family over the other may have direct consequences on the morphological properties of the bars that can be constructed from them, properties such as face-on bar thinness and strength as well as the boxiness of the outer isophotes.

(From Boonyasait, Patsis and Gottesman, 2005)

Using both observations and theoretical techniques, we show that the barred spiral galaxy NGC 3359 contains two pattern speeds. The faster pattern speed for the bar is obtained from isophotal analysis and stellar orbit theory. To explain the spiral arms and the observed velocity field of the disk, a slower pattern speed is required. Nonlinear resonance coupling is the supporting theory for the existence of two pattern speeds for the galaxy. The best match of our models with the observed data indicates a pattern speed for the bar of 39.17 km/sec/kpc and a value between 10 and 16 km/sec/kpc for the spiral.

This is the best theoretical representation for the (inner 5 kpc) morphology of the galaxy NGC 3359. It combines x1 orbits from two models rotating with two different pattern speeds. The white circle denotes the extent of the stellar bar. Orbits with the same color belong to the same model.

(From Patsis, Athanassoula, Quillen 1997, ApJ 483,717)

In a paper by Patsis, Athanassoula and Quillen (1997) we found the main families of simple periodic orbits in and around the bar of NGC 4314 and examined their stability. We have given special attention to the orbital behavior at the ultraharmonic resonance region, and we investigated all possibilities offered by our study in explaining the boxy structure at the end of the bar. It has been shown that the outer boxy isophotes in this and other early type bars, are in a large extent due to the chaotic orbits at the region. The contribution of chaotic orbits to the boxiness of the bar is described at the figure above. It shows three chaotic orbits, integrated for a few pattern rotations, suppoorting a boxy structure.

  • Patsis, P. A.; Athanassoula, E.; Quillen, A. C.: Orbits in the Bar of NGC 4314, 1997 ApJ...483..731
  • Patsis, P. A.; Guivarch, B.; Grosbøl, P. Line-of-Sight Velocity Profiles at the End of Weak Bars, 2001 ASPC..230..243
  • Patsis, P. A.; Skokos, Ch.; Athanassoula, E.: On the 3D dynamics and morphology of inner rings, 2003 MNRAS.346.1031
  • Patsis, P. A.; Skokos, Ch.; Athanassoula, E.: Formation of inner rings in 3D potentials of barred galaxies, International Astronomical Union Symposium no. 220, Eds: S. D. Ryder, D. J. Pisano, M. A. Walker, and K. C. Freeman. San Francisco: Astronomical Society of the Pacific., p.275
  • Kaufmann, David E.; Patsis, Panos A.: Propeller Orbits in Barred Galaxy Models, 2005 ApJ...624..693
  • Patsis, P. A.: On the relation between orbital structure and observed bar morphology 2005 MNRAS.358..305
  • Veera Boonyasait, P A Patsis and S T Gottesman: The Two Pattern Speeds of NGC 3359. Ann. N.Y. Acad. Sci. 1045: 203-224 (2005)
  • Contopoulos G., Patsis P.A. : "Outer dynamics and escapes in barred galaxies", 2006 MNRAS in press
  • P.A. Patsis: "The stellar dynamics of spiral arms in barred spiral galaxies", MNRAS, 2006 in press