The value of the pattern speed of density waves (or equivalent the location of the main resonances) is still an unresolved issue for several types of spiral galaxies. The exact estimation of this value is very important for the understanding of the spiral structure but cannot be measured directly. Usually it is estimated by associating major resonances (e.g. 4:1, corotation or -2:1) to spiral features such as the end of the arms.

The figure below is from a work done in collaboration with D. Kaufmann (Patsis and Kaufmann 1999). In N-body simulations of galactic disks where a main bisymmetric spiral mode dominates for 5-7 pattern rotations of the spiral we considered the phases of the dominating bisymmetric spiral for the saved snapshots during this period. Then the resulting diagrams have been rotated with the found pattern speed of the spiral so that they can be overplotted in a single frame. Such a result is depicted below. The numbers on the axes correspond to kpc.

The circles represent the 2:1, 4:1, corotation, and -2:1 resonances. It is clear that the spiral we found rotates as slow as to put corotation beyond the end of the strong symmetric spiral. The strong symmetric part of the spiral ends at the inner 4:1 resonance, and only a weaker extension reaches resonances beyond it.

Contopoulos and Grosbol (1986;1988) indicated that strong open spirals terminate at the inner 4:1 resonance, due to the abrupt change of the orientation of the x1 orbits at the region of this resonance.

Patsis, Contopoulos and Grosbol (1991) found that the self-consistency of orbital models for Sa and Sb galaxies (relation between imposed and response density) was better if a strong symmetric spiral was assumed ending at the 4:1 resonance, than in models where the end of the strong symmetric part was placed at corotation.
The weak, tightly wound spirals of the Sa galaxies could continue through the 4:1 resonance.

Later (see Hydrodynamics, SPH simulations by Patsis, Hiotelis, Contopoulos and Grosbol (1994) and Patsis, Grosbol and Hiotelis (1997) have shown that gaseous response models could reproduce a spiral structure along the potential minima of the imposed spiral up to the inner 4:1 resonance. A major role for the reproduction of morphological features observed in grand design spiral galaxies plays the inclusion of an m=1 component in the imposed potential (Patsis et al. 1997).

  • Patsis, P. A.; Contopoulos, G.; Grosbol, P.: Self-consistent spiral galactic models, 1991 A&A...243..373
  • Patsis, P. A.; Grosbol, P.: Gaseous and stellar responses to spiral perturbations detected in the NIR, 1996 in New Extragalactic Perspectives in the New South Africa (ed. Block, Greenberg), p.554
  • Grosbol, P.; Patsis, P. A.: Periodic Orbits in Three-armed Galaxies, 1998 in IAU Colloq. 172: Impact of Modern Dynamics in Astronomy, p.40
  • Patsis, P. A.; Grosbol, P.: Stellar and gaseous models of spiral galaxies, 1998, in Dynamics of Galaxies and Galactic Nuclei (ed. Duschl, Einsel), p.85
  • Patsis, P. A.; Kaufmann, D.: Signature of Density Wave Resonances in N-body Simulations of Spiral Galaxies, 1999, in Numerical Astrophysics, Edited by Shoken M. Miyama, Kohji Tomisaka, and Tomoyuki Hanawa. Boston, Mass. : Kluwer Academic, 1999. (Astrophysics and space science library ; v. 240), p.65
  • Grosbøl, Preben J.; Patsis, Panos A.: The Three-Armed Galaxy NGC 7137, Galaxy Dynamics, 1999, ASP Conference Series vol. 182 (San Francisco: ASP), edited by David R. Merritt, Monica Valluri, and J. A. Sellwood
  • Patsis, P. A.; Kaufmann, D. E.: Resonances and the morphology of spirals in N-body simulations, 1999, A&A...352..469