![]() It has been shown that these orbits can collaborate so that the imposed model matches with the response model of spiral arms (see Contopoulos 1970, 1971, 1975 Berman & Mark 1977 Monet & Vandervoort 1978 Contopoulos & Grosbøl 1986 Patsis et al. Many papers have studied these periodic orbits, in models of grand design galaxies. ![]() In the density wave theory, the periodic orbits are close to precessing ellipses that support the shape of the spiral structure. Lindblad (1955) pioneered the orbital description of spiral density waves. This theory was first developed by Lindblad (1940, 1961), and it was extended by Lin & Shu (1964, 1966). The density wave theory fits the description of spiral arms better when the spiral amplitude does not exceed a value of 10%–20% over a few pattern rotations. In the case of grand design galaxies, the “density wave” theory remains a valid dynamical model with which the spiral structure of many disk galaxies can be described. There are two main theories that prevail nowadays concerning the building blocks of the spiral arms in galaxies. Subscribe to A&A to support open access publication. This article is published in open access under the Subscribe-to-Open model. Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License ( ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The superposition of these perturbed preccesing ellipses for all the energy levels of the Hamiltonian creates a slightly perturbed symmetrical spiral density wave. In this case, the stable elliptical orbits that support the spiral density wave (in the case of grand design galaxies) are transformed into quasiperiodic orbits (or 2D tori) with a certain thickness. In the present study, we consider an alternative scenario in the case where the bar rotates fast enough in comparison with the spiral arms and the bar potential can be considered as a perturbation of the spiral potential. The theory that prevails in explaining the formation of the spiral arms in the case of a barred spiral galaxy with two pattern speeds is the manifold theory, where the orbits that support the spiral density wave are chaotic, and are related to the manifolds emanating from the Lagrangian points L 1 and L 2 at the end of the bar. The main conclusion from the bibliography is that the bar rotates faster than the spiral arms with a double or even a triple value of angular velocity. Research Center for Astronomy and Applied Mathematics, Academy of Athens, Soranou Efessiou 4, 115 27 Athens, GreeceĮ-mail: of Mathematics, Tullio Levi-Civita, University of Padua, Via Trieste, 63, 35121 Padova, ItalyĮ-mail: and simulations of barred spiral galaxies have shown that, in general, the spiral arms rotate at a different pattern speed to that of the bar. Astronomical objects: linking to databases.Including author names using non-Roman alphabets.Suggested resources for more tips on language editing in the sciences Punctuation and style concerns regarding equations, figures, tables, and footnotes
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