×

A three-dimensional dynamical model for double-barred galaxies, escape dynamics and the role of the NHIMs. (English) Zbl 1466.85001

Summary: A new analytic multi-component gravitational model with three degrees of freedom to describe the orbital properties of stars in a double-barred galaxy is introduced. We assume that the galaxy contains two bars: the primary one, parallel to the disc and the secondary one which is perpendicular to the primary bar. By following the trajectories, belonging to large sets of starting conditions, we manage to distinguish between localized (chaotic, sticky or regular) and escaping motion of stars. The character of orbits is revealed by presenting modern colour-coded diagrams on several choices of planes of two dimensions. Additionally, we investigate the properties of the normally hyperbolic invariant manifolds (NHIMs), associated with the index-1 saddle points of the system. The dynamics near the index-1 saddle points is demonstrated by presenting the bifurcation diagrams of the Lyapunov periodic orbits, and by visualizing the restriction of the Poincaré maps to the NHIMs. Useful conclusions are drawn by comparing our results with previous related ones, from other types of Hamiltonian systems.

MSC:

85A05 Galactic and stellar dynamics
85A15 Galactic and stellar structure
85-10 Mathematical modeling or simulation for problems pertaining to astronomy and astrophysics
70F15 Celestial mechanics
37N05 Dynamical systems in classical and celestial mechanics

Software:

Mathematica
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Aguirre, J.; Vallejo, J. C.; Sanjuán, M. A.F., Wada basins and chaotic invariant sets in the Hénon-Heiles system, Phys Rev E, 64, 066208 (2001)
[2] Binney, J.; Tremaine, S., Galactic dynamics (2008), Princeton Univ. Press: Princeton Univ. Press Princeton, USA · Zbl 1136.85001
[3] Buta, R.; Crocker, D. A., Metric characteristics of nuclear rings and related features in spiral galaxies, AJ, 105, 1344-1357 (1993)
[4] de Vaucouleurs, G., Southern galaxies. VII - The remarkable lenticular barred galaxy NGC 1291, ApJS, 29, 193-218 (1975)
[5] Emsellem, E.; Greusard, D.; Combes, F., A&A, 368, 52 (2001)
[6] Ernst, A.; Just, A.; Spurzem, R.; Porth, O., Escape from the vicinity of fractal basin boundaries of a star cluster, MNRAS, 383, 897-906 (2008)
[7] Ernst, A.; Peters, T., Fractal basins of escape and the formation of spiral arms in a galactic potential with a bar, MNRAS, 443, 2579-2589 (2014)
[8] Erwin, P., Double-barred galaxies. i. a catalog of barred galaxies with stellar secondary bars and inner disks, A&A, 415, 941-957 (2004)
[9] Erwin, P.; Sparke, L. S., Double bars, inner disks, and nuclear rings in early-type disk galaxies, AJ, 124, 65-77 (2002)
[10] Friedli, D.; Martinet, L., Bars within bars in lenticular and spiral galaxies - a step in secular evolution, A&A, 277, 27 (1993)
[11] Friedli, D.; Wozniak, H.; Rieke, M.; Martinet, L.; Bratschi, P., Disc galaxies with multiple triaxial structures. II. JHK surface photometry and numerical simulations, A&AS, 118, 461-479 (1996)
[12] Gonzalez, F.; Drotos, G.; Jung, C., The decay of a normally hyperbolic invariant manifold to dust in a three degrees of freedom scattering system, J Phys A, 47, 045101 (2014) · Zbl 1292.70011
[13] Guckenheimer, J.; Holmes, P., Nonlinear oscillations, dynamical systems, and bifurcations of vector fields (1983), Springer Verlag: Springer Verlag New York · Zbl 0515.34001
[14] Hénon, M., Numerical exploration of the restricted problem, A&A, 1, 223-238 (1969) · Zbl 0177.27703
[15] Jung, C.; Zotos, E. E., Introducing a new 3d dynamical model for barred galaxies, PASA, 32, e042 (2015)
[16] Jung, C.; Zotos, E. E., Orbital and escape dynamics in barred galaxies - I. The 2d system, MNRAS, 457, 2583-2603 (2016)
[17] Jung, C.; Zotos, E. E., Orbital and escape dynamics in barred galaxies - II. The 3d system: exploring the role of the normally hyperbolic invariant manifolds, MNRAS, 463, 3965-3988 (2016)
[18] Jungwiert, B.; Combes, F.; Axon, D. J., Near-IR photometry of disk galaxies: search for nuclear isophotal twist and double bars, A&AS, 125, 479-496 (1997)
[19] Kormendy, J., Rotation of the bulge components of barred galaxies, ApJ, 257, 75-88 (1982)
[20] Laine, S.; Shlosman, I.; Knapen, J. H.; Peletier, R. F., Nested and single bars in seyfert and non-seyfert galaxies, ApJ, 567, 97-117 (2002)
[21] Lyapunov, A. M., Problème genérál de la stabilité du mouvement, Ann Fac Sci Toulouse, 9, 203-475 (1907)
[22] Maciejewski, W.; Sparke, L. S., Regular orbits and periodic loops in multiply barred galactic potentials, ApJ, 484, L117-L120 (1997)
[23] Miyamoto, M.; Nagai, R., Three-dimensional models for the distribution of mass in galaxies, PASJ, 27, 533-543 (1975)
[24] Moiseev, A. V.; Valdés, J. R.; Chavushyan, V. H., Structure and kinematics of candidatedouble-barred galaxies, A&A, 421, 433-453 (2004)
[25] Nagler, J., Crash test for the copenhagen problem, Phys Rev E, 69, 066218 (2004)
[26] Nagler, J., Crash test for the restricted three-body problem, Phys Rev E, 71, 026227 (2005)
[27] Press, H. P.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P., Numerical recipes in FORTRAN 77 (1992), Cambridge Univ. Press: Cambridge Univ. Press Cambridge, USA · Zbl 0778.65002
[28] Schinnerer, E.; Maciejewski, W.; Scoville, N.; Moustakas, L. A., Toward the secondary bar: gas morphology and dynamics in NGC 4303, ApJ, 575, 826-844 (2002)
[29] Shlosman, I.; Frank, J.; Begelman, M. C., Bars within bars - a mechanism for fuelling active galactic nuclei, Nature, 338, 45-47 (1989)
[30] Skokos, C., Alignment indices: a new, simple method for determining the ordered or chaotic nature of orbits, J Phys A, 34, 10029 (2001) · Zbl 1004.37021
[31] Skokos, C.; Antonopoulos, C.; Bountis, T. C.; Vrahatis, M. N., Detecting order and chaos in hamiltonian systems by the SALI method, J Phys A, 37, 6269-6284 (2004)
[32] Waalkens, H.; Burbanks, A.; Wiggins, S., Letter to the Editor: a computational procedure to detect a new type of high-dimensional chaotic saddle and its application to the 3d Hill’s problem, J Phys A, 37, L257-L265 (2004)
[33] Waalkens, H.; Burbanks, A.; Wiggins, S., Escape from planetary neighbourhoods, MNRAS, 361, 763-775 (2005)
[34] Waalkens, H.; Schubert, R.; Wiggins, S., Wigner’s dynamical transition state theory in phase space: classical and quantum, Nonlinearity, 21, R1-R118 (2008) · Zbl 1153.81017
[35] Wiggins, S., Normally hyperbolic invariant manifolds in dynamical systems (1994), Springer Verlag: Springer Verlag Berlin · Zbl 0812.58001
[36] Wolfram, S., The mathematica book (2003), Wolfram Media: Wolfram Media Champaign
[37] Wozniak, H.; Friedli, D.; Martinet, L.; Martin, P.; Bratschi, P., Disc galaxies with multiple triaxial structures. I. BVRI and ha surface photometry, A&A, 111, 115 (1995)
[38] Zotos, E. E., Revealing the escape mechanism of three-dimensional orbits in a tidally limited star cluster, MNRAS, 446, 770-792 (2015)
[39] Zotos, E. E., Orbit classification in the hill problem: I. The classical case, Nonlinear Dyn, 89, 901-923 (2017) · Zbl 1430.70094
[40] Zotos, E. E.; Jung, C., Unravelling the escape dynamics and the nature of the normally hyperbolic invariant manifolds in tidally limited star clusters, MNRAS, 465, 525-546 (2017)
[41] Zotos, E. E.; Jung, C., Orbital and escape dynamics in barred galaxies - III. The 3d system: correlations between the basins of escape and the NHIMs, MNRAS, 473, 806-825 (2018)
[42] Zotos, E. E.; Jung, C., Correlating the escape dynamics and the role of the normally hyperbolic invariant manifolds in a binary system of dwarf spheroidal galaxies, Int J Non-Linear Mech, 99, 182-203 (2018)
[43] Zotos, E. E.; Jung, C., Orbital and escape dynamics in barred galaxies - IV. Heteroclinic connections, MNRAS, 487, 1233-1247 (2019)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.