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Chaos and integrability in galactic disks

Grant number: 15/10577-9
Support type:Scholarships in Brazil - Post-Doctorate
Effective date (Start): August 01, 2015
Effective date (End): July 31, 2018
Field of knowledge:Physical Sciences and Mathematics - Astronomy
Principal Investigator:Tatiana Alexandrovna Michtchenko
Grantee:Ronaldo Savioli Sumé Vieira
Home Institution: Instituto de Astronomia, Geofísica e Ciências Atmosféricas (IAG). Universidade de São Paulo (USP). São Paulo , SP, Brazil


This project aims to study the Hamiltonian dynamics of test particles in Newtonian and relativistic discoidal systems, with emphasis mainly in the dynamics of stars in spiral galaxies (especially in the Milky Way). Our goal is to advance in the description of the Hamiltonian dynamics in these systems, focusing on two different aspects: (i) the regular motion around equilibrium points and stable equatorial periodic orbits, through a third integral of motion determined by physical observables (for off-equatorial orbits), according to the recently obtained results regarding the axially symmetric case, and (ii) the chaotic motion near resonances of the spiral pattern and the relation with the recent discoveries about the Galaxy structure near these radii. The second topic will be analyzed mainly by the "Spectral Analysis Method", developed by the Dynamical Astronomy group of IAG--USP, and successfully applied to planetary systems and asteroid motion. The resemblance between the two formalisms for the motion in planetary systems and in galaxies allows us to apply it also to galactic dynamics problems, since both correspond to the dynamics of a particle subject to an external gravitational potential.As a second part of the project, we intend to apply the aforementioned method to the dynamics of test particles in general relativity, with focus on systems containing bidimensional or three-dimensional disks, using the Hamiltonian formalism for the geodesic flow. The study of chaos in relativistic disk models is recent. Our main goal is to analyze how chaos appears in disk systems with known Newtonian analogue, as well as to verify if the relativistic extensions of Newtonian systems with integrable dynamics present chaos, and in this case to study the reason for this behavior. A last problem is the dynamical analysis of orbits in post-Newtonian disk systems (1PN), following the Hamiltonian formulation for test particles recently developed by the candidate, comparing with the Newtonian case. We expect that the rotation in stationary disks introduces qualitative effects in the phase-space structure already in the 1PN approximation, without the necessity of an exact relativistic approach.

Scientific publications (10)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
VIEIRA, RONALDO S. S.; MICHTCHENKO, TATIANA A. Relativistic chaos in the anisotropic harmonic oscillator. CHAOS SOLITONS & FRACTALS, v. 117, p. 276-282, DEC 2018. Web of Science Citations: 1.
MICHTCHENKO, TATIANA A.; LEPINE, JACQUES R. D.; PEREZ-VILLEGAS, ANGELES; VIEIRA, RONALDO S. S.; BARROS, DOUGLAS A. On the Stellar Velocity Distribution in the Solar Neighborhood in Light of Gaia DR2. Astrophysical Journal Letters, v. 863, n. 2 AUG 20 2018. Web of Science Citations: 4.
MICHTCHENKO, T. A.; LEPINE, J. R. D.; BARROS, D. A.; VIEIRA, R. S. S. Combined dynamical effects of the bar and spiral arms in a Galaxy model. Application to the solar neighbourhood. Astronomy & Astrophysics, v. 615, JUL 6 2018. Web of Science Citations: 3.
LEPINE, JACQUES R. D.; MICHTCHENKO, TATIANA A.; BARROS, DOUGLAS A.; VIEIRA, RONALDO S. S. The Dynamical Origin of the Local Arm and the Sun's Trapped Orbit. ASTROPHYSICAL JOURNAL, v. 843, n. 1 JUL 1 2017. Web of Science Citations: 7.
VIEIRA, RONALDO S. S.; KLUZNIAK, WLODEK; ABRAMOWICZ, MAREK. Curvature dependence of relativistic epicyclic frequencies in static, axially symmetric spacetimes. Physical Review D, v. 95, n. 4 FEB 8 2017. Web of Science Citations: 1.
MICHTCHENKO, T. A.; VIEIRA, R. S. S.; BARROS, D. A.; LEPINE, J. R. D. Modelling resonances and orbital chaos in disk galaxies Application to a Milky Way spiral model. Astronomy & Astrophysics, v. 597, JAN 2017. Web of Science Citations: 7.
VIEIRA, RONALDO S. S.; RAMOS-CARO, JAVIER; SAA, ALBERTO. Vertical stability of circular orbits in relativistic razor-thin disks. Physical Review D, v. 94, n. 10 NOV 7 2016. Web of Science Citations: 5.
VIEIRA, RONALDO S. S.; RAMOS-CARO, JAVIER. Integrability of motion around galactic razor-thin disks. CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, v. 126, n. 4, p. 483-500, NOV 2016. Web of Science Citations: 3.
LASOTA, J. -P.; VIEIRA, R. S. S.; SADOWSKI, A.; NARAYAN, R.; ABRAMOWICZ, M. A. The slimming effect of advection on black-hole accretion flows. Astronomy & Astrophysics, v. 587, MAR 2016. Web of Science Citations: 15.
GOLUCHOVA, KATERINA; KULCZYCKI, KONRAD; VIEIRA, RONALDO S. S.; STUCHLIK, ZDENEK; KLUZNIAK, WLODEK; ABRAMOWICZ, MAREK. Horava's quantum gravity illustrated by embedding diagrams of the Kehagias-Sfetsos spacetimes. GENERAL RELATIVITY AND GRAVITATION, v. 47, n. 11 NOV 2015. Web of Science Citations: 2.

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