Physical characteristics of the Galaxy defining the oscillation period of librating orbits near the OLR of the bar
Abstract
We studied librating orbits of stars near the Outer Lindblad Resonance (OLR) of the bar using the angle-action variables of Hamiltonian dynamics. The librating orbits change the direction of their elongation relative to the major axis of the bar in a limited range of angles. To calculate orbits, we used the model of the Galaxy with an analytical bar which reproduces well the distributions of the observed stellar velocities along the Galactocentric distance R derived from the Gaia DR3 data. We compared the values of the orbital oscillation period of a typical star obtained from the theory and with the use of numerical simulation. Both values were found to be in good agreement and are equal to 2.0 Gyr. It was shown that the change in the average orbital radius, , of a star, calculated over the time interval of one radial oscillation, is regulated by the change in the direction of orbital elongation. As the orbit is tilted relative to the minor axis of the bar in the sense of Galactic rotation, the angular momentum of the star, L, decreases, on average, causing a decrease in . As the orbit is tilted in the opposite direction, and increase. We derived a general formula for the oscillation frequency, omega, of orbits captured by libration near the OLR of the bar. It turned out that the ratio of the frequency of orbit oscillations to the epicyclic frequency, omega/kappa, is determined by the parameters q_R and , where the factor q_R is the ratio of the amplitude of the radial force generated by the bar to the average radial force produced by the entire galaxy at the distance of the OLR, and the parameter characterizes the average elongation of orbits captured by libration near the OLR.
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BibTeX
@misc{melnik2026physical,
title = {{Physical characteristics of the Galaxy defining the oscillation period of librating orbits near the OLR of the bar}},
author = {A. M. Melnik and E. N. Podzolkova},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17255},
eprint = {2610.17255},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17255},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Physical characteristics of the Galaxy defining the oscillation period of librating orbits near the OLR of the bar
AU - A. M. Melnik
AU - E. N. Podzolkova
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.17255
UR - https://arxiv.org/abs/2610.17255
AB - We studied librating orbits of stars near the Outer Lindblad Resonance (OLR) of the bar using the angle-action variables of Hamiltonian dynamics. The librating orbits change the direction of their elongation relative to the major axis of the bar in a limited range of angles. To calculate orbits, we used the model of the Galaxy with an analytical bar which reproduces well the distributions of the observed stellar velocities along the Galactocentric distance R derived from the Gaia DR3 data. We compared the values of the orbital oscillation period of a typical star obtained from the theory and with the use of numerical simulation. Both values were found to be in good agreement and are equal to 2.0 Gyr. It was shown that the change in the average orbital radius, , of a star, calculated over the time interval of one radial oscillation, is regulated by the change in the direction of orbital elongation. As the orbit is tilted relative to the minor axis of the bar in the sense of Galactic rotation, the angular momentum of the star, L, decreases, on average, causing a decrease in . As the orbit is tilted in the opposite direction, and increase. We derived a general formula for the oscillation frequency, omega, of orbits captured by libration near the OLR of the bar. It turned out that the ratio of the frequency of orbit oscillations to the epicyclic frequency, omega/kappa, is determined by the parameters q_R and , where the factor q_R is the ratio of the amplitude of the radial force generated by the bar to the average radial force produced by the entire galaxy at the distance of the OLR, and the parameter characterizes the average elongation of orbits captured by libration near the OLR.
ER -