Resonant Stellar Orbits in Spiral Galaxies. 111. Applications and Numerical Tests of the General Epicyclic Theory

This paper reviews a series of investigations of the orbits of stars in the regions of the Lindblad resonances of a spiral galaxy. The analysis is formulated in an epicyclic approximation. Analytic solutions of the epicyclic equations of motion are obtained by the method of harmonic balance of Bogoliubov and Mitropolsky. These solutions represent the resonance phenomena exhibited by the orbits in generally excellent agreement with numerical solutions.

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Resonant stellar orbits in spiral galaxies. IV - Hydrodynamic flows in the regions of the Lindblad resonances

The Astrophysical Journal Supplement Series ◽

10.1086/190541 ◽

1978 ◽

Vol 37 ◽

pp. 519 ◽

Cited By ~ 1

Author(s):

P. O. Vandervoort ◽

J. Keene

Keyword(s):

Spiral Galaxies ◽

Stellar Orbits

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Galactic spiral structure

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2009.0036 ◽

2009 ◽

Vol 465 (2111) ◽

pp. 3425-3446 ◽

Cited By ~ 9

Author(s):

Charles Francis ◽

Erik Anderson

Keyword(s):

Pitch Angle ◽

Milky Way ◽

Spiral Galaxies ◽

Stellar Orbits ◽

Grand Design ◽

Galactic Spiral Structure ◽

Pattern Speed ◽

Galactic Spiral ◽

Almost All ◽

Spiral Arm

We describe the structure and composition of six major stellar streams in a population of 20 574 local stars in the New Hipparcos Reduction with known radial velocities. We find that, once fast moving stars are excluded, almost all stars belong to one of these streams. The results of our investigation have led us to re-examine the hydrogen maps of the Milky Way, from which we identify the possibility of a symmetric two-armed spiral with half the conventionally accepted pitch angle. We describe a model of spiral arm motions that matches the observed velocities and compositions of the six major streams, as well as the observed velocities of the Hyades and Praesepe clusters at the extreme of the Hyades stream. We model stellar orbits as perturbed ellipses aligned at a focus in coordinates rotating at the rate of precession of apocentre. Stars join a spiral arm just before apocentre, follow the arm for more than half an orbit, and leave the arm soon after pericentre. Spiral pattern speed equals the mean rate of precession of apocentre. Spiral arms are shown to be stable configurations of stellar orbits, up to the formation of a bar and/or ring. Pitch angle is directly related to the distribution of orbital eccentricities in a given spiral galaxy. We show how spiral galaxies can evolve to form bars and rings. We show that orbits of gas clouds are stable only in bisymmetric spirals. We conclude that spiral galaxies evolve toward grand design two-armed spirals. We infer from the velocity distributions that the Milky Way evolved into this form about 9 billion years ago (Ga).

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Gravitoelectromagnetism and stellar orbits in galaxies

International Journal of Modern Physics D ◽

10.1142/s0218271821501029 ◽

2021 ◽

pp. 2150102

Author(s):

Viktor T. Toth

Keyword(s):

General Relativity ◽

Dark Matter ◽

Gravitational Field ◽

Magnetic Force ◽

Milky Way ◽

Spiral Galaxies ◽

Observable Effect ◽

Stellar Orbits ◽

Gravitational Fields ◽

The Impact

Beyond the Newtonian approximation, gravitational fields in general relativity can be described using a formalism known as gravitoelectromagnetism. In this formalism, a vector potential, the gravitomagnetic potential, arises as a result of moving masses, in strong analogy with the magnetic force due to moving charges in Maxwell’s theory. Gravitomagnetism can affect orbits in the gravitational field of a massive, rotating body. This raises the possibility that gravitomagnetism may serve as the dominant physics behind the anomalous rotation curves of spiral galaxies, eliminating the need for dark matter. In this essay, we methodically work out the magnitude of the gravitomagnetic equivalent of the Lorentz force and apply the result to the Milky Way. We find that the resulting contribution is too small to produce an observable effect on these orbits. We also investigate the impact of cosmological boundary conditions on the result and find that these, too, are negligible.

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