Stellar orbits in angle variables

Ratcliff, S. J.; Chang, K. M.; Schwarzschild, M.

doi:10.1086/161925

Cited by 17 publications

(10 citation statements)

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“…In point of historical fact, Martin Schwarzschild himself took the first step towards torus modelling (Ratcliff et al 1984).…”

Section: Poisson Noise and Modelling Strategymentioning

confidence: 99%

Orbital tori for non-axisymmetric galaxies

Binney¹

2017

Monthly Notices of the Royal Astronomical Society

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Our Galaxy's bar makes the Galaxy's potential distinctly non-axisymmetric. All orbits are affected by non-axisymmetry, and significant numbers are qualitatively changed by being trapped at a resonance with the bar. Orbital tori are used to compute these effects. Thick-disc orbits are no less likely to be trapped by corotation or a Lindblad resonance than thin-disc orbits. Perturbation theory is used to create non-axisymmetric orbital tori from standard axisymmetric tori, and both trapped and untrapped orbits are recovered to surprising accuracy. Code is added to the TorusModeller library that makes it as easy to manipulate non-axisymmetric tori as axisymmetric ones. The augmented TorusModeller is used to compute the velocity structure of the solar neighbourhood for bars of different pattern speeds and a simple action-based distribution function. The technique developed here can be applied to any non-axisymmetric potential that is stationary in a rotating from -hence also to classical spiral structure.

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“…In point of historical fact, Martin Schwarzschild himself took the first step towards torus modelling (Ratcliff et al 1984).…”

Section: Poisson Noise and Modelling Strategymentioning

confidence: 99%

Orbital tori for non-axisymmetric galaxies

Binney¹

2017

Monthly Notices of the Royal Astronomical Society

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“…This method actually goes back to many years ago (e.g., Ratcliff, Chang & Schwarzschild 1984), but recent work by the Oxford group (e.g., Kaasalainen Figure 3: A planar loop orbit in various cuts of the phase space. The top panel shows the phase space torus of the orbit, which will be populated uniformly after integrating the orbit for a long time.…”

Section: Spectral Dynamics Methodsmentioning

confidence: 99%

Building Galaxy Models with Schwarzschild Method and Spectral Dynamics

Zhao¹

1999

Impact of Modern Dynamics in Astronomy

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Tremendous progress has been made recently in modelling the morphology and kinematics of centers of galaxies. Increasingly realistic models are built for central bar, bulge, nucleus and black hole of galaxies, including our own. The newly revived Schwarzschild method has played a central role in these theoretical modellings. Here I will highlight some recent work at Leiden on extending the Schwarzschild method in a few directions. After a brief discussion of (i) an analytical approach to include stochastic orbits (Zhao 1996), and (ii) the "pendulum effect" of loop and boxlet orbits (Zhao, Carollo, de Zeeuw 1999), I will concentrate on the very promising (iii) spectral dynamics method, with which not only can one obtain semi-analytically the actions of individual orbits as previously known, but also many other physical quantities, such as the density in configuration space and the line-ofsight velocity distribution of a superposition of orbits (Copin, Zhao & de Zeeuw 1999). The latter method also represents a drastic reduction of storage space for the orbit library and an increase in accuracy over the grid-based Schwarzschild method.

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“…This criterion can be based on either the 'theoretical' Hamiltonian flow (found by the normal form) fitting the true Hamiltonian flow of the system, or the theoretical tori, viewed as geometrical objects, fitting the real tori of the system. Such fitting methods were introduced in galactic dynamics by Ratcliff et al (1984), McGill and Binney (1990) and Kent and de Zeeuw (1991).…”

Section: Axisymmetric Systems and The 'Third Integral' Of Motionmentioning

confidence: 99%