Probing a regular orbit with spectral dynamics

Y. Copin*, H. S. Zhao, P. T. De Zeeuw

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


We have extended the spectral dynamics formalism introduced by Binney & Spergel, and have implemented a semi-analytic method to represent regular orbits in any potential, making full use of their regularity. We use the spectral analysis code of Carpintero & Aguilar to determine the nature of an orbit (irregular, regular, resonant, periodic) from a short-time numerical integration. If the orbit is regular, we approximate it by a truncated Fourier time series of a few tens of terms per coordinate. Switching to a description in action-angle variables, this corresponds to a reconstruction of the underlying invariant torus. We then relate the uniform distribution of a regular orbit on its torus to the non-uniform distribution in the space of observables by a simple Jacobian transformation between the two sets of coordinates. This allows us to compute, in a cell-independent way, all the physical quantities needed in the study of the orbit, including the density and the line-of-sight velocity distribution, with much increased accuracy. The resulting flexibility in the determination of the orbital properties, and the drastic reduction of storage space for the orbit library, provide a significant improvement in the practical application of Schwarzschild's orbit superposition method for constructing galaxy models. We test and apply our method to two-dimensional orbits in elongated discs, and to the meridional motion in axisymmetric potentials, and show that for a given accuracy, the spectral dynamics formalism requires an order of magnitude fewer computations than the more traditional approaches.

Original languageEnglish
Pages (from-to)781-797
Number of pages17
JournalMonthly Notices of the Royal Astronomical Society
Issue number3
Publication statusPublished - 1 Nov 2000


  • Celestial mechanics, stellar dynamics
  • Galaxies: kinematics and dynamics


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