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Probing a regular orbit with spectral dynamics | | Y. Copin
; H.S. Zhao
; P.T. de Zeeuw
; | | Date: |
13 Dec 1999 | | Journal: | Mon.Not.Roy.Astron.Soc. 318 (2000) 781 | | Subject: | astro-ph | | Affiliation: | CRAL -- Observatoire de Lyon, France, Sterrewacht Leiden, The Netherlands | | Abstract: | 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 in 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. | | Source: | arXiv, astro-ph/9912255 | | Services: | Forum | Review | PDF | Favorites | |
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