Torusfitting method for obtaining action variables in twodimensional Galactic potentials
Abstract
A phasespace distribution function of the steady state in galaxy models that admits regular orbits overall in the phase space can be represented by a function of three action variables. This type of distribution function in Galactic models is often constructed theoretically for comparison of the Galactic models with observational data as a test of the models. On the other hand, observations give Cartesian phasespace coordinates of stars. Therefore, it is necessary to relate action variables and Cartesian coordinates in investigating whether the distribution function constructed in galaxy models can explain observational data. Generating functions are very useful in practice for this purpose, because calculations of relations between action variables and Cartesian coordinates by generating functions do not require a lot of computational time or computer memory in comparison with direct numerical integration calculations of stellar orbits. Here, we propose a new method called a torusfitting method, by which a generating function is derived numerically for models of the Galactic potential in which almost all orbits are regular. We confirmed that the torusfitting method can be applied to major orbit families (box and loop orbits) in some twodimensional potentials. Furthermore, the torusfitting method is still applicable to resonant orbit families, besides major orbit families. Hence, the torusfitting method is useful for analysing real Galactic systems in which a lot of resonant orbit families might exist.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 November 2014
 DOI:
 10.1093/mnras/stu1490
 arXiv:
 arXiv:1405.2393
 Bibcode:
 2014MNRAS.444.2218U
 Keywords:

 galaxies: kinematics and dynamics;
 Astrophysics  Astrophysics of Galaxies;
 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 12 pages, 14 figures