Frequency map analysis of the orbital structure in elliptical galaxies

We present an application of the frequency map analysis to an elliptical galaxy which is represented by a generalization of a double-power-law spherical mass model. The density distribution of this model varies as r−γ close to the centre and as r−4 at large radii. We study the case with γ = 1, which is known as the ‘weak-cusp’ model and which represents well the density profile of the ‘core’ galaxies observed by the Hubble Space Telescope. The final objective of our work is to improve our understanding of the dynamics of elliptical galaxies in a similar way to Merritt & Fridman, finding the regions of stochasticity, looking for resonances that might play an important role in sustaining the triaxial morphology, and analysing the diffusion of orbits. To this end, we use the frequency map analysis of Laskar, which has been applied widely in the field of celestial mechanics but which is a relatively new technique in the area of galactic dynamics. Finally, we show some useful features of this method in understanding the global dynamical structure of the system.