Role of dark matter haloes on the predictability of computed orbits

¹ European Space Astronomy Centre, PO Box 78, 28691 Villanueva de la Canada, Madrid Spain
e-mail: Juan.Carlos.Vallejo@esa.int
² Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipan s/n, 28933 Mostoles, Madrid, Spain
e-mail: miguel.sanjuan@urjc.es

Received: 29 June 2016
Accepted: 17 August 2016

Abstract

Aims. The predictability of a system indicates how often a computed orbit is close to a real orbit of the system, independent of its stability or chaotic nature. We explore the effect of dark halo shapes on the predictability of computed orbits in a Milky Way mean field model. We also present the sources for the low predictability found in some orbits.

Methods. We derived a predictability index from the distributions of the finite-time Lyapunov exponents. We computed those distributions and analysed the evolution of their shapes when the finite-time interval sizes are varied. The predictability index can be computed using the interval lengths corresponding to the timescales when the flow dynamics leaves the local regime and enters the global regime.

Results. These analyses reveal that not all chaotic orbits have the same predictability and that the predictability of some orbits is more affected than others by the orientation and shape of the dark halo. We show that the lowest predictability may be linked to strong unstable dimension variability.