On the relevance of chaos for halo stars in the solar neighbourhood II

Abstract

In a previous paper based on dark matter only simulations we show that, in the approximation of an analytic and static potential describing the strongly triaxial and cuspy shape of Milky Way-sized haloes, diffusion due to chaotic mixing in the neighbourhood of the Sun does not efficiently erase phase space signatures of past accretion events. In this second paper we further explore the effect of chaotic mixing using multicomponent Galactic potential models and solar neighbourhood-like volumes extracted from fully cosmological hydrodynamic simulations, thus naturally accounting for the gravitational potential associated with baryonic components, such as the bulge and disc. Despite the strong change in the global Galactic potentials with respect to those obtained in dark matter only simulations, our results confirm that a large fraction of halo particles evolving on chaotic orbits exhibit their chaotic behaviour after periods of time significantly larger than a Hubble time. In addition, significant diffusion in phase space is not observed on those particles that do exhibit chaotic behaviour within a Hubble time.

Phase correlations in chaotic dynamics: a Shannon entropy measure

“…Notice that near I 2 = 1 diffusion spreads out of the chaotic layer of the resonance ω 1 = 0 where the motion is under the influence of at least three resonances, ω 1 = 0, ω 1 ± ω 2 = 0 and ω 1 = ±1. Thus, the numerical results confirm that for ω 0 2 2 the map (25) does no longer describe the diffusion along the chaotic layer of the main resonance.…”

“…5 we present a three dimensional visualization of the diffusion for the smaller four values of κ ∈ K for the section |θ 2 | ≤ 10 −5 where we observe that at least up to t = 10 6 the diffusion is almost irrelevant. Again, we take for the map an ensemble of n p = 1000 random initial conditions with y ≤ 10 −5 , |ω 2 − ω 0 2 | ≤ 10 −5 , τ = 10 −5 , β = 0 and iterate the map (25) up to N = 10 6 . We normalize both phases τ and θ 2 to the unit interval and compute the information (11) and the time derivative (13) after time intervals of length ∆ = 10 3 with q = 10 3 .…”

“…Therefore for these large values of the perturbation parameters we numerically investigate the Hamiltonian (21) instead of the map (25). To this aim, we take an ensemble of n p = 100 random initial conditions on the separatrix of the resonance ω 1 = 0.…”

“…Left panel) Evolution of I for np = 1000 initial values of τ ∈ (0, 1) for the map(25) for ε = 0.05, µ = 10 −3 ε and eight values of ω 0 2 = κ √ The analytically expected behavior for random motion given by(12) is also included for N = np × t. (Right panel) Similar to the plot at the left but for the phase θ 2 ∈ (0, 1).…”

Simulating cosmological substructure in the solar neighbourhood

“…2 with the CHDYN sample selection cuts. Potential energies for stars in the mocks are computed using a 3 component fit to the galactic potential following Maffione et al (2018). For aurigaia stars we assign the [Fe/H] and [α/Fe] abundances of parent particles to all child stars.…”