Transient chaos and resonant phase mixing in violent relaxation

Abstract

This paper explores how orbits in a galactic potential can be impacted by large amplitude time-dependences of the form that one might associate with galaxy or halo formation or strong encounters between pairs of galaxies. A period of time-dependence with a strong, possibly damped, oscillatory component can give rise to large amounts of transient chaos, and it is argued that chaotic phase mixing associated with this transient chaos could play a major role in accounting for the speed and efficiency of violent relaxation. Analysis of simple toy models involving time-dependent perturbations of an integrable Plummer potential indicates that this chaos results from a broad, possibly generic, resonance between the frequencies of the orbits and harmonics thereof and the frequencies of the time-dependent perturbation. Numerical computations of orbits in potentials exhibiting damped oscillations suggest that, within a period of 10 dynamical times t_D or so, one could achieve simultaneously both `near-complete' chaotic phase mixing and a nearly time-independent, integrable end state.Comment: 11 pages and 12 figures: an extended version of the original manuscript, containing a modified title, one new figure, and approximately one page of additional text, to appear in Monthly Notices of the Royal Astronomical Societ

Chaos and chaotic phase mixing in cuspy triaxial potentials

“…Given, however, that there is only one natural time‐scale for the problem, namely the dynamical t D , which sets both the characteristic orbital time‐scale and the pulsation time, one would anticipate that, throughout most of the galaxy, the frequencies will be sufficiently close to trigger the resonance. Simple toy models involving an integrable Plummer sphere subjected to damped oscillations can, within a time ∼10 t D , exhibit both near‐complete chaotic phase mixing and an approach towards a nearly time‐independent state (Kandrup et al 2003a).…”

Interplay between chaotic and regular motion in a time-dependent barred galaxy model

“…Defining the orbital complexity n(k), of an orbital segment as the number of frequencies in its discrete Fourier spectrum that contain a k-fraction of its total power [43], one may compare n(k) with the short-time evolution of the LEs for TD models [44]. In [45] the case of a cosmological model is discussed, where orbits may experience regular and/or chaotic motion during their time evolution, while in [46] the effects of a black hole, friction, noise and periodic driving are studied on a triaxial elliptic galaxy model, in which a type of transient chaos was found caused by a damped, oscillatory component [47,48]. Finally, in [49] the so-called "pattern method" was used to study a Hénon-Heiles potential to which an exponential function of time is added, while the dynamics of some simple TD galactic models was investigated in [50,51].…”

A Derivation of (Half) the Dark Matter Distribution Function

“…It may also be associated with dynamical effects, like radial orbit instability (Henriksen 2009;Bellovary et al 2008), or phase mixing or violent relaxation (Lynden-Bell 1967; Kandrup et al 2003). Alternatively, it could just be a "coincidence," since all structures have been built up through similar processes of mergers and accretion Salvador-Sole et al 2007).…”