Spherical symmetry breaking in cold gravitational collapse of isolated systems

Abstract

We study, using N -body simulation, the shape evolution in gravitational collapse of cold uniform spherical system. The central interest is on how the deviation from spherical symmetry depends on particle number N . By revisit of the spherical collapse model, we hypothesize that the departure from spherical symmetry is regulated by the finite-N density fluctuation. Following this assumption, the estimate of the flattening of relaxed structures is derived to be N −1/3 . In numerical part, we find that the virialized states can be characterized by the core-halo structures and the flattenings of the cores fit reasonably well with the prediction. Moreover the results from large N systems suggest the divergence of relaxation time to the final shapes with N . We also find that the intrinsic shapes of the cores are considerably diverse as they vary from nearly spherical, prolate, oblate or completely triaxial in each realization. When N increases, this variation is suppressed as the final shapes do not differ much from initial symmetry. In addition, we observe the stable rotation of the virialized states. Further investigation reveals that the origin of this rotation is related in some way to the initial density fluctuation.

Generation of angular momentum in cold gravitational collapse

“…A similar decrease in amplitude, with an exponent of about the same value, has been observed for the case α = 0 in Worrakitpoonpon (2015). In our simulations of initial conditions from elliptical conditions, we have not been able to detect a clear trend for L p b to decrease as N increases within the significant scatter of different realisations at given N. This is probably because of a weaker N-dependence in this case, as the spherical symmetry is "mostly" broken by ι(0) 0, which does not depend on N. In contrast, the lack of evidence for any N dependence in the final ι -once N is sufficiently large so that collisional relaxation plays no role on the time scales probedmay be indicative of the true physical behaviour: in the limit of exact spherical symmetry of a perfectly cold system, it is expected that symmetry will be broken because of a so-called radial orbit instability.…”

“…The most popular theory to account for angular momentum in virialised structures is the so-called tidal torque theory, in which the virialised structure gains angular momentum by the action of the torque that is caused by the tidal fields generated by surrounding structures (Peebles 1969). Here, we explore a distinct mechanism which, despite its simplicity, appears not to have been considered in the literature, apart from in one recent study of cold spherical collapse (Worrakitpoonpon 2015): generation of angular momentum by ejection of matter in violent relaxation. Indeed violent relaxation of self-gravitating structures is characterised by very large amplitude variations of the mean field potential of a structure, which can give enough energy to particles to escape, even if all the mass is initially bound.…”

“Virtual Planetarium” Code for Astrophysical Objects Modeling: Mathematical Model, Methodology and First Results

“…В нашей модельной задаче мы будем исследовать поведение ансамбля частиц газа при различных значениях дисперсии скоростей  . Проблема исследования фрагментации вращающегося холодного облака особенно интересна в контексте эволюции эллиптических галактик [10].…”

Gravitational collapse from cold uniform asymmetric initial conditions

“…The evolution under Newtonian self-gravity of an isolated distribution of particles that start from initial conditions (ICs) in which the particles are initially at rest and are randomly distributed in a sphere with uniform mean density has been studied by numerous authors since the earliest numerical simulations of such systems. Numerous variants have also been explored, notably with initial velocity dispersion (using radially dependent density profiles) and for spheroidal boundaries (Henon, 1964(Henon, , 1973van Albada, 1982;Merritt & Aguilar, 1985;Aarseth et al, 1988;Aguilar & Merritt, 1990;Theis & Spurzem, 1999;Boily et al, 2002;Roy & Perez, 2004;Boily & Athanassoula, 2006;Barnes et al, 2009;Joyce et al, 2009;Sylos Labini, 2012, 2013Worrakitpoonpon, 2015;Sylos Labini et al, 2015;Benhaiem et al, 2016;Benhaiem & Sylos Labini, 2017;Spera & Capuzzo-Dolcetta, 2017;Worrakitpoonpon, 2020). Such systems provide a natural and simple setting to explore the rich complexity of the nonlinear phase of gravitational dynamics relevant to many different problems in astrophysics and cosmology.…”