On the generation of triaxiality in the collapse of cold spherical self-gravitating systems

Abstract

Initially cold and spherically symmetric self-gravitating systems may give rise to a virial equilibrium state which is far from spherically symmetric, and typically triaxial. We focus here on how the degree of symmetry breaking in the final state depends on the initial density profile. We note that the most asymmetric structures result when, during the collapse phase, there is a strong injection of energy preferentially into the particles which are localized initially in the outer shells. These particles are still collapsing when the others, initially located in the inner part, are already reexpanding; the motion of particles in a time varying potential allow them to gain kinetic energy -in some cases enough to be ejected from the system. We show that this mechanism of energy gain amplifies the initial small deviations from perfect spherical symmetry due to finite N fluctuations. This amplification is more efficient when the initial density profile depends on radius, because particles have a greater spread of fall times compared to a uniform density profile, for which very close to symmetric final states are obtained. These effects lead to a distinctive correlation of the orientation of the final structure with the distribution of ejected mass, and also with the initial (very small) angular fluctuations.

Generation of angular momentum in cold gravitational collapse

“…We report here the results for the range of α with 0 ≤ α ≤ 2. We restrict ourselves to this range since, in a previous study (Sylos Labini 2012;Sylos Labini et al 2015), we observed that for α > 2, there is negligible ( 1%) mass ejection. As shown in the same study, and except for α very close to zero, the evolution leads to virial equilibria that are very non-spherically symmetric and typically triaxial.…”

“…All results presented here are for simulations in which energy is conserved to within one tenth of a percent over the timescale evolved, with maximal deviations at any time of less than half a percent (see Sylos Labini et al 2015, for more details). This accuracy was attained using values of the essential numerical parameters in the Gadget2 code [0.025 for the η parameter, which controls the time-step, and a force accuracy of α F = 0.001] in the range of typically used values for this code.…”

“…Henon 1973;van Albada 1982;Aarseth et al 1988;Theis & Spurzem 1999;Boily et al 2002;Joyce et al 2009;Sylos Labini 2012, 2013aSylos Labini et al 2015), with an emphasis, in particular, on the study of the shape and profile of the virialised structure. Because the system is initially cold, in all cases it undergoes a strong collapse in a time of order 1/ √ Gρ 0 , where ρ 0 is the initial mean density, followed by a re-expansion, which leads rapidly to virialisation of most of the mass.…”

“…Essentially, the amount of mass ejected depends on the degree of violence of the relaxation, which can be quantified roughly by the maximal contraction attained by the system during the collapse phase. The reason for this correlation between the ejection of mass and the violence of collapse is easier to understand when the mechanism for ejection is studied (Joyce et al 2009;Carucci et al 2014;Sylos Labini et al 2015): The ejected particles are essentially those whose fall times to the centre of the structure during collapse are longest. As a consequence, they pass through the centre of the whole structure when it begins to re-expand, which means that they travel into a deeper potential than the one they travel out of.…”

“…Further, given that violent relaxation starting from a wide range of initially cold conditions is often characterised by a very strong breaking of spherical symmetry, leading to triaxial relaxed structures (e.g. Merritt & Aguilar 1985;Barnes et al 2009;Sylos Labini et al 2015) the effect might be far from negligible.…”