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 re-expanding; 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.
An isolated, initially cold and ellipsoidal cloud of self-gravitating particles represents a relatively simple system in which to study the effects of deviations from spherical symmetry in the mechanism of violent relaxation. Initial deviations from spherical symmetry are shown to play a dynamical role that is equivalent to that of density fluctuations in the case of an initially spherical cloud. Indeed, these deviations control the amount of particle-energy change and thus determine the properties of the final energy distribution, particularly the appearance of two species of particles: bound and free. Ejection of mass and energy from the system, together with the formation of a density profile decaying as ρ(r) ∼ r−4 and a Keplerian radial velocity dispersion profile, are prominent features similar to those observed after the violent relaxation of spherical clouds. In addition, we find that ejected particles are characterized by highly non-spherical shapes, the features of which can be traced in the initial deviations from spherical symmetry that are amplified during the dynamical evolution: particles can indeed form anisotropic configurations, like bars and/or discs, even though the initial cloud was very close to spherical.