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Initially cold and spherically symmetric self-gravitating systems may giverise to a virial equilibrium state which is far from spherically symmetric, andtypically triaxial. We focus here on how the degree of symmetry breaking in thefinal state depends on the initial density profile. We note that the mostasymmetric structures result when, during the collapse phase, there is a stronginjection of energy preferentially into the particles which are localizedinitially in the outer shells. These particles are still collapsing when theothers, initially located in the inner part, are already re-expanding; themotion of particles in a time varying potential allow them to gain kineticenergy --- in some cases enough to be ejected from the system. We show thatthis mechanism of energy gain amplifies the initial small deviations fromperfect spherical symmetry due to finite $N$ fluctuations. This amplificationis more efficient when the initial density profile depends on radius, becauseparticles have a greater spread of fall times compared to a uniform densityprofile, for which very close to symmetric final states are obtained}. Theseeffects lead to a distinctive correlation of the orientation of the finalstructure with the distribution of ejected mass, and also with the initial(very small) angular fluctuations.

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