Chaos in violent relaxation dynamics

Aims . Violent relaxation is often regarded as the mechanism that leads stellar systems to collisionless meta equilibrium via rapid changes in the collective potential. Methods . We investigate the role of chaotic instabilities on single particle orbits in leading to nearly invariant phase-space distributions, aiming at disentangling their role from that of the chaos induced by collective oscillations in the self-consistent potential. Results . We explore, as a function of the system’s size (i.e. number of particles N ), the chaoticity in terms of the largest Lyapunov exponent of test trajectories in a simplified model of gravitational cold collapse, mimicking an N -body calculation via a time-dependent smooth potential and a noise-friction process accounting for the discreteness effects. A new numerical method to evaluate effective Lyapunov exponents for stochastic models is presented and tested. Conclusions . We find that the evolution of the phase-space of independent trajectories reproduces rather well what is observed in self-consistent N -body simulations of dissipationless collapses. The chaoticity of test orbits rapidly decreases with N for particles that remain weakly bounded in the model potential, while it decreases with different power laws for more bound orbits, consistently with what was observed in previous self-consistent N -body simulations. The largest Lyapunov exponents of ensembles of orbits starting from initial conditions uniformly sampling the accessible phase-space are somewhat constant for N ≲ 10 9 , while decreases towards the continuum limit with a power-law trend. Moreover, our numerical results appear to confirm the trend of a specific formulation of dynamical entropy and its relation with Lyapunov timescales.