Phase-space structure analysis of self-gravitating collisionless
  spherical systems
  In the mean field limit, isolated gravitational systems often evolve towards
a steady state through a violent relaxation phase. One question is to
understand the nature of this relaxation phase, in particular the role of
radial instabilities in the establishment/destruction of the steady profile.
Here, through a detailed phase-space analysis based both on a spherical Vlasov
solver, a shell code and a $N$-body code, we revisit the evolution of
collisionless self-gravitating spherical systems with initial power-law density
profiles $\rho(r) \propto r^n$, $0 \leq n \leq -1.5$, and Gaussian velocity
dispersion. Two sub-classes of models are considered, with initial virial
ratios $\eta=0.5$ ("warm") and $\eta=0.1$ ("cool"). Thanks to the numerical
techniques used and the high resolution of the simulations, our numerical
analyses are able, for the first time, to show the clear separation between two
or three well known dynamical phases: (i) the establishment of a spherical
quasi-steady state through a violent relaxation phase during which the
phase-space density displays a smooth spiral structure presenting a morphology
consistent with predictions from self-similar dynamics, (ii) a quasi-steady
state phase during which radial instabilities can take place at small scales
and destroy the spiral structure but do not change quantitatively the
properties of the phase-space distribution at the coarse grained level and
(iii) relaxation to non spherical state due to radial orbit instabilities for
$n \leq -1$ in the cool case.
