  The evolution of self-gravitating systems, and long-range interacting systems
more generally, from initial configurations far from dynamical equilibrium is
often described as a simple two phase process: a first phase of violent
relaxation bringing it to a quasi-stationary state in a few dynamical times,
followed by a slow adiabatic evolution driven by collisional processes. In this
context the complex spatial structure evident, e.g., in spiral galaxies is
understood either in terms of instabilities of quasi-stationary states, or a
result of dissipative non-gravitational interactions. We illustrate here, using
numerical simulations, that purely self-gravitating systems evolving from quite
simple initial configurations can in fact give rise easily to structures of
this kind of which the lifetime can be large compared to the dynamical
characteristic time, but short compared to the collisional relaxation time
scale. More specifically, for a broad range of non-spherical and non-uniform
rotating initial conditions, gravitational relaxation gives rise quite
generically to long-lived non-stationary structures of a rich variety,
characterized by spiral-like arms, bars and even ring-like structures in
special cases. These structures are a feature of the intrinsically
out-of-equilibrium nature of the system's collapse, associated with a part of
the system's mass while the bulk is well virialized. They are characterized by
predominantly radial motions in their outermost parts, but also incorporate an
extended flattened region which rotates coherently about a well virialized core
of triaxial shape with an approximately isotropic velocity dispersion. We
discuss the possible relevance of these simple toy models to the observed
structure of real galaxies emphasizing the difference between dissipative and
dissipationless disc formation.
