  (Abridged) We present numerical hydrodynamical simulations of the formation,
evolution and gravitational collapse of isothermal molecular cloud cores. A
compressive wave is set up in a constant sub-Jeans density distribution of
radius r = 1 pc. As the wave travels through the simulation grid, a
shock-bounded spherical shell is formed. The inner shock of this shell reaches
and bounces off the center, leaving behind a central core with an initially
almost uniform density distribution, surrounded by an envelope consisting of
the material in the shock-bounded shell, with a power-law density profile that
at late times approaches a logarithmic slope of -2 even in non-collapsing
cases. The resulting density structure resembles a quiescent core of radius <
0.1 pc, with a Bonnor-Ebert-like (BE-like) profile, although it has significant
dynamical differences: it is initially non-self-gravitating and confined by the
ram pressure of the infalling material, and consequently, growing continuously
in mass and size. With the appropriate parameters, the core mass eventually
reaches an effective Jeans mass, at which time the core begins to collapse.
Thus, there is necessarily a time delay between the appearance of the core and
the onset of its collapse, but this is not due to the dissipation of its
internal turbulence as it is often believed. These results suggest that
pre-stellar cores may approximate Bonnor-Ebert structures which are however of
variable mass and may or may not experience gravitational collapse, in
qualitative agreement with the large observed frequency of cores with BE-like
profiles.
