We present numerical hydrodynamical simulations of the formation , evolution and gravitational collapse of isothermal molecular cloud cores induced by turbulent compressions in spherical geometry .
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 central core and the envelope are separated by a mild shock .
The resulting density structure resembles a quiescent core of radius \lesssim 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 , until finally a singularity is formed .
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 , but rather to the time necessary for it to reach its Jeans mass .
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 .
In our collapsing simulations , a time \sim 0.5 Myr typically elapses between the formation of the core and the time at which it becomes gravitationally unstable , and another \sim 0.5 Myr are necessary for it to complete the collapse .