Protostellar Collapse Induced by Compression
  We present numerical simulations of the evolution of low-mass, isothermal, molecular cores which are subjected to an increase in external pressure $P\xt$. If $P\xt$ increases very slowly, the core approaches instability quite quasistatically. However, for larger (but still quite modest) $dP\xt/dt$ a compression wave is driven into the core, thereby triggering collapse from the outside in. If collapse of a core is induced by increasing $P\xt$, this has a number of interesting consequences. (i) The density profile is approximately flat in the centre during the prestellar phase (i.e. before the compression wave converges on the centre creating the central protostar). (ii) During the prestellar phase there are (subsonic) inward velocities in the outer layers of the core, whilst the inner parts are still approximately at rest. (iii) There is an initial short phase of rapid accretion (notionally the Class 0 phase), followed by a longer phase of slower accretion (the Class I phase). All these features accord well with observation, but are at variance with the predictions of the standard theory of star formation based on the inside-out collapse of a singular isothermal sphere. We note that the setting up of a coherent inward velocity field appears to be a generic feature of compression waves; and we speculate that interactions and interference between such velocity fields may play a crucial r\^ole in initiating the fragmentation of cores and the genesis of multiple star systems. 
P. Hennebelle, A. P. Whitworth, P. P. Gladwin, Ph. Andre