  We investigate, through a series of numerical calculations, the evolution of
dense cores that are accreting external gas up to and beyond the point of star
formation. Our model clouds are spherical, unmagnetized configurations with
fixed outer boundaries, across which gas enters subsonically. When we start
with any near-equilibrium state, we find that the cloud's internal velocity
also remains subsonic for an extended period, in agreement with observations.
However, the velocity becomes supersonic shortly before the star forms.
Consequently, the accretion rate building up the protostar is much greater than
the benchmark value c_s^3/G, where c_s is the sound speed in the dense core.
This accretion spike would generate a higher luminosity than those seen in even
the most embedded young stars. Moreover, we find that the region of supersonic
infall surrounding the protostar races out to engulf much of the cloud, again
in violation of the observations, which show infall to be spatially confined.
Similar problematic results have been obtained by all other hydrodynamic
simulations to date, regardless of the specific infall geometry or boundary
conditions adopted. Low-mass star formation is evidently a quasi-static
process, in which cloud gas moves inward subsonically until the birth of the
star itself. We speculate that magnetic tension in the cloud's deep interior
helps restrain the infall prior to this event.
