A recent homogeneous study of outflow activity in low-mass embedded young stellar objects ( YSOs ) ( Bontemps et al .
1996 ) suggests that mass ejection and mass accretion both decline significantly with time during protostellar evolution .
In the present paper , we propose that this rapid decay of accretion/ejection activity is a direct result of the non-singular density profiles characterizing pre-collapse clouds .
Submillimeter dust continuum mapping indicates that the radial profiles of pre-stellar cores flatten out near their centers , being much flatter than \rho ( r ) \propto r ^ { -2 } at radii less than a few thousand AU ( Ward-Thompson et al .
1994 ) .
In some cases , sharp edges are observed at a finite core radius .
Here we show , through Lagrangian analytical calculations , that the supersonic gravitational collapse of pre-stellar cloud cores with such centrally peaked , but flattened density profiles leads to a transitory phase of energetic accretion immediately following the formation of the central hydrostatic protostar .
Physically , the collapse occurs in various stages .
The first stage corresponds to the nearly isothermal , dynamical collapse of the pre-stellar flat inner region , which ends with the formation of a finite-mass stellar nucleus .
This phase is essentially non-existent in the ‘ standard ’ singular model developed by Shu and co-workers .
In a second stage , the remaining cloud core material accretes supersonically onto a non-zero point mass .
Because of the significant infall velocity field achieved during the first collapse stage , the accretion rate is initially higher than in the Shu model .
This enhanced accretion persists as long as the gravitational pull of the initial point mass remains significant .
The accretion rate then quickly converges towards the characteristic value \sim a ^ { 3 } / G ( where a is the sound speed ) , which is also the constant rate found by Shu ( 1977 ) .
If the model pre-stellar core has a finite outer boundary , there is a terminal decline of the accretion rate at late times due to the finite reservoir of mass . We suggest that the initial epoch of vigorous accretion predicted by our non-singular model coincides with Class 0 protostars , which would explain their unusually powerful jets compared to the more evolved Class I YSOs .
We use a simple two-component power-law model to fit the diagrams of outflow power versus envelope mass observed by Bontemps et al .
( 1996 ) , and suggest that Taurus and \rho Ophiuchi YSOs follow different accretion histories because of differing initial conditions .
While the isolated Class I sources of Taurus are relatively well explained by the standard Shu model , most of the Class I objects of the \rho Oph cluster may be effectively in their terminal accretion phase .