TIME-DEPENDENT ACCRETION AND EJECTION IMPLIED BY PRE-STELLAR DENSITY PROFILES

A recent homogeneous study of outflow activity in low-mass embedded yo ung stellar objects (YSOs) (Bontemps et al. 1996) suggests that mass e jection nod mass accretion both decline significantly with time during protostellar evolution. In the present paper, we propose that this ra pid decay of accretion/ejection activity is a direct result of the non -singular density profiles characterizing pre-collapse clouds. Submill imeter dust continuum mapping indicates that the radial profiles of pr e-stellar cores flatten out near their centers, being much flatter tha n rho(r) proportional to r(-2) at radii less than a few thousand AU (W ard-Thompson et al. 1994). In some cases, sharp edges are observed at a finite core radius. Here we show, through Lagrangian analytical calc ulations, that the supersonic gravitational collapse of pre-stellar cl oud cores with such centrally peaked, but flattened density profiles l eads to a transitory phase of energetic accretion immediately followin g 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 re gion, which ends with the formation of a finite-mass stellar nucleus. This phase is essentially non-existent in the 'standard' singular mode l developed by Shu and co-workers. In a second stage, the remaining cl oud core material accretes supersonically onto a non-zero point mass. Because of the significant infall velocity field achieved during the f irst collapse stage, the accretion rate is initially higher than in th e Shu model. This enhanced accretion persists as long as the gravitati onal pull of the initial point mass remains significant. The accretion rate then quickly converges towards the characteristic value similar to a(3)/G (where a is the sound speed), which is also the constant rat e found by Shu (1977). If the model pre-stellar core has a finite oute r 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 coinc ides with Class 0 protostars, which would explain their unusually powe rful jets compared to the more evolved Class I YSOs. We use a simple t wo-component power-law model to fit the diagrams of outflow power vers us envelope mass observed by Bontemps et al. (1996), and suggest that Taurus and rho Ophiuchi YSOs follow different accretion histories beca use of differing initial conditions. While the isolated Class I source s of Taurus are relatively well explained by the standard Shu model, m ost of the Class I objects of the rho Oph cluster may be effectively i n their terminal accretion phase.