Astron. Astrophys. 323, 549-565 (1997)

Time-dependent accretion and ejection implied by pre-stellar density profiles

R. Henriksen ^{1, 2}, P. André ^{* 1} and S. Bontemps <sup>1, 3

1</sup> CEA, DSM, DAPNIA, Service d'Astrophysique, C.E. Saclay, F-91191 Gif-sur-Yvette Cedex, France
² Department of Physics, Queen's University at Kingston, Ontario, Canada
³ Stockholm Observatory, S-133 36 Saltsjöbaden, Sweden

Received 5 August 1996 / Accepted 2 January 1997

Abstract

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 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 (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 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 Oph cluster may be effectively in their terminal accretion phase.

Key words: stars: formation circumstellar matter Interstellar medium: clouds ISM: jets and outflows stars: pre-main sequence

* (andre@sapvxg.saclay.cea.fr)

Send offprint requests to: P. André

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Contents

• 1. Introduction
• 2. Relevant observations
  • 2.1. Constraints on initial conditions: flattened pre-stellar density profiles
  • 2.2. Decline of outflow power with time
• 3. Relevant theory
  • 3.1. Overview of known spherical collapse solutions
  • 3.2. Justification of our pressure-free analytical approach
    • 3.2.1. Neglect of magnetic field and rotation
    • 3.2.2. Lagrangian treatment of isothermal self-similarity
    • 3.2.3. The case for starting from strictly flat inner density profiles
  • 3.3. Accretion phase history
    • 3.3.1. General formulation
    • 3.3.2. Two-component power-law model
• 4. Discussion: implications for protostellar evolution
  • 4.1. Predicted versus observed accretion histories
  • 4.2. Accretion luminosities of Class 0 and Class I sources
  • 4.3. Differences between Ophiuchi and Taurus
• 5. Summary and conclusions
• Acknowledgements
• Appendix A
• Appendix A: Lagrangian collapse and self-similarity
• Appendix B: asymptotic value of the accretion rate
• References

© European Southern Observatory (ESO) 1997

Online publication: June 5, 1998

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