The effect of a finite mass reservoir on the collapse of spherical isothermal clouds and the evolution of protostellar accretion
Bibliographic record
Abstract
Motivated by recent observations which detect an outer boundary for starless cores, and evidence for time-dependent mass accretion in the Class 0 and Class I protostellar phases, we reexamine the case of spherical isothermal collapse in the case of a finite mass reservoir. The presence of a core boundary results in the generation of an inward propagating rarefaction wave. This steepens the gas density profile from r^{-2} to r^{-3} or steeper. After a protostar forms, the mass accretion rate \\dot{M} evolves through three distinct phases: (1) an early phase of decline in \\dot{M}, which is a non-self-similar effect due to spatially nonuniform infall in the prestellar phase; (2) for large cores, an intermediate phase of near-constant \\dot{M} from the infall of the outer part of the self-similar density profile; (3) a late phase of rapid decline in \\dot{M} when accretion occurs from the region affected by the inward propagating rarefaction wave. Our model clouds of small to intermediate size make a direct transition from phase (1) to phase (3) above. Both the first and second phase are characterized by a temporally increasing bolometric luminosity L_bol, while L_bol is decreasing in the third (final) phase. We identify the period of temporally increasing L_bol with the Class 0 phase, and the later period of terminal accretion and decreasing L_bol with the Class I phase. The peak in L_bol corresponds to the evolutionary time when 50% \\pm 10% of the cloud mass has been accreted by the protostar. This is in agreement with the classification scheme proposed by Andre et al. (1993). We show how our results can be used to explain tracks of envelope mass M_env versus L_bol for protostars in Taurus and Ophiuchus. We also develop an analytic formalism which reproduces the protostellar accretion rate.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".