The Transition from a Lognormal to a Power-law Column Density Distribution in Molecular Clouds: An Imprint of the Initial Magnetic Field and Turbulence
Bibliographic record
Abstract
Abstract We introduce a theory for the development of a transitional column density ΣTP between the lognormal and the power-law forms of the probability distribution function in a molecular cloud. Our turbulent magnetohydrodynamic simulations show that the value of ΣTP increases as the strength of both the initial magnetic field and turbulence increases. We develop an analytic expression for ΣTP based on the interplay of turbulence, a (strong) magnetic field, and gravity. The transition value ΣTP scales with , the square of the initial sonic Mach number, and β 0, the initial ratio of gas pressure to magnetic pressure. We fit the variation of ΣTP among different model clouds as a function of or, equivalently, the square of the initial Alfvénic Mach number . This implies that the transition value ΣTP is an imprint of cloud initial conditions and is set by turbulent compression of a magnetic cloud. Physically, the value of ΣTP denotes the boundary above which the mass-to-flux ratio becomes supercritical and gravity drives the evolution.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 source (direct Gemma or distilled Codex), 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".