Hall equilibria with toroidal and poloidal fields: application to neutron stars
Bibliographic record
Abstract
We present solutions for Hall equilibria applicable to neutron star crusts. Such magnetic configurations satisfy a Grad–Shafranov-type equation, which is solved analytically and numerically. The solutions presented cover a variety of configurations, from purely poloidal fields connected to an external dipole to poloidal–toroidal fields connected to an external vacuum field, or fully confined within the star. We find that a dipole external field should be supported by a uniformly rotating electron fluid. The energy of the toroidal magnetic field is generally found to be a few per cent of the total magnetic field energy for the fields with an external component. We discuss the evolution due to Ohmic dissipation which leads to slowing down of the electron fluid. We also find that the transition from an MHD equilibrium to a state governed by Hall effect generates spontaneously an additional toroidal field in regions where the electron fraction changes.
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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 | 0.000 | 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 | 0.000 | 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".