Powering Stellar Magnetism: Energy Transfers in Cyclic Dynamos of Sun-like Stars
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Bibliographic record
Abstract
Abstract We use the anelastic spherical harmonic code to model the convective dynamo of solar-type stars. Based on a series of 15 3D MHD simulations spanning four bins in rotation and mass, we show what mechanisms are at work in these stellar dynamos with and without magnetic cycles and how global stellar parameters affect the outcome. We also derive scaling laws for the differential rotation and magnetic field based on these simulations. We find a weaker trend between differential rotation and stellar rotation rate, ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:mi mathvariant="normal">Ω</mml:mi> <mml:mo>∝</mml:mo> <mml:msup> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mo stretchy="false">∣</mml:mo> <mml:mi mathvariant="normal">Ω</mml:mi> <mml:mo stretchy="false">∣</mml:mo> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant="normal">Ω</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⊙</mml:mo> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:mrow> <mml:mn>0.46</mml:mn> </mml:mrow> </mml:msup> </mml:math> ) in the MHD solutions than in their HD counterpart <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mo stretchy="false">∣</mml:mo> <mml:mi mathvariant="normal">Ω</mml:mi> <mml:mo stretchy="false">∣</mml:mo> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant="normal">Ω</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⊙</mml:mo> </mml:mrow> </mml:msub> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mn>0.66</mml:mn> </mml:mrow> </mml:msup> </mml:math> ), yielding a better agreement with the observational trends based on power laws. We find that for a fluid Rossby number between 0.15 ≲ Ro f ≲ 0.65, the solutions possess long magnetic cycle, if Ro f ≲ 0.42 a short cycle and if Ro f ≳ 1 (antisolar-like differential rotation), a statistically steady state. We show that short-cycle dynamos follow the classical Parker–Yoshimura rule whereas the long-cycle period ones do not. We also find efficient energy transfer between reservoirs, leading to the conversion of several percent of the star's luminosity into magnetic energy that could provide enough free energy to sustain intense eruptive behavior at the star’s surface. We further demonstrate that the Rossby number dependency of the large-scale surface magnetic field in the simulation ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>B</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">L</mml:mi> <mml:mo>,</mml:mo> <mml:mi>surf</mml:mi> </mml:mrow> </mml:msub> <mml:mo>∼</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi mathvariant="italic">Ro</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">f</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1.26</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> ) agrees better with observations ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>B</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>V</mml:mi> </mml:mrow> </mml:msub> <mml:mo>∼</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi mathvariant="italic">Ro</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">s</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1.4</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.1</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> ) and differs from dynamo scaling based on the global magnetic energy ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>B</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>bulk</mml:mi> </mml:mrow> </mml:msub> <mml:mo>∼</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi mathvariant="italic">Ro</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">f</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.5</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> ).
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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 | 0.001 |
| 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 it