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arxiv: 2605.18151 · v1 · pith:3X26KW6Jnew · submitted 2026-05-18 · 🌌 astro-ph.SR

Testing the reliability of magnetic field strength measurements for M dwarfs

I. Amateis , O. Kochukhov , A. Hahlin This is my paper

Pith reviewed 2026-05-20 00:40 UTC · model grok-4.3

classification 🌌 astro-ph.SR
keywords M dwarfsmagnetic fieldsZeeman broadeningsynthetic spectramodel selectionTi I linesstellar atmospheres
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The pith

Zeeman broadening recovers magnetic fields in M dwarfs but its accuracy hinges on choices of statistical criteria and line strength treatment.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper generates synthetic Stokes I spectra of Ti I lines from three-dimensional magnetohydrodynamic simulations paired with MARCS atmospheres to test how well Zeeman broadening diagnostics recover known magnetic field strengths. Different combinations of surface field, rotation speed, and viewing angle are examined using polarised radiative transfer and Markov chain Monte Carlo fitting. The authors compare information criteria for deciding the number of magnetic components and contrast two ways of handling line strengths. In most models the criteria agree, but in active fast rotators BIC and AIC tend to pick fewer components and return lower fields, while WAIC stays closer to the input values. Treating each line strength as an independent free parameter underestimates the field by 30 to 50 percent, whereas a single joint abundance plus continuum scaling recovers the input field more faithfully.

Core claim

Synthetic tests demonstrate that Zeeman broadening diagnostics can recover the input magnetic field strengths in M dwarfs when the number of filling factors is chosen with WAIC or when line strengths are handled through a joint element abundance and continuum scaling; BIC and AIC sometimes select too few components in active rapid rotators and thereby underestimate the field, while free line strengths produce systematic underestimates of 30-50 percent.

What carries the argument

Synthetic Stokes I spectra of Ti I lines generated from 3D magnetohydrodynamic simulations combined with MARCS atmospheres, analysed with polarised radiative transfer and MCMC inference to compare model-selection criteria and line-strength treatments.

If this is right

  • WAIC yields field estimates closer to the true values than BIC or AIC for active, rapidly rotating M dwarfs.
  • Fitting a joint element abundance together with continuum scaling recovers the input field strength reliably, whereas treating individual line strengths as free parameters underestimates it by 30-50 percent.
  • In most cases BIC, AIC and WAIC select the same number of magnetic components, but the choice matters for rapidly rotating active stars.
  • The overall reliability of Zeeman broadening holds across a range of field strengths, rotational velocities and inclination angles when the better-performing methodological options are used.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Earlier measurements that treated line strengths independently may have systematically underestimated magnetic fields in active M dwarfs.
  • Observers could improve consistency by reporting results from both WAIC and BIC/AIC and by adopting joint-abundance fitting as a default.
  • The same synthetic-test framework can be extended to other spectral lines or to time-series data to check whether the same methodological sensitivities appear.

Load-bearing premise

The three-dimensional magnetohydrodynamic simulations combined with MARCS atmospheres produce sufficiently realistic temperature structures and Ti I line formation to stand in for real M dwarf photospheres.

What would settle it

Apply the same analysis pipeline to real high-resolution optical spectra of well-studied M dwarfs whose fields have been measured independently with infrared lines or Zeeman Doppler imaging and check whether the recovered values match within the stated uncertainties.

Figures

Figures reproduced from arXiv: 2605.18151 by A. Hahlin, I. Amateis, O. Kochukhov.

Figure 1
Figure 1. Figure 1: MHD magnetic field structure from Yadav et al. (2015) employed in our study. The four panels display rectangular maps of the radial, meridional, and azimuthal field components as well as the field modulus. Colour bars span the range encompassing 95% of the data values [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Comparison between simulated input spectra (black histograms) and model spectra corresponding to median parameters [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Inferred values of the hemispheric average magnetic field [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Results of the inference with the number of magnetic field components minimised by BIC (red circles), AIC (blue squares), [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Inferred values of the hemispheric average magnetic field [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Inferred distributions of magnetic filling factors (red symbols with error bars) and corresponding input probability distribution [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Difference, averaged over the rotation phases, between the hemispheric-surface-average inferred magnetic field and the input field as a function of the inferred projected rotational ve￾locity for the input cases s = 0.5, ve sin i = 1, 3, 5 km s−1 , i = 45◦ . The green squares are the result of the inference with continuum scaling factors as free parameters. The red circles are the results of the inference … view at source ↗
read the original abstract

M dwarfs host strong magnetic fields that can be measured using several complementary techniques. However, the impact of key methodological choices on Zeeman broadening diagnostics has not been systematically quantified. We assess the reliability of different approaches for inferring magnetic fields in M dwarfs using synthetic Stokes $I$ spectra of Ti I lines generated from three-dimensional magnetohydrodynamic simulations combined with MARCS model atmospheres. Synthetic observations were produced for different surface magnetic field strengths, projected rotational velocities, and inclination angles. Zeeman broadening and intensification were analysed using polarised radiative transfer calculations coupled with Markov chain Monte Carlo inference. We evaluated several statistical criteria (BIC, AIC, and WAIC) for selecting the number of magnetic filling factors and compared alternative strategies for treating line strengths. In most cases, BIC, AIC, and WAIC favoured the same number of components. For some active and rapidly rotating models, BIC and AIC selected fewer components and yielded lower field estimates, while WAIC generally produced closer agreement with the input field strengths. Treating individual line strengths as free parameters underestimated the field strength by 30--50%, whereas fitting a joint element abundance together with continuum scaling recovered the input field more reliably. Our results show that Zeeman broadening diagnostics can robustly recover magnetic fields in M dwarfs, but their accuracy depends strongly on methodological choices.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript tests the reliability of Zeeman broadening diagnostics for inferring magnetic field strengths in M dwarfs. It generates synthetic Stokes I spectra of Ti I lines from 3D magnetohydrodynamic simulations combined with MARCS model atmospheres for varying field strengths, v sin i, and inclinations, then recovers the input fields via polarised radiative transfer and MCMC inference. The study compares model-selection criteria (BIC, AIC, WAIC) for choosing the number of magnetic filling factors and evaluates two line-strength treatments (individual free parameters versus joint element abundance plus continuum scaling).

Significance. If the results hold, the work provides a controlled, quantitative assessment of how methodological choices affect field recovery accuracy on synthetic data with known inputs. Strengths include direct recovery tests against prescribed field strengths and the demonstration that WAIC tends to yield closer agreement with inputs than BIC/AIC while joint-abundance fitting avoids the 30-50% underestimation seen with per-line strengths. This supplies practical guidance for observers even if the absolute applicability to real M dwarfs requires further checks.

major comments (2)
  1. [Abstract and §4] Abstract and §4 (results on model selection): the central claim that 'Zeeman broadening diagnostics can robustly recover magnetic fields in M dwarfs' is load-bearing for the paper's title and conclusions, yet it rests on the untested assumption that the 3D MHD + MARCS forward model reproduces real Ti I line formation and field distributions; no section compares synthetic profiles or recovered quantities to observed high-resolution M dwarf spectra or alternative forward models (e.g., non-LTE or different MHD codes).
  2. [Methods] Methods section describing synthetic spectrum generation: the choice of MARCS atmospheres plus the specific 3D MHD snapshots is invoked to generate the test data, but the manuscript provides no sensitivity tests to variations in temperature structure, magnetic topology, or line-formation physics that would quantify how robust the reported methodological differences are to those modeling assumptions.
minor comments (2)
  1. Figure captions and axis labels should explicitly state which statistical criterion and line-strength treatment each panel or curve corresponds to, to facilitate direct comparison of the recovery biases reported in the text.
  2. [Abstract] The abstract states 'in most cases' BIC/AIC/WAIC agree; adding the exact fraction of models or the specific conditions (e.g., active vs. quiet, slow vs. rapid rotators) would improve precision.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive report. Our study is a controlled test of methodological choices on synthetic spectra with known inputs; we address the comments by clarifying scope and adding caveats rather than expanding the computational scope of the present work.

read point-by-point responses

  1. Referee: [Abstract and §4] Abstract and §4 (results on model selection): the central claim that 'Zeeman broadening diagnostics can robustly recover magnetic fields in M dwarfs' is load-bearing for the paper's title and conclusions, yet it rests on the untested assumption that the 3D MHD + MARCS forward model reproduces real Ti I line formation and field distributions; no section compares synthetic profiles or recovered quantities to observed high-resolution M dwarf spectra or alternative forward models (e.g., non-LTE or different MHD codes).

    Authors: We agree that the phrasing in the abstract and §4 could be read as implying direct applicability to real data. The manuscript tests recovery accuracy under the specific assumptions of the 3D MHD snapshots and MARCS atmospheres; it does not claim the forward model exactly reproduces nature. We will revise the abstract and the final paragraph of §4 to state explicitly that the diagnostics recover the prescribed fields reliably within these modeling assumptions, and we will add a short discussion of the need for future validation against observed spectra and alternative forward models. revision: yes

  2. Referee: [Methods] Methods section describing synthetic spectrum generation: the choice of MARCS atmospheres plus the specific 3D MHD snapshots is invoked to generate the test data, but the manuscript provides no sensitivity tests to variations in temperature structure, magnetic topology, or line-formation physics that would quantify how robust the reported methodological differences are to those modeling assumptions.

    Authors: We accept that explicit sensitivity tests would be desirable. Generating additional MHD snapshots with varied temperature structures or topologies and repeating the full radiative-transfer and MCMC analysis is computationally prohibitive within the scope of this study. We will instead expand the methods and discussion sections to justify the adopted model choices, provide a qualitative assessment of how plausible variations could affect the relative performance of the tested methods, and flag full sensitivity experiments as future work. revision: partial

Circularity Check

0 steps flagged

No significant circularity; validation uses independent synthetic benchmarks

full rationale

The paper generates synthetic Stokes I spectra from 3D MHD simulations with independently prescribed magnetic field strengths, rotational velocities, and inclinations, then tests recovery via MCMC fitting of Zeeman broadening under varying statistical criteria and line-strength treatments. This is a standard forward-model validation against external truth values set by the simulation inputs rather than any fitted quantity or self-referential loop. No equation or claim reduces the recovered field strengths to the fitting procedure by construction, and no load-bearing step relies on self-citation chains or ansatzes imported from prior author work. The derivation chain remains self-contained against the stated synthetic benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The reliability assessment rests on standard stellar atmosphere modeling assumptions and the fidelity of radiative transfer for Zeeman effects, with no new entities postulated.

free parameters (2)
  • number of magnetic filling factors
    Selected via BIC, AIC, or WAIC during MCMC inference on synthetic spectra
  • line strength treatment
    Alternative strategies tested: individual free parameters versus joint abundance plus continuum scaling
axioms (2)
  • domain assumption MARCS model atmospheres combined with 3D MHD simulations accurately capture M dwarf photospheric conditions and Ti I line formation
    Used to generate synthetic observations with prescribed magnetic fields for recovery tests
  • standard math Polarized radiative transfer correctly models Zeeman broadening and intensification in the chosen lines
    Foundation for the inference procedure applied to synthetic data

pith-pipeline@v0.9.0 · 5767 in / 1521 out tokens · 74866 ms · 2026-05-20T00:40:21.495937+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

100 extracted references · 100 canonical work pages · 21 internal anchors

  1. [1]

    , keywords =

    Comparative study of small-scale magnetic fields on Boo A using optical and near-infrared spectroscopy. , keywords =. doi:10.1051/0004-6361/202453016 , archivePrefix =. 2503.04519 , primaryClass =

    work page doi:10.1051/0004-6361/202453016

  2. [2]

    , keywords =

    Multi-scale magnetic field investigation of the M-dwarf eclipsing binary CU Cancri. , keywords =. doi:10.1051/0004-6361/202348750 , archivePrefix =. 2402.00721 , primaryClass =

    work page doi:10.1051/0004-6361/202348750

  3. [3]

    Physics of Magnetic Stars , date-added =

    work page

  4. [4]

    doi:10.1086/519017 , eprint =

    , keywords =. doi:10.1086/519017 , eprint =

    work page doi:10.1086/519017

  5. [5]

    arXiv , author =:1401.5250 , journal =

    work page internal anchor Pith review Pith/arXiv arXiv

  6. [6]

    Magnetic Field of the Eclipsing M Dwarf Binary YY Gem

    doi:10.3847/1538-4357/ab06c5 , eid =. arXiv , author =:1902.04157 , journal =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-4357/ab06c5 1902

  7. [7]

    doi:10.1093/mnras/stad3144 , eprint =

    , keywords =. doi:10.1093/mnras/stad3144 , eprint =

    work page doi:10.1093/mnras/stad3144

  8. [8]

    Magnetic Inhibition of Convection and the Fundamental Properties of Low-Mass Stars. II. Fully Convective Main Sequence Stars

    doi:10.1088/0004-637X/789/1/53 , eid =. arXiv , author =:1405.1767 , journal =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/789/1/53

  9. [9]

    doi:10.1038/s41550-017-0284-0 , eprint =

    Nature Astronomy , keywords =. doi:10.1038/s41550-017-0284-0 , eprint =

    work page doi:10.1038/s41550-017-0284-0

  10. [10]

    , keywords =

    Why Observations at Mid-infrared Wavelengths Partially Mitigate M Dwarf Star Host Stellar Activity Contamination in Exoplanet Transmission Spectroscopy. , keywords =. doi:10.3847/1538-4357/ad509a , adsurl =

    work page doi:10.3847/1538-4357/ad509a

  11. [11]

    arXiv , author =:2202.07949 , journal =

    doi:10.3847/1538-4357/ac54b8 , eid =. arXiv , author =:2202.07949 , journal =

    work page doi:10.3847/1538-4357/ac54b8

  12. [12]

    Effects of M dwarf magnetic fields on potentially habitable planets

    doi:10.1051/0004-6361/201321504 , eid =. arXiv , author =:1306.4789 , journal =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201321504

  13. [13]

    doi:10.1093/mnras/stt2265 , eprint =

    , keywords =. doi:10.1093/mnras/stt2265 , eprint =

    work page doi:10.1093/mnras/stt2265

  14. [14]

    , keywords =

    The CARMENES search for exoplanets around M dwarfs: The impact of rotation and magnetic fields on the radial velocity jitter in cool stars. , keywords =. doi:10.1051/0004-6361/202450836 , archivePrefix =. 2412.07691 , primaryClass =

    work page doi:10.1051/0004-6361/202450836

  15. [15]

    Long-term magnetic activity of a sample of M-dwarf stars from the HARPS program . II. Activity and radial velocity. , keywords =. doi:10.1051/0004-6361/201118598 , archivePrefix =. 1202.1564 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201118598

  16. [16]

    M., & Grevesse, N

    doi:10.1051/0004-6361/202140445 , eid =. arXiv , author =:2105.01661 , journal =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/202140445

  17. [17]

    Intrinsic Colors, Temperatures, and Bolometric Corrections of Pre-Main Sequence Stars

    doi:10.1088/0067-0049/208/1/9 , eid =. arXiv , author =:1307.2657 , journal =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0067-0049/208/1/9

  18. [18]

    Magnetic fields in M dwarfs from the CARMENES survey

    2019 , bdsk-url-1 =. doi:10.1051/0004-6361/201935315 , eid =. arXiv , author =:1904.12762 , journal =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201935315 2019

  19. [19]

    , keywords =

    , keywords =. doi:10.1111/j.1365-2966.2010.17101.x , eprint =

    work page doi:10.1111/j.1365-2966.2010.17101.x 2010

  20. [20]

    J., & Gao, L

    , keywords =. doi:10.1111/j.1365-2966.2008.13809.x , eprint =

    work page doi:10.1111/j.1365-2966.2008.13809.x 2008

  21. [21]

    J., & Gao, L

    , keywords =. doi:10.1111/j.1365-2966.2008.13799.x , eprint =

    work page doi:10.1111/j.1365-2966.2008.13799.x 2008

  22. [22]

    doi:10.1051/0004-6361/200913149 , eprint =

    , keywords =. doi:10.1051/0004-6361/200913149 , eprint =

    work page doi:10.1051/0004-6361/200913149

  23. [23]

    doi:10.1088/0031-8949/90/5/054005 , eid =

    , month = may, number = 5, pages =. doi:10.1088/0031-8949/90/5/054005 , eid =

    work page doi:10.1088/0031-8949/90/5/054005

  24. [24]

    doi:10.12942/lrsp-2005-8 , eid =

    Living Reviews in Solar Physics , keywords =. doi:10.12942/lrsp-2005-8 , eid =

    work page doi:10.12942/lrsp-2005-8 2005

  25. [25]

    Three-dimensional simulations of near-surface convection in main-sequence stars. III. The structure of small-scale magnetic flux concentrations

    doi:10.1051/0004-6361/201525788 , eid =. arXiv , author =:1505.04739 , journal =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201525788

  26. [26]

    doi:10.1086/498634 , eprint =

    , keywords =. doi:10.1086/498634 , eprint =

    work page doi:10.1086/498634

  27. [27]

    doi:10.1086/527432 , eprint =

    , keywords =. doi:10.1086/527432 , eprint =

    work page doi:10.1086/527432

  28. [28]

    arXiv , author =:2012.01259 , journal =

    doi:10.1051/0004-6361/202040049 , eid =. arXiv , author =:2012.01259 , journal =

    work page doi:10.1051/0004-6361/202040049 2012

  29. [29]

    arXiv , author =:2305.16447 , journal =

    doi:10.1051/0004-6361/202244666 , eid =. arXiv , author =:2305.16447 , journal =

    work page doi:10.1051/0004-6361/202244666

  30. [30]

    arXiv , author =:2204.00342 , journal =

    doi:10.1051/0004-6361/202243251 , eid =. arXiv , author =:2204.00342 , journal =

    work page doi:10.1051/0004-6361/202243251

  31. [31]

    Explaining the coexistence of large-scale and small-scale magnetic fields in fully convective stars

    doi:10.1088/2041-8205/813/2/L31 , eid =. arXiv , author =:1510.05541 , journal =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/2041-8205/813/2/l31 2041

  32. [32]

    , keywords =

    Magnetic fields of M dwarfs. , keywords =. doi:10.1007/s00159-020-00130-3 , archivePrefix =. 2011.01781 , primaryClass =

    work page doi:10.1007/s00159-020-00130-3 2011

  33. [33]

    The global and small-scale magnetic fields of fully convective, rapidly spinning M dwarf pair GJ65A and B

    The Global and Small-scale Magnetic Fields of Fully Convective, Rapidly Spinning M Dwarf Pair GJ65 A and B. , keywords =. doi:10.3847/2041-8213/835/1/L4 , archivePrefix =. 1702.02946 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/2041-8213/835/1/l4 2041

  34. [34]

    Strong dipole magnetic fields in fast rotating fully convective stars

    Strong dipole magnetic fields in fast rotating fully convective stars. Nature Astronomy , keywords =. doi:10.1038/s41550-017-0184 , archivePrefix =. 1801.08571 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1038/s41550-017-0184

  35. [35]

    A grid of MARCS model atmospheres for late-type stars. I. Methods and general properties. , keywords =. doi:10.1051/0004-6361:200809724 , archivePrefix =. 0805.0554 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361:200809724

  36. [36]

    Least squares deconvolution of the stellar intensity and polarization spectra

    Least-squares deconvolution of the stellar intensity and polarization spectra. , keywords =. doi:10.1051/0004-6361/201015429 , archivePrefix =. 1008.5115 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201015429

  37. [37]

    , keywords =

    Small-scale magnetic fields of the spectroscopic binary T Tauri stars V1878 Ori and V4046 Sgr. , keywords =. doi:10.1051/0004-6361/202142425 , archivePrefix =. 2201.04978 , primaryClass =

    work page doi:10.1051/0004-6361/202142425

  38. [38]

    , keywords =

    Solar Bayesian Analysis Toolkit A New Markov Chain Monte Carlo IDL Code for Bayesian Parameter Inference. , keywords =. doi:10.3847/1538-4365/abc5c1 , archivePrefix =. 2005.05365 , primaryClass =

    work page doi:10.3847/1538-4365/abc5c1 2005

  39. [39]

    Markov Chain Monte Carlo Methods for Bayesian Data Analysis in Astronomy

    Markov Chain Monte Carlo Methods for Bayesian Data Analysis in Astronomy. , keywords =. doi:10.1146/annurev-astro-082214-122339 , archivePrefix =. 1706.01629 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1146/annurev-astro-082214-122339

  40. [40]

    Magnetic fields of non-degenerate stars

    Magnetic Fields of Nondegenerate Stars. , keywords =. doi:10.1146/annurev-astro-082708-101833 , archivePrefix =. 0904.1938 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1146/annurev-astro-082708-101833 1938

  41. [41]

    Structure and evolution of low-mass stars

    Structure and evolution of low-mass stars. , keywords =. doi:10.48550/arXiv.astro-ph/9704118 , archivePrefix =. astro-ph/9704118 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.astro-ph/9704118

  42. [42]

    , year = 2014, month = aug, volume =

    Solar Dynamo Theory. , year = 2014, month = aug, volume =. doi:10.1146/annurev-astro-081913-040012 , adsurl =

    work page doi:10.1146/annurev-astro-081913-040012 2014

  43. [43]

    , keywords =

    On the Generation of the Largescale and Turbulent Magnetic Fields in the Solar Type Stars. , keywords =. doi:10.1007/BF00690652 , adsurl =

    work page doi:10.1007/bf00690652

  44. [44]

    Masses and Radii of Low-Mass Stars: Theory versus Observations

    Masses and Radii of Low-Mass Stars: Theory Versus Observations. , keywords =. doi:10.1007/s10509-006-9081-4 , archivePrefix =. astro-ph/0511431 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/s10509-006-9081-4

  45. [45]

    On the Correlation between the Magnetic Activity Levels, the Metallicities and the Radii of Low-Mass Stars

    On the Correlation between the Magnetic Activity Levels, Metallicities, and Radii of Low-Mass Stars. , keywords =. doi:10.1086/513142 , archivePrefix =. astro-ph/0701702 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/513142

  46. [46]

    Observations of Cool-Star Magnetic Fields

    Observations of Cool-Star Magnetic Fields. Living Reviews in Solar Physics , keywords =. doi:10.12942/lrsp-2012-1 , archivePrefix =. 1203.0241 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.12942/lrsp-2012-1 2012

  47. [47]

    Estimating magnetic filling factors from Zeeman-Doppler magnetograms

    Estimating Magnetic Filling Factors from Zeeman-Doppler Magnetograms. , keywords =. doi:10.3847/1538-4357/ab1096 , archivePrefix =. 1903.05595 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-4357/ab1096 1903

  48. [48]

    , keywords =

    Characterising the surface magnetic fields of T Tauri stars with high-resolution near-infrared spectroscopy. , keywords =. doi:10.1051/0004-6361/201935695 , archivePrefix =. 1909.04965 , primaryClass =

    work page doi:10.1051/0004-6361/201935695 1909

  49. [49]

    , keywords =

    Hidden magnetic fields of young suns. , keywords =. doi:10.1051/0004-6361/201937185 , archivePrefix =. 2002.10469 , primaryClass =

    work page doi:10.1051/0004-6361/201937185 2002

  50. [50]

    , keywords =

    Determination of small-scale magnetic fields on Sun-like stars in the near-infrared using CRIRES ^ +. , keywords =. doi:10.1051/0004-6361/202346314 , archivePrefix =. 2305.06873 , primaryClass =

    work page doi:10.1051/0004-6361/202346314

  51. [51]

    , keywords =

    The magnetic field and multiple planets of the young dwarf AU Mic. , keywords =. doi:10.1093/mnras/stad1193 , archivePrefix =. 2304.09642 , primaryClass =

    work page doi:10.1093/mnras/stad1193

  52. [52]

    , keywords =

    Rotational modulation and long-term evolution of the small-scale magnetic fields of M dwarfs observed with SPIRou. , keywords =. doi:10.1051/0004-6361/202554902 , archivePrefix =. 2508.04569 , primaryClass =

    work page doi:10.1051/0004-6361/202554902

  53. [53]

    D., Cohen , O., Drake , J

    Alvarado-G \'o mez , J. D., Cohen , O., Drake , J. J., et al. 2022, , 928, 147

    work page 2022

  54. [54]

    A., Nakariakov , V

    Anfinogentov , S. A., Nakariakov , V. M., Pascoe , D. J., & Goddard , C. R. 2021, , 252, 11

    work page 2021

  55. [55]

    M., & Grevesse , N

    Asplund , M., Amarsi , A. M., & Grevesse , N. 2021, , 653, A141

    work page 2021

  56. [56]

    H., & Reiners , A

    Beeck , B., Sch \"u ssler , M., Cameron , R. H., & Reiners , A. 2015, , 581, A42

    work page 2015

  57. [57]

    Berdyugina , S. V. 2005, Living Reviews in Solar Physics, 2, 8

    work page 2005

  58. [58]

    Browning , M. K. 2008, , 676, 1262

    work page 2008

  59. [59]

    & Baraffe , I

    Chabrier , G. & Baraffe , I. 1997, , 327, 1039

    work page 1997

  60. [60]

    2014, , 52, 251

    Charbonneau , P. 2014, , 52, 251

    work page 2014

  61. [61]

    I., Donati , J

    Cristofari , P. I., Donati , J. F., Moutou , C., et al. 2023, , 526, 5648

    work page 2023

  62. [62]

    2006, , 638, 336

    Dobler , W., Stix , M., & Brandenburg , A. 2006, , 638, 336

    work page 2006

  63. [63]

    Donati , J. F. & Landstreet , J. D. 2009, , 47, 333

    work page 2009

  64. [64]

    F., Morin , J., Petit , P., et al

    Donati , J. F., Morin , J., Petit , P., et al. 2008, , 390, 545

    work page 2008

  65. [65]

    R., De Young , D

    Durney , B. R., De Young , D. S., & Roxburgh , I. W. 1993, , 145, 207

    work page 1993

  66. [66]

    Feiden , G. A. & Chaboyer , B. 2014, , 789, 53

    work page 2014

  67. [67]

    C., Bonfils , X., et al

    Gomes da Silva , J., Santos , N. C., Bonfils , X., et al. 2012, , 541, A9

    work page 2012

  68. [68]

    2008, , 486, 951

    Gustafsson , B., Edvardsson , B., Eriksson , K., et al. 2008, , 486, 951

    work page 2008

  69. [69]

    & Kochukhov , O

    Hahlin , A. & Kochukhov , O. 2022, , 659, A151

    work page 2022

  70. [70]

    D., et al

    Hahlin , A., Kochukhov , O., Rains , A. D., et al. 2023, , 675, A91

    work page 2023

  71. [71]

    Johns-Krull , C. M. 2007, , 664, 975

    work page 2007

  72. [72]

    K \"a pyl \"a , P. J. 2021, , 651, A66

    work page 2021

  73. [73]

    G., Noack , L., Johnstone , C

    Kislyakova , K. G., Noack , L., Johnstone , C. P., et al. 2017, Nature Astronomy, 1, 878

    work page 2017

  74. [74]

    2007, in Physics of Magnetic Stars, ed

    Kochukhov , O. 2007, in Physics of Magnetic Stars, ed. I. I. Romanyuk & D. O. Kudryavtsev , 109--118

    work page 2007

  75. [75]

    2021, , 29, 1

    Kochukhov , O. 2021, , 29, 1

    work page 2021

  76. [76]

    J., & Wehrhahn , A

    Kochukhov , O., Hackman , T., Lehtinen , J. J., & Wehrhahn , A. 2020, , 635, A142

    work page 2020

  77. [77]

    & Lavail , A

    Kochukhov , O. & Lavail , A. 2017, , 835, L4

    work page 2017

  78. [78]

    2010, , 524, A5

    Kochukhov , O., Makaganiuk , V., & Piskunov , N. 2010, , 524, A5

    work page 2010

  79. [79]

    & Shulyak , D

    Kochukhov , O. & Shulyak , D. 2019, , 873, 69

    work page 2019

  80. [80]

    Lavail , A., Kochukhov , O., & Hussain , G. A. J. 2019, , 630, A99

    work page 2019

Showing first 80 references.