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arxiv: 2604.11568 · v1 · submitted 2026-04-13 · 🌌 astro-ph.SR

The magnetic sensitivity of the Ca II H and K lines

M. Kriginsky , J. Leenaarts , J. de la Cruz Rodriguez , S. Danilovic , O. Andriienko This is my paper

Pith reviewed 2026-05-10 15:31 UTC · model grok-4.3

classification 🌌 astro-ph.SR
keywords Ca II H lineCa II K linesolar chromospheremagnetic field sensitivitypolarizationradiative transferweak-field approximation
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The pith

The Ca II H and K lines reliably measure magnetic fields in the upper solar chromosphere via their circular polarization.

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

This paper aims to demonstrate that the Ca II H and K lines can probe magnetic fields in the upper chromosphere. It does so by performing detailed radiative transfer calculations on semi-empirical models matched to solar observations. The analysis shows that circular polarization signals are strong enough for detection and that the weak-field approximation works to infer the line-of-sight magnetic field. A reader would care because accurate magnetic field measurements in this layer help understand how energy is transported and how the solar atmosphere is structured.

Core claim

Both lines are sensitive to magnetic fields in the upper chromosphere. The K line forms slightly higher due to its larger opacity. The H line shows stronger magnetic sensitivity owing to its higher effective response factor and longer wavelength. For typical chromospheric field strengths, linear polarization stays below 1.7 percent while circular polarization can reach more than 10 percent in strong-field areas. The weak-field approximation allows reliable inference of the line-of-sight magnetic field from these signals.

What carries the argument

Response functions and synthetic inversions applied to radiative transfer calculations in semi-empirical atmospheric models, which quantify how the polarization signals depend on magnetic field strength and formation height.

If this is right

  • Both the H and K lines serve as diagnostics for the magnetic structure of the upper chromosphere.
  • The K line provides information from a slightly higher layer than the H line.
  • Circular polarization signals from these lines can be used with the weak-field approximation to determine the line-of-sight magnetic field.
  • Linear polarization signals are generally too weak to detect under typical conditions, but circular ones are accessible in strong fields.

Where Pith is reading between the lines

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

  • Combining measurements from these lines with other chromospheric diagnostics could reveal the vertical structure of magnetic fields.
  • These lines might help model the role of the chromosphere in solar energy balance and activity.
  • Extensions to three-dimensional atmospheric models could test how well the sensitivity holds in more complex magnetic configurations.

Load-bearing premise

Semi-empirical atmospheric models combined with high-resolution observations accurately represent the thermodynamic and magnetic conditions in the chromosphere.

What would settle it

Comparing the modeled circular polarization values in strong magnetic regions to those actually observed, to check if the predicted formation heights and field inferences hold.

Figures

Figures reproduced from arXiv: 2604.11568 by J. de la Cruz Rodriguez, J. Leenaarts, M. Kriginsky, O. Andriienko, S. Danilovic.

Figure 1
Figure 1. Figure 1: Image of active region NOAA 13465 in the line core of the Ca ii 854.2 nm line. The marked pixels are the locations of 45 representative line profiles that sample the variety of line profiles present in the observations as determined by k-means clustering (see Sec. 2.4). an overview of the active region NOAA 13465 as it neared the disc centre. Spectropolarimetric observations of the Ca ii 854.2 nm line were… view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of linear polarisation of the Ca ii H and K lines computed with the multiterm (MT, solid curves) and multilevel (ML, dashed curves) formalisms for different values of the heliocentric angle µ for the case of zero magnetic field. The colours represent the different values of µ as given in the legend. For µ = 1 no scattering polarisation is produced and both curves are identically zero. 3.1.1. Non… view at source ↗
Figure 3
Figure 3. Figure 3: Fractional linear polarisation of the Ca ii H and K lines under the multilevel and multiterm formalisms. As in [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Fractional circular polarisation of the Ca ii H and K lines under the multilevel and multiterm formalisms for different values of B when observed at disc centre. Again, as in [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Line profiles, response functions, and magnetic fields in three representative atmosphere models. Top row: Intensity of the Ca ii H line before (blue) and after (orange) being convolved with a spectral PSF of 130 mÅ. Second row: Circular polarisation of the Ca ii H line before (blue) and after (orange) being convolved with a spectral PSF of 130 mÅ. Third row: Image of the response functions of Stokes V in … view at source ↗
Figure 6
Figure 6. Figure 6: Top row: Line-of-sight magnetic field (BLoS) at log ξ = −4 from the input model (a), compared with the weak-field estimates obtained from the original synthetic spectra (b), and from the same spectra after convolution with the CHROMIS spectral PSF with (c), and without noise (d). Bottom row: Logarithmic density plots comparing the input BLoS with the weak-field results, for the case without the convolution… view at source ↗
read the original abstract

The solar chromosphere is a transition layer between the cool, dense photosphere and the hot, rarefied corona. This boundary region plays a key role in regulating energy transport and structuring the magnetic field throughout the solar atmosphere. Understanding its thermodynamic and magnetic properties is essential to model and interpret solar phenomena. This study investigates the theoretical properties and diagnostic potential of the polarisation signals in the Ca II H and K lines, with particular emphasis on their capability to probe magnetic fields in the upper chromosphere with the CHROMIS instrument at the Swedish 1-m solar telescope. We combine semi-empirical atmospheric models with high-resolution solar observations to model the formation of the Ca II H and K lines using non-local thermodynamic equilibrium radiative transfer calculations. The sensitivity of the lines to the magnetic field is examined through response functions and synthetic inversions, enabling an assessment of their diagnostic performance under realistic chromospheric conditions. For typical chromospheric field strengths, the linear polarisation of the Ca ii H & K lines is less than 1.7%, below the expected detection threshold of CHROMIS. However, their circular polarisation reaches more than 10% in strong-field regions, which is detectable by CHROMIS. Both lines are sensitive to magnetic fields in the upper chromosphere, with the K line forming slightly higher due to its larger opacity, and the H line exhibiting a somewhat stronger Zeeman sensitivity owing to its higher effective Lande factor and longer wavelength. Using the weak-field approximation, the line of sight magnetic field can be reliably inferred. These results confirm that the Ca II H & K lines constitute powerful diagnostics for studying the magnetic structure of the upper solar chromosphere.

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

1 major / 2 minor

Summary. The paper investigates the magnetic sensitivity of the Ca II H and K lines in the solar chromosphere. Using non-LTE radiative transfer calculations in semi-empirical atmospheric models combined with high-resolution observations, the authors compute polarization signals and employ response functions and synthetic inversions to assess diagnostic capabilities for the CHROMIS instrument. They find that linear polarization is generally below 1.7% while circular polarization can exceed 10% in strong magnetic field regions. The K line forms slightly higher than the H line, the H line has stronger Zeeman sensitivity, and the weak-field approximation allows reliable inference of the line-of-sight magnetic field. The conclusion is that these lines are powerful diagnostics for the upper chromospheric magnetic structure.

Significance. If the modeling and checks hold, this provides a useful theoretical basis for interpreting Ca II H and K polarization observations with CHROMIS to probe upper-chromospheric magnetic fields. The differential formation heights and Zeeman sensitivities between the lines, along with the use of response functions and synthetic inversions, offer a concrete framework for assessing their diagnostic value in a regime important for solar energy transport studies.

major comments (1)
  1. Abstract and results on WFA application: The claim that the line-of-sight magnetic field can be reliably inferred using the weak-field approximation is central to the diagnostic conclusions. However, circular polarization is stated to reach >10% in strong-field regions (detectable by CHROMIS), yet there is no explicit verification that Zeeman splitting remains ≪ Doppler width or quantification of WFA recovery errors from the synthetic inversions in those regimes. This check is load-bearing for the reliability assertion.
minor comments (2)
  1. The effective Landé factor values used for the H and K lines should be explicitly stated or referenced in the methods or modeling section for reproducibility.
  2. Figure captions for response functions should clearly indicate the derived formation height differences between the H and K lines.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. The point raised about verifying the weak-field approximation in strong-field regimes is well taken and central to our diagnostic claims. We address it in detail below and will revise the manuscript accordingly to provide the requested explicit checks.

read point-by-point responses

  1. Referee: Abstract and results on WFA application: The claim that the line-of-sight magnetic field can be reliably inferred using the weak-field approximation is central to the diagnostic conclusions. However, circular polarization is stated to reach >10% in strong-field regions (detectable by CHROMIS), yet there is no explicit verification that Zeeman splitting remains ≪ Doppler width or quantification of WFA recovery errors from the synthetic inversions in those regimes. This check is load-bearing for the reliability assertion.

    Authors: We agree that an explicit verification of the weak-field approximation (WFA) validity is essential to substantiate the reliability claim, especially where circular polarization exceeds 10%. Our synthetic inversions did apply the WFA to recover the line-of-sight field from the full set of computed Stokes profiles, including models with strong fields, and the response functions were used to confirm sensitivity in the upper chromosphere. However, we did not include a dedicated quantification of Zeeman splitting relative to Doppler width or a tabulation of WFA recovery errors specifically binned by polarization amplitude in the strong-field limit. To address this directly, we will add a new paragraph in the results section (and update the abstract if needed for precision) that: (i) computes the Zeeman splitting for the relevant field strengths and compares it to the local Doppler width (incorporating thermal, microturbulent, and instrumental broadening), confirming the splitting remains ≪ width; and (ii) reports the WFA inversion errors from the synthetic tests, demonstrating that the recovered B_los matches the input values to within a few percent even for cases with V/I > 10%. These additions will be illustrated with a supplementary figure showing error versus field strength. This revision will make the diagnostic conclusions more robust without altering the overall findings. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on external models and prior literature

full rationale

The paper combines semi-empirical atmospheric models with non-LTE radiative transfer, response functions, and synthetic inversions to assess Ca II H & K magnetic sensitivity. The weak-field approximation for LOS B inference is invoked as an established technique from prior literature rather than derived or fitted within the paper's own equations. No load-bearing step reduces by construction to a self-definition, a renamed fit, or a self-citation chain; the central claims about formation heights, Zeeman sensitivity, and detectability remain independent of the paper's inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard domain assumptions in solar spectroscopy about atmospheric structure and radiative transfer that are not derived within the paper.

axioms (2)
  • domain assumption Non-local thermodynamic equilibrium conditions govern the formation and polarization of Ca II H and K lines in the chromosphere.
    Invoked throughout the modeling and response function calculations described in the abstract.
  • domain assumption Semi-empirical atmospheric models provide a sufficiently accurate representation of real chromospheric thermodynamic and magnetic conditions.
    Used as the basis for combining with observations to model line formation.

pith-pipeline@v0.9.0 · 5621 in / 1521 out tokens · 86992 ms · 2026-05-10T15:31:55.213594+00:00 · methodology

discussion (0)

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Reference graph

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