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Quantifying the effect of passband on observations in the Ca II K line

This study utilizes high-resolution observations from the Sunrise III mission to derive empirical power-law relationships that quantify the effects of spectral passband and spatial resolution variations, thereby enabling improved cross-calibration of historical and modern Ca II K solar archives to construct a consistent century-long time series of solar activity.

Original authors: Ajay Kumar Yadav, Theodosios Chatzistergos, Natalie Krivova, Sami K. Solanki, Francisco A. Iglesias, Ilaria Ermolli, Andreas Lagg, Achim Gandorfer, Jose Carlos del Toro Iniesta, Yukio Katsukawa, Pietr

Published 2026-05-29

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CC BY 4.0

Original authors: Ajay Kumar Yadav, Theodosios Chatzistergos, Natalie Krivova, Sami K. Solanki, Francisco A. Iglesias, Ilaria Ermolli, Andreas Lagg, Achim Gandorfer, Jose Carlos del Toro Iniesta, Yukio Katsukawa, Pietro Bernasconi, Thomas Berkefeld, Alex Feller, Tino L. Riethmüller, Alberto Álvarez-Herrero, Masahito Kubo, H. N. Smitha, David Orozco Suárez, Bianca Grauf, Michael Carpenter, Alexander Bell, Valentín Martínez Pillet, Laurent Gizon, Johannes Hoelken, Francisco Javier Bailén, Julian Blanco Rodríguez, Juan Sebastián Castellanos Durán, Edvarda Harnes, Ryohtaroh T. Ishikawa, Yusuke Kawabata, Takuma Matsumoto, Takayoshi Oba, Azaymi L. Siu-Tapia, Hanna Strecker, Dušan Vukadinović, Yasuhito Narita

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the Sun as a giant, glowing stage. For over a century, astronomers have been taking photos of this stage through different colored glasses (filters) to study the "actors" on it—specifically, bright, magnetic storms called plages (which are like the chromospheric cousins of sunspots).

The problem is that every observatory has used a different pair of glasses. Some lenses are very narrow and sharp (like a high-definition camera), while others are wider and blurrier (like a standard phone camera). Because of this, the photos don't match up. A bright spot in one photo might look dimmer in another, not because the Sun changed, but because the "glasses" were different. This makes it hard to stitch together a single, consistent history of solar activity.

This paper is like a universal translator for these solar photos. Here is how the authors solved the puzzle:

1. The "Super-Camera" (The Data)

To fix the mismatch, the authors didn't just guess; they used the most advanced solar camera ever flown: the Sunrise III mission. This balloon-borne observatory took incredibly detailed, high-resolution pictures of the Sun's surface. Think of it as having a master photo taken with a perfect, ultra-sharp lens that can see every tiny detail.

2. The "Digital Glasses" (The Method)

Since they couldn't go back in time to put the exact same glasses on old telescopes, they used a clever trick. They took their perfect "master photo" and digitally simulated what it would look like if viewed through the specific, imperfect glasses of old observatories (like the ones in Rome and Meudon).

The Passband Analogy: Imagine looking at a bright light through a narrow slit versus a wide window. The narrow slit lets you see the intense core of the light clearly. The wide window lets in more light but blurs the edges and mixes in more of the surrounding dimness. The authors figured out the exact mathematical recipe to translate what you see through the "narrow slit" into what you would see through the "wide window," and vice versa.
The Resolution Analogy: They also simulated what happens if you take a sharp photo and blur it to match the grainy quality of older, ground-based telescopes.

3. The "Magic Formula" (The Result)

After running thousands of simulations, they discovered that the relationship between these different views isn't a simple straight line. Instead, it follows a power law (a specific type of curve).

Think of it like a recipe for adjusting volume. If you have a song playing on a high-quality speaker (narrow passband) and you want to know how loud it would sound on a cheap speaker (wide passband), you can't just turn the volume knob up by the same amount. You need a specific formula to get it right. The authors found that formula.

They tested this formula by taking real photos from two different observatories (Rome and Meudon) taken on the same day.

Before: The photos looked different. The Rome photo (wider filter) showed lower contrast than the Meudon photo (narrower filter).
After: They applied their new formula to the Meudon photo to "translate" it into the Rome style. Suddenly, the two photos matched almost perfectly. The bright spots lined up, and the differences vanished.

4. One-Way Street

The authors also found an interesting quirk: It is much easier to translate a narrow view into a wide view than the other way around.

Analogy: Imagine you have a high-resolution photo of a landscape. You can easily blur it to look like a low-resolution photo (you just lose detail). But if you start with a blurry photo, you can't magically invent the missing sharp details to make it high-resolution. Similarly, converting a narrow-band image to a wide-band one works well, but trying to guess what a narrow-band image would have looked like from a wide-band one is less accurate because the detailed information was already lost.

Why This Matters (According to the Paper)

The paper states that this "universal translator" allows scientists to finally combine historical solar photos from the last 100+ years with modern ones into one consistent record. By doing this, they can:

Create a single, long timeline of solar magnetic activity.
Improve models that try to figure out how much energy the Sun sends to Earth (solar irradiance).
Better understand the Sun's internal "dynamo" (the engine that drives its magnetic field).

In short, the paper provides the mathematical key to unlock a century of solar history, turning a messy pile of mismatched photos into a clear, unified story of our Sun's activity.

Technical Summary: Quantifying the effect of passband on observations in the Ca ii K line

Problem Statement
Full-disk observations of the Sun in the Calcium II (Ca ii) K line have been conducted globally since the late 19th century, offering a unique opportunity to extend records of solar magnetic activity and facular coverage into the pre-satellite era. These records are critical for reducing discrepancies in solar irradiance reconstructions and advancing solar dynamo studies. However, constructing a consistent, century-long composite record is hindered by significant inhomogeneities between archives. Different observatories utilize distinct instrumental setups with varying spectral passbands and spatial resolutions. Consequently, images from different sources sample different atmospheric heights and spatial scales. Previous attempts to combine these datasets often failed to properly account for these instrumental differences, leading to spurious trends and inhomogeneities. While some normalization methods exist, they often assume linear relationships or rely on regional averages, lacking a robust, pixel-by-pixel framework for converting observations between arbitrary instrumental configurations.

Methodology
To address these limitations, the authors utilized high-spectral and high-spatial resolution data from the Sunrise III mission's UV Spectropolarimeter and Imager (SUSI). The dataset includes observations of a plage region and two emerging flux regions, providing spectra around the Ca ii K line with a spectral sampling of 10 mÅ pixel⁻¹ and spatial sampling of 0.03″ pixel⁻¹.

The core methodology involved:

Passband Emulation: The high-resolution SUSI spectra were convolved with Gaussian profiles of varying Full Width at Half-Maximum (FWHM) to emulate observations from historical instruments with passbands ranging from 0.1 Å to 9 Å.
Spatial Resolution Degradation: SUSI images were convolved with 2D Gaussians to match target spatial resolutions between 1″ and 6″, simulating the lower resolution of ground-based telescopes.
Normalization: All images were normalized by the mean intensity of selected Quiet Sun (QS) regions to establish a consistent contrast scale.
Derivation of Relationships: The authors analyzed pixel-by-pixel contrast relationships between pairs of emulated passbands. They tested linear, logarithmic, and power-law models, restricting the analysis to "bright pixels" (plage regions with contrast above the QS level) to avoid the non-linear behavior of dark features like sunspots.
Validation: The derived empirical relationships were applied to real-world ground-based data from the Meudon heliograph (1.4 Å passband) and the Rome/PSPT (2.5 Å passband) to test their efficacy in cross-calibration.

Key Contributions

Empirical Power-Law Model: The study establishes that the relationship between Ca ii K contrasts in different passbands is best described by a power law of the form $y = ax^b + c$ .
Comprehensive Coefficient Tables: The authors provide coefficients ( $a, b, c$ ) and their uncertainties for a wide range of passband combinations (0.1–9 Å) and spatial resolutions (1″–6″), available in supplementary material.
Quantification of Resolution vs. Passband Effects: The analysis demonstrates that while spatial resolution affects the contrast-contrast relationship, the effect of passband width is significantly more dominant.
Directional Asymmetry: The study identifies that converting narrow-band observations to broad-band equivalents is more effective than the reverse, as broad-band data inherently averages out information that cannot be statistically recovered.

Results

Model Accuracy: The power-law fit reproduces the data significantly better than linear or logarithmic fits, yielding the lowest reduced $\chi^2$ values. For example, converting a 1.4 Å image to a 2.5 Å equivalent at 4″ resolution resulted in a root-mean-square (RMS) difference of only 0.0342 between the reconstructed and original 2.5 Å image, compared to 0.2161 for the uncorrected 1.4 Å vs. 2.5 Å comparison.
Cross-Calibration Success: When applied to the Meudon and Rome/PSPT datasets, the derived relationship successfully reduced the RMS difference in contrast across the solar disk from 0.0940 to 0.0492. The scatter in the contrast-contrast plot concentrated around the $y=x$ line, eliminating systematic offsets.
Center-to-Limb Variation (CLV): Tests confirmed that the conversion relationship remains valid across the solar disk, with no significant CLV effects detected.
Robustness: The method proved effective even for extreme passband mismatches, such as converting a 0.15 Å spectroheliograph passband to a 2.5 Å filtergram.

Significance
The paper claims that these results provide a foundational tool for the cross-calibration of Ca ii K images from diverse observatories. By enabling the translation of observations obtained with different passbands and resolutions into a common framework, this work lays the groundwork for constructing a consistent, century-long time series of solar plage and magnetic field records. Such a homogeneous dataset is essential for improving solar irradiance reconstructions based directly on facular information, resolving discrepancies among existing models, and facilitating long-term studies of the solar magnetic field and dynamo. The authors emphasize that while the method relies on idealized Gaussian assumptions for passbands, it offers a practical and necessary step toward homogenizing historical solar data.

1. The "Super-Camera" (The Data)

2. The "Digital Glasses" (The Method)

3. The "Magic Formula" (The Result)

4. One-Way Street

Why This Matters (According to the Paper)

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