Height expansion of plage chromospheric magnetic fields and their causal connection to localized chromospheric heating

Solar plage regions — patches of concentrated magnetic field where hot coronal loops root — have well-measured photospheric fields but poorly known chromospheric fields, and the mechanism that heats the plage chromosphere is unresolved. High-sensitivity spectropolarimetry with the Daniel K. Inouye Solar Telescope's Visible Spectro-Polarimeter (DKIST/ViSP) (da Silva Santos et al. 2023) measured $`\sim`$200–300 G fields in plage fibrils, found a clear field-strength/$\lambda8542$-emission correlation over the whole field of view that weakens inside plage, and detected supersonic downflows at the plage periphery, but could not determine how the field expands with height, whether the Ca II 8542 Å line quantitatively traces chromospheric cooling rates, or whether current systems at flux-tube edges cause the observed localized heating. The open problem is to establish the three-dimensional structure of the plage chromospheric magnetic field — its weakening and expansion with height, measured systematically across heliocentric angles and plage samples — together with the three-dimensional distribution of radiative cooling rates in the lower chromosphere, and to determine whether the magnetic topology (including edge-localized currents, i.e. the curl of $\mathbf{B}$) causally shapes the heating, including the origin of the peripheral supersonic downflows.

Background

Plage regions are patches of strong, predominantly unipolar magnetic field in the solar photosphere, seen in chromospheric diagnostics as bright Ca II emission; they are the footpoint regions of hot coronal loops. The chromosphere — the $`\sim`$10,000 K layer between the photosphere and the corona — is heated by mechanisms that remain unidentified, and in plage the heating is known to be magnetic in origin. Spectropolarimetry measures the four Stokes parameters ($I$, intensity; $Q$, $U$, linear polarization; $V$, circular polarization) of a spectral line; the Ca II 8542 Å line ($\lambda8542$, of the infrared Ca II triplet) forms in the low-to-middle chromosphere and is sensitive to magnetic fields through the Zeeman effect. Because its polarization signals are weak, plage chromospheric fields are commonly inferred with the weak-field approximation (WFA, a linear relation between Stokes $V$ and the line-of-sight field valid for weak fields) or with Milne–Eddington (ME) inversions, which assume a simplified one-component atmosphere; full non-local thermodynamic equilibrium (NLTE) inversions retrieve height-resolved atmosphere models by fitting the line formation physics. The magnetic canopy is the fan of expanding, highly inclined field lines spreading from photospheric flux concentrations and traced by dark fibrils in chromospheric images.

Photospheric plage fields are strong (kilogauss) and well characterized, but chromospheric values were scarce before DKIST: spatially-regularized WFA applied to Swedish 1-m Solar Telescope data found canopy field stratification over one plage (Morosin et al. 2020), and CLASP2 (the Chromospheric Lyman-Alpha Spectro-Polarimeter sounding-rocket experiment, second flight) spectropolarimetry of the Mg II h and k lines mapped longitudinal fields from the photosphere to the upper chromosphere in active regions (Ishikawa et al. 2021). Semi-empirical models established that the Ca II lines dominate chromospheric radiative losses (Vernazza, Avrett & Loeser 1981), and observations show enhanced $\lambda8542$ emission near magnetic elements, offset from the strongest fields — interpreted as resistive heating at the edges of flux tubes (de la Cruz Rodríguez et al. 2013) — while NLTE inversions of one plage found heating concentrated away from the field maxima (Morosin et al. 2022). Co-spatial Ca II K / Ca II 8542 spectropolarimetry of one active-region plage has since established the height expansion directly (Juanikorena Berasategi et al. 2026), confirming the effect qualitatively for a single region but not supplying the systematic multi-region, multi-heliocentric-angle sampling needed to separate viewing-angle effects from intrinsic field geometry.

The source paper (da Silva Santos et al. 2023) used the Daniel K. Inouye Solar Telescope (DKIST) Visible Spectro-Polarimeter (ViSP) to observe one extended, decaying plage with $`\sim`$2 G noise. It found $`\sim`$200–300 G total fields in fibrils, an average line-of-sight chromospheric field of $\sim$-210 G, a clear field-strength/cooling-proxy correlation over the whole field of view that weakens inside plage, and supersonic ($`\sim`$15 km s$^{-1}$) downflows at the plage periphery. Its conclusions state what remains open: the height expansion of the plage magnetic field (requiring a larger sample and a range of heliocentric angles $\mu$, the cosine of the viewing angle, to separate viewing effects from intrinsic geometry), the three-dimensional distribution of heating rates (the source notes that if heating is resistive at flux-tube edges, emission should correlate with the curl of $\mathbf{B}$ — the electric current density — rather than with $\mathbf{B}$ itself), whether $\lambda8542$ integrated intensity quantitatively traces the radiative cooling rates in plage, the origin and energetics of the supersonic downflows, and — as enabling capabilities — improved $\lambda8542$-arm calibration, NLTE multi-line inversions, and extended chromospheric magnetograms suitable for extrapolating fields into the corona and heliosphere for comparison with in situ Parker Solar Probe measurements.

Problem Statement

Establish the three-dimensional structure of the plage chromospheric magnetic field and its causal relationship to localized chromospheric heating. Concretely, for solar plage regions: (i) measure how the magnetic field weakens and expands with height from the kilogauss photospheric concentrations through the chromospheric canopy, systematically over a sample of plage regions and a range of heliocentric angles $\mu$ (the cosine of the angle between the line of sight and the local solar vertical), so that viewing-angle effects are separated from intrinsic field geometry; (ii) determine the three-dimensional distribution of radiative cooling rates in the lower chromosphere of plage and quantify whether Ca II 8542 Å integrated intensity is a faithful proxy for those rates; (iii) establish or exclude a causal link between the magnetic topology and the localized heating — in particular whether enhanced $\lambda8542$ emission at flux-tube edges is produced by resistive heating associated with edge currents, i.e. whether it correlates with the curl of $\mathbf{B}$ rather than with the field strength $\mathbf{B}$ itself; and (iv) as part of the plage dynamics this structure governs, determine the origin (draining of cold material, shock formation, or reconnection outflows) and energetic significance of the supersonic ($`\sim`$15 km s$^{-1}$) downflows at plage peripheries. These four components are all required and jointly answer one question — what is the 3D magnetic structure of plage and does that structure cause the observed chromospheric heating? — with improved $\lambda8542$ calibration, NLTE multi-line inversions, and extended chromospheric magnetograms serving as the means that enable it.

References

1. J. M. da Silva Santos, K. Reardon, G. Cauzzi, T. Schad, V. Martinez Pillet, A. Tritschler, F. Wöger, R. Hofmann, J. Stauffer, H. Uitenbroek, 'Magnetic Fields in Solar Plage Regions: Insights from High-sensitivity Spectropolarimetry', The Astrophysical Journal Letters 954, L35 (2023), DOI 10.3847/2041-8213/acf21f, arXiv:2308.10983, https://arxiv.org/abs/2308.10983
2. D. Kuridze, H. Uitenbroek, F. Wöger, M. Mathioudakis, H. Morgan, R. Campbell, C. Fischer, G. Cauzzi, T. Schad, K. Reardon, J. M. da Silva Santos, C. Beck, A. Tritschler, T. Rimmele, 'Insight into the Solar Plage Chromosphere with DKIST', The Astrophysical Journal (2024), DOI 10.3847/1538-4357/ad2702, arXiv:2402.04545, https://arxiv.org/abs/2402.04545
3. J. M. da Silva Santos, M. Molnar, I. Milić, M. Rempel, K. Reardon, J. de la Cruz Rodríguez, 'Constraints on Acoustic Wave Energy Fluxes and Radiative Losses in the Solar Chromosphere from Non-LTE Inversions', The Astrophysical Journal (2024), DOI 10.3847/1538-4357/ad81d4, arXiv:2408.15908, https://arxiv.org/abs/2408.15908
4. H. Li, Tanausú del Pino Alemán, Javier Trujillo Bueno, Ryohko Ishikawa, Ernest Alsina Ballester, David E. McKenzie, Luca Belluzzi, Donguk Song, Takenori J. Okamoto, Ken Kobayashi, Laurel A. Rachmeler, Christian Bethge, Frédéric Auchère, 'Mapping the Longitudinal Magnetic Field in the Atmosphere of an Active Region Plage from the Inversion of the Near-ultraviolet CLASP2.1 Spectropolarimetric Data', The Astrophysical Journal (2024), DOI 10.3847/1538-4357/ad6dfb, arXiv:2408.06094, https://arxiv.org/abs/2408.06094
5. Hao Li, T. del Pino Alemán, J. Trujillo Bueno, R. Ishikawa, E. Alsina Ballester, David E. McKenzie, Frédéric Auchère, Ken Kobayashi, Takenori J. Okamoto, Laurel A. Rachmeler, Donguk Song, 'Tomography of a Solar Plage with the Tenerife Inversion Code', The Astrophysical Journal 945, 144 (2023), DOI 10.3847/1538-4357/acb76e, arXiv:2301.12792, https://arxiv.org/abs/2301.12792
6. Iñigo Juanikorena Berasategi, Ernest Alsina Ballester, Javier Trujillo Bueno, Francisco A. Iglesias, Yusuke Kawabata, Juan Sebastián Castellanos Durán, Masahito Kubo, Alex Feller, Yukio Katsukawa, Sami K. Solanki, Jose Carlos del Toro Iniesta, Andreas Lagg, Achim Gandorfer, Pietro Bernasconni, Thomas Kerkefeld, Tino L. Riethmüller, Yoshihiro Naito, Alberto Álvarez-Herrero, H. N. Smitha, David Orozco Suárez, Bianca Grauf, Michael Carpenter, Alexander Bell, Valentín Martínez Pillet, Francisco Javier Bailén, Julian Blanco Rodríguez, Edvarda Harnes, Johannes Hölken, Ryohtaroh T. Ishikawa, Takuma Matsumoto, Takayoshi Oba, Azaymi L. Siu-Tapia, Hanna Strecker, Dušan Vukadinović, 'Magnetic Field Stratification in Active-Region Plage from Ca II K and Ca II 8542 Å Spectropolarimetry', The Astrophysical Journal Letters (accepted, 2026), arXiv:2607.28102, https://arxiv.org/abs/2607.28102
7. Souvik Bose, Bart De Pontieu, Viggo Hansteen, Alberto Sainz Dalda, Sabrina Savage, Amy Winebarger, 'Chromospheric and coronal heating in an active region plage by dissipation of currents from braiding', Nature Astronomy (2024), DOI 10.1038/s41550-024-02241-8, arXiv:2211.08579, https://arxiv.org/abs/2211.08579
8. Robert Jarolim, Benoit Tremblay, Matthias Rempel, Momchil Molnar, Astrid M. Veronig, Julia K. Thalmann, Tatiana Podladchikova, 'Advancing Solar Magnetic Field Extrapolations through Multiheight Magnetic Field Measurements', The Astrophysical Journal Letters (2024), DOI 10.3847/2041-8213/ad2450, arXiv:2312.06823, https://arxiv.org/abs/2312.06823
9. Sanjay Gosain, 'Temperature Diagnostics of Chromospheric Fibrils using DKIST/ViSP Observations: K-Means Clustering Approach', The Astrophysical Journal (accepted, 2026), arXiv:2606.06886, https://arxiv.org/abs/2606.06886
10. R. Morosin, J. de la Cruz Rodríguez, C. J. Díaz Baso, J. Leenaarts, 'Spatio-temporal analysis of chromospheric heating in a plage region', Astronomy & Astrophysics 664, A8 (2022), DOI 10.1051/0004-6361/202243461, arXiv:2203.01688, https://arxiv.org/abs/2203.01688
11. R. Morosin, J. de la Cruz Rodríguez, G. J. M. Vissers, R. Yadav, 'Stratification of canopy magnetic fields in a plage region. Constraints from a spatially-regularized weak-field approximation method', Astronomy & Astrophysics 642, A210 (2020), DOI 10.1051/0004-6361/202038754, arXiv:2006.14487, https://arxiv.org/abs/2006.14487
12. J. de la Cruz Rodríguez, B. De Pontieu, M. Carlsson, L. H. M. Rouppe van der Voort, 'Heating of the magnetic chromosphere: observational constraints from Ca II 8542 spectra', The Astrophysical Journal Letters 764, L11 (2013), DOI 10.1088/2041-8205/764/1/L11, arXiv:1301.3141, https://arxiv.org/abs/1301.3141
13. K. Sowmya, A. Lagg, S. K. Solanki, J. S. Castellanos Durán, 'Magnetized supersonic downflows in the chromosphere. A statistical study using the He I 10830 Å lines', Astronomy & Astrophysics 661, A122 (2022), DOI 10.1051/0004-6361/202142850, arXiv:2202.11679, https://arxiv.org/abs/2202.11679
14. R. Ishikawa, J. Trujillo Bueno, T. del Pino Alemán, T. Okamoto, D. E. McKenzie, F. Auchère, R. Kano, D. Song, M. Yoshida, L. A. Rachmeler, K. Kobayashi, H. Hara, M. Kubo, N. Narukage, T. Sakao, T. Shimizu, Y. Suematsu, C. Bethge, B. De Pontieu, A. Sainz Dalda, G. D. Vigil, A. Winebarger, E. Alsina Ballester, L. Belluzzi, J. Štěpán, A. Asensio Ramos, M. Carlsson, J. Leenaarts, 'Mapping solar magnetic fields from the photosphere to the base of the corona with the CLASP2 sounding-rocket experiment', Science Advances 7, eabe8406 (2021), DOI 10.1126/sciadv.abe8406, https://www.science.org/doi/10.1126/sciadv.abe8406
15. J. E. Vernazza, E. H. Avrett, R. Loeser, 'Structure of the solar chromosphere. III. Models of the EUV brightness components of the quiet Sun from the computed ultraviolet and extreme-ultraviolet spectra', The Astrophysical Journal Supplement Series 45, 635 (1981), DOI 10.1086/190731, https://ui.adsabs.harvard.edu/abs/1981ApJS...45..635V