The solar chromosphere requires a mechanical energy input of order 10610^6–10710^7 erg cm−2^{-2} s−1^{-1} to balance its radiative losses, yet which physical processes dominate this deposition — shock dissipation of convectively driven acoustic waves, dissipation in reconnecting current sheets, or other mechanisms — has remained unsettled for decades. A 2025–2026 series of 3D radiation-magnetohydrodynamic simulations with the Bifrost code quantified, for one quiet-Sun model, a partition in which shocks supply up to 59% of the mechanical heating near z≈1.2z\approx1.2 Mm and current sheets dominate the upper chromosphere, the two together powering 66% of the height-averaged heating — but this partition is single-code, numerics-dependent, and unverified by observations, and a companion study shows the shock share collapses from 23% to 5% as the sub-photospheric magnetic flux increases. Establish a quantitative, mechanism-resolved partition of chromospheric heating as a function of height and magnetic environment, robust across independent models and heating definitions, and confronted with observations capable of discriminating among the mechanisms, so that the chromospheric energy budget closes against the measured radiative losses and thermal structure.

Background

The solar chromosphere is the roughly 2–3 Mm thick layer of the solar atmosphere lying between the 5772 K photosphere and the million-degree corona. It cannot be explained by radiative equilibrium: sustaining its temperature structure requires a mechanical energy input of order 10610^6–10710^7 erg cm−2^{-2} s−1^{-1} to balance radiative losses — about an order of magnitude more than the corona needs. The convection zone contains ample kinetic energy, but identifying which physical processes actually deposit this energy in the chromosphere — the chromospheric heating problem — has remained open for decades, as the authoritative review of Carlsson, De Pontieu & Hansteen (2019) makes explicit.

Candidate mechanisms are conventionally grouped as follows. "AC" (alternating-current) heating dissipates magnetohydrodynamic waves: acoustic waves generated by convection steepen into shocks as they propagate upward through the falling density, converting kinetic energy into heat. "DC" (direct-current) heating dissipates magnetic energy: horizontal convective motions braid magnetic field lines and build up electric currents, which are released in current sheets — thin layers of intense magnetic-field gradient where magnetic reconnection, a topological reconfiguration of the field converting magnetic energy into kinetic and thermal energy, takes place. Both operate in a plasma whose character changes with height: the plasma beta β\beta (the ratio of gas pressure to magnetic pressure) falls from above unity near the photosphere to well below unity in the upper chromosphere, so mechanical (shock) processes tend to give way to magnetic (current-sheet) processes as altitude increases. A third, subtler term is compressive heating — the irreversible part of the work done by adiabatic compression — which classical energy budgets often neglect but which is significant inside chromospheric shocks.

The evidence to date is layered but inconclusive. One-dimensional simulations of upward-propagating acoustic shocks reproduce the bright Ca II H and K line cores (the resonance lines of singly ionized calcium) of the quiet Sun (Carlsson & Stein 1992), establishing shocks as a real lower-chromospheric heating agent; yet the acoustic flux actually observed appears insufficient above roughly 1.4 Mm, implicating magnetic processes higher up. The observational flux estimates themselves conflict: Abbasvand et al. (2020a, b) concluded that deposited acoustic flux (frequencies up to about 20 mHz) can balance radiative losses in parts of the quiet Sun, while Molnar et al. (2021), combining the IBIS (Interferometric Bidimensional Spectrometer) imaging spectrograph and ALMA (Atacama Large Millimeter/submillimeter Array) millimetric observations (5–50 mHz), inferred at most about 1 kW m−2^{-2} (roughly 10610^6 erg cm−2^{-2} s−1^{-1}) in the middle chromosphere — not enough to maintain the quiet chromosphere — and Molnar et al. (2023) showed that systematic methodological differences in such studies are large enough to decide their conclusions. Chromospheric inference is intrinsically hard: chromospheric spectral lines form out of non-local thermodynamic equilibrium (non-LTE, meaning the atomic level populations are not determined by the local temperature alone), so velocities, magnetic fields, and electric currents at chromospheric heights are difficult to recover, and the heating events themselves — shocks and current sheets — are intermittent, small-scale, and faint in the quiet Sun.

Three-dimensional radiation-magnetohydrodynamic (rMHD) modeling, chiefly with the Bifrost code (Gudiksen et al. 2011; publicly released enhanced-network simulation of Carlsson et al. 2016), can now follow the convection-zone-to-corona system self-consistently and has shown that photospheric braiding can sustain a hot corona through Poynting-flux (electromagnetic energy flux) injection. Within this framework, Noraz, Carlsson & Aulanier (published as A&A 705, A86, 2026) performed the first event-resolved quantification of both shock and current-sheet heating in a quiet-Sun 3D simulation: applying physics-based detection criteria, they found shocks supply up to 59% of the mechanical heating rate near z≈1.2z\approx1.2 Mm, current sheets dominate above z≈1.5z\approx1.5 Mm as β\beta and the Mach number (flow speed over sound speed) drop, and the two together power 66% of the height-averaged mechanical heating (shocks 23%, current sheets 55%, with 13% of the heating in co-spatial shock–current-sheet events) — with compressive heating a major, previously under-counted local term. The authors themselves stress that this partition comes from a single simulation with an open, coronal-hole-like magnetic topology (field lines opening into interplanetary space); that shock and current-sheet thickness is set by the numerical diffusion scheme rather than physical kinetics; that ambipolar diffusion (heating and diffusion arising from ion–neutral drift in the partially ionized gas) and non-equilibrium ionization were neglected; and that their strict detection thresholds make the quoted shares lower bounds. Their companion study (Noraz et al. 2026, A&A 710, A175) confirmed strong regime dependence: increasing the sub-photospheric magnetic flux collapses the shock share from 23% to 5% while current sheets hold near 50%. What is still missing — and what the source itself identifies as the open issues — is a partition that is robust across independent models and numerical treatments, and observations capable of resolving and discriminating the intermittent, small-scale dynamics that carry it. Adjacent results underline both the stakes and the difficulty: in strong-field plage — the compact regions of intense magnetic flux surrounding active regions — coordinated IRIS (Interface Region Imaging Spectrograph) and Hi-C (High-resolution Coronal Imager) observations support current-dissipation heating (Bose et al. 2024), while simulations show lower-chromospheric shocks pumping magnetic energy into the upper chromosphere that current sheets then dissipate (Martínez-Sykora et al. 2019) — the mechanisms are coupled, which is precisely why quantitative attribution by partition is the crux.

Problem Statement

Which physical processes dominate energy deposition in the solar chromosphere, and how is chromospheric heating partitioned among them?

Determine, quantitatively, the partition of chromospheric heating among shock dissipation of acoustic and magnetoacoustic waves, current-sheet (magnetic reconnection) dissipation of magnetic energy, and the remaining processes (for example dissipation of linear-wave dynamics, ambipolar-diffusion-related and vorticity-related heating), as a function of atmospheric height and of magnetic-field environment — from the weak-field quiet-Sun internetwork (the interiors of convective cells, between magnetic concentrations), through the magnetic network (concentrations of flux outlining convective-cell boundaries), to plage (compact strong-field regions adjacent to active regions) — such that the resulting accounting:

  1. closes the chromospheric energy budget, with the mechanism-resolved deposition balancing the observed chromospheric radiative losses and reproducing the observed thermal structure and chromospheric diagnostics;
  2. is demonstrably robust — not an artifact of one numerical scheme, resolution, heating definition (including the treatment of compressive work), or event-attribution criterion;
  3. is confronted with observations capable of discriminating among the mechanisms — in particular resolving, or uniquely diagnosing, the intermittent small-scale shock and current-sheet dynamics that current models identify as the dominant agents and that couple energy transport between atmospheric layers.

The single scientific objective uniting these requirements is an accepted, observationally constrained, mechanism-resolved energy budget of the solar chromosphere. An answer may take one of two forms, and in either form it must cover the full chromospheric height range — from the temperature minimum to the transition region — and all three magnetic environments identified above (internetwork, network, and plage). A validated model-based partition that survives independent verification and observational confrontation must discharge all three requirements over that scope. A decisive observational determination that establishes or excludes dominance of mechanism families over stated height and regime ranges must discharge requirement 3 and is accepted as a resolution without separately having to deliver the budget closure of requirement 1. Only an answer that discharges the requirements set for its form, over the full stated scope, counts as resolved.

References

  1. Noraz, Q., Carlsson, M., Aulanier, G. 2026, 'Chromosphere of the quiet sun I. Shock and current-sheet dynamics and heating', Astronomy & Astrophysics 705, A86 (arXiv:2511.01858, posted 2025-11-03). DOI: 10.1051/0004-6361/202556375; https://doi.org/10.1051/0004-6361/202556375; arXiv: https://arxiv.org/abs/2511.01858
  2. Noraz, Q., Carlsson, M., Aulanier, G. 2026, 'Chromosphere of the quiet Sun II. Atmospheric response to small-scale magnetic flux emergence', Astronomy & Astrophysics 710, A175. DOI: 10.1051/0004-6361/202660067; https://doi.org/10.1051/0004-6361/202660067
  3. Carlsson, M., De Pontieu, B., Hansteen, V. H. 2019, 'New View of the Solar Chromosphere', Annual Review of Astronomy and Astrophysics 57, 189. DOI: 10.1146/annurev-astro-081817-052044; https://doi.org/10.1146/annurev-astro-081817-052044
  4. Carlsson, M., Stein, R. F. 1992, 'Non-LTE radiating acoustic shocks and Ca II K2V bright points', The Astrophysical Journal 397, L59. DOI: 10.1086/186544; https://doi.org/10.1086/186544
  5. Gudiksen, B. V., Carlsson, M., Hansteen, V. H., Hayek, W., Leenaarts, J., Martínez-Sykora, J. 2011, 'The stellar atmosphere simulation code Bifrost', Astronomy & Astrophysics 531, A154. DOI: 10.1051/0004-6361/201116520; https://doi.org/10.1051/0004-6361/201116520
  6. Carlsson, M., Hansteen, V. H., Gudiksen, B. V., Leenaarts, J., De Pontieu, B. 2016, 'A publicly available simulation of an enhanced network region of the Sun', Astronomy & Astrophysics 585, A4. DOI: 10.1051/0004-6361/201527226; https://doi.org/10.1051/0004-6361/201527226
  7. Martínez-Sykora, J., Hansteen, V. H., Gudiksen, B., Carlsson, M., De Pontieu, B., Gošić, M. 2019, 'On the Origin of the Magnetic Energy in the Quiet Solar Chromosphere', The Astrophysical Journal 878, 40. DOI: 10.3847/1538-4357/ab1f0b; https://doi.org/10.3847/1538-4357/ab1f0b
  8. Udnæs, E. R., Pereira, T. M. D. 2025, 'Characteristics of acoustic-wave heating in simulations of the quiet Sun chromosphere', Astronomy & Astrophysics 699, A25. DOI: 10.1051/0004-6361/202453028; https://doi.org/10.1051/0004-6361/202453028
  9. Abbasvand, V., Sobotka, M., Heinzel, P., Švanda, M., Jurčák, J., del Moro, D., Berrilli, F. 2020, 'Chromospheric Heating by Acoustic Waves Compared to Radiative Cooling. II. Revised Grid of Models', The Astrophysical Journal 890, 22. DOI: 10.3847/1538-4357/ab665f; https://doi.org/10.3847/1538-4357/ab665f
  10. Abbasvand, V., Sobotka, M., Švanda, M., Heinzel, P., García-Rivas, M., Denker, C., Balthasar, H., Verma, M., Kontogiannis, I., Koza, J., Korda, D., Kuckein, C. 2020, 'Observational study of chromospheric heating by acoustic waves', Astronomy & Astrophysics 642, A52. DOI: 10.1051/0004-6361/202038559; https://doi.org/10.1051/0004-6361/202038559
  11. Molnar, M. E., Reardon, K. P., Cranmer, S. R., Kowalski, A. F., Chai, Y., Gary, D. 2021, 'High-frequency Wave Power Observed in the Solar Chromosphere with IBIS and ALMA', The Astrophysical Journal 920, 125. DOI: 10.3847/1538-4357/ac1515; https://doi.org/10.3847/1538-4357/ac1515
  12. Molnar, M. E., Reardon, K. P., Cranmer, S. R., Kowalski, A. F., Milić, I. 2023, 'Constraining the Systematics of (Acoustic) Wave Heating Estimates in the Solar Chromosphere', The Astrophysical Journal 945, 154. DOI: 10.3847/1538-4357/acbc75; https://doi.org/10.3847/1538-4357/acbc75
  13. Bose, S., De Pontieu, B., Hansteen, V., Sainz Dalda, A., Savage, S., Winebarger, A. 2024, 'Chromospheric and coronal heating in an active region plage by dissipation of currents from braiding', Nature Astronomy 8, 697–705. DOI: 10.1038/s41550-024-02241-8; https://doi.org/10.1038/s41550-024-02241-8