Coordinated SST/IRIS observations showed that cancellations of quiet-Sun internetwork (IN) magnetic fields produce real but strictly local chromospheric heating, with a population-aggregated energy input about one order of magnitude below the roughly 10−110^{-1} erg cm−3^{-3} s−1^{-1} needed to sustain the internetwork chromosphere at the sensitivity then available (about 24 G at the 3-sigma noise level). Because deep spectropolarimetry indicates the IN is nearly fully covered by weak fields of order 20 Mx cm−2^{-2}, cancellations of such sub-threshold fields could in principle close this deficit, but no observation has yet combined the polarimetric sensitivity, spatial resolution, field of view, duration, and chromospheric diagnostics needed to count them. The problem is to determine, observationally and with realistic modeling, the frequency, per-event energy, and area coverage of IN cancellations down to the weak-field population, and thereby to decide whether their aggregated energy release balances the internetwork chromospheric radiative losses — closing, or definitively excluding closure of, the one-order-of-magnitude deficit.

Background

The solar chromosphere — the layer between the visible photosphere and the million-degree corona — is maintained at temperatures of roughly 6,000–20,000 K against persistent radiative losses that must be continuously resupplied by mechanical and magnetic energy from below. In quiet, active-region-free Sun, the chromospheric demand adopted in the source work is of order 10−110^{-1} erg cm−3^{-3} s−1^{-1}; identifying what supplies it is one of the classic unsolved problems of solar physics.

The quiet photosphere is organized into supergranular convection cells whose boundaries (the network) concentrate strong kilogauss fields, while the cell interiors — the internetwork (IN) — harbor weak (tens of gauss), small, short-lived magnetic elements. IN regions cover most of the solar surface, and very deep observations with the Hinode Spectro-Polarimeter (an instrument measuring the full polarization state of spectral lines) indicate that the IN is nearly fully seeded by weak fields of order 20 Mx cm−2^{-2}, most of which are invisible to routine magnetograms. A magnetogram is a map of the line-of-sight magnetic field inferred from the circular polarization of a spectral line; its sensitivity, i.e. the noise level of the map, sets the weakest field it can detect (about 24 G at three times the noise sigma for the Mg I 5173 Å data used in the source study).

Flux cancellation is the apparent loss of magnetic flux when opposite-polarity patches converge and mutually diminish. It can be the photospheric signature of magnetic reconnection — field lines of opposite polarity reconnecting in the chromosphere above, converting magnetic energy into heat, jets, and plasma motion — or of the submergence of U-shaped loops below the surface. The source study, Gošić et al. 2018, used coordinated observations with the Swedish 1-m Solar Telescope (SST) and the Interface Region Imaging Spectrograph (IRIS) to identify 411 cancelling IN events, about 76% of them cospatial with transient brightenings in IRIS 1400 Å slit-jaw images. Multi-line non-LTE inversions of the Mg II h and k lines — that is, fitting observed line profiles with atmospheric models computed outside local thermodynamic equilibrium — showed local temperature increases exceeding 10310^{3} K, establishing that individual cancellation events do heat the upper photosphere and chromosphere.

The deficit is in the aggregate budget. Averaged over the IN field of view and the observing time, the magnetic energy released by the detected cancellations was only about 1×10−21\times10^{-2} erg cm−3^{-3} s−1^{-1}, an order of magnitude below the chromospheric requirement, because the events are localized and cover a small fraction of the area. Gošić et al. noted, however, that if the ubiquitous weak fields of order 20 Mx cm−2^{-2} hinted at by deep Hinode spectropolarimetry dissipate through cancellations on the same timescales as the stronger elements they could resolve, the missing factor of ten could plausibly be supplied. Settling this requires polarimetric sensitivity near the photon limit (about 10−410^{-4} of the continuum intensity), spatial resolution of order 20 km, large area coverage, and long time series — the domain of the 4-m Daniel K. Inouye Solar Telescope (DKIST) and the planned European Solar Telescope (EST).

The question sits inside a broader landscape of proposed quiet-chromosphere heating channels: analytical cancellation-nanoflare models and radiation-MHD simulations argue that converging opposite-polarity flux can heat the chromosphere and corona; small-scale-dynamo simulations suggest that weak IN fields in aggregate carry enough energy; acoustic shocks and Poynting-flux transport by magnetoconvection are competing suppliers. None of these, however, substitutes for the specific observational determination asked for here: a closure-tested energy budget for IN flux cancellation, including the population currently hidden below magnetogram sensitivity.

Problem Statement

Determine the total contribution of quiet-Sun internetwork (IN) magnetic-flux cancellations — including the weak, small-scale fields below current magnetogram detection thresholds (about 24 G at 3 sigma in the source dataset, down to the roughly 20 Mx cm−2^{-2} fields indicated by deep Hinode spectropolarimetry) — to the heating of the internetwork chromosphere. Concretely: (1) measure, with a completeness-corrected census combining sufficient polarimetric sensitivity, spatial resolution, field of view, and duration, the frequency, per-event magnetic-energy release, and area coverage of cancellations of sub-threshold IN fields, quantifying and removing the selection effects that limited earlier surveys; and (2) decide whether the aggregated energy input, averaged over the internetwork, balances the chromospheric radiative losses of order 10−110^{-1} erg cm−3^{-3} s−1^{-1} — that is, whether it closes, or definitively excludes closing, the roughly one-order-of-magnitude deficit found by Gošić et al. 2018. These are components of one objective: a closure-tested observational energy budget for internetwork-field cancellation heating of the quiet chromosphere, with quantified selection effects and uncertainties. Answers restricted to single events or to resolved fields only, without the aggregated budget, do not address the problem.

References

  1. Gošić, M., de la Cruz Rodríguez, J., De Pontieu, B., Bellot Rubio, L. R., Carlsson, M., Esteban Pozuelo, S., Ortiz, A., Polito, V. (2018). Chromospheric heating due to cancellation of quiet Sun internetwork fields. The Astrophysical Journal 857, 48. DOI: 10.3847/1538-4357/aab1f0. https://arxiv.org/abs/1802.07392
  2. Ledvina, V. E., Kazachenko, M. D., Criscuoli, S., Tilipman, D., Ermolli, I., Falco, M., Guglielmino, S., Jafarzadeh, S., Rouppe van der Voort, L., Zuccarello, F. (2022). Quantifying Properties of Photospheric Magnetic Cancellations in the Quiet Sun Internetwork. The Astrophysical Journal 934, 38. DOI: 10.3847/1538-4357/ac7785. https://arxiv.org/abs/2206.04644
  3. Park, S.-H. (2020). An Observational Test of Solar Plasma Heating by Magnetic Flux Cancellation. The Astrophysical Journal 897, 49. DOI: 10.3847/1538-4357/ab93ca. https://arxiv.org/abs/2005.07953
  4. Priest, E. R., Chitta, L. P., Syntelis, P. (2018). A Cancellation Nanoflare Model for Solar Chromospheric and Coronal Heating. The Astrophysical Journal Letters 862, L24. DOI: 10.3847/2041-8213/aad4fc. https://arxiv.org/abs/1807.08161
  5. Gošić, M., De Pontieu, B., Sainz Dalda, A. (2024). Global Impact of Emerging Internetwork Fields on the Low Solar Atmosphere. The Astrophysical Journal 964, 175. DOI: 10.3847/1538-4357/ad2e03. https://arxiv.org/abs/2211.09111
  6. Gošić, M., De Pontieu, B., Bellot Rubio, L. R., Sainz Dalda, A., Esteban Pozuelo, S. (2021). Emergence of Internetwork Magnetic Fields through the Solar Atmosphere. The Astrophysical Journal 911, 41. DOI: 10.3847/1538-4357/abe7e0. https://arxiv.org/abs/2103.02213
  7. Giannattasio, F., Consolini, G., Berrilli, F., Del Moro, D. (2020). Magnetic Energy Balance in the Quiet Sun on Supergranular Spatial and Temporal Scales. The Astrophysical Journal 904, 7. DOI: 10.3847/1538-4357/abbb36. https://doi.org/10.3847/1538-4357/abbb36
  8. Campbell, R. J., Keys, P. H., Mathioudakis, M., Wöger, F., Schad, T. A., Tritschler, A., de Wijn, A. G., Smitha, H. N., Beck, C. A., Christian, D. J., Jess, D. B., Erdélyi, R. (2023). DKIST Unveils the Serpentine Topology of Quiet Sun Magnetism in the Photosphere. The Astrophysical Journal Letters 955, L36. DOI: 10.3847/2041-8213/acf85d. https://arxiv.org/abs/2309.05836
  9. Liu, J., Sun, X., Schuck, P. W., Jaeggli, S. A. (2025). What Can DKIST/DL-NIRSP Tell Us About Quiet-Sun Magnetism? The Astrophysical Journal 979, 139. DOI: 10.3847/1538-4357/ad98e7. https://arxiv.org/abs/2411.18735
  10. Trelles Arjona, J. C. (2025). Quiet Sun Magnetism from ViSP Data Multiline Inversions Around 630.1 nm. The Astrophysical Journal 986, 169. DOI: 10.3847/1538-4357/adceca. https://arxiv.org/abs/2506.14076
  11. Przybylski, D., Cameron, R., Solanki, S. K., Rempel, M., Danilovic, S., Leenaarts, J. (2025). Structure and dynamics of the internetwork solar chromosphere: results of a small-scale dynamo simulation. Astronomy & Astrophysics 703, A148. DOI: 10.1051/0004-6361/202554656. https://arxiv.org/abs/2508.19809
  12. Tang, Z., Shen, Y., Zhou, C., Yao, S., Liu, D. (2025). High-resolution Observations of a Small-scale Cancellation Nanoflare: Supporting Evidence for the Cancellation Nanoflare Model. The Astrophysical Journal Letters 985, L11. DOI: 10.3847/2041-8213/adca3a. https://arxiv.org/abs/2504.02396
  13. Moreno-Insertis, F., Hansteen, V. H., Nóbrega-Siverio, D. (2025). Magnetic Flux Cancellation in the Solar Atmosphere through 3D Realistic Numerical Modeling. The Astrophysical Journal 995, 137. DOI: 10.3847/1538-4357/ae14fb. https://arxiv.org/abs/2510.19993