High-resolution 3D radiative magnetohydrodynamic simulations showed that the quiet solar chromosphere can amplify its own magnetic field in situ: magnetoacoustic shocks in the lower chromosphere convert kinetic energy into magnetic energy, with the horizontally averaged field strength saturating at roughly 4–30 G in structures poorly connected to the photosphere. A direct 2023 sequel established that this locally grown magnetic energy can indeed be dissipated into heat when ambipolar diffusion and non-equilibrium hydrogen ionization are included. What remains open is whether this mechanism is a general and observable source of chromospheric magnetic energy and heating on the Sun: how amplification and dissipation behave outside the idealized weakest-internetwork setup (network-scale flux, different connectivity, explicit flux emergence), and whether the predicted weak, transient structures can be confirmed spectro-polarimetrically in the chromospheric lines identified by the source (Ca II H, Ca II 8542 Å, Na I D 5896 Å, Mg I 5173 Å).

Background

The solar chromosphere is the roughly 2000 km thick, weakly ionized layer between the visible photosphere and the transition region; in quiet (non-active) regions it is divided into the network (concentrated magnetic flux along supergranular cell boundaries) and the internetwork (weak, highly dynamic fields in the cell interiors). Observations show the internetwork photosphere is filled with magnetic field produced by a small-scale dynamo (turbulent convection amplifying field) and by intermittent small-scale flux emergence, but weak photospheric field largely fails to expand into the chromosphere because convection, the entropy drop with height, and strong downdrafts recycle it back into deeper layers.

The source of this problem is a study using the Bifrost code, which solves the magnetohydrodynamic (MHD) equations coupled to radiative energy exchange — specifically with non-gray, non-local-thermodynamic-equilibrium (non-LTE, meaning the radiation field is not in equilibrium with the local matter) radiative transfer and thermal conduction along magnetic field lines. Martínez-Sykora et al. (2019) simulated a very quiet internetwork region with a weak initial field and no injection of new flux through the boundaries, and found: (1) the net photospheric magnetic flux cannot maintain the chromospheric field on average; (2) in the lower chromosphere, where magnetoacoustic shocks (steepened sound waves in a magnetized, stratified plasma) dominate, kinetic energy is converted into magnetic energy through stretch-twist-fold of field lines plus reconnection — a linear (not exponential) growth, so not a classical fast turbulent dynamo; (3) the chromospheric magnetic energy grows linearly in time until the horizontal-average rms field strength saturates at roughly 4–30 G; (4) the resulting magnetic features are localized to this layer and only weakly connected to deeper layers. This raised a natural agenda: whether that in-situ magnetic energy can be dissipated into heat, whether the mechanism survives in more magnetized environments, whether the structures are observable, and how robust the numbers are to numerical choices.

Two physical ingredients are central to the dissipation question. The chromosphere is partially ionized, and ion–neutral collisions give rise to ambipolar diffusion: in the generalized Ohm's law, currents flowing perpendicular to the magnetic field drift through the neutrals and dissipate magnetic energy as heat. Its efficiency depends on the ionization fraction, which is set by non-equilibrium ionization (NEQI) — the lag of the hydrogen ionization state behind local thermodynamic equilibrium in dynamic plasma. Khomenko et al. (2018) had shown in local-dynamo magneto-convection simulations that ambipolar diffusion can dissipate dynamo-generated magnetic energy, but without chromospheric radiative transfer or NEQI; Martínez-Sykora et al. (2020) quantified how NEQI changes ambipolar heating in shocks.

The source paper itself resolved the dissipation question with a direct sequel: Martínez-Sykora et al. (2023) added ambipolar diffusion and time-dependent NEQ hydrogen ionization to a higher-resolution version of the same model, finding that the in-situ growth of the lower-chromospheric field continues nearly unchanged, while ambipolar diffusion dissipates the locally grown magnetic energy in the upper chromosphere, heating it above roughly 10410^4 K, with synthetic Mg II line profiles correspondingly closer to observations. A companion preprint (Martínez-Sykora et al. 2022, arXiv:2210.15150) synthesized full Stokes profiles (the four Stokes parameters II, QQ, UU, VV encoding intensity and linear/circular polarization of a spectral line, which carry magnetic information via the Zeeman effect) from the model for photospheric iron and chromospheric Ca II lines, predicting circular polarization signals large enough for the 4-meter Daniel K. Inouye Solar Telescope (DKIST) to detect.

That leaves the surviving questions this record addresses. Observationally, the relevant diagnostics are full-Stokes spectropolarimetry in chromospheric lines — Ca II H (3968 Å), Ca II 8542 Å, Na I D (5896 Å), and Mg I 5173 Å — from facilities such as DKIST, the planned European Solar Telescope (EST), and the balloon-borne Sunrise III with its SCIP spectropolarimeter; the weak-field approximation (relating the circular-polarization amplitude to the line-of-sight field for weak fields) is the standard inference tool at these signal levels. Very recent Sunrise III/SCIP observations reveal thread-like chromospheric field structures over internetwork regions with no obvious photospheric counterpart — morphologically suggestive of the prediction — but without any test of the in-situ-amplification interpretation. On the simulation side, adjacent Bifrost studies of quiet-Sun chromospheric heating (Noraz et al. 2026, Papers I and II of their quiet-Sun chromosphere series) quantify shock and current-sheet heating and the response to injected small-scale flux, but include neither ambipolar diffusion and NEQI nor an analysis of in-situ magnetic-energy growth, so the dependence of the mechanism on the magnetic environment has been quantified only in the single weakest-internetwork setup.

Problem Statement

Determine whether the in-situ amplification of chromospheric magnetic field found in the idealized quiet-internetwork simulation of Martínez-Sykora et al. (2019) — conversion of kinetic energy of magnetoacoustic shocks into magnetic energy in the lower chromosphere, saturating at a horizontal-average rms field strength of roughly 4–30 G — is a general and observable source of magnetic energy and heating in the quiet solar chromosphere. Concretely:

(a) Generality across magnetic environments: with self-consistent radiative MHD simulations that include ambipolar diffusion and non-equilibrium ionization (as in the 2023 follow-up), quantify how the amplitude, growth rate, saturation level, height distribution, and ambipolar dissipation of the in-situ-generated field change in environments other than the weakest internetwork case — regions with network-scale mean flux, different large-scale connectivity, and explicit flux emergence through the lower boundary.

(b) Observational signature and confirmation: complete the forward modeling with full synthetic Stokes profiles in the chromospheric lines named by the source — Ca II H, Ca II 8542 Å, Na I D 5896 Å, and Mg I 5173 Å (the last two not yet synthesized), including realistic instrumental treatment for DKIST/EST-class telescopes — and determine observationally whether the predicted weak, transient, locally confined structures with weak photospheric connectivity exist on the Sun, distinguishing them from magnetic-canopy fields (the horizontally expanding network field overlying the internetwork chromosphere) and from photospheric flux that is emerging or submerging.

The common objective uniting these deliverables is a verdict on whether in-situ amplification is a real, general contributor to the quiet-Sun chromosphere's magnetic-energy budget and heating, rather than an artifact or edge case of one idealized simulation.

Completion of the task requires a verdict on this common objective: (a) and (b) are both required, and an answer that covers only part of the environments or lines listed above must state which parts remain uncovered and why they cannot change the verdict.

References

  1. 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(1), 40, DOI 10.3847/1538-4357/ab1f0b, https://doi.org/10.3847/1538-4357/ab1f0b (arXiv:1904.04464, https://arxiv.org/abs/1904.04464)
  2. Martínez-Sykora, J., de la Cruz Rodríguez, J., Gošić, M., Sainz Dalda, A., Hansteen, V. H., & De Pontieu, B. 2023, 'Chromospheric Heating from Local Magnetic Growth and Ambipolar Diffusion under Nonequilibrium Conditions', The Astrophysical Journal Letters 943(1), L14, DOI 10.3847/2041-8213/acafe9, https://doi.org/10.3847/2041-8213/acafe9 (arXiv:2211.08472, https://arxiv.org/abs/2211.08472)
  3. Martínez-Sykora, J., Sainz Dalda, A., Gošić, M., & De Pontieu, B. 2022, 'Small-scale chromospheric spectropolarimetric observables in the internetwork from a 3D radiative MHD model', arXiv:2210.15150, https://arxiv.org/abs/2210.15150 (preprint)
  4. Martínez-Sykora, J., Leenaarts, J., De Pontieu, B., Nóbrega-Siverio, D., Hansteen, V. H., Carlsson, M., & Szydlarski, M. 2020, 'Ion–neutral Interactions and Nonequilibrium Ionization in the Solar Chromosphere', The Astrophysical Journal 889(2), 95, DOI 10.3847/1538-4357/ab643f, https://doi.org/10.3847/1538-4357/ab643f
  5. Nóbrega-Siverio, D., Moreno-Insertis, F., Martínez-Sykora, J., Carlsson, M., & Szydlarski, M. 2020, 'Nonequilibrium ionization and ambipolar diffusion in solar magnetic flux emergence processes', Astronomy & Astrophysics 633, A66, DOI 10.1051/0004-6361/201936944, https://doi.org/10.1051/0004-6361/201936944
  6. Khomenko, E., Vitas, N., Collados, M., & de Vicente, A. 2018, 'Three-dimensional simulations of solar magneto-convection including effects of partial ionization', Astronomy & Astrophysics 618, A87, DOI 10.1051/0004-6361/201833048, https://doi.org/10.1051/0004-6361/201833048
  7. Khomenko, E., Vitas, N., Collados, M., & Modestov, M. 2025, 'Convergence study of ambipolar diffusion in realistic simulations of magneto-convection', Astronomy & Astrophysics 697, A29, DOI 10.1051/0004-6361/202452284, https://doi.org/10.1051/0004-6361/202452284
  8. Noraz, Q., Carlsson, M., & Aulanier, G. 2026, 'Chromosphere of the quiet Sun -- I. Shock and current-sheet dynamics and heating', Astronomy & Astrophysics 705, A86, DOI 10.1051/0004-6361/202556375, https://doi.org/10.1051/0004-6361/202556375 (arXiv:2511.01858, https://arxiv.org/abs/2511.01858)
  9. 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 (arXiv:2605.03019, https://arxiv.org/abs/2605.03019)
  10. Kubo, M., Katsukawa, Y., Kawabata, Y., Oba, T., Hara, H., et al. 2026, 'Three-dimensional Magnetic Field Structure of a Quiet-Sun Region Revealed by SUNRISE III/SCIP', The Astrophysical Journal Letters 1008, L9, DOI 10.3847/2041-8213/ae909b, https://doi.org/10.3847/2041-8213/ae909b (arXiv:2607.26353, https://arxiv.org/abs/2607.26353)
  11. Campbell, R. J., Quintero Noda, C., Collados, M., Mathioudakis, M., Lagg, A., et al. 2026, 'Horizontal Magnetic Fields Dominate the Quiet Sun Internetwork in Sunrise III Observations. Evidence from Traditional and Transformer-Based Inversions', arXiv:2608.03776, https://arxiv.org/abs/2608.03776