Robustness and observational testability of the shock–current-sheet heating partition in the quiet-Sun chromosphere

State-of-the-art 3D radiation-magnetohydrodynamic simulations of the weakly magnetized quiet-Sun (QS) chromosphere show that its heating is dominated by two intermittent structures: acoustic shocks in the lower chromosphere and reconnecting current sheets in the upper chromosphere, together powering about 66% of the mechanical heating (Noraz, Carlsson and Aulanier 2026, Paper I). The follow-up parametric study (Paper II) showed that as small-scale magnetic flux increases, current sheets persistently provide roughly half of the chromospheric heating while the shock share falls from 23% to 5%. This quantification, however, rests on ideal-MHD simulations that omit ambipolar diffusion and Hall currents and assume instantaneous (LTE) hydrogen and helium ionization, covers only a limited flux-emergence family of magnetic configurations, lacks a high-resolution convergence study of the scales of energy deposition, and has not been translated into observational diagnostics. The open problem is to determine how, and whether, the shock-versus-current-sheet heating partition changes when the partially ionized, non-ideal physics of the chromosphere is included; how it behaves across the remaining QS magnetic regimes and topologies; whether the time and spatial scales of energy deposition and the viscous-to-Ohmic ratio converge at higher resolution; and which spectral or imaging signatures can observationally discriminate shock- from current-sheet-dominated heating and identify the transition of shocks back into linear waves near the transition region.

Background

The solar chromosphere — the roughly 2–3 Mm thick layer between the 5772 K photosphere and the million-degree corona — radiates away between $10^{6}$ and $10^{7}$ erg cm$^{-2}$ s$^{-1}$ under quiet-Sun conditions, about an order of magnitude more than the corona, and identifying the processes that deposit this energy is one of the classic open problems of solar physics. In quiet-Sun (QS) regions — areas away from sunspots and active regions, with weak average magnetic fields — two candidate mechanisms have long coexisted: dissipation of acoustic waves that steepen into shocks as they propagate upward into the low-density atmosphere, and dissipation of magnetic energy in current sheets (CS), thin layers of intense magnetic-field gradient where magnetic reconnection converts field energy into heat and bulk motion. Shocks reproduce the bright calcium grains — transient bright points seen in the calcium K spectral line — of the QS chromosphere in 1D simulations (Carlsson and Stein 1992), but observations of acoustic-flux dissipation cannot by themselves balance QS radiative losses (Abbasvand et al. 2020a, 2020b), leaving the magnetic channel essential.

Paper I of the Noraz–Carlsson–Aulanier series gave this dichotomy its first quantitative, volumetric treatment in a 3D radiation-magnetohydrodynamic (rMHD) simulation — a model that solves compressible magnetohydrodynamics coupled to radiative transfer and a realistic equation of state. Run with the Bifrost code — a widely used solar radiation-MHD code — it models a weakly magnetized QS box (12 × 12 Mm horizontal extent, $512^{3}$ grid, 23 km horizontal resolution, open coronal-hole-like magnetic topology, mean unsigned photospheric vertical field $\langle |B_z| \rangle = 21$ G, at the low end of QS values) spanning the convection zone to the corona. The authors introduce physics-based detection criteria: a grid cell is flagged as a shock when the velocity convergence exceeds a threshold set by the local sound speed and grid spacing, and as a reconnecting CS when the current density parallel to the magnetic field, normalized by field strength, exceeds an analogous threshold. Heating is decomposed into viscous ($Q_{\nu}$), Ohmic ($Q_{\eta}$), and positive compressive ($Q_{\rm comp}$) contributions, whose sum defines the mechanical heating $Q_{\rm mech}$. Shocks dominate the lower chromosphere (up to 59% of the mechanical heating near $z = 1.2$ Mm); CS dominate the upper chromosphere ($1.5 \lesssim z \lesssim 2.5$ Mm) as the plasma beta ($\beta = 8\pi P/B^{2}$, the ratio of thermal to magnetic pressure) and the Mach number drop. Averaged over the chromosphere, shocks supply 23%, CS 55%, their overlap region 13%, and their union 66% of $Q_{\rm mech}$.

Two structural caveats motivate the open problem. First, the chromosphere is partially ionized, so the ideal-MHD Ohm's law is only an approximation: ambipolar diffusion (the drift of weakly magnetized neutrals relative to ions across field lines, which dissipates energy where the two species decouple) and the Hall effect (the separation of ion and electron motions at small scales) both modify magnetic diffusion and dissipation, while hydrogen and helium ionization does not obey local thermodynamic equilibrium (LTE) — their ionization-recombination timescales exceed the dynamic timescales of magneto-acoustic shocks, so a non-equilibrium ionization (NEI) treatment changes how much shock energy is stored in ionization rather than released as heat. Earlier studies established that these effects materially alter chromospheric thermodynamics — ambipolar heating (Martínez-Sykora et al. 2012; Nóbrega-Siverio et al. 2020), the joint action of Hall and ambipolar terms in QS magneto-convection (González-Morales et al. 2020), and ion-neutral and NEI effects (Martínez-Sykora et al. 2020) — but none was combined with the shock/CS detection-and-partition framework. Second, Bifrost's numerical stability relies on hyper-diffusivity, which selectively enhances viscosity and resistivity at unresolved sharp gradients; it renders the integrated dissipation resolution-independent but sets artificial thicknesses (typically six grid cells) for shocks and CS and leaves the exact viscous-to-Ohmic ratio scheme-dependent.

Paper II of the series extended the reference model by injecting horizontal magnetic-flux sheets of increasing amplitude ($B_y = 200$ G and 800 G) into the subsurface convection zone. Chromospheric temperature and mechanical heating rise monotonically with field strength; current sheets maintain about half of the chromospheric heating (55–47%) while the shock share falls from 23% to 5%; and the coronal-base temperature responds non-monotonically, because heating- and emergence-driven mass loading amplifies radiative losses that dominate the coronal energy balance. The first-order magnetization dependence of the partition is thus now established for the flux-emergence family of QS configurations — while the non-ideal physics, the remaining magnetic regimes (e.g., the network: the stronger-field concentrations outlining supergranular boundaries), numerical convergence, and observability remain open, and are the subject of this problem.

Problem Statement

Starting from the shock/current-sheet heating quantification of the quiet-Sun chromosphere established in Paper I and its flux-emergence parametric extension in Paper II — both performed with ideal-MHD, LTE-ionization Bifrost simulations and physics-based shock/CS detection criteria — determine the robustness and observational testability of this multi-process heating partition. The components of the problem, which jointly serve this single objective, are:

1. How does the shock-versus-current-sheet partition of chromospheric mechanical heating, and its decomposition into viscous, Ohmic, and compressive contributions ($Q_{\nu}$, $Q_{\eta}$, $Q_{\rm comp}$), change when the generalized Ohm's law terms relevant to the partially ionized chromosphere — ambipolar diffusion and Hall currents — and non-equilibrium ionization of hydrogen and helium are included? In particular, does the upper-chromospheric dominance of current-sheet heating and the ~13% shock–CS overlap persist, weaken, or redistribute?

2. How does the partition behave across the quiet-Sun magnetic parameter space beyond the flux-emergence family already studied — for example network-field strengths and topologies, and a denser sampling of mean photospheric field strengths — i.e., is the multi-process heating scenario universal across quiet-Sun regimes or regime-dependent in a way that the three existing runs do not capture?

3. Do the time and spatial scales of energy deposition and the viscous-to-Ohmic dissipation ratio converge at higher numerical resolution, given that the hyper-diffusivity scheme currently sets the thicknesses of shocks and current sheets?

4. Which observationally testable diagnostics — spectral or imaging signatures — robustly distinguish shock-dominated from current-sheet-dominated heating, so that the partition can be confronted with high-resolution observations from facilities such as the European Solar Telescope (a planned 4-m class solar telescope optimized for chromospheric spectroscopy)?

5. What is the observable signature of the transition of shocks back to linear waves near the transition region (the thin interface layer separating the chromosphere from the corona)?

These five components are each required for a complete answer: an answer that addresses only a subset of them leaves the stated objective unresolved.

A defensible answer must apply the same physics-based detection framework consistently across ideal and non-ideal runs and across configurations, so that the reported changes in the partition are attributable to the added physics or the changed magnetic regime rather than to analysis differences. Such an answer need not be exhaustive: it must answer each component quantitatively where the component poses a quantitative question, must state the configurations, resolution, and diagnostics actually analysed, and must confine its conclusions to those cases.

References

1. Q. Noraz, M. Carlsson, G. Aulanier, 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)
2. Q. Noraz, M. Carlsson, G. Aulanier, 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)
3. M. Carlsson, R. F. Stein, 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
4. J. Martínez-Sykora, B. De Pontieu, V. Hansteen, 2012, 'Two-dimensional radiative magnetohydrodynamic simulations of the importance of partial ionization in the chromosphere', The Astrophysical Journal 753, 161, DOI: 10.1088/0004-637X/753/2/161, https://doi.org/10.1088/0004-637X/753/2/161
5. D. Nóbrega-Siverio, J. Martínez-Sykora, F. Moreno-Insertis, M. Carlsson, 2020, 'Ambipolar diffusion in the Bifrost code', Astronomy & Astrophysics 638, A79, DOI: 10.1051/0004-6361/202037809, https://doi.org/10.1051/0004-6361/202037809
6. P. A. González-Morales, E. Khomenko, N. Vitas, M. Collados, 2020, 'Joint action of Hall and ambipolar effects in 3D magneto-convection simulations of the quiet Sun', Astronomy & Astrophysics 642, A220, DOI: 10.1051/0004-6361/202037938, https://doi.org/10.1051/0004-6361/202037938
7. J. Martínez-Sykora, J. Leenaarts, B. De Pontieu, D. Nóbrega-Siverio, V. H. Hansteen, M. Carlsson, M. Szydlarski, 2020, 'Ion–neutral interactions and nonequilibrium ionization in the solar chromosphere', The Astrophysical Journal 889, 95, DOI: 10.3847/1538-4357/ab643f, https://doi.org/10.3847/1538-4357/ab643f
8. V. Abbasvand, M. Sobotka, P. Heinzel, M. Švanda, J. Jurčák, D. del Moro, F. Berrilli, 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
9. V. Abbasvand, M. Sobotka, M. Švanda, P. Heinzel, M. García-Rivas, C. Denker, H. Balthasar, M. Verma, I. Kontogiannis, J. Koza, D. Korda, C. Kuckein, 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
10. E. R. Udnæs, T. M. D. Pereira, 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 (arXiv:2505.21047, https://arxiv.org/abs/2505.21047)
11. M. O. Sand, Q. Noraz, G. Aulanier, J. Martínez-Sykora, M. Carlsson, L. Rouppe van der Voort, 2025, 'Shock-induced magnetic reconnection driving Ellerman bomb emission and a spicule', arXiv:2512.19547, https://arxiv.org/abs/2512.19547 (accepted in Astronomy & Astrophysics)
12. G. Cherry, B. Gudiksen, A. J. Finley, Q. Noraz, 2026, 'Decomposing wave activity in the solar atmosphere: Shocks, jets and swirls in the quiet Sun', Astronomy & Astrophysics 705, A42, DOI: 10.1051/0004-6361/202557226, https://doi.org/10.1051/0004-6361/202557226 (arXiv:2509.11179, https://arxiv.org/abs/2509.11179)
13. R. Chaurasiya, S. Srivastava, P. Chatterjee, S. Dey, R. Erdélyi, A. R. Bayanna, 2026, 'On the Relationship between Solar Spicules and Propagating Coronal Disturbances: The Role of Shocks', The Astrophysical Journal 1005, 111, DOI: 10.3847/1538-4357/ae75eb, https://doi.org/10.3847/1538-4357/ae75eb (arXiv:2606.02516, https://arxiv.org/abs/2606.02516)