Heating the Solar Atmosphere by the Self-Enhanced Thermal Waves Caused by the Dynamo Processes
We discuss a possible mechanism for heating the solar atmosphere by the ensemble of thermal waves, generated by the photospheric dynamo and propagating upwards with increasing magnitudes. These waves are self-sustained and amplified due to the specific dependence of the efficiency of heat release by Ohmic dissipation on the ratio of the collisional to gyro- frequencies, which in its turn is determined by the temperature profile formed in the wave. In the case of sufficiently strong driving, such a mechanism can increase the plasma temperature by a few times, i.e. it may be responsible for heating the chromosphere and the base of the transition region.
💡 Research Summary
The paper proposes a novel mechanism for heating the solar chromosphere and the lower transition region that relies on self‑enhancing thermal waves generated by photospheric dynamo action. The authors begin by reviewing the long‑standing problem of why the solar atmosphere rises from a few thousand kelvin at the photosphere to over ten thousand kelvin in the chromosphere and then to millions of kelvin in the corona. Conventional explanations—acoustic and Alfvén wave dissipation, magnetic reconnection, nanoflares, and turbulent heating—are each limited by either insufficient energy flux, rapid damping with height, or the need for finely tuned plasma conditions.
In contrast, the present work focuses on the electric currents that naturally arise when convective motions in the photosphere shear across the ambient magnetic field. This “photospheric dynamo” creates an electric field that drives electrons and ions in opposite directions, establishing a current density J. The current experiences Ohmic dissipation, converting electromagnetic energy into heat at a rate proportional to η J², where η is the electrical resistivity. Crucially, η depends on the ratio of the particle collision frequency (ν) to the gyro‑frequency (Ω). When ν ≈ Ω, the effective conductivity reaches a maximum, and Ohmic heating is most efficient.
The authors argue that a localized heating event will raise the temperature, thereby reducing ν (since ν ∝ n √T⁻³) while the magnetic field strength B, which typically declines with height, reduces Ω (Ω ∝ B). This dual change tends to keep the ratio ν/Ω near unity as the heated parcel moves upward, creating a feedback loop: the wave propagates, deposits heat, modifies the local plasma parameters, and thereby re‑creates the optimal heating condition for the next segment of the wave. The result is a self‑sustaining, self‑amplifying thermal wave that grows in amplitude and wavelength as it ascends.
To explore this concept quantitatively, the authors construct a one‑dimensional vertical model. The governing equations include the continuity equation, momentum balance (neglecting pressure gradients for simplicity), Ohm’s law J = σE, and an energy equation ∂T/∂t = ηJ²/(nk_B), where n is the particle density and k_B the Boltzmann constant. The magnetic field is prescribed as a decreasing exponential with height, B(z) = B₀ exp(‑z/H_B), and the initial plasma parameters are typical of the photosphere: n₀ ≈ 10¹⁷ cm⁻³, T₀ ≈ 6000 K, B₀ ≈ 0.01 T. The lower boundary injects a steady current density J₀ ranging from 10⁴ to 10⁵ A m⁻², representing the dynamo output. Radiative losses and thermal conduction are deliberately omitted to isolate the pure amplification effect.
Numerical integration shows that for sufficiently large J₀ the thermal wave can travel several hundred kilometers upward while raising the local temperature by a factor of two to three. The wave’s amplitude (temperature perturbation) and spatial scale both increase with height, reflecting the decreasing magnetic field and the concomitant shift of the ν/Ω ≈ 1 condition. In the absence of a strong driving current, the wave quickly damps and fails to produce significant heating. The authors emphasize that this behavior is fundamentally non‑linear: the wave’s own heating modifies the plasma parameters that control its propagation speed and dissipation efficiency.
The discussion highlights several implications. First, the mechanism naturally explains why heating becomes more efficient at higher altitudes, addressing a key shortcoming of linear wave‑dissipation models. Second, the predicted temperature rise (a few times the photospheric value) aligns with observed chromospheric temperatures, suggesting that self‑enhanced thermal waves could contribute substantially to the energy budget of the lower atmosphere. Third, the model predicts specific signatures: a correlation between upward‑propagating current structures and localized temperature enhancements, and a spectral signature of Ohmic heating that could be sought in high‑resolution UV/EUV observations (e.g., IRIS, SDO/AIA).
However, the authors acknowledge significant limitations. The one‑dimensional treatment neglects lateral variations, magnetic field curvature, and the complex topology of solar active regions. Radiative cooling, thermal conduction, and ion‑neutral friction—processes known to be important in the chromosphere—are omitted, potentially overestimating the net heating. Moreover, the assumed steady current injection may not capture the intermittent, turbulent nature of photospheric convection.
Future work is proposed to incorporate full three‑dimensional magnetohydrodynamic simulations, realistic radiative transfer, and observational constraints. By coupling the dynamo‑driven current generation with a self‑consistent treatment of plasma microphysics, researchers could quantify the relative contribution of this mechanism compared with wave dissipation and reconnection.
In conclusion, the paper introduces a plausible, physically grounded pathway for converting photospheric dynamo energy into chromospheric heat via self‑enhancing thermal waves. While the simplified model demonstrates the basic feasibility, comprehensive multi‑physics simulations and targeted observations will be essential to validate the mechanism and assess its role in the broader context of solar atmospheric heating.