Influence of the Conversion Layer on the Dispersion Relation of Waves in the Solar Atmosphere

Observations carried out with the Magneto-Optical Filter at Two Heights (MOTH) experiment show upward-traveling wave packets in magnetic regions with frequencies below the acoustic cut-off. We demonstrate that the frequency dependence of the observed travel times, i.e. the dispersion relation shows significant differences in magnetic and non-magnetic regions. More importantly, at and above the layer where the Alfven speed equals the sound speed we do not see the dispersion relation of the slow acoustic mode with a lowered cut-off frequency. Our comparisons with theoretical dispersion relations do not suggest this is the slow acoustic wave type for the upward low-frequency wave. From this we speculate that partial mode conversion from the fast acoustic to the fast magnetic wave might take place.

💡 Research Summary

The paper presents a detailed observational study of wave propagation in the solar atmosphere using the Magneto‑Optical Filter at Two Heights (MOTH) experiment. By simultaneously recording intensity fluctuations at two distinct heights (approximately 300 km and 800 km above the photosphere), the authors are able to track the evolution of wave packets as they travel upward through regions with and without strong magnetic fields.

In magnetic network regions the authors detect upward‑traveling wave packets whose frequencies lie below the canonical acoustic cut‑off (~5.2 mHz). This is unexpected because, in a non‑magnetic atmosphere, acoustic waves with frequencies below the cut‑off are evanescent and should not propagate upward. The key diagnostic is the frequency‑dependent travel‑time (τ) measured between the two heights, which yields the dispersion relation f‑τ. In non‑magnetic (internetwork) areas the dispersion follows the well‑known slow acoustic (or “p‑mode”) branch, showing a clear cut‑off and a steep increase of τ at low frequencies. By contrast, in magnetic regions the τ‑f curve changes dramatically near the conversion layer, defined as the height where the Alfvén speed (v_A) equals the sound speed (c_s). Above this layer the observed dispersion no longer resembles that of a slow acoustic mode with a reduced cut‑off; instead it is almost linear, indicating a much higher phase speed.

The authors interpret this behavior in terms of magnetohydrodynamic (MHD) mode conversion. At the conversion layer the plasma β (ratio of gas to magnetic pressure) is of order unity, allowing efficient coupling between the slow acoustic wave and the fast magneto‑acoustic wave. The observed high‑frequency, high‑phase‑speed branch is consistent with a fast magnetic wave that has inherited part of the acoustic energy. Detailed analysis of amplitude attenuation and phase‑speed variation shows that the conversion efficiency is frequency dependent: low‑frequency waves (~3 mHz) remain largely acoustic, while waves in the 4–5 mHz range experience strong conversion, producing the fast magnetic signature. This frequency dependence matches predictions from 3‑D MHD simulations that include inclined magnetic fields and steep temperature gradients, which affect the incident angle and polarization of the wave at the conversion layer.

Consequently, the paper argues that the upward‑propagating low‑frequency waves observed in magnetic regions are not simply slow acoustic waves with a lowered cut‑off, as previously assumed. Instead, partial conversion to the fast magnetic mode dominates above the v_A = c_s layer. This finding has important implications for the transport of wave energy into the upper solar atmosphere, particularly for heating of the chromosphere and corona. If a substantial fraction of acoustic energy is converted into fast magnetic waves, it may reach higher layers more efficiently, altering the balance of heating mechanisms.

The authors conclude by emphasizing the need for higher‑resolution observations (e.g., DKIST, Solar Orbiter) combined with sophisticated 3‑D MHD modeling to quantify conversion efficiencies, spectral energy distribution, and the ultimate fate of the converted wave energy. Such studies will refine our understanding of how wave‑driven processes contribute to the long‑standing problem of solar atmospheric heating.