Velocity Acoustic Oscillations in Sunspots

• VAOs are periodic velocity fluctuations caused by acoustic and magnetoacoustic waves propagating in plasmas, notably observed as three-minute oscillations in sunspot regions.
• Observations using instruments like SDO/HMI and spectral diagnostics reveal distinct phase shifts that differentiate upward propagating slow magnetoacoustic waves from standing wave modes.
• Advanced signal processing methods, including narrow-band frequency filtering and spatial FFT analysis, enable detailed mapping of wave modes and insights into energy transfer in the solar atmosphere.

Velocity Acoustic Oscillations (VAOs) are periodic velocity fluctuations resulting from the propagation of acoustic (sound) or magnetoacoustic waves in plasmas and cosmological media. In solar and astrophysical settings, VAOs are strongly influenced by magnetic field geometry, fluid stratification, and localized inhomogeneities, manifesting as three-minute oscillations in sunspot penumbrae and superpenumbrae detectable in line-of-sight (LOS) velocity measurements. The precise classification of these oscillations—whether magnetoacoustic or Alfvénic—is crucial for understanding energy transport and wave coupling in the solar atmosphere.

1. Observational Overview of Three-Minute VAOs in Sunspot Vicinity

Sunspot penumbrae and superpenumbrae exhibit dominant 3-minute LOS velocity oscillations observable in photospheric and chromospheric layers through spectral lines such as Fe I 6173 Å and Si I 10827 Å. These oscillations extend to the transition region and lower coronal layers above active regions. High-cadence spectroscopic timeseries, typically over 90 minutes, reveal sharp periodic signals when subjected to narrow-band frequency filtration (5.6–5.8 mHz). Phase comparisons between LOS velocity and intensity show a ∼180° phase shift in the penumbra—a haLLMark of propagating waves—while the superpenumbra presents mixed signatures, with phase shifts near both 180° and 90°, suggestive of propagating and standing modes respectively. This empirical distribution aligns with the idea that wave propagation and reflection are modulated by local magnetic field topology.

2. Magnetoacoustic versus Alfvénic Wave Classification

The central finding of recent analyses is that 3-minute oscillations in LOS velocity signals are best explained by magnetoacoustic waves—acoustic waves modified by the local magnetic field—propagating upward from the photosphere (Chelpanov et al., 24 Sep 2024). The ∼180° phase relationship between LOS velocity and intensity is diagnostic of upward propagating slow magnetoacoustic waves. In contrast, phase shifts close to 90° signify standing wave configurations, often found further from the sunspot core, where magnetic field lines are more horizontal.

However, the presence of oscillations in LOS magnetic field signals, occasionally decoupled from velocity and intensity oscillations, hints at the existence of Alfvénic modes. These transverse or torsional oscillations may be present in the photosphere, even if they do not dominate the velocity signal. This nuanced multi-modal behavior reflects the complexity and diversity of wave phenomena in structured magnetic environments and suggests coexisting magnetoacoustic and Alfvénic waveforms in certain regions.

3. Methodological Considerations in VAO Detection

The detection and classification of VAOs rely on multi-instrument, multi-channel methodologies. Space-based instruments such as SDO/HMI provide measurements of intensity, LOS velocity, and magnetic field using the Fe I 6173 Å line, while AIA supplements higher-layer imaging. Ground-based telescopes add spectral diagnostics (Si I 10827 Å) at complementary heights.

Signal processing involves narrow-band frequency filtering using wavelets (e.g., sixth-order Morlet as per Torrence and Compo, 1998), followed by spatial FFT analysis, often normalized by time series variance. Spatial phase analysis involves shifting intensity and velocity signals to optimize cross-correlation, identifying phase differences that distinguish between propagating and standing wave modes. This approach enables mapping the spatial distribution of oscillation character and the separation of regions with distinct wave behavior.

4. VAOs in the Context of Solar Magnetohydrodynamics

The predominance of magnetoacoustic wave behavior in LOS velocity oscillations ties VAOs to slow magnetoacoustic waves—compressive, longitudinal oscillations whose propagation is guided and modulated by the sunspot’s magnetic field. The observed transition from propagating to standing wave characteristics across penumbra and superpenumbra correlates with changes in field inclination and magnetic topology. Regions with more vertical field lines favor upward propagation, while horizontal fields promote the formation of wave cavities and mode conversion.

The intermittent detection of independent oscillations in the LOS magnetic field signals implies that Alfvénic dynamics may initiate already in the photosphere. These signals could witness torsional or kink-type Alfvénic oscillations, revealed in the data as autonomous magnetic field fluctuations unaccompanied by strong velocity or intensity oscillations.

5. Implications for VAO Theory and Future Research

The preponderance of magnetoacoustic wave signatures in observed 3-minute LOS velocity oscillations reinforces their interpretation as VAOs within the broader context of acoustic and MHD wave theory. However, the auxiliary presence of Alfvénic activity mandates caution—isolated magnetic signals already in the photosphere suggest that comprehensive VAO analyses should account for a possible mode superposition.

To rigorously disentangle magnetoacoustic and Alfvénic contributions, future research must employ simultaneous observations of LOS velocity, magnetic field strength, spectral line width, and intensity at multiple atmospheric heights. Enhanced spectral analyses may resolve fine distinctions between compressive (magnetoacoustic) and non-compressive (Alfvénic) waveforms. Additionally, higher spatial and temporal magnetic measurements are required to clarify the "uncombed" field topology in superpenumbral regions, parsewave coupling, and assess energy transport mechanisms.

6. Broader Impact and Controversies

The present findings challenge previous interpretations that favored purely Alfvénic wave origins for 3-minute oscillations in sunspot surroundings (Chelpanov et al., 24 Sep 2024). While certain studies had classified these oscillations as predominantly Alfvénic, detailed phase analyses and cross-correlation mapping point more robustly toward upward propagating slow magnetoacoustic waves, with occasional Alfvénic activity detected in magnetic field signatures. This evolving picture underlines the necessity for multi-modal diagnostics and highlights the complexity of MHD wave environments in the lower solar atmosphere.

In conclusion, sunspot penumbrae and superpenumbrae are domains where 3-minute VAOs provide critical insight into magnetoacoustic wave propagation, reflection, and coupling, with potential secondary Alfvénic contributions. Untangling these wave modes is paramount for advancing solar seismology, diagnosing energy transfer processes, and improving theoretical models of solar atmospheric dynamics.