Transverse energy injection scales at the base of the solar corona

The outer atmospheres of solar-like stars reach temperatures exceeding a million degrees, emitting X-ray and extreme-ultraviolet radiation and generating hot, magnetized winds that cause sustained mass loss. These phenomena influence planetary system evolution and habitability and play a pivotal role in stellar angular momentum loss through magnetic braking. However, the energy conversion mechanisms powering these dynamics are poorly understood. A promising candidate is the dissipation of Alfvénic waves, supported by numerical models of wave propagation through stellar atmospheres. These models use turbulence (e.g., incompressible magnetohydrodynamic turbulence, instabilities) to cascade energy from driving to dissipation scales. While these models show promise in predicting solar wind parameters, simulating environments around exoplanets, and studying stellar evolution, they often include critical but unconstrained parameters that significantly affect energy transport and deposition. One such parameter is the perpendicular correlation length (L⊥), representing the effective transverse length of the largest turbulence eddies. L⊥ phenomenologically relates to the turbulent heating rate and controls energy deposition in the coronal plasma, influencing wind speed, which in turn affects magnetic braking. Although L⊥'s influence on maximum coronal temperature, mass-loss rate, and the Alfvén critical zone location is weaker, its impact is comparable to variations in a star's rotation period. Previous measurements of L⊥ were limited to the outer corona and heliosphere, far from the coronal base where Alfvénic waves are injected. This distance makes it challenging to extrapolate these measurements back to the Sun's base, as the Alfvénic waves may undergo substantial evolution due to fine-scale plasma inhomogeneities.

Numerous studies have investigated Alfvénic wave turbulence models in the context of stellar atmospheres and the solar wind (citations 4-16, 18-20). These models often rely on phenomenological approaches to describe the turbulent processes involved in energy dissipation and heating. The importance of the perpendicular correlation length (L⊥) in these models has been highlighted in several studies, showing its influence on parameters such as coronal heating, wind speed, and magnetic braking (citations 10, 12, 16). However, direct observational constraints on L⊥, particularly close to the Sun, have been lacking. Previous attempts to measure L⊥ have been limited to the outer corona and heliosphere (citations 28-35), significantly limiting the applicability of these measurements to models of wave generation at the coronal base. This study aims to address this limitation by providing direct measurements of L⊥ at the base of the solar corona.

This research used observations from the Coronal Multi-channel Polarimeter (CoMP) and its upgraded version (UCoMP) to measure the perpendicular correlation length in the inner corona. CoMP and UCoMP observe the off-limb solar corona in near-infrared passbands. The data used include intensity and line-of-sight (LOS) Doppler velocity estimations from the Fe XIII (1074.7 nm) emission line, enabling the identification of ubiquitous propagating Alfvénic fluctuations. To analyze the spatial scales of these fluctuations, an artificial slit was placed across coronal loops perpendicular to the local magnetic field. The temporal mean was subtracted from the Doppler velocities, and a frequency filter (centered on 3.5 mHz) was applied to reveal wave fronts. The mean-squared coherence (MSC) was calculated between the filtered LOS Doppler velocity time-series at each pixel and its neighbors to characterize the transverse length scales. The MSC magnitudes were estimated using Fourier cross-spectra. Because Alfvénic fluctuations propagate along the magnetic field, the coherence distribution is elongated along this direction. The elongated regions of high coherence (MSC > 0.5) were modeled using a two-dimensional Gaussian function to obtain orthogonal length scales, specifically the standard deviation (σ⊥), representing length scales perpendicular to the propagation direction. A global map of the perpendicular coherence (σ⊥) was created, and probability density distributions from multiple datasets were generated to determine the peak values and corresponding perpendicular correlation length scales (L⊥). The analysis considered multiple data sets from both CoMP and UCoMP, spanning a period of several years, and included data from various coronal regions (active regions, equatorial coronal holes, and pseudostreamers). Comparisons were made between closed and open magnetic field topologies to assess variability. Finally, the L⊥ results were compared to previous measurements from radio and in-situ observations in the outer corona and interplanetary medium, along with two theoretical models describing radial L⊥ evolution. The uncertainties associated with Doppler velocity estimation were considered, incorporating photon, background, readout, and seeing noise.

The study found that the perpendicular correlation length (L⊥) in the inner corona, at heights of 1.05–1.3 R⊙, is sharply peaked around 7.6–9.3 Mm (1/e folding). This value is remarkably homogeneous throughout the quiescent corona, with no significant differences observed between closed and open magnetic field topologies. The measured L⊥ is comparable to the average supergranular cell diameter in the solar photosphere, suggesting a link to the expansion of intense magnetic fields from the photosphere to the corona. This value is consistent across the nine years of observations. The results from the coronal base are crucial, representing the transverse injection scales of Alfvénic waves that will propagate outwards into the solar wind. Comparison with previous measurements (radio and in-situ) in the outer corona and interplanetary medium revealed a significant discrepancy. The current models (M1 and M2) which explain the observed L⊥ values in the outer corona and interplanetary medium underpredict the values observed in the inner corona by almost an order of magnitude. These models suggest much smaller L⊥ values at the coronal base (~1 Mm). Rescaling the M1 model to match the inner coronal measurements implied a much larger photospheric correlation length (~1.5 Mm), comparable to the scale of granulation, but overestimated L⊥ at 1 AU when compared to in-situ data. The discrepancy suggests that existing global Alfvén wave turbulence models, which often assume homogeneous plasma, are missing key physical processes. The observations suggest the corona is inhomogeneous perpendicular to the magnetic field, implying surface Alfvén modes and resonances that could concentrate energy to smaller scales through Alfvénic-to-Alfvénic mode conversion. The measured correlation length might also be specific to Alfvénic waves around 3.5 mHz, potentially associated with acoustic mode conversion.

The key finding of this study is the determination of the perpendicular correlation length (L⊥) at the base of the solar corona, a previously elusive parameter. This value, significantly larger than predicted by current models, challenges existing assumptions about Alfvén wave propagation and energy dissipation in the solar atmosphere. The discrepancy indicates the need to refine global Alfvén wave turbulence models to incorporate the effects of plasma inhomogeneity, surface Alfvén modes, and potential multiple populations of Alfvénic waves with different drivers and correlation lengths. The observed L⊥ of 7.6–9.3 Mm, matching supergranulation scales, suggests a connection between photospheric dynamics and coronal heating. Future studies should incorporate inhomogeneous plasma conditions, multiple wave drivers, and more comprehensive descriptions of wave-wave and wave-flow interactions into global models to enhance their predictive capabilities. This research strongly emphasizes the importance of direct measurements near the Sun's surface for validating and refining theoretical models.

This study provides the closest-to-the-Sun measurements of the perpendicular correlation length (L⊥) of Alfvénic waves at the coronal base (1.05–1.3 R⊙), revealing values of 7.6–9.3 Mm, consistent with supergranulation scales. These results significantly constrain global Alfvén wave turbulence models, highlighting the shortcomings of existing models that assume homogeneous plasma and the necessity for incorporating more realistic plasma conditions and wave physics. Future research should focus on developing improved models that incorporate these effects to better predict solar wind properties and the dynamics of stellar coronae.

The study focused on specific frequency ranges of Alfvénic waves (around 3.5 mHz), potentially limiting the generalizability of the results to other frequency ranges. The LOS measurements of Doppler velocities suffer from degradation due to line-of-sight and spatial averaging, underestimating the true wave amplitudes. Also, the lack of absolute wavelength calibration in CoMP and UCoMP data restricts the interpretation of absolute Doppler shifts, though fluctuations remain unaffected.