Transverse energy injection scales at the base of the solar corona

The outer atmospheres of solar-like stars are heated to over a million degrees and shed hot, magnetized winds that influence stellar evolution, angular momentum loss, and planetary habitability. A promising mechanism for energy transport and deposition is the dissipation of Alfvénic waves through turbulence and shocks. Global Alfvén-wave-based models depend critically on parameters that control the turbulent cascade and heating, notably the perpendicular correlation length L⊥, which influences where and how wave energy is deposited, the wind speed, and aspects of coronal plasma properties. Despite its importance, L⊥ near the coronal base has remained unconstrained; previous estimates exist only in the outer corona and heliosphere, far from where waves are injected. This study aims to measure the transverse (perpendicular) correlation length of Alfvénic fluctuations at the base of the corona (1.05–1.3 R⊙) using CoMP and UCoMP observations, thereby providing a direct constraint for turbulence models of the corona and solar wind.

Phenomenological and MHD turbulence-based models have shown promise for predicting solar wind and coronal properties, but employ unconstrained parameters including L⊥ (e.g., Cranmer et al. 2007; Chandran et al. 2011; van der Holst et al. 2014; Shoda et al. 2018). Prior measurements of perpendicular correlation lengths were obtained only in the outer corona (>10 R⊙) via radio techniques and in situ in the heliosphere and at 1 au (e.g., Matthaeus & Goldstein 1982; Spangler 2005; Wicks et al. 2009, 2010; Matthaeus et al. 2005; Cuesta et al. 2022). These values have been used to build radial evolution models for L⊥ (e.g., Cranmer & van Ballegooijen 2012), often assuming homogeneous plasma and scaling with flux-tube expansion or coupling to flows. However, observations show the corona is structured perpendicular to the magnetic field to large heights, implying surface Alfvén waves and potential resonances that can transfer energy to smaller scales, challenging the homogeneous assumptions. No direct measurements existed at the coronal base where Alfvénic waves are injected, motivating the present work.

Data: Multiple datasets from CoMP (2013, 2015, 2016) and UCoMP (2022) were used. CoMP observes 1.05–1.3 R⊙ at 30 s cadence with 4.46″ pixels; UCoMP observes 1.03–1.95 R⊙ at 30 s cadence with 3″ pixels. The Fe XIII 1074.7 nm line was sampled at three wavelengths. Level-2 data from MLSO were used; bad frames were removed and short gaps linearly interpolated. Spectral profiles were fit with a single Gaussian per pixel to derive intensity, LOS Doppler velocity, and width. Uncertainties incorporate photon, background, readout, and seeing noise; no absolute wavelength calibration is available, but only fluctuations are analyzed. Additional K-Cor white-light data (1.05–3 R⊙, 15 s cadence) were used for contextual imaging. Signal preparation: For selected structures, an artificial slit perpendicular to local field-aligned loops was extracted. At each pixel, temporal mean was removed and a Gaussian frequency filter (center 3.5 mHz, σ ≈ 1.5 mHz) applied in Fourier space to isolate enhanced Alfvénic power. Mean-squared coherence (MSC): In local 64×64 Mm neighborhoods centered on a reference pixel, MSC between the reference and each neighbor was computed from cross- and auto-spectral densities. A weighted sum around 3.5 mHz (Gaussian weighting) emphasized the targeted Alfvénic frequencies. The resulting 2D MSC maps typically show elongated islands aligned with the magnetic field (parallel) and shorter coherence perpendicular to it. Length-scale estimation: Pixels with MSC > 0.5 were retained and the coherence island was fit with a 2D Gaussian with rotation, G(x,y)=exp[−(ax²+2bxy+cy²)], parameterized by orthogonal standard deviations (σ1, σ2) and orientation θ. Fits used L2-regularized maximum likelihood with a free noise parameter φ to stabilize edge cases. The perpendicular standard deviation σ⊥ (short axis) was taken as the coherence scale perpendicular to the field. To compare with prior 1/e autocorrelation-based definitions, the perpendicular correlation length was defined as L⊥=√2 σ⊥. This procedure was repeated for all pixels to form global maps. Distribution estimation: Kernel density estimation with bandwidth chosen via fivefold cross-validation was used to obtain probability density functions of σ⊥ (and hence L⊥) across datasets. Quality considerations: LOS and spatial averaging reduce apparent Doppler amplitudes, but do not bias coherence scales. Low SNR regions (notably near poles) were excluded where fits were unreliable.

• First direct measurements of perpendicular correlation lengths at the coronal base (1.05–1.3 R⊙) for Alfvénic fluctuations using CoMP/UCoMP.
• Perpendicular coherence scales (σ⊥) typically range from about 2 to 20 Mm; their probability density peaks at σ⊥ ≈ 5–6.5 Mm, corresponding to L⊥ ≈ 7.6–9.3 Mm (1/e folding length).
• Global maps show L⊥ values are relatively homogeneous throughout the inner corona and show no significant differences between open-field regions (e.g., equatorial coronal holes) and closed-field regions (e.g., bases of pseudostreamers).
• The measured L⊥ is comparable to supergranulation scales, consistent with expansion of intense kilogauss magnetic fields from the photosphere into the corona.
• Results are consistent across datasets spanning about nine years, suggesting little solar cycle variation (noting a five-year observational gap around solar minimum).
• Comparison with existing radial-evolution models (M1: flux-tube expansion scaling; M2: includes coupling to flows) reveals tension: models tuned to in-situ measurements imply inner-coronal L⊥ ~1 Mm, nearly an order of magnitude smaller than measured here. Rescaling M1 to match the inner corona implies a photospheric L⊥ ~1.5 Mm (granulation-like), but then overestimates at 1 au.

These measurements directly constrain the transverse energy injection scales of Alfvénic fluctuations at the coronal base, addressing a key unknown in turbulence-based coronal heating and solar/stellar wind models. The finding that L⊥ ≈ 7.6–9.3 Mm and is broadly homogeneous across inner-coronal structures implies that wave-driven turbulent heating and subsequent energy deposition are organized on supergranular scales. This provides a stringent input for models controlling heating rates and wind acceleration. The discrepancy between the measured inner-coronal L⊥ and values inferred from outer-corona and heliospheric observations suggests that current models are missing relevant physics in the low-to-middle corona. Observations indicate significant transverse inhomogeneity, implying surface Alfvén modes and resonant processes that can transfer energy to smaller scales as waves propagate, counteracting the growth of L⊥ expected from magnetic expansion. Such processes, potentially active below and through the Alfvén critical zone (≈10–20 R⊙), could reconcile large L⊥ near the Sun with smaller in-situ scales. Additionally, the present measurements target waves near 3.5 mHz, where enhanced Alfvénic power is linked to acoustic-mode conversion, hinting at frequency- or driver-dependent correlation lengths and multiple wave populations not typically represented in global models. Overall, incorporating structured-plasma wave physics and potentially multiple driving populations may be necessary to match the full radial evolution of L⊥.

The study provides the closest-to-Sun measurements of the perpendicular correlation length of Alfvénic fluctuations, finding L⊥ ≈ 7.6–9.3 Mm at 1.05–1.3 R⊙. These supergranulation-scale, relatively homogeneous values across inner-coronal structures offer a critical constraint for Alfvén-wave-based coronal heating and solar/stellar wind models, which have historically treated L⊥ as a tunable parameter. Comparisons with theoretical radial-evolution models and prior outer-corona/heliospheric measurements indicate that additional physics—such as effects of transverse structuring, surface Alfvén modes, resonances, and potential changes across the Alfvén critical zone—are needed to explain the evolution of L⊥ with distance. Future work should: (1) incorporate structured-plasma wave physics and multiple driver populations into global models; (2) explore the frequency dependence of L⊥; (3) obtain continuous multi-height observations (e.g., with UCoMP and heliospheric assets) to map the radial evolution of L⊥; and (4) expand coverage across the solar cycle and diverse magnetic topologies.

• Frequency specificity: Coherence and L⊥ were measured around 3.5 mHz; correlation lengths may be frequency-dependent and differ for other drivers.
• Observational gaps: A five-year period near solar minimum lacks observations, limiting assessment of solar-cycle variability.
• Spatial coverage and SNR: Low signal-to-noise regions (e.g., near poles) were excluded; estimates could not be made for some pixels.
• LOS and spatial averaging: These reduce apparent Doppler amplitudes (though not expected to bias coherence scales), complicating amplitude-based interpretations.
• No absolute wavelength calibration: Absolute Doppler shifts are uncertain, although fluctuation analyses are unaffected.
• Methodological assumptions: Thresholding at MSC > 0.5 and Gaussian modeling of coherence islands may omit more complex coherence morphologies; conversion to 1/e correlation length assumes equivalence with prior autocorrelation-based definitions (L⊥=√2σ⊥).
• Height range and line sensitivity: Results are limited to 1.05–1.3 (CoMP) and up to ~1.95 R⊙ (UCoMP) and to plasma sampled by Fe XIII 1074.7 nm; generalization to other heights/temperatures requires further study.