Turbulent characteristics in the intensity fluctuations of a solar quiescent prominence observed by the textit{Hinode} Solar Optical Telescope

We focus on Hinode Solar Optical Telescope (SOT) calcium II H-line observations of a solar quiescent prominence (QP) that exhibits highly variable dynamics suggestive of turbulence. These images capture a sufficient range of scales spatially ($\sim$0.1-100 arc seconds) and temporally ($\sim$16.8 s - 4.5 hrs) to allow the application of statistical methods used to quantify finite range fluid turbulence. We present the first such application of these techniques to the spatial intensity field of a long lived solar prominence. Fully evolved inertial range turbulence in an infinite medium exhibits multifractal \emph{scale invariance} in the statistics of its fluctuations, seen as power law power spectra and as scaling of the higher order moments (structure functions) of fluctuations which have non-Gaussian statistics; fluctuations $\delta I(r,L)=I(r+L)-I(r)$ on length scale $L$ along a given direction in observed spatial field $I$ have moments that scale as $<\delta I(r,L)^p>\sim L^{\zeta(p)}$. For turbulence in a system that is of finite size, or that is not fully developed, one anticipates a generalized scale invariance or extended self-similarity (ESS) $<\delta I(r,L)^p>\sim G(L)^{\zeta(p)}$. For these QP intensity measurements we find scaling in the power spectra and ESS. We find that the fluctuation statistics are non-Gaussian and we use ESS to obtain ratios of the scaling exponents $\zeta(p)$: these are consistent with a multifractal field and show distinct values for directions longitudinal and transverse to the bulk (driving) flow. Thus, the intensity fluctuations of the QP exhibit statistical properties consistent with an underling turbulent flow.

💡 Research Summary

This paper presents the first application of statistical turbulence diagnostics to the spatial intensity field of a long‑lived solar quiescent prominence (QP) observed with the Hinode Solar Optical Telescope (SOT) in the Ca II H line. The authors analyse a 4.5‑hour data set (≈1000 frames) with a cadence of 16.8 s and a spatial resolution of 0.108 arcsec per pixel (≈77 km on the solar surface), covering scales from ∼0.1 arcsec to ∼100 arcsec (∼70 km to ∼70 Mm).

Data handling and geometry
The prominence is observed near the north‑west limb (90° W 52° N). The authors define five vertical strips (L1–L5) aligned with the bulk upward/downward flow and five horizontal strips (T1–T5) perpendicular to it. Each strip is 10 pixels wide; intensity averages are taken over the 10 rows (or columns) within a strip to improve statistics. For temporal analysis, five 21 × 21 pixel boxes (A–E) are selected, and the mean intensity of each box is tracked through the entire sequence.

Power spectral analysis
Spatial power spectral densities (PSDs) of the intensity along each strip display two distinct regimes. At low wave‑numbers the spectra follow a k⁻² law, characteristic of a Brownian (additive noise) process. At higher wave‑numbers the spectra steepen to k⁻α with α ranging from ≈2.3 to 2.9, significantly different from the Kolmogorov α = 5/3 expectation for fully developed inertial‑range turbulence. The authors attribute this deviation to line‑of‑sight integration and the fact that intensity is a proxy rather than a direct measurement of velocity or magnetic field fluctuations. Temporal PSDs of the box‑averaged intensities exhibit an approximate 1/f (f⁻¹) scaling over 1–20 mHz, which they interpret as a “random telegraph” process: the cadence (16.8 s) is too coarse to resolve the rapid passage of structures moving at the bulk flow speed (~25 km s⁻¹), resulting in decorrelated temporal signals.

Probability density functions (PDFs) and Gaussianity
The PDFs of spatial intensity differences δI(r,L) (with L = 1 pixel) are markedly non‑Gaussian: they are more peaked and possess heavier tails than a normal distribution. The excess kurtosis is measured as k_excess ≈ 2.44 ± 0.1, confirming strong intermittency. Quantile‑quantile (Q‑Q) plots further demonstrate deviation from Gaussianity. By contrast, PDFs of temporal differences δI(t,τ) (τ = 16.8 s) have kurtosis close to zero and Q‑Q plots that lie on the diagonal, indicating near‑Gaussian statistics. The authors argue that the temporal Gaussianity is an artifact of the insufficient temporal resolution rather than an intrinsic property of the flow.

Structure functions and Extended Self‑Similarity (ESS)
Higher‑order structure functions S_p(L) = ⟨|δI|^p⟩ are computed for orders p = 1–6. Direct power‑law scaling S_p ∝ L^{ζ(p)} is not evident over the limited inertial range, but when plotted against each other (e.g., S_p versus S_2) the data collapse onto clear power‑law relationships, demonstrating ESS. From the ESS slopes the ratios ζ(p)/ζ(2) are extracted; these ratios are nonlinear in p, indicating multifractal scaling rather than simple self‑similar (fractal) behaviour. Moreover, the ζ(p) curves differ between the vertical (flow‑aligned) and horizontal (cross‑flow) strips, revealing anisotropy in the turbulent cascade.

Physical interpretation
The authors treat the observed intensity as a passive scalar proportional to the square of the plasma density, assuming that bright structures trace the underlying plasma motions. Under this assumption, the non‑Gaussian PDFs, multifractal ESS scaling, and anisotropic ζ(p) spectra constitute strong evidence that the QP harbours a finite‑size, partially developed MHD turbulent flow. The estimated Reynolds number (~10⁵) and observed upflow speeds (~25 km s⁻¹) support the plausibility of turbulence in this low‑β, dense prominence plasma.

Limitations and future work
Key limitations include line‑of‑sight integration (which can smear out velocity‑related signatures), the use of intensity rather than direct velocity or magnetic field measurements, and the relatively coarse temporal cadence that masks temporal intermittency. The authors suggest that simultaneous high‑cadence Doppler imaging or spectropolarimetry would allow a direct comparison between intensity fluctuations and true plasma dynamics, enabling a more rigorous test of turbulence theories (e.g., Kolmogorov vs. Iroshnikov‑Kraichnan).

Conclusions
The study demonstrates that intensity fluctuations in a solar quiescent prominence exhibit statistical hallmarks of turbulence: power‑law spectra, heavy‑tailed PDFs, multifractal ESS scaling, and directional anisotropy. These results provide the first observational confirmation that finite‑size, partially developed turbulent cascades can exist in solar prominences, opening a new avenue for investigating MHD turbulence in the solar atmosphere using high‑resolution imaging data.