Characteristic Length of Energy-Containing Structures at the Base of a Coronal Hole

TL;DR

This study measures the characteristic length scales of energy-containing structures in coronal holes using solar observations, providing key parameters to improve models of coronal heating and solar wind acceleration.

Contribution

The paper presents the first detailed measurements of the characteristic length scales of velocity and magnetic field fluctuations in coronal holes using high-resolution solar data.

Findings

Characteristic length of velocity fluctuations is approximately 1260 km.

Magnetic field fluctuation length scale is about 950 km.

Measured lengths are significantly smaller than those used in previous models.

Abstract

An essential parameter for models of coronal heating and fast solar wind acceleration that rely on the dissipation of MHD turbulence is the characteristic energy-containing length $\lambda_{\bot}$ of the squared velocity and magnetic field fluctuations ($u^2$ and $b^2$) transverse to the mean magnetic field inside a coronal hole (CH) at the base of the corona. The characteristic length scale defines directly the heating rate. We use a time series analysis of solar granulation and magnetic field measurements inside two CHs obtained with the New Solar Telescope (NST) at Big Bear Solar Observatory. A data set for transverse magnetic fields obtained with the Solar Optical Telescope/Spectro-Polarimeter (SOT/SP) aboard {\it Hinode} spacecraft was utilized to analyze the squared transverse magnetic field fluctuations $b_t^2$. Local correlation tracking (LCT) was applied to derive the squared transverse velocity fluctuations $u^2$. We find that for $u^2$-structures, Batchelor integral scale $\lambda$ varies in a range of 1800 - 2100 km, whereas the correlation length $\varsigma$ and the $e$-folding length $L$ vary between 660 and 1460 km. Structures for $b_t^2$ yield $\lambda \approx 1600$ km, $\varsigma \approx 640$ km, and $L \approx 620$ km. An averaged (over $\lambda, \varsigma$, and $L$) value of the characteristic length of $u^2$-fluctuations is 1260$\pm$500 km, and that of $b_t^2$ is 950$\pm$560 km. The characteristic length scale in the photosphere is approximately 1.5-50 times smaller than that adopted in previous models (3-30$\times10^3$ km). Our results provide a critical input parameter for current models of coronal heating and should yield an improved understanding of fast solar wind acceleration.