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

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 $λ_{\bot}$ 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 $λ$ varies in a range of 1800 - 2100 km, whereas the correlation length $ς$ and the $e$-folding length $L$ vary between 660 and 1460 km. Structures for $b_t^2$ yield $λ\approx 1600$ km, $ς\approx 640$ km, and $L \approx 620$ km. An averaged (over $λ, ς$, 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.