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

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_ of the squared velocity and magnetic field fluctuations (u² and b²) 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 { Hinode} spacecraft was utilized to analyze the squared transverse magnetic field fluctuations bₜ². Local correlation tracking (LCT) was applied to derive the squared transverse velocity fluctuations u². We find that for u²-structures, Batchelor integral scale λ varies in a range of 1800 - 2100 km, whereas the correlation length and the e-folding length L vary between 660 and 1460 km. Structures for bₜ² yield λ ≈ 1600 km, ≈ 640 km, and L ≈ 620 km. An averaged (over λ,, and L) value of the characteristic length of u²-fluctuations is 1260±500 km, and that of bₜ² is 950±560 km. The characteristic length scale in the photosphere is approximately 1.5-50 times smaller than that adopted in previous models (3-30×10³ 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.