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_τ 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 directly defines 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 at Big Bear Solar Observatory. A data set for transverse magnetic fields obtained with the Solar Optical Telescope/Spectro-Polarimeter on board the Hinode spacecraft was utilized to analyze the squared transverse magnetic field fluctuations . Local correlation tracking was applied to derive the squared transverse velocity fluctuations u ². We find that for u ² structures, the 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 yield λ ≈ 1600 km, ς ≈ 640 km, and L ≈ 620 km. An averaged (over λ, ς, and L) value of the characteristic length of u ² fluctuations is 1260 ± 500 km, and that of 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.