The Number of Magnetic Null Points in the Quiet Sun Corona |
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Authors: | D W Longcope C E Parnell |
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Institution: | (1) Department of Physics, Montana State University, Bozeman, MT 59717, USA;(2) School of Mathematics and Statistics, University of St Andrews, St Andrews, Fife, KY16 9SS, UK |
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Abstract: | The coronal magnetic field above a particular photospheric region will vanish at a certain number of points, called null points.
These points can be found directly in a potential field extrapolation or their density can be estimated from the Fourier spectrum
of the magnetogram. The spectral estimate, in which the extrapolated field is assumed to be random and homogeneous with Gaussian
statistics, is found here to be relatively accurate for quiet Sun magnetograms from SOHO’s MDI. The majority of null points
occur at low altitudes, and their distribution is dictated by high wavenumbers in the Fourier spectrum. This portion of the
spectrum is affected by Poisson noise, and as many as five-sixths of null points identified from a direct extrapolation can
be attributed to noise. The null distribution above 1500 km is found to depend on wavelengths that are reliably measured by
MDI in either its low-resolution or high-resolution mode. After correcting the spectrum to remove white noise and compensate
for the modulation transfer function we find that a potential field extrapolation contains, on average, one magnetic null
point, with altitude greater than 1.5 Mm, above every 322 Mm2 patch of quiet Sun. Analysis of 562 quiet Sun magnetograms spanning the two latest solar minima shows that the null point
density is relatively constant with roughly 10% day-to-day variation. At heights above 1.5 Mm, the null point density decreases
approximately as the inverse cube of height. The photospheric field in the quiet Sun is well approximated as that from discrete
elements with mean flux 〈|φ|〉=1.0×1019 Mx distributed randomly with density n=0.007 Mm−2. |
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Keywords: | MHD Sun: Corona Sun: Magnetic fields |
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