  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 Fourier spectrum of the magnetogram. The spectral estimate, which assumes
that the extrapolated field is random, homogeneous and has 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 square Mm patch of quiet Sun. Analysis of 562 quiet Sun
magnetograms spanning the two latest solar minimum 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 1.0e19 Mx
distributed randomly with density n=0.007 per square Mm.

Astrophysics