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 { Mm } ^ { 2 } 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 { \langle { | \phi| } \rangle } = 1.0 \times 10 ^ { 19 } Mx distributed randomly with density n = 0.007 { Mm } ^ { -2 } .