Instrumental and Observational Artifacts in Quiet Sun Magnetic Flux Cancellation Functions

Under the assumption that the photospheric quiet Sun magnetic field is turbulent, the cancellation function has previously been used to estimate the true, resolution-independent mean, unsigned vertical flux 〈|Bz|〉true. We show that the presence of network elements, noise, and seeing complicate the measurement of accurate cancellation functions and their power law exponents κ. Failure to exclude network elements previously led to estimates that were too low for both the cancellation exponent κ and 〈|Bz|〉true. However, both κ and 〈|Bz|〉true are overestimated due to noise in magnetograms. While no conclusive value can be derived with data from current instruments, our Hinode/SP results of κ⪅0.38 and 〈|Bz|〉true⪅270 gauss can be taken as upper bounds.