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, resolutionindependent mean, unsigned vertical flux <vertical bar B-z vertical bar >(true). We show that the presence of network elements, noise, and seeing complicate the measurement of accurate cancellation functions and their power law exponents kappa. Failure to exclude network elements previously led to estimates that were too low for both the cancellation exponent kappa and <vertical bar B-z vertical bar >(true). However, both kappa and <vertical bar Bz vertical bar >(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 kappa less than or similar to 0.38 and <vertical bar B-z vertical bar >(true) less than or similar to 270 gauss can be taken as upper bounds.