Instrumental and Observational Artifacts in Quiet Sun Magnetic Flux Cance llation 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 $<|B_z|>_{\mathrm{true}}$. 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 too low estimates of both the cancellation exponent $κ$ and of $<|B_z|>_{\mathrm{true}}$. However, both $κ$ and $<|B_z|>_{\mathrm{true}}$ are over-estimated due to noise in magnetograms. While no conclusive value can be derived with data from current instruments, our {\it Hinode}/SP results of $κ\lessapprox0.38$ and $<|B_z|>_{\mathrm{true}}\lessapprox 270 $gauss can be taken as upper bounds.