The relationship between X-ray radiance and magnetic flux

We use soft X-ray and magnetic field observations of the Sun (quiet Sun, X-ray bright points, active regions, and integrated solar disk) and active stars (dwarf and pre-main-sequence) to study the relationship between total unsigned magnetic flux, Phi, and X-ray spectral radiance, L-X. We find that Phi and L-X exhibit a very nearly linear relationship over 12 orders of magnitude, albeit with significant levels of scatter. This suggests a universal relationship between magnetic flux and the power dissipated through coronal heating. If the relationship can be assumed linear, it is consistent with an average volumetric heating rate (Q) over bar similar to (B) over bar /L, where (B) over bar is the average field strength along a closed field line and L is its length between footpoints. The Phi-L-X relationship also indicates that X-rays provide a useful proxy for the magnetic flux on stars when magnetic measurements are unavailable.