The brightness of magnetic field concentrations in the quiet Sun

In addition to the `facular' brightening of active regions, the quiet Sun also contains a small scale magnetic field with associated brightenings in continuum radiation. We measure this contribution of quiet regions to the Sun's brightness from high spatial resolution (0"16-0"32) observations of the Swedish 1-m Solar Telescope (SST) and Hinode satellite. The line-of-sight magnetic field and continuum intensity near \ion{Fe}{i} 6302.5 \AA\ are used to quantify the correlation between field strength and brightness. The data show that magnetic flux density contains a significant amount of intrinsically weak fields that contribute little to brightness. We show that with data of high spatial resolution a calibration of magnetic flux density as a proxy for brightness excess is possible. In the SST data, the magnetic brightening of a quiet region with an average (unsigned) flux density of 10 G is about 0.15%. In the Hinode data, and in SST data reduced to Hinode resolution, the measured brightening is some 40% lower. With appropriate correction for resolution, magnetic flux density can be used as a reliable proxy in regions of small scale mixed polarity. The measured brightness effect is larger than the variation of irradiance over a solar cycle. It is not clear, however, if this quiet Sun contribution actually varies significantly. \keywords{Sun: surface magnetism -- photosphere -- solar-terrestrial relations}