The quiet Sun's magnetic flux estimated from CaIIH bright inter-granular G-band structures

We determine the number density and area contribution of small-scale inter-granular calcium-II bright G-band structures in images of the quiet Sun as tracers of kilo-Gauss magnetic flux-concentrations. In a 149" x 117" G-band image of the disk center at the activity minimum, 7593 small inter-granular structures ['IGS']were segmented with the `multiple-level tracking' pattern recognition algorithm ['MLT_4']. The scatter-plot of the continuum versus the G-band brightness shows the known magnetic and non-magnetic branches. These branches are largely disentangled by applying an intrinsic Ca-II excess criterion. The thus obtained 2995 structures contain 1152 G-band bright points ['BP'] and 1843 G-band faint points ['FP']. They show a tendency of increasing size with decreasing G-band excess, as expected from the `hot wall' picture. Their Ca-H and G-band brightness are slightly related, resembling the known relation of Ca-II and magnetic field strength. The magnetic flux density of each individual BP and FP is estimated from their G-band brightness according to MHD-model calculations. The entity of BP and FP covers the total field-of-view ['FOV'] with a number density of 0.32/Mm^2 and a total area contribution of 2.0%. Their individual calibrations yield a mean flux density of 20 Mx/cm^2 in the entire FOV and 13 Mx/cm^2 for inter-network regions.