Panel A: histograms of the continuum intensity for a fixed B_z = 150 G for AR 10923 (blue) and AR 11041 (red). These are horizontal cuts across the two histograms shown in Fig. 4 along the dashed horizontal lines. The arrows show the intensity I_C, fil corresponding to the maximum of the region of the histograms that affected by the filaments (as indicated by the red circles in Fig. 4. Panel B:I_C, fil for all the spots in our sample as a function of the total size of the umbra. The red line shows a fit to the data (I_C, fil = 0.91−0.02log A_U).