Analytical fit of the scaling relations. The red SUEs show the data of panel d of Fig. 8 and panel b of Fig. 12. The blue curve in panel a shows the analytical fit of Eq. (8) modified by Eq. (9). The blue curve in panel b shows the analytical fit of Eq. (10). In both panels, the dashed lines display the envelope encompassing 68% of the sources, and the dotted lines, the envelope encompassing 95% of the sources. We show here the decimal logarithm of the Z_dust and q_AF.