Dust mass as a function of the stellar mass of our lensed galaxy sample (red circles) compared to other high-z (filled symbols) and local galaxy samples (open symbols). The stellar masses used here come from the energy conserving models presented in Table 6. Red triangles and blue squares (both open) show local spirals and ULIRGs; filled black circles show high-z SMGs; all data are taken from Fig. 1 of Santini et al. (2010). Filled magenta circles show the z ~ 0.5−3.5 SMG sample of Michałowski et al. (2010); yellow squares 17 z > 1 galaxies observed with Herschel in GOODS-N (Magnelli et al. 2012b); filled magenta triangles the z ~ 0.5−3 galaxies from Magdis et al. (2012a); filled black triangle the z ~ 1−2 (U)LIRG from Lo Faro et al. (2013). The green dashed line shows the location of the sequence observed by the H-ATLAS/GAMA survey at z ~ 0−0.35 (Bourne et al. 2012); the green solid line the median value of Md/M⋆ = −2.63 obtained by Smith et al. (2012) from the H-ATLAS survey after adjustment to the Salpeter IMF used here. The red solid (dotted) line shows the predictions from the chemical- and dust-evolution models of Pipino et al. (2011) for galaxies leading to the formation of ellipticals with masses of 1010 (1011) M⊙ at z = 0.; blue lines the dwarf, M101, and Milky Way models of Calura et al. (2008). The blacked shaded area (black line) shows the 68% confidence interval (median) predicted by the semi-analytical models of Lagos et al. (2012) for z ~ 1.5. The inferred dust and stellar masses of our galaxies seem to follow a simple M⋆−Md relation also extending to the SMGs. They do not show significant offsets from low redshift galaxies, and are in good agreement with the models.
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