We report the discovery of a well-defined correlation between B-band face-on central optical depth due to dust, tau^f_B, and the stellar mass surface density, mu_{*}, of nearby (z < 0.13) spiral galaxies: log(tau^f_B) = 1.12(+-0.11)log(mu_{*}/M_sol kpc^2)-8.6(+-0.8). This relation was derived from a sample of spiral galaxies taken from the Galaxy and Mass Assembly (GAMA) survey and detected in the FIR/submm in the Herschel-ATLAS survey. Using a quantitative analysis of the NUV attenuation-inclination relation for complete samples of GAMA spirals categorized according to mu_{*} we demonstrate that this correlation can be used to statistically correct for dust attenuation purely on the basis of optical photometry and Sersic-profile morphological fits. Considered together with previously established empirical relationships between stellar mass, metallicity and gas mass, the near linearity and high constant of proportionality of the tau^f_B-mu_{*} relation disfavors a stellar origin for the bulk of refractory grains in spiral galaxies, instead being consistent with the existence of a ubiquitous and very rapid mechanism for the growth of dust in the ISM. We use the tau^f_B-mu_{*} relation in conjunction with the radiation transfer model for spiral galaxies of Popescu & Tuffs (2011) to derive intrinsic scaling relations between specific star formation rate (sSFR), stellar mass, and mu_{*}, in which the attenuation of the UV light used to measure the SFR is corrected on an object-to-object basis. A marked reduction in scatter in these relations is achieved which is demonstrably due to correction of both the inclination-dependent and face-on components of attenuation. Our results are consistent with a picture of spiral galaxies in which most of the submm emission originates from grains residing in translucent structures, exposed to UV in the diffuse interstellar radiation field.
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