  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 S'ersic-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.
