The First Maps of $\kappa_{d}$ -- the Dust Mass Absorption Coefficient
  -- in Nearby Galaxies, with DustPedia
  The dust mass absorption coefficient, $\kappa_{d}$, is the conversion
function used to infer physical dust masses from observations of dust emission.
However, it is notoriously poorly constrained, and it is highly uncertain how
it varies, either between or within galaxies. Here we present the results of a
proof-of concept study, using the DustPedia data for two nearby face-on spiral
galaxies M74 (NGC 628) and M83 (NGC 5236), to create the first ever maps of
$\kappa_{d}$ in galaxies. We determine $\kappa_{d}$ using an empirical method
that exploits the fact that the dust-to-metals ratio of the interstellar medium
is constrained by direct measurements of the depletion of gas-phase metals. We
apply this method pixel-by-pixel within M74 and M83, to create maps of
$\kappa_{d}$. We also demonstrate a novel method of producing metallicity maps
for galaxies with irregularly-sampled measurements, using the machine learning
technique of Gaussian process regression. We find strong evidence for
significant variation in $\kappa_{d}$. We find values of $\kappa_{d}$ at 500
$\mu$m spanning the range 0.11-0.25 ${\rm m^{2}\,kg^{-1}}$ in M74, and
0.15-0.80 ${\rm m^{2}\,kg^{-1}}$ in M83. Surprisingly, we find that
$\kappa_{d}$ shows a distinct inverse correlation with the local density of the
interstellar medium. This inverse correlation is the opposite of what is
predicted by standard dust models. However, we find this relationship to be
robust against a large range of changes to our method - only the adoption of
unphysical or highly unusual assumptions would be able to suppress it.
