The Herschel Exploitation of Local Galaxy Andromeda (HELGA): IV. Dust
  scaling relations at sub-kpc resolution
  The imprints of dust-starlight interactions are visible in scaling relations
between stellar characteristics, star formation parameters and dust properties.
We aim to examine dust scaling relations on a sub-kpc resolution in the
Andromeda galaxy (M31) by comparing the properties on a local and global scale
to other galaxies of the local universe. New Herschel observations are combined
with available data from GALEX, SDSS, WISE and Spitzer to construct a dataset
covering UV to submm wavelengths. We work at the resolution of the SPIRE $500\;
\mu$m beam, with pixels corresponding to physical regions of 137 x 608 pc in
the galaxy's disk. A panchromatic spectral energy distribution was modelled for
each pixel and several dust scaling relations are investigated. We find, on a
sub-kpc scale, strong correlations between $M_d/M_\star$ and NUV-r, and between
$M_d/M_\star$ and $\mu_\star$ (the stellar mass surface density). Striking
similarities with corresponding relations based on integrated galaxies are
found. We decompose M31 in four macro-regions based on their FIR morphology;
the bulge, inner disk, star forming ring and the outer disk. All regions
closely follow the galaxy-scale average trends. The specific star formation
characteristics we derive for these macro-regions give strong hints of an
inside-out formation of the bulge-disk geometry, as well as an internal
downsizing process. However, within each macro-region, a great diversity in
individual micro-regions is found. Furthermore, we confirm that dust in the
bulge of M31 is heated only by the old stellar populations. In general, the
local dust scaling relations indicate that the dust content in M31 is
maintained by a subtle interplay of past and present star formation. The
similarity with galaxy-based relations strongly suggests that they are in situ
correlations, with underlying processes that must be local in nature. (Abriged)
