  Understanding the spatial distribution of metals within galaxies allows us to
study the processes of chemical enrichment and mixing in the interstellar
medium (ISM). In this work, we map the two-dimensional distribution of metals
using a Gaussian Process Regression (GPR) for 19 star-forming galaxies observed
with the Very Large Telescope/Multi Unit Spectroscopic Explorer (VLT-MUSE) as
part of the PHANGS-MUSE survey. We find that 12 of our 19 galaxies show
significant two-dimensional metallicity variation. Those without significant
variations typically have fewer metallicity measurements, indicating this is
due to the dearth of HII regions in these galaxies, rather than a lack of
higher-order variation. After subtracting a linear radial gradient, we see no
enrichment in the spiral arms versus the disc. We measure the 50 per cent
correlation scale from the two-point correlation function of these
radially-subtracted maps, finding it to typically be an order of magnitude
smaller than the fitted GPR kernel scale length. We study the dependence of the
two-point correlation scale length with a number of global galaxy properties.
We find no relationship between the 50 per cent correlation scale and the
overall gas turbulence, in tension with existing theoretical models. We also
find more actively star forming galaxies, and earlier type galaxies have a
larger 50 per cent correlation scale. The size and stellar mass surface density
do not appear to correlate with the 50 per cent correlation scale, indicating
that perhaps the evolutionary state of the galaxy and its current star
formation activity is the strongest indicator of the homogeneity of the metal
distribution.
