Measuring the mixing scale of the ISM within nearby spiral galaxies
  The spatial distribution of metals reflects, and can be used to constrain,
the processes of chemical enrichment and mixing. Using PHANGS-MUSE optical
integral field spectroscopy, we measure the gas phase oxygen abundances
(metallicities) across 7,138 HII regions in a sample of eight nearby disc
galaxies. In Paper I (Kreckel et al. 2019) we measure and report linear radial
gradients in the metallicities of each galaxy, and qualitatively searched for
azimuthal abundance variations. Here, we examine the two-dimensional variation
in abundances once the radial gradient is subtracted, Delta(O/H), in order to
quantify the homogeneity of the metal distribution and to measure the mixing
scale over which HII region metallicities are correlated. We observe low
(0.03--0.05 dex) scatter in Delta(O/H) globally in all galaxies, with
significantly lower (0.02--0.03 dex) scatter on small (<600 pc) spatial scales.
This is consistent with the measurement uncertainties, and implies the
two-dimensional metallicity distribution is highly correlated on scales of <600
pc. We compute the two point correlation function for metals in the disc in
order to quantify the scale lengths associated with the observed homogeneity.
This mixing scale is observed to correlate better with the local gas velocity
dispersion (of both cold and ionized gas) than with the star formation rate.
Selecting only HII regions with enhanced abundances relative to a linear radial
gradient, we do not observe increased homogeneity on small scales. This
suggests that the observed homogeneity is driven by the mixing introducing
material from large scales rather than by pollution from recent and on-going
star formation.
