2021MNRAS.508..489M

Thanks to recent advances in integral field spectroscopy, modern surveys of nearby galaxies are capable of resolving metallicity maps of H II regions down to scales of ∼50 pc. However, statistical analyses of these metallicity maps has seldom gone beyond fitting basic linear regressions and comparing parameters to global galaxy properties. In this paper (the first of a series), we introduce techniques from spatial statistics that are well suited for detailed analysis of both small- and large-scale metallicity variations within the interstellar medium (ISM) of local galaxies. As a first application, we compare the observed structure of small-scale metallicity fluctuations within seven local galaxies observed by the Physics at High Angular resolution in Nearby GalaxieS (PHANGS) collaboration to predictions from a stochastic, physically motivated, analytical model developed by Krumholz & Ting. We show that while the theoretical model underestimates the amount of correlated scatter in the galactic metallicity distributions by 3-4 orders of magnitude, it provides good estimates of the physical scale of metallicity correlations. We conclude that the ISM of local spiral galaxies is far from homogeneous, with regions of size ∼1 kpc showing significant departures from the mean metallicity at each galactocentric radius.