A geostatistical analysis of multiscale metallicity variations in galaxies – I. Introduction and comparison of high-resolution metallicity maps to an analytical metal transport model

Thanks to recent advances in integral field spectroscopy (IFS), modern surveys of nearby galaxies are capable of resolving metallicity maps of Hii regions down to scales of ~50pc. However, statistical analysis 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 media (ISMs) of local galaxies. As a first application, we compare the observed structure of small-scale metallicity fluctuations within 7 local galaxies observed by the 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.