The MOSDEF Survey: Probing Resolved Stellar Populations at $z\sim2$ Using a New Bayesian-defined Morphology Metric Called Patchiness

We define a new morphology metric called "patchiness" ($P$) that is sensitive to deviations from the average of a resolved distribution, does not require the galaxy center to be defined, and can be used on the spatially-resolved distribution of any galaxy property. While the patchiness metric has a broad range of applications, we demonstrate its utility by investigating the distribution of dust in the interstellar medium of 310 star-forming galaxies at spectroscopic redshifts $1.36<z<1.66$ observed by the MOSFIRE Deep Evolution Field (MOSDEF) survey. The stellar continuum reddening distribution, derived from high-resolution multi-waveband CANDELS/3D-HST imaging, is quantified using the patchiness, Gini, and $M_{20}$ coefficients. We find that the reddening maps of high-mass galaxies, which are dustier and more metal-rich on average, tend to exhibit patchier distributions (high $P$) with the reddest components concentrated within a single region (low $M_{20}$). Our results support a picture where dust is uniformly distributed in low-mass galaxies ($\lesssim$10$^{10}$ $M_\odot$), implying efficient mixing of dust throughout the interstellar medium. On the other hand, the dust distribution is patchier in high-mass galaxies ($\gtrsim$10$^{10}$ $M_\odot$). Dust is concentrated near regions of active star formation and dust mixing timescales are expected to be longer in high-mass galaxies, such that the outskirt regions of these physically larger galaxies remain relatively unenriched. This study presents direct evidence for patchy dust distributions on scales of a few kpc in high-redshift galaxies, which previously has only been suggested as a possible explanation for the observed differences between nebular and stellar continuum reddening, SFR indicators, and dust attenuation curves.