Chaos iv: Gas-phase abundance trends from the first four chaos galaxies

The chemical abundances of spiral galaxies, as probed by H ii regions across their disks, are key to understanding the evolution of galaxies over a wide range of environments. We present Large Binocular Telescope/Multi-Object Double Spectrographs spectra of 52 H ii regions in NGC 3184 as part of the CHemical Abundances Of Spirals (CHAOS) project. We explore the direct-method gas-phase abundance trends for the first four CHAOS galaxies, using temperature measurements from one or more auroral-line detections in 190 individual H ii regions. We find that the dispersion in T_e T_e relationships is dependent on ionization, as characterized by, and so we recommend ionization-based temperature priorities for abundance calculations. We confirm our previous results that [N ii] and [S iii] provide the most robust measures of electron temperature in low-ionization zones, while [O iii] provides reliable electron temperatures in high-ionization nebula. We measure relative and absolute abundances for O, N, S, Ar, and Ne. The four CHAOS galaxies marginally conform with a universal O/H gradient, as found by empirical integral field unit studies when plotted relative to effective radius. However, after adjusting for vertical offsets, we find a tight universal N/O gradient of dex/R _e with σ _tot. = 0.08 for R _g/R_e < 2.0, where N is dominated by secondary production. Despite this tight universal N/O gradient, the scatter in the N/O-O/H relationship is significant. Interestingly, the scatter is similar when N/O is plotted relative to O/H or S/H. The observable ionic states of S probe lower ionization and excitation energies than O, which might be more appropriate for characterizing abundances in metal-rich H ii regions.