The Outflowing [O ii ] Nebulae of Compact Starburst Galaxies at z ∼ 0.5

High-velocity outflows are ubiquitous in compact, massive (M * ∼ 1011 M ⊙), z ∼ 0.5 galaxies with extreme star formation surface densities (ΣSFR ∼ 2000 M ⊙ yr−1 kpc−2). We have previously detected and characterized these outflows using Mg ii absorption lines. To probe their full extent, we present Keck/KCWI integral field spectroscopy of the [O ii] and Mg ii emission nebulae surrounding all of the 12 galaxies in this study. We find that [O ii] is more effective than Mg ii in tracing low surface brightness, extended emission in these galaxies. The [O ii] nebulae are spatially extended beyond the stars, with radial extent R 90 between 10 and 40 kpc. The nebulae exhibit nongravitational motions, indicating galactic outflows with maximum blueshifted velocities ranging from −335 to −1920 km s−1. The outflow kinematics correlate with the bursty star formation histories of these galaxies. Galaxies with the most recent bursts of star formation (within the last