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

High-velocity outflows are ubiquitous in compact, massive ( M _* ∼ 10 ^11 M _⊙ ), z ∼ 0.5 galaxies with extreme star formation surface densities (Σ _SFR ∼ 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