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

High-velocity outflows are ubiquitous in compact, massive (M-* similar to 10(11)M(circle dot)), z similar to 0.5 galaxies with extreme star formation surface densities (Sigma(SFR) similar to 2000 M-circle dot 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 <3 Myr) exhibit the highest central velocity dispersions (sigma greater than or similar to 400 km s(-1)), while the oldest bursts have the lowest-velocity outflows. Many galaxies exhibit both high-velocity cores and more extended, slower-moving gas indicative of multiple outflow episodes. The slower, larger outflows occurred earlier and have decelerated as they propagate into the circumgalactic medium and mix on timescales greater than or similar to 50 Myr.