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 <3 Myr) exhibit the highest central velocity dispersions (σ ≳ 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 ≳50 Myr.
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