We present the discovery of compact, obscured star formation in galaxies at z ~ 0.6 that exhibit >1000 km/s outflows. Using optical morphologies from the Hubble Space Telescope and infrared photometry from the Wide-field Infrared Survey Explorer, we estimate star formation rate (SFR) surface densities that approach Sigma_SFR ~ 3000 Msun/yr/kpc^2, comparable to the Eddington limit from radiation pressure on dust grains. We argue that feedback associated with a compact starburst in the form of radiation pressure from massive stars and ram pressure from supernovae and stellar winds is sufficient to produce the high-velocity outflows we observe, without the need to invoke feedback from an active galactic nucleus.
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