We use ultradeep 20 cm data from the Karl G. Jansky Very Large Array and 850 micron data from SCUBA-2 and the Submillimeter Array of an 124 arcmin^2 region of the Chandra Deep Field-north to analyze the high radio power (P_20cm>10^31 erg s^-1 Hz^-1) population. We find that 20 (42+/-9%) of the spectroscopically identified z>0.8 sources have consistent star formation rates (SFRs) inferred from both submillimeter and radio observations, while the remaining sources have lower (mostly undetected) submillimeter fluxes, suggesting that active galactic nucleus (AGN) activity dominates the radio power in these sources. We develop a classification scheme based on the ratio of submillimeter flux to radio power versus radio power and find that it agrees with AGN and star-forming galaxy classifications from Very Long Baseline Interferometry. Our results provide support for an extremely rapid drop in the number of high SFR galaxies above about a thousand solar masses per year (Kroupa initial mass function) and for the locally determined relation between X-ray luminosity and radio power for star-forming galaxies applying at high redshifts and high radio powers. We measure far-infrared (FIR) luminosities and find that some AGNs lie on the FIR-radio correlation, while others scatter below. The AGNs that lie on the correlation appear to do so based on their emission from the AGN torus. We measure a median radio size of 1.0+/-0.3 arcsecond for the star-forming galaxies. The radio sizes of the star-forming galaxies are generally larger than those of the AGNs.
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