The rapid transition from star-formation to AGN dominated rest-frame UV light at z ~ 4

With the advent of deep optical-to-near-infrared extragalactic imaging on the degree scale, samples of high-redshift sources are being selected that contain both bright star-forming (SF) galaxies and faint active galactic nuclei (AGN). In this study we investigate the transition between SF and AGN-dominated systems at $z \simeq 4$ in the rest-frame UV. We find a rapid transition to AGN-dominated sources bright-ward of $M_{\rm UV} \simeq -23.2$. The effect is observed in the rest-frame UV morphology and size-luminosity relation, where extended clumpy systems become point-source dominated, and also in the available spectra for the sample. These results allow us to derive the rest-frame UV luminosity function for the SF and AGN-dominated sub-samples. We find the SF-dominated LF is best fit with a double-power law, with a lensed Schechter function being unable to explain the existence of extremely luminous SF galaxies at $M_{\rm UV} \simeq -23.5$. If we identify AGN-dominated sources according to a point-source morphology criterion we recover the relatively flat faint-end slope of the AGN LF determined in previous studies. If we instead separate the LF according to the current spectroscopic AGN fraction, we find a steeper faint-end slope of $\alpha = -1.83 \pm 0.11$. Using a simple model to predict the rest-frame AGN LF from the $z = 4 $ galaxy LF we find that the increasing impact of host galaxy light on the measured morphology of faint AGN can explain our observations.