The GLEAMing of the first supermassive black holes: III. Radio sources with ultra-faint host galaxies

We present deep near-infrared K-s-band imaging for 35 of the 53 sources from the high-redshift (z > 2) radio galaxy candidate sample defined in Broderick et al. (2022, PASA, 39, e061). These images were obtained using the High-Acuity Widefield K-band Imager (HAWK-I) on the Very Large Telescope. Host galaxies are detected for 27 of the sources, with K-s approximate to 21.6-23.0 mag (2 '' diameter apertures; AB). The remaining eight targets are not detected to a median 3 sigma 3 sigma depth of K-s approximate to 23.3 mag (2 '' diameter apertures). We examine the radio and near-infrared flux densities of the 35 sources, comparing them to the known z > 3 powerful radio galaxies with 500-MHz radio luminosities L-500MHz > 10(27) W Hz(-1). By plotting 150-MHz flux density versus K-s-band flux density, we find that, similar to the sources from the literature, these new targets have large radio to near-infrared flux density ratios, but extending the distribution to fainter flux densities. Five of the eight HAWK-I deep non-detections have a median 3 sigma lower limit of K-s greater than or similar to 23.8 mag (1.'' 5 diameter apertures); these five targets, along with a further source from Broderick et al. (2022, PASA, 39, e061) with a deep non-detection (Ks greater than or similar to 23.7 mag; 3 sigma; 2 '' diameter aperture) in the Southern H-ATLAS Regions K-s-band Survey, are considered candidates to be ultra-high-redshift (z > 5) radio galaxies. The extreme radio to near-infrared flux density ratios (>10(5)) for these six sources are comparable to TN J0924-2201, GLEAM J0856 + 0223 and TGSS J1530 + 1049, the three known powerful radio galaxies at z > 5. For a selection of galaxy templates with different stellar masses, we show that z greater than or similar to 4.2 is a plausible scenario for our ultra-high-redshift candidates if the stellar mass M* greater than or similar to 10(10.5 )M(circle dot). In general, the 35 targets studied have properties consistent with the previously known class of infrared-faint radio sources. We also discuss the prospects for finding more UHzRG candidates from wide and deep near-infrared surveys.