A complete search for redshift z>6.5 quasars in the VIKING survey

We present the results of a new, deeper, and complete search for high-redshift $z > 6.5$ quasars over 977 square degrees of the VISTA Kilo-Degree Infrared Galaxy Survey (VIKING) survey, that is sensitive out to $z \sim 9.3$. This exploits a new list-driven dataset providing aperture fluxes and uncertainties in all bands $ZYJHK_s$, for all sources detected by VIKING in $J$. We used the Bayesian model comparison (BMC) selection method of Mortlock et al., producing a ranked list of just 21 candidates. The sources ranked 1, 2, 3 and 5 are the four known $z > 6.5$ quasars in this field. Additional observations of the other 17 candidates, primarily DESI Legacy Survey photometry and ESO FORS2 spectroscopy, confirm that none is a quasar. This is the first complete sample (i.e., all candidates followed up) from the VIKING survey, and we provide the computed selection function. We also compute selection functions for samples produced by two other methods: colour cuts and minimum chi-square SED fitting. Comparison of the efficiency (fraction of candidates that are quasars) and the depth of the three methods leads to the following conclusions: i) BMC produces eight times fewer false positives than colour cuts, while also reaching 0.3 mag. deeper, ii) the SED fitting method is extremely efficient but reaches 0.7 mag less deep than the BMC method, picking out only one of the four known quasars. By additionally following up BMC candidates rejected because their photometric SEDs have high $\chi^2$ values, we identify a population of galaxies where very strong [OIII]$\lambda\lambda$4959,5007 emission in the $Y$ band can mimic the colours of quasars, i.e., from Ly$\alpha$ and a blue continuum. This is a potential additional contaminant population in future searches for faint high-redshift quasars (such as in Euclid), not previously identified as such, and that requires better characterisation.