Paving the way forEuclid and JWST via probabilistic selection of high-redshift quasars

We introduce a probabilistic approach to select 6 ≤ $z$ ≤ 8 quasar candidates for spectroscopic follow-up, which is based on density estimation in the high-dimensional space inhabited by the optical and near-infrared photometry. Densities are modelled as Gaussian mixtures with principled accounting of errors using the extreme deconvolution (XD) technique, generalizing an approach successfully used to select lower redshift ($z$ ≤ 3) quasars. We train the probability density of contaminants on 1902 071 7-d flux measurements from the 1076 deg2 overlapping area from the Dark Energy Camera Legacy Survey (DECaLS) ($z$), VIKING (YJHKs), and unWISE (W1W2) imaging surveys, after requiring they dropout of DECaLS g and r, whereas the distribution of high-$z$ quasars are trained on synthetic model photometry. Extensive simulations based on these density distributions and current estimates of the quasar luminosity function indicate that this method achieves a completeness of $\ge 56{{\ \rm per\ cent}}$ and an efficiency of $\ge 5{{\ \rm per\ cent}}$ for selecting quasars at 6 < $z$ < 8 with JAB < 21.5. Among the classified sources are 8 known 6 < $z$ < 7 quasars, of which 2/8 are selected suggesting a completeness $\simeq 25{{\ \rm per\ cent}}$, whereas classifying the 6 known (JAB < 21.5) quasars at $z$ > 7 from the entire sky, we select 5/6 or a completeness of $\simeq 80{{\ \rm per\ cent}}$. The failure to select the majority of 6 < $z$ < 7 quasars arises because our quasar density model is based on an empirical quasar spectral energy distribution model that underestimates the scatter in the distribution of fluxes. This new approach to quasar selection paves the way for efficient spectroscopic follow-up of Euclid quasar candidates with ground-based telescopes and James Webb Space Telescope.