A strategy for astrometric quasar selection with Gaia DR3 and its application to discover new luminous z>2 quasars

We provide a cookbook for a purely astrometric selection of quasars with Gaia DR3 and provide an example of its use for the identification of very luminous z>2 quasars. We analysed the Gaia DR3 astrometry of confirmed quasars and stationary sources. The proper motion signal-to-noise ratio μ/σ_μ follows a Rayleigh-like distribution. We also show the importance of properly taking the correlation between proper motions in right ascension and declination into account, as well as the non-linear error propagation. We adopted the Mahalanobis distance to the null proper-motion hypothesis. A scaled ̧hi^2 distribution with k=2 and scale s=1.1485 was fitted to Gaia-CRF3; the corresponding pm2σ Gaussian-equivalent threshold is D^2_ M(μ) <7.097. The final criteria combine this with the parallax condition and mathrm ruwe <1.4. When we applied the new criteria to the SDSS DR16Q confirmed quasars, the recovery rate was 90.25%. The suggested purely astrometric selection significantly improves completeness and purity compared to other strategies used in the literature, reaching a quasar purity of approximately 95% (sim2σ Gaussian-equivalent). It can be used to improve the selection purity and completeness for future quasar surveys. As an example, we used the suggested strategy to locate 24 very bright z>2 quasars without redshifts in the literature. Our proposed astrometric selection strategy recovers 95% of the known quasars. Its potential use for new discoveries was demonstrated by the identification of 24 very luminous z>2 quasars. Of these, 10 are new discoveries, and for an additional 7, we corrected the redshifts determined by other methods.