Predicting the Yields of $z$ > 6.5 Quasar Surveys in the Era of Roman and Rubin
Around 70 $z>6.5$ luminous quasars have been discovered, strongly biased toward the bright end, thus not providing a comprehensive view on quasar abundance beyond cosmic dawn. We present the predicted results of Roman/Rubin high-redshift quasar survey, yielding 3 times more, $2-4$ magnitudes deeper quasar samples, probing high-redshift quasars across broad range of luminosities, especially faint quasars at $L_\mathrm{bol}\sim 10^{10}\;L_{\odot}$ or $M_\mathrm{1450} \sim-22$ that are currently poorly explored. We include high-$z$ quasars, galactic dwarfs and low-$z$ compact galaxies with similar colors as quasar candidates. We create mock catalogs based on population models to evaluate selection completeness and efficiency. We utilize classical color dropout method in $z$ and $Y$ bands to select primary quasar candidates, followed up with Bayesian selection method to identify quasars. We show that overall selection completeness $> 80\%$ and efficiency $\sim 10\%$ at $6.5 6.5$, 20 at $z > 7.5$ and 2 at $z > 8.5$. The quasar yields depend sensitively on the assumed quasar luminosity shape and redshift evolution. Brown dwarf rejection through proper motion up to 50$\%$ can be made for stars brighter than 25 mag, low-$z$ galaxies dominate at fainter magnitude. Our results show that Roman/Rubin are able to discover a statistical sample of the earliest and faintest quasars in the Universe. The new valuable datasets worth follow up studies with James Webb Space Telescope and Extremely Large Telescopes, to determine quasar luminosity function faint end slope and constraint the supermassive black holes growth in the early Universe.