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An example of effective coverage maps (for the same regions) measured by HEALPix with three different starting resolution levels, Levels 9 (top panel), 10 (middle panel), and 11 (bottom panel). We use Level 10 as our starting resolution level (see the main text for the details).
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We present the discovery of nine quasars at $z\sim6$ identified in the Sloan Digital Sky Survey (SDSS) imaging data. This completes our survey of $z\sim6$ quasars in the SDSS footprint. Our final sample consists of 52 quasars at $5.7<z\le6.4$, including 29 quasars with $z_{\rm AB}\le20$ mag selected from 11,240 deg$^2$ of the SDSS single-epoch imag...
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... have tried different starting resolution levels, and found that HEALPix Level 10 (i.e., the HEALPix base resolution is divided 10 times) is the best for the SDSS. Figure 5 shows an example that com- pares the results from three different starting resolution levels, Levels 9 (top panel), 10 (middle panel), and 11 (bottom panel). The added 'holes' from Level 9 to Level 10 are almost all real, primarily caused by missing data and very bright stars. ...
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... pixels in the second category (hereafter boundary pixels) are the close neighbors to the pixels in the first category, i.e., each boundary pixel has at least one neighboring pixel in the first category. The boundary pixels include outer boundaries and inner boundaries (the edges of the inner 'holes', see Figure 5). The third category contains all remaining pixels (here- after non-boundary pixels). ...
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... Over the last two decades of quasar research, ground-based surveys have unveiled the existence of a large population of luminous quasars at z ∼ 6; residing well within the epoch of reionization (EOR), these quasars have black hole masses 10 9 M e Wu et al. 2015;Bañados et al. 2016;Jiang et al. 2016;Wang et al. 2019b;Yang et al. 2019Yang et al. , 2021Fan et al. 2023). These rare quasars, powered by such massive black holes, require that the black holes must have grown to their current state in less than 1 Gyr after the Big Bang. ...
We study the environment of the z = 6.33 ultraluminous quasar SDSS J010013.02+280225.8 (J0100) to understand its association with large-scale structure. Theoretical models propose high-redshift quasars as markers of galaxy overdensities residing in the most massive dark matter halos (DMHs) in the early Universe. J0100 is an ultraluminous quasar with the most massive black hole known at z ≳ 6, suggesting a high likelihood of residing in a massive DMH. We present wide-field (∼522 arcmin ² ) imaging in the r , i , and z bands from the Large Binocular Cameras on the Large Binocular Telescope, with Y- and J -band imaging from the Wide-field Infrared Camera on the Canada–France–Hawaii Telescope, centered on J0100. Applying color selections, we identify 23 objects as i -dropout Lyman break galaxy (LBG) candidates in the J0100 field. We use the deep photometric catalog in the 1.27 deg ² COSMOS field to calculate the density of LBGs in a blank field, and to estimate the selection completeness and purity. The observed surface density of LBG candidates in the J0100 field corresponds to a galaxy overdensity of δ = 4 (at 8.4 σ ). This large-scale overdensity suggests that the ∼22 arcmin ² overdensity found by Kashino et al. using JWST data extends out to much larger scales. We calculate the angular autocorrelation function of the candidates and find a positive correlation on ≲10′ scales as well as evidence of asymmetries in their spatial distribution, further suggesting the direct detection of large-scale structure in the field of the ultraluminous quasar J0100.
... The James Webb Space Telescope (JWST) is transforming the observational landscape of supermassive black holes (SMBHs). Prior to JWST, the observed BH population at high redshifts (z ∼ 4 − 7.5) was confined to the most luminous quasars powered by BHs between ∼ 10 9 −10 10 M⊙ (Fan et al. 2001;Willott et al. 2010;Mortlock et al. 2011;Venemans et al. 2015;Jiang et al. 2016;Bañados et al. 2016;Reed et al. 2017;Matsuoka et al. 2018;Wang et al. 2018;Bañados et al. 2018;Matsuoka et al. 2019;Yang et al. 2019;Wang et al. 2021). JWST is pushing these frontiers by revealing a large population of fainter broad line (BL) Active Galactic Nuclei (AGN) candidates at z ∼ 4 − 11 (Onoue et al. 2023;Harikane et al. 2023;Kocevski et al. 2023;Maiolino et al. 2023;Larson et al. 2023;Greene et al. 2023;Kocevski et al. 2024;Andika et al. 2024). ...
JWST has recently revealed a large population of accreting black holes (BHs) in the early Universe. Even after accounting for possible systematic biases, the high-z $M_*-M_{\rm \rm bh}$ relation derived from these objects by Pacucci et al. (2023 P23 relation) is above the local scaling relation by $>3\sigma$. To understand the implications of potentially overmassive high-z BH populations, we study the BH growth at $z\sim4-7$ using the $[18~\mathrm{Mpc}]^3$ BRAHMA suite of cosmological simulations with systematic variations of heavy seed models that emulate direct collapse black hole (DCBH) formation. In our least restrictive seed model, we place $\sim10^5~M_{\odot}$ seeds in halos with sufficient dense and metal-poor gas. To model conditions for direct collapse, we impose additional criteria based on a minimum Lyman Werner flux (LW flux $=10~J_{21}$), maximum gas spin, and an environmental richness criterion. The high-z BH growth in our simulations is merger dominated, with a relatively small contribution from gas accretion. For the most restrictive simulation that includes all the above seeding criteria for DCBH formation, the high-z $M_*-M_{\rm bh}$ relation falls significantly below the P23 relation (by factor of $\sim10$ at $z\sim4$). Only by excluding the spin and environment based criteria, and by assuming $\lesssim750~\mathrm{Myr}$ delay times between host galaxy mergers and subsequent BH mergers, are we able to reproduce the P23 relation. Overall, our results suggest that if high-z BHs are indeed systematically overmassive, assembling them would require more efficient heavy seeding channels, higher initial seed masses, additional contributions from lighter seeds to BH mergers, and / or more efficient modes for BH accretion.
... Recent advancements in deep imaging surveys, coupled with the enhanced capabilities of near-infrared (NIR) spectroscopy on large telescopes, have substantially expanded the sample size of quasars with > 6 to more than 200 (e.g., Fan et al. 2023). This has extended the quasar frontier beyond > 7.5, moving deep into the epoch of reionization (EoR; e.g., Mortlock et al. 2011;Jiang et al. 2016;Mazzucchelli et al. 2017;Bañados et al. 2016Bañados et al. , 2018Fan et al. 2019;Reed et al. 2019;Matsuoka et al. 2019a,b;Venemans et al. 2013Venemans et al. , 2015Wang et al. 2018Wang et al. , 2019Yang et al. 2019Yang et al. , 2020Yang et al. , 2021Wang et al. 2021a). Furthermore, recent observations from the James Webb Space Telescope (JWST) have already uncovered new high-active galactic nuclei (AGNs) with lower luminosity and black hole mass, promising to deliver additional breakthroughs in our understanding (e.g., Labbe et al. 2023;Maiolino et al. 2023a,b;Larson et al. 2023;Fujimoto et al. 2023;Goulding et al. 2023;Furtak et al. 2023;Kokorev et al. 2023;Greene et al. 2023;Kokorev et al. 2024;Pérez-González et al. 2024;Matthee et al. 2024;Andika et al. 2024). ...
We present optical and near-infrared (NIR) spectroscopic observations for a sample of $45$ quasars at $6.50 < z \leq 7.64$ with absolute magnitudes at $1450$ {\AA} in the range $-28.82 \leq M_{1450} \leq -24.13$ and their composite spectrum. The median redshift and $M_{1450}$ of the quasars in the sample are $z_{\rm{median}}=6.71$ and $M_{1450,\rm{median}} \simeq -26.1$, respectively. The NIR spectra are taken with echelle spectrographs, complemented with additional data from optical long slit instruments, and then reduced consistently using the open-source Python-based spectroscopic data reduction pipeline PypeIt. The median value of the mean signal-to-noise ratios of the spectra in J, H, and K band (median $\langle \rm{SNR}_{\lambda} \rangle$) is: median $\langle \rm{SNR}_{J} \rangle=9.7$, median $\langle \rm{SNR}_{H} \rangle=10.3$, and median $\langle \rm{SNR}_{K} \rangle=11.7$; demonstrating the good data quality. This work presents the largest medium/moderate-resolution sample of quasars at $z>6.5$ from ground-based instruments. Its homogeneity and reproducibility make it ideally suited for several scientific goals, i.e., the study of the quasar proximity zones and damping wings, the Ly$\alpha$ forest, the intergalactic medium's metal content, as well as other properties such as the distribution of SMBH masses and Eddington ratios. Our composite spectrum is compared to others at both high and low-$z$ from the literature, showing differences in the strengths of many emission lines, probably due to differences in luminosity among the samples, but a consistent continuum slope, which proves that the same spectral features are preserved in quasars at different redshift ranges.
... The most direct quasar demographic studies are based on the quasar luminosity function which has been used to measure active galactic nuclei (AGN) populations and their evolution across a wide range of redshifts (e.g. Willott et al. 2010a;Jiang et al. 2016;Yang et al. 2016;Akiyama et al. 2018;Matsuoka et al. 2018;McGreer et al. 2018;Niida et al. 2020;Onken et al. 2022;Matsuoka et al. 2023). Demographic analyses on high-redshift quasars become increasingly difficult due to declining quasar spatial densities, requiring deeper wide-area surveys (e.g. ...
... The Wu et al. (2022) mass function utilised a sample of 29 quasars with mostly Mg ii-based virial black hole mass estimates and just over 100 quasars with 1450 estimates from a fixed power-law continuum extrapolation. The quasars with black hole mass estimates are split into two samples (see Jiang et al. 2016), hence there can be two estimates for the spatial density in the same mass bin. At high masses, the Wu et al. (2022) binned spatial density is more consistent with the ∼ 5 spatial density than with other ∼ 6 mass functions, but the two highest mass bins which appear to deviate from the mass function of Willott et al. (2010b), contain only 5 quasars, including J0100+2802 ( = 6.3), which is the sole occupant of the highest mass bin. ...
We investigate the black hole mass function at $z\sim5$ using XQz5, our recent sample of the most luminous quasars between the redshifts $4.5 < z < 5.3$. We include 72 quasars with black hole masses estimated from velocity-broadened emission-line measurements and single-epoch virial prescriptions in the footprint of a highly complete parent survey. The sample mean Eddington ratio and standard deviation is $\log\lambda \approx -0.20\pm0.24$. The completeness-corrected mass function is modelled as a double power-law, and we constrain its evolution across redshift assuming accretion-dominated mass growth. We estimate the evolution of the mass function from $z=5-4$, presenting joint constraints on accretion properties through a measured dimensionless e-folding parameter, $k_{\rm{ef}} \equiv \langle\lambda\rangle U (1-\epsilon)/\epsilon = 1.79\pm0.06$, where $\langle\lambda\rangle$ is the mean Eddington ratio, $U$ is the duty cycle, and $\epsilon$ is the radiative efficiency. If these supermassive black holes were to form from seeds smaller than $10^8\,M_{\odot}$, the growth rate must have been considerably faster at $z\gg5$ than observed from $z=5-4$. A growth rate exceeding $3\times$ the observed rate would reduce the initial heavy seed mass to $10^{5-6}\,M_{\odot}$, aligning with supermassive star and/or direct collapse seed masses. Stellar mass ($10^2\,M_{\odot}$) black hole seeds would require $\gtrsim4.5\times$ the observed growth rate at $z\gg5$ to reproduce the measured active black hole mass function. A possible pathway to produce the most extreme quasars is radiatively inefficient accretion flow, suggesting black holes with low angular momentum or photon trapping in supercritically accreting thick discs.
... In the past two decades, about 300 quasars at z > 6 have been discovered, indicating that SMBHs with M BH 10 9 M e already existed when the Universe was less than 1 Gyr old (e.g., Mortlock et al. 2011;Jiang et al. 2016;Matsuoka et al. 2018;Wang et al. 2019bWang et al. , 2021Yang et al. 2020;Bañados et al. 2023). This quasar sample enables studies of SMBH-host coevolution in the early Universe. ...
We report JWST/NIRCam measurements of quasar host galaxy emissions and supermassive black hole (SMBH) masses for six quasars at 5.9 < z < 7.1 in the Emission-line galaxies and Intergalactic Gas in the Epoch of Reionization (EIGER) project. We obtain deep NIRCam imaging in the F115W, F200W, and F356W bands, as well as F356W grism spectroscopy of the quasars. We use bright unsaturated stars to construct models of the point-spread functions (PSFs) and estimate the errors of these PSFs. We then measure or constrain the fluxes and morphology of the quasar host galaxies by fitting the quasar images as a point source plus an exponential disk. We successfully detect the host galaxies of three quasars, which have host-to-quasar-flux ratios of ∼1%–5%. Spectral energy distribution fitting suggests that these quasar host galaxies have stellar masses of M * ≳ 10 ¹⁰ M ⊙ . For quasars with host galaxy nondetections, we estimate the upper limits of their stellar masses. We use the grism spectra to measure the H β line profile and the continuum luminosity, then estimate the SMBH masses for the quasars. Our results indicate that the positive relation between SMBH masses and host galaxy stellar masses already exists at redshift z ≳ 6. The quasars in our sample show a high BH-to-stellar-mass ratio of M BH / M * ∼ 0.15, which is about ∼2 dex higher than local relations. We find that selection effects only contribute partially to the high M BH / M * ratios of high-redshift quasars. This result hints at a possible redshift evolution of the M BH – M * relation.
... Observations of high-redshift quasars within the first few billion years of cosmic history have benefited from wide-field surveys such as the Sloan Digital Sky Survey (SDSS; Jiang et al. 2016;Wu et al. 2022), Pan-Starrs 1 (Morganson et al. 2012;Bañados et al. 2023), the Dark Energy Spectroscopic Instrument (Yang et al. 2023), and the Hyper Suprime-Cam (HSC) Subaru Strategic Program (Matsuoka et al. 2016(Matsuoka et al. , 2018Akiyama et al. 2018;Niida et al. 2020). Extensive efforts in spectroscopic follow-up observations have revealed that supermassive black holes (SMBHs) have formed and grown in mass to M • 10 9 M e within a short amount of cosmic time (1 Gyr at z 6; Wu et al. 2015;Shen et al. 2019;Wang et al. 2021; see also a recent review by Fan et al. 2023). ...
The James Webb Space Telescope (JWST) has recently uncovered the presence of low-luminosity active galactic nuclei (AGNs) at z = 4–11. Spectroscopic observations have provided estimates of the nuclear black hole (BH) masses for these sources, extending the low-mass boundary down to M • ∼ 10 6–7 M ⊙ . Despite this breakthrough, the observed lowest mass of BHs is still ≳1–2 orders of magnitude heavier than the predicted mass range of their seed population, thereby leaving the initial mass distribution of massive BHs poorly constrained. In this paper, we focus on UV-to-optical (in the rest frame) flares of stellar tidal disruption events (TDEs) embedded in low-luminosity AGNs as a tool for exploring low-mass BH populations with ≲10 4–6 M ⊙ . We provide an estimate of the TDE rate over z = 4–11, associated with the properties of JWST-detected AGN host galaxies, and we find that deep and wide survey programs with JWST and the Roman Space Telescope (RST) can detect and identify TDEs up to z ≃ 4–7. The predicted detection numbers of TDEs at z > 4 in 1 yr are N TDE ∼ 2 – 10 ( 0.2 – 2 ) for the JADES-Medium (and COSMOS-Web) survey with JWST and N TDE ∼ 2 – 10 ( 8 – 50 ) for the deep (and wide) tiers of the High Latitude Time Domain Survey with RST. We further discuss survey strategies for hunting for transient high-redshift TDEs in wide-field surveys with RST, as well as a joint observation campaign with the Vera C. Rubin Observatory for enhancing the detection number. The high-redshift TDE search will give us a unique opportunity to probe the mass distribution of early BH populations.
... A comprehensive comparison can be found in [71], which demonstrated that differences are minimal so long as the window function is implemented properly. 6 It is unclear whether this factor should still be included when considering asymmetric probability distribution functions, as in the case of non-Gaussianities. We retain it nevertheless since this is an ultimately inconsequential O(1) effect. ...
There is controversy surrounding the origin and evolution of our universe's largest supermassive black holes (SMBHs). In this study, we consider the possibility that some of these black holes formed from the direct collapse of primordial density perturbations. Since the mass of a primordial black hole is limited by the size of the cosmological horizon at the time of collapse, these SMBHs must form rather late, and are naively in conflict with constraints from CMB spectral distortions. These limits can be avoided, however, if the distribution of primordial curvature perturbations is highly non-Gaussian. After quantifying the departure from Gaussianity needed to evade these bounds, we explore a model of multi-field inflation — a non-minimal, self-interacting curvaton model — which has all the necessary ingredients to yield such dramatic non-Gaussianities. We leave the detailed model building and numerics to a future study, however, as our goal is to highlight the challenges associated with forming SMBHs from direct collapse and to identify features that a successful model would need to have. This study is particularly timely in light of recent observations of high-redshift massive galaxy candidates by the James Webb Space Telescope as well as evidence from the NANOGrav experiment for a stochastic gravitational wave background consistent with SMBH mergers.
... Due to their potential for extreme luminosities, quasars can be observed at very early cosmic periods, into the epoch of reionization, the last major phase change of the Universe, at z 6 (e.g. Wu et al. 2015 ;Jiang et al. 2016 ;Reed et al. 2019 ;Shen et al. 2019 ;Yang et al. 2021 ;D'Odorico et al. 2023 ). The highest redshift quasars are disco v ered up to z ∼ 7.5 (e.g. ...
Bright quasar samples at high redshift are useful for investigating active galactic nuclei evolution. In this study, we describe XQz5, a sample of 83 ultraluminous quasars in the redshift range 4.5 < z < 5.3 with optical and near-infrared spectroscopic observations, with unprecendented completeness at the bright end of the quasar luminosity function. The sample is observed with the Southern Astrophysical Research Telescope, the Very Large Telescope, and the ANU 2.3m Telescope, resulting in a high-quality, moderate-resolution spectral atlas of the brightest known quasars within the redshift range. We use established virial mass relations to derive the black hole masses by measuring the observed Mg ii λ2799 Å emission-line and we estimate the bolometric luminosity with bolometric corrections to the UV continuum. Comparisons to literature samples show that XQz5 bridges the redshift gap between other X-shooter quasar samples, XQ-100 and XQR-30, and is a brighter sample than both. Luminosity-matched lower-redshift samples host more massive black holes, which indicate that quasars at high redshift are more active than their counterparts at lower-redshift, in concordance with recent literature.
... Recent successful high-redshift quasar surveys have increased the number of known z 5 quasars to ∼600 (e.g., Fan et al. 2006;Willott et al. 2010;Mortlock et al. 2011;Venemans et al. 2015;Wu et al. 2015;Bañados et al. 2016;Jiang et al. 2016;Mazzucchelli et al. 2017;McGreer et al. 2018;Reed et al. 2019;Matsuoka et al. 2019aMatsuoka et al. , 2019bWang et al. 2016Wang et al. , 2018Wang et al. , 2019Yang et al. 2017Yang et al. , 2019aYang et al. , 2019bRoss & Cross 2020;Yang et al. 2021), with the three most distant quasars at z > 7.5 (Bañados et al. 2018;Yang et al. 2020a;Wang et al. 2021). After the end of high-redshift quasar searches using the Sloan Digital Sky Survey I-IV (e.g., Schneider et al. 2010;Pâris et al. 2017;Lyke et al. 2020), recent discoveries of high-redshift quasars are mainly based on single-object observations, which have a limited efficiency of spectroscopy. ...
... The red points on the track represent quasars at z = 5.0, 5.5, 6.0, and 6.5. The blue crosses denote all existing quasars known at 4.8 z 6.8 (e.g., Fan et al. 2006;Willott et al. 2010;Mortlock et al. 2011;Venemans et al. 2015;Wu et al. 2015;Bañados et al. 2016Bañados et al. , 2018Jiang et al. 2016;Mazzucchelli et al. 2017;McGreer et al. 2018;Matsuoka et al. 2019aMatsuoka et al. , 2019bPâris et al. 2017;Reed et al. 2019;Wang et al. 2016Wang et al. , 2018Wang et al. , 2019Wang et al. , 2021Yang et al. 2017Yang et al. , 2019aYang et al. , 2019bYang et al. , 2020aYang et al. , 2021, while the gray points and the black squares show the loci of M and L/T dwarfs (Kirkpatrick et al. 2011;Mace 2014;Best et al. 2015), respectively. The orange dashed lines bound the selected regions for z ∼ 5 and z ∼ 6 quasar candidates. ...
We report the first results of a high-redshift ( z ≳ 5) quasar survey using the Dark Energy Spectroscopic Instrument (DESI). As a DESI secondary target program, this survey is designed to carry out a systematic search and investigation of quasars at 4.8 < z < 6.8. The target selection is based on the DESI Legacy Imaging Surveys (the Legacy Surveys) DR9 photometry, combined with the Pan-STARRS1 data and J -band photometry from public surveys. A first quasar sample has been constructed from the DESI Survey Validation 3 (SV3) and first-year observations until 2022 May. This sample includes more than 400 new quasars at redshift 4.7 ≤ z < 6.6, down to 21.5 magnitude (AB) in the z band, discovered from 35% of the entire target sample. Remarkably, there are 220 new quasars identified at z ≥ 5, more than one-third of existing quasars previously published at this redshift. The observations so far result in an average success rate of 23% at z > 4.7. The current spectral data set has already allowed analysis of interesting individual objects (e.g., quasars with damped Ly α absorbers and broad absorption line features), and statistical analysis will follow the survey’s completion. A set of science projects will be carried out leveraging this program, including quasar luminosity function, quasar clustering, intergalactic medium, quasar spectral properties, intervening absorbers, and properties of early supermassive black holes. Additionally, a sample of 38 new quasars at z ∼ 3.8–5.7 discovered from a pilot survey in the DESI SV1 is also published in this paper.
... Fan (1999) proposes an empirical method to construct a quasar spectrum using observed continuum slope and emission line strengths, assuming the shape of quasar SEDs does not evolve with redshift, as well as models of intergalactic absorption blueward of Lyα emission. This approach has been extended to include higher redshift quasars in a number of recent works (e.g., McGreer et al. 2013;Jiang et al. 2016;Yang et al. 2016;McGreer et al. 2018;Wang et al. 2019). In this section, we briefly describe the spectral model and extend the simulation to include z = 6-10 quasars. ...
... where M 1450 is the absolute magnitude at 1450 Å, α and β are the faint end and bright end slopes, respectively, * M 1450 is the characteristic absolute magnitude or break magnitude measured at 1450 Å (assume no redshift evolution), and Φ * is the normalization of the luminosity function (LF). With high completeness quasar samples, the QLF has been measured at z ∼ 5 and extended to z = 6 across wide luminosity ranges of ( Willott et al. 2010;McGreer et al. 2013;Jiang et al. 2016;McGreer et al. 2018). Previous studies of SDSS quasars at z > 3.5 show that k = −0.47, ...
... However, the measurement of the QLF at z 5 remains highly uncertain because of the small sample sizes, especially at fainter magnitudes (e.g., Willott et al. 2010;McGreer et al. 2013;Venemans et al. 2013;Kashikawa et al. 2015;Venemans et al. 2015;Jiang et al. 2016; ) use a complete bright quasar samples at 6.4 < z < 6.9 and find k = −0.78 ± 0.18 at z = 6.0 −6.7, further strengthening the claim of a rapid declination in quasar spatial density from z = 3.0−5.0 to z > 6.0. ...
About 70 luminous quasars discovered at z > 6.5 are strongly biased toward the bright end, thus not providing a comprehensive view of quasar abundance beyond the cosmic dawn. We present the predicted results of the Roman/Rubin high-redshift quasar survey, yielding 3 times more, 2–4 mag deeper quasar samples, probing high-redshift quasars across a broad range of luminosities, especially faint quasars at L bol ∼ 10 ¹⁰ L ⊙ or M 1450 ∼ −22, which 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 the classical color dropout method in the z and Y bands to select primary quasar candidates, followed up with the Bayesian selection method to identify quasars. We show that overall selection completeness >80% and efficiency ∼10% at 6.5 < z < 9, with 180 quasars at z > 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 data sets are worth follow-up studies with JWST and Extremely Large Telescopes to determine the quasar luminosity function faint end slope and constraint the supermassive black holes growth in the early Universe.
