arXiv subjects

Xuheng Ding

Publications and source records attributed to Xuheng Ding.

At least 19 recordsLinked to original sources

arXiv2026

SHELLQs. Black Hole Mass and Eddington Ratio Distributions of Intermediate-Luminosity Quasars at 6<z<7

We present near-infrared spectroscopy of 21 quasars at 6.07 < z < 6.90 obtained with JWST/NIRSpec and Subaru/MOIRCS. These targets have absolute ultraviolet magnitudes of -25 < M_1450 < -22 and are drawn from a sample of z>6 quasars identified in the Subaru High-z Exploration of Low-Luminosity Quasars (SHELLQs) project. These quasars occupy the intermediate-luminosity regime between luminous quasars and the faint high-redshift AGNs uncovered by JWST. We detect broad Balmer emission lines and MgII 2798 with underlying continua from the NIRSpec and MOIRCS targets, respectively. The virial black hole masses of this sample span a wide range of 7.2 < log M_BH/M_sun < 9.4, with Eddington ratios of -1.3 < log L_bol/L_Edd < 0.4. Combining these measurements with our previous mass estimates for other SHELLQs quasars, we construct a sample of 27 quasars with M_BH estimates at 6 < z < 7 and derive the distributions of M_BH and L_bol/L_Edd. When compared with luminosity-matched quasars at z ~ 1.3, we find median offsets of delta log M_BH/M_sun = -0.4 and Delta log L_bol/L_Edd = 0.2 in the high-redshift sample. In addition, 11% of the high-redshift quasars are accreting near or above the Eddington limit. As a systematic check, adopting the Eddington-ratio-dependent calibration of single-epoch M_BH estimates increases the inferred super-Eddington fraction to 22%. These results indicate that a representative population of distant supermassive black holes undergo a rapid accretion phase, although not as extreme as that seen in the most luminous quasar population, consistent with the anti-hierarchical growth scenario of supermassive black holes.

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arXiv2026

Hidden in Pixels. I. Discovery of dual "little red dots" indicates excess clustering on kilo-parsec scales

``Little Red Dots'' (LRDs) are an abundant high-redshift population newly discovered by the James Webb Space Telescope (JWST) and considered to be an early growth phase of supermassive black holes (SMBHs). Using a method of pixel-by-pixel color selection and relaxing the compactness criteria, we identify four dual LRD candidates in the COSMOS-Web survey with projected separations of $0.\!\!^{\prime\prime}2$-$1.\!\!^{\prime\prime}2$. A comparison between existing LRD samples and mock data reveals that the projected separations of these dual LRD candidates are unlikely to result from chance projections of objects at different redshifts. Furthermore, two of the four systems are covered by COSMOS-3D slitless spectroscopy, and a single-line detection at the same observed wavelength for each LRD in a pair strongly supports that they are at identical redshifts. Assuming that the detected lines are H$α$ based on their high equivalent width and broad profile, the spectroscopic redshifts of $z=5.822$ and $5.464$ for the two pairs are consistent with their photometric redshifts, yielding projected separations of $1.64$ and $7.36\,{\rm kpc}$. These discoveries suggest that the angular auto-correlation function (ACF) of LRDs exhibits an excess ($\sim20$-$30$ times) on sub-arcsec (kilo-parsec) separations compared to an extrapolation of a power-law ACF of JWST-found AGNs measured over $10^{\prime\prime}$-$100^{\prime\prime}$. Our sample is likely to represent precursors of mergers between LRDs, and such mergers may be one of the mechanisms that can drive the rapid growth of SMBHs in their early evolutionary stages.

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arXiv2026

The Intermediate-Mass Black Hole Reverberation Mapping Project: Scientific Overview and Sample Characteristics

Recent discoveries with the James Webb Space Telescope of massive black holes at high redshift have highlighted fundamental questions about black hole seed formation and the coevolution of black holes with their host galaxies. Because the initial seed population cannot yet be observed directly, nearby intermediate-mass black holes provide a complementary fossil record of black hole formation and early growth. Motivated by this opportunity, we present the Intermediate-Mass Black Hole Reverberation Mapping (IMBH-RM) project and construct a homogeneous Sloan Digital Sky Survey sample of active broad-line IMBHs by uniformly reanalyzing literature candidates with consistent spectral decomposition and black hole mass estimation. Our sample contains 192 reliable IMBH candidates at $z\lesssim0.3$ with $\log(M_{\rm BH}/M_\odot)<6$, including four particularly compelling sources with $\log(M_{\rm BH}/M_\odot)<5$. The primary goal of IMBH-RM is to obtain reliable black hole masses from direct measurements and characteristic sizes of the broad-line region and accretion disk for a carefully selected subsample. These measurements will provide robust low-mass anchors for calibrating single-epoch black hole mass estimates and extending black hole--galaxy scaling relations into the IMBH regime. By building a statistically meaningful reverberation-mapped sample spanning $10^4-10^6\,M_\odot$, we aim to constrain the local IMBH mass distribution and place observational constraints on competing black hole seed formation scenarios. The future Multi-Channel Imager aboard the Chinese Space-station Survey Telescope provides a particularly promising platform for achieving these goals.

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arXiv2026

Extended Components of Little Red Dots in the Rest-Frame Optical

Recent JWST observations have revealed a population of red, compact, high-redshift objects called Little Red Dots (LRDs), whose host components have remained largely unconstrained, possibly due to their extreme compactness. Current morphological studies suggest the presence of extended emission in LRDs at rest-frame ultraviolet wavelengths. However, in the rest-frame optical regime, investigations have been limited by small sample sizes and insufficient imaging depth, hindering reliable separation between point-like and potential extended components. Here we perform the image stacking analysis of 217 LRDs in four NIRCam bands, a large and homogeneous sample observed with the COSMOS-Web survey. Our results reveal the detection of faint extended emission in the F444W band, with a typical size of ~200 parsecs and magnitude of ~27.7 AB at z~6.5. We perform four-band photometric spectral energy distribution fitting based on galaxy templates and derive an average stellar mass of log(M*/M_sun) = 9.02 +0.20/-0.18. Given this stellar mass, the host galaxy is compact, that is, ~2.5 times smaller than star-forming galaxies of similar mass at comparable redshifts. This work provides direct observational evidence for the existence of LRD host galaxies at rest-frame optical wavelengths and offers new insights into the stellar buildup of these systems within the first billion years after the Big Bang.

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arXiv2026

Magnetically Arrested Discs Powering Jets in a Large Sample of Low-Accretion FR I Radio Galaxies

We study a sample of 289 Fanaroff-Riley type I (FR I) radio galaxies selected from the LOFAR Two-Metre Sky Survey (LoTSS) DR1, identified by their edge-darkened radio morphologies. Using Sloan Digital Sky Survey (SDSS) DR17 optical photometry and spectroscopy, we derive Eddington-scaled accretion rates spanning -6.84 < log $\dot{m}$ < -0.87 (median $\approx$ -2.84). The vast majority of sources lie below $\dot{m}$ = 0.01, indicating that their central engines are well described by advection-dominated accretion flows (ADAFs). However, even for a rapidly spinning black hole with a = 0.95, the maximum jet power predicted by the Blandford-Znajek mechanism in the standard ADAF regime is lower than the observed jet power (estimated from 151 MHz radio luminosity) for approximately 70% of the sample. We demonstrate that the magnetically arrested disc (MAD) scenario, in which large-scale poloidal magnetic flux accumulates near the event horizon, can fully account for the powerful jets observed in these low-accretion systems. Within the MAD framework, the data are consistent with slow-spinning black holes with $a < 0.5$. This large, uniformly selected LoTSS sample extends the MAD requirement previously established for the bright 3CR FR I population, indicating that magnetically arrested discs are common in FR I radio galaxies across a wide range of luminosities.

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arXiv2026

COSMOS-Web: A Multi-wavelength Morphological Catalog of ~780,000 Galaxies

We present multi-wavelength morphological measurements for all galaxies in the COSMOS-Web survey, i.e., $\sim$780,000 galaxies contained in the COSMOS2025 catalog. We perform both parametric (e.g., single and double Sérsic modeling) and non-parametric (e.g., Gini-$M_{20}$) morphology analyses in four NIRCam bands, independently. Our parametric fits reveal a strong correlation between galaxy structure and star formation activity up to $z\sim4$, as evidenced by the dependence of the Sérsic index ($n_{\rm sérsic}$) and bulge-to-total ratio ($B/T$) on the position of the star formation rate-stellar mass plane. A tight correlation between $n_{\rm sérsic}$ and $B/T$ is observed. The evolution of $n_{\rm sérsic}$ and $B/T$ depends on stellar mass; for example, the median $n_{\rm sérsic}$ increases from $\sim1$ at $z\sim6$ to $\sim2.5$ at $z\sim2$ for massive galaxies with $M_*>10^{10.5} M_{\odot}$, while lower mass galaxies remain $n_{\rm sérsic}\sim1.2$ at all epochs. The UV $n_{\rm sérsic}$ values are systematically smaller than those in the optical, although both exhibit similar evolutionary trends. From non-parametric analyses, we demonstrate the distribution of galaxies on the Gini-$M_{20}$ and asymmetry-concentration planes, and find that morphological classifications based on non-parametric indicators are consistent with those derived from the Sérsic index. The resulting catalog provides the largest and most detailed set of JWST multi-wavelength morphological measurements to date, serving as a valuable community resource for studies of structural transformation, bulge growth, and galaxy-supermassive black hole coevolution across cosmic time.

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arXiv2026

Varstrometry for Off-nucleus and Dual Subkiloparsec AGN (VODKA): Three Quadruply Lensed Quasars at Cosmic Noon in HST and JWST

We present results from imaging observations of three quadruply lensed quasars by Hubble Space Telescope (HST) and James Webb Space Telescope (JWST) at redshifts $z = 2.550$, 2.975, and 1.500. We model our targets assuming a singular isothermal ellipsoid mass profile and an elliptical SÃ\c{opyright}rsic profile for the lensing galaxies, and reconstruct the geometric configuration of each system with measured Einstein radii of 0.44$'$, 0.58$'$, and 0.49$'$. While no spectroscopic measurements are available for the lenses, we constrain the redshift of each lens to $0.5 < z < 1.2$, $1.0 < z < 1.5$, and $0.4 < z < 0.9$. For all three lenses, the best-fit light model yield a typical de Vaucouleurs $n_{\rm S\acute{e}rsic} \sim 4$ profile and an effective radius $R_e$ around $\sim 1.5 - 3.5$ kpc. We accordingly classify the three lenses as early-type galaxies at an intermediate to high redshift, a common type for strong lensing galaxies. Compared to other known quadruple lenses, the lensing galaxies in this work are at the lower end of the distribution of Einstein radii and upper end of the distribution of the lens redshifts. They represent an interesting quadrant of subarcsecond-separation lenses in the population of single-galaxy strong lensing which have been largely unexplored yet and will be great targets of interest in upcoming high-resolution lensing surveys.

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arXiv2026

Mock Catalogs of Strongly Lensed Gravitational Waves via A Halo Model Approach with Ground-based Detectors

As plans for the construction of third-generation gravitational wave (GW) detectors advance, research into strongly lensed GWs has become increasingly critical. It is anticipated that hundreds of multi-image lensed GWs will be detected annually. We present a comprehensive suite of lensed GW mock catalog derived from a composite lens mass model incorporating dark matter halos, galaxies, and subhalos. We analyze three source populations with four detector network configurations considering the earth rotation. Our simulations encompass not only conventional doublets and quadruplets but also subhalo-lensed events, highly magnified systems, and complete three or five image systems with a detectable central image, a feature distinct from optical lensing. For the joint ET+CE network, we forecast an annual detection rate of approximately 400 doublets and 36 quadruplets. Notably, this population includes roughly 107 events lensed by subhalos and 20 complete systems with detectable central images. Furthermore, we analyze high-magnification events ($μ> 3$), predicting approximately 360 such cases. Under a more relaxed selection criterion that requires only at least one lensed signal to exceed the detection threshold, we estimate a total of approximately 617 lensed events. We also investigate the impact of variations in lens mass models and stellar evolution models on event rates, as well as the distributions of SNR pairs and time delays. These results establish a more physically grounded statistical prior for the future identification and authentication of lensed GW signals. The Gravitational Waves-Lensing Mock Catalog (GW-LMC) have been made publicly available.

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arXiv2026

A Bending in the Size-mass Relation of Star-forming Galaxies across $0.5 < z < 6.0$ at a Critical Stellar Mass of $10^{10}M_\odot$ Revealed by JWST

We investigate the rest-frame optical size-stellar mass relation of galaxies at $0.5 M_{\rm p}$, an increasing fraction of SFGs decouple from halo growth and become compact, likely associated with rapid bulge (and black hole) growth in $M_{\rm h} \gtrsim 10^{12} M_{\odot}$ halos. These compact SFGs are promising progenitors of massive QGs, as evidenced by their similar masses, surface brightness profiles, and morphologies. Their high number densities can account for the observed buildup of massive QGs at $z > 2$, suggesting that the compaction pathway, rather than major mergers of extended SFGs, dominates the formation of high-z massive QGs.

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arXiv2026

Gas Fraction and Depletion Time Drive the Main-Sequence Scatter in Massive Galaxies at $z\sim1.5$

We present ALMA Band 7 dust continuum observations of 57 massive ($M_\ast \gtrsim 10^{10.8}~M_\odot$) star-forming galaxies at $1.45 3σ$ detections for 55 galaxies. Combining the ALMA data with multiwavelength photometry, we reliably derive dust masses and infer molecular gas masses using metallicity-dependent gas-to-dust ratios estimated from individual metallicity measurements. The derived molecular gas mass ratio spans $μ_\mathrm{gas} = M_\mathrm{gas}/M_\ast=0.11\text{--}2.8$, with a median value of 0.65, corresponding to gas reservoirs more than an order of magnitude larger than in local galaxies at fixed stellar mass. The integrated Schmidt--Kennicutt relation is consistent with previous measurements over $z=0\text{--}2$. Across the MS, both molecular gas mass ratio and star formation efficiency scale approximately as $(\mathrm{sSFR}/\mathrm{sSFR}_\mathrm{MS})^{0.5}$, indicating that the MS scatter is driven nearly equally by variations in gas content and depletion time. The intrinsic scatter of $0.19$~dex suggests additional galaxy-to-galaxy diversity in star formation efficiency. Our results provide a controlled test of the unified gas scaling framework in the massive regime at $z\sim1.5$, demonstrating that the fundamental regulation of star formation through coupled modulation of gas supply and efficiency is already in place at cosmic noon.

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arXiv2026

Spectroscopic confirmation of dual and offset quasars from the Subaru HSC-SSP program

We present a spectroscopic follow-up program targeting closely-separated dual quasar candidates selected from imaging of SDSS quasars with the Subaru Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP). Using two-dimensional image decomposition, our selection identifies PSF-like companions within 0.6-4 arcsec separation (< 30 kpc) around the SDSS quasar. We newly confirm six broad-line dual quasars and eleven offset quasars (quasar-galaxy pairs), spanning 1.5 < z < 3.3 for the duals and predominantly z < 0.6 for the offset systems. No obvious lensed quasars were discovered from this program. We obtained 99 spectra of these candidates from NTT/EFOSC2, Gemini/GMOS-N, Keck/NIRES, and Subaru/FOCAS. From the spectra, we measure the emission-line properties of these dual black holes (BH). At z > 1.5, the confirmed duals exhibit high black hole mass ($M_{\rm BH}$ $=10^{8.5}$-$10^{10} M_{\odot}$) with high bolometric luminosities ($L_{bol}$ $=10^{45.5}$-$10^{47.5}$ erg s$^{-1}$), yet accrete at moderate Eddington ratios ($λ_{\rm Edd}=$0.01-0.4). From the spectroscopically-confirmed samples, we estimate the dual fraction of SDSS quasars with separations of 0.6-4 arcsec to be 0.2%-1.2% at z<0.8, 0.08%-0.24% at 0.8<z<1.5, and 0.06% at 1.5<z<3.3. These values are broadly consistent with other recent optical studies, but lower than theoretical expectations of a rising dual fraction at cosmic noon. However, we note that these fractions, especially at high $z$, still need a more accurate assessment of selection and observation effects.

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arXiv2026

Breaking the Mass-sheet Degeneracy in Time-delay Cosmology with Lensed and Unlensed Type Ia Supernovae

This study introduces an innovative framework aimed at overcoming the ongoing issue of mass-sheet degeneracy (MSD) in time-delay cosmography by incorporating observations of both gravitationally lensed and unlensed Type Ia supernovae (SNe Ia). By simultaneously using lensing magnification measurements $μ^{\rm{obs}}$ and cosmic distance ratios ($D_s/D_{ds}$), we develop a Bayesian framework capable of breaking the MSD. Specifically, we reconstruct the distance-redshift and magnitude-redshift relations from unlensed Type Ia supernovae using Gaussian process to avoid dependence on specific cosmological models. Our framework shows substantial efficacy in resolving the MSD by imposing constraints on the MSD parameter $λ$. Furthermore, we extend this framework to analyze multiple gravitational lensing systems. The results show strong agreement with the fiducial MSD parameters used in the data simulation, confirming our method's effectiveness in mitigating the MSD. Ultimately, this technique enables the derivation of corrected time-delay distance measurements under the MSD, improving the precision of cosmological parameters inferred from strong lensing systems.

astro-ph.CO↗

arXiv2026

The Host Galaxies of Active Galactic Nuclei with Direct Black Hole Mass Measurements

Reverberation mapping (RM) determines the mass of black holes (BH) in active galactic nuclei (AGNs) by resolving the BH gravitational sphere of influence in the time domain. Recent RM campaigns yielded direct BH masses through dynamical modeling for a sample of 32 objects, spanning a wide range of AGN luminosities and BH masses. In addition, accurate BH masses have been determined by spatially resolving the broad-line region with GRAVITY for a handful of AGNs. Here, we present a detailed analysis of Hubble Space Telescope images using surface-brightness profile fitting with state-of-the-art programs. We derive AGN luminosity and host-galaxy properties, such as radii and luminosities for spheroid, disk, and bar (if present). The spheroid effective radii were used to measure stellar velocity dispersion from integral-field spectroscopy. Since the BH masses of our sample do not depend on any assumption of the virial factor needed in single-epoch spectroscopic mass estimates, we can show that the resulting scaling relations between the mass of the supermassive BHs and their host galaxies match those of quiescent galaxies, naturally extending to lower masses in these (predominantly) spiral galaxies. We find that the inner AGN orientation, as traced by the broad-line region inclination angle, is uncorrelated with the host-galaxy disk. Our sample has the most direct and accurate MBH measurements of any AGN sample and provides a fundamental local benchmark for studies of the evolution of massive black holes and their host galaxies across cosmic time.

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arXiv2026

Obscured AGN at z < 1.5: X-ray to Far-Infrared SEDs and Host Galaxy Morphologies in the GOODS Fields

We present an analysis of spectral energy distributions (SEDs), galaxy light profiles, and visual morphological classifications for 194 X-ray luminous AGN (intrinsic absorption-corrected log10 LX(0.5 to 7 keV) less than 42.5, with a maximum of 45.2 ergs per second) at redshift z less than 1.5 in the GOODS fields. We generate X-ray to far-infrared SEDs normalized at 1 micron for all AGN and sort them according to their emission slopes in the ultraviolet and infrared. We visually classify their host galaxy morphologies and compute their bulge-to-total light ratios using the software Galaxy Shapes of Light (galight). Most (94 percent) GOODS AGN exhibit obscured SEDs, defined by diminished ultraviolet and/or mid-infrared emission, while only 6 percent show unobscured, quasar-like SEDs. Secular processes appear to play a large role in stimulating AGN emission, as only around one-third of galaxies are undergoing interactions. We also describe the morphological identification of a population of suspected post-merger spheroid galaxies with obscured ultraviolet and infrared SEDs, and distinguish them from the host galaxies of AGN with less obscuration in the ultraviolet or infrared.

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arXiv2026

Through Thick and Thin: The Cosmic Evolution of Disk Scale Height

To investigate the formation and evolution of vertical structures in disk galaxies, we measure global $\operatorname{sech}^2$ scale heights, averaging thin and thick components when present, for 2631 edge-on disk galaxies with $M_*>10^{10} M_\odot$ at $0 1.5$, but rises to $4.0\pm0.4$ at $z=0.25$. These results imply that the high-redshift progenitors of present-day thick disks were of intermediate thickness, neither thin nor thick, yet dynamically hot and dense. The observed radial variation of scale height is consistent with the artificial flaring expected from observational effects, disfavoring minor mergers as the primary mechanism of disk thickening. Instead, we suggest that the high-redshift intermediate-thickness disks were single-component systems that increased their vertical scale height through decreasing surface mass density and/or violent gravitational instabilities, eventually producing thick disks. Thin-disk growth begins at $z\approx2$ and dominates at $z\lesssim1$, yielding a vertically more compact system with decreasing scale heights from $z\approx1$ to $0$. The inferred thin-disk mass fraction increases from $0.1\pm0.03$ at $z=1$ to $0.6\pm0.1$ at $z=0$. Together, these findings reveal a continuous evolutionary link between high-redshift single-component disks and present-day thick thin disk systems.

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arXiv2026

Galactic bars are already mature at Cosmic Noon: bar strength and flatness at z ~ 1.5

In this work, we explore the nature of $z>1$ galactic bars. Once thought to be highly transient, our results demonstrate otherwise. Our sample consists of nine massive ($>10^{10.5}\,\rm M_{\odot}$) star-forming barred-spiral galaxies at $z_{\rm spec} \sim 1.5$. Using rest-frame near-IR (F444W) JWST/NIRCam imaging, we apply ellipse fitting along with 1D and 2D morphological modeling to directly measure bar properties. We find that five galaxies host flat surface brightness profiles (bar Sérsic index $<0.4$), indicative of highly evolved, "mature" bars. By contrast, only two galaxies show exponential profiles, characteristic of young bars, and these are also shorter in absolute length than the flat bars. We therefore conclude that a large fraction of bars at this epoch have already matured, thereby indicating the presence of well-settled disks required to facilitate bar formation and sustained evolution well before $z\sim1.5$. To assess the gravitational impact of the bars, we calculate the maximum transverse-to-radial force ratio ($Q_{b}$). We find that $Q_{b}$ values are comparable to, or weaker than, those of bars in the local Universe, Seven of the nine bars show only a marginal increase in strength with maturity (from exponential to flat bars). Contrarily however, the remaining two bars are flat, but have the lowest $Q_{b}$ values in our sample. We hence propose that the mature bars at $z\sim 1.5$ may experience phases of weakening due to rapid gas inflows and/or minor mergers. In conclusion, our work sheds light on the rapidly evolving nature of high-z bars and paves the way for larger statistical studies.

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arXiv2025

SHELLQs. Bridging the Gap: JWST Unveils Obscured Quasars in the Most Luminous Galaxies at z > 6

The unprecedented sensitivity of the James Webb Space Telescope (JWST) has uncovered a surprisingly abundant population of mildly obscured, low-luminosity active galactic nuclei (AGNs) in the epoch of reionization (EoR). However, the link between these objects and classical unobscured quasars remains a mystery. Here we report the discovery of obscured quasars hosted by the most luminous galaxies at z > 6, possibly bridging the gap between the two AGN populations. The 13 objects presented here were originally selected from a rest-frame ultraviolet (UV) imaging survey over >1000 deg2, and were known to have luminous (>10^{43} erg/s) narrow Ly-alpha emission. With JWST/NIRSpec follow-up observations, we found that 7 out of 11 objects with narrow Ly-alpha exhibit a broad component in H I Balmer lines and He I lines, but not in [O III] and other forbidden lines. Mild dust obscuration (0 < Av < 3) is inferred from the Balmer decrements. The estimated intrinsic luminosities suggest that our broad line (BL) objects are the long-sought UV-obscured counterparts of luminous quasars in the EoR. They host supermassive black holes (SMBHs) with masses 10^(7.8-9.1) Msun, undergoing sub-Eddington to Eddington accretion. Most of the BL objects are spatially unresolved, and are close to "little red dots" with their blue rest-UV and red rest-optical colors. We estimate the AGN number density among similarly luminous Ly-alpha emitters to be larger than 2 x 10^(-8) /Mpc3. This density is comparable to that of classical quasars with similar continuum luminosities, suggesting that a substantial fraction of active SMBHs are obscured in the EoR and have been overlooked in past rest-UV surveys.

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arXiv2025

SHELLQs-JWST perspective on the intrinsic mass relation between supermassive black holes and their host galaxies at z > 6

The relation between the masses of supermassive black holes (SMBHs) and their host galaxies encodes information on their mode of growth, especially at the earliest epochs. The James Webb Space Telescope (JWST) has opened such investigations by detecting the host galaxies of AGN and more luminous quasars within the first billion years of the universe (z > 6). Here, we evaluate the relation between the mass of SMBHs and the total stellar mass of their host galaxies using a sample of nine quasars at 6.18 < z < 6.4 from the Subaru High-z Exploration of Low-luminosity Quasars (SHELLQs) survey with NIRCam and NIRSpec observations. We find that the observed location of these quasars in the SMBH-galaxy mass plane (log M_BH/Msun ~ 8-9; log M_*/Msun ~ 9.5-11) is consistent with a non-evolving intrinsic mass relation with dispersion (0.80_{-0.28}^{+0.23} dex) higher than the local value (~0.3-0.4 dex) of their more massive descendants. Our analysis is based on a forward model of systematics and includes a consideration of the impact of selection effects and measurement uncertainties with an assumption on the slope of the mass relation. While degeneracies between parameters persist, the best-fit solution has a reasonable AGN fraction (2.3%) of galaxies at z ~ 6 with an actively growing UV-unobscured black hole. In particular, models with a substantially higher normalisation in M_BH would require an unrealistically low intrinsic dispersion (~0.22 dex). Consequently, our results predict a large population of AGNs at lower black hole masses, as are now just starting to be discovered in focused efforts with JWST.

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