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Andreas Schulze

Publications and source records attributed to Andreas Schulze.

At least 19 recordsLinked to original sources

The Physical Origin of Extreme Emission Line Galaxies at High redshifts: Strong {\sc [Oiii]} Emission Lines Produced by Obscured AGNs

We present deep Subaru/FOCAS spectra for two extreme emission line galaxies (EELGs) at $z\sim 1$ with strong {\sc[Oiii]}$λ$5007 emission lines, exhibiting equivalent widths (EWs) of $2905^{+946}_{-578}$ Å and $2000^{+188}_{-159}$ Å, comparable to those of EELGs at high redshifts that are now routinely identified with JWST spectroscopy. Adding a similarly large {\sc [Oiii]} EW ($2508^{+1487}_{-689}$ Å) EELG found at $z\sim 2$ in the JWST CEERS survey to our sample, we explore for the physical origins of the large {\sc [Oiii]} EWs of these three galaxies with the Subaru spectra and various public data including JWST/NIRSpec, NIRCam, and MIRI data. While there are no clear signatures of AGN identified by the optical line diagnostics, we find that two out of two galaxies covered by the MIRI data show strong near-infrared excess in the spectral energy distributions (SEDs) indicating obscured AGN. Because none of the three galaxies show clear broad H$β$ lines, the upper limits on the flux ratios of broad-H$β$ to {\sc [Oiii]} lines are small, $\lesssim 0.15$ that are comparable with Seyfert $1.8-2.0$ galaxies. We conduct \texttt{Cloudy} modeling with the stellar and AGN incident spectra, allowing a wide range of parameters including metallicities and ionization parameters. We find that the large {\sc [Oiii]} EWs are not self-consistently reproduced by the spectra of stars or unobscured AGN, but obscured AGN that efficiently produces O$^{++}$ ionizing photons with weak nuclear and stellar continua that are consistent with the SED shapes.

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Black hole mass and Eddington ratio distributions of less-luminous quasars at $z\sim4$ in the Subaru Hyper Suprime-Cam Wide field

We investigate the black hole mass function (BHMF) and Eddington ratio distribution function (ERDF) of broad-line AGNs at z=4, based on a sample of 52 quasars with i<23.2 at 3.50 < z < 4.25 from the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) S16A-Wide2 dataset, and 1,462 quasars with i<20.2 in the same redshift range from the Sloan Digital Sky Survey (SDSS) DR7 quasar catalog. Virial BH masses of quasars are estimated using the width of the CIV 1549Å line and the continuum luminosity at 1350Å. To obtain the intrinsic broad-line AGN BHMF and ERDF, we correct for the incompleteness in the low-mass and/or low-Eddington-ratio ranges caused by the flux-limited selection. The resulting BHMF is constrained down to $\log M_{\rm BH}/M_{\odot}\sim7.5$. In comparison with broad-line AGN BHMFs at z=2 in the literature, we find that the number density of massive SMBHs peaks at higher redshifts, consistent with the "down-sizing" evolutionary scenario. Additionally, the resulting ERDF shows a negative dependence on BH mass, suggesting more massive SMBHs tend to accrete at lower Eddington ratios at z=4. With the derived intrinsic broad-line AGN BHMF, we also evaluate the active fraction of broad-line AGNs among the entire SMBH population at z=4. The resulting active fraction may suggest a positive dependence on BH mass. Finally, we examine the time evolution of broad-line AGN BHMF between z=4 and 6 through solving the continuity equation. The results suggest that the broad-line AGN BHMFs at z=4-6 only show evolution in their normalization, but with no significant changes in their shape.

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The Hobby-Eberly Telescope Dark Energy Experiment (HETDEX) Survey Design, Reductions, and Detections

We describe the survey design, calibration, commissioning, and emission-line detection algorithms for the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX). The goal of HETDEX is to measure the redshifts of over a million Ly$α$ emitting galaxies between 1.88<z<3.52, in a 540 deg^2 area encompassing a co-moving volume of 10.9 Gpc^3. No pre-selection of targets is involved; instead the HETDEX measurements are accomplished via a spectroscopic survey using a suite of wide-field integral field units distributed over the focal plane of the telescope. This survey measures the Hubble expansion parameter and angular diameter distance, with a final expected accuracy of better than 1%. We detail the project's observational strategy, reduction pipeline, source detection, and catalog generation, and present initial results for science verification in the COSMOS, Extended Groth Strip, and GOODS-N fields. We demonstrate that our data reach the required specifications in throughput, astrometric accuracy, flux limit, and object detection, with the end products being a catalog of emission-line sources, their object classifications, and flux-calibrated spectra.

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Star Formation in Luminous LoBAL Quasars at 2.0<z<2.5

Low-ionisation broad absorption line quasars (LoBALs) mark an important, yet poorly understood, population of quasars showing direct evidence for energetic mass outflows. We outline a sample of 12 luminous (L$_{\rm{bol}}$ $>$10$^{46}$ergs$^{-1}$) LoBALs at 2.0$<$z$<$2.5 - a key epoch in both star formation and black hole accretion, which have been imaged as part of a targeted program with the \textit{Herschel} Spectral and Photometric Imaging REceiver (SPIRE). We present K-band NOTCam spectra for three of these targets, calculating their spectroscopic redshifts, black hole masses and bolometric luminosities, and increasing the total number of LoBAL targets in our sample with spectral information from five to eight. Based on FIR obeservations from \textit{Herschel} SPIRE, we derive prolific SFRs ranging 740 - 2380M$_{\rm{\odot}}$yr$^{-1}$ for the detected targets, consistent with LoBALs existing in an evolutionary phase associated with starburst activity. Furthermore, an upper limit of $<$440M$_{\rm{\odot}}$yr$^{-1}$ is derived for the non-detections, meaning moderate-to-high SFRs cannot be ruled out, even among the undetected targets. Indeed, we detect an enhancement in both the SFRs and FIR fluxes of LoBALs compared to HiBAL and non-BAL quasars, further supporting the evolutionary LoBAL paradigm. Despite this enhancement in SFR however, the environments of LoBALs appear entirely consistent with the general galaxy population at 2.0$<$z$<$2.5.

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Circumnuclear Molecular Gas in Low-redshift Quasars and Matched Star-forming Galaxies

A series of gravitational instabilities in a circumnuclear gas disk (CND) are required to trigger gas transport to a central supermassive black hole (SMBH) and ignite Active Galactic Nuclei (AGNs). A test of this scenario is to investigate whether an enhanced molecular gas mass surface density ($Σ_{\rm mol}$) is found in the CND-scale of quasars relative to a comparison sample of inactive galaxies. Here we performed sub-kpc resolution CO(2-1) observations with ALMA of four low-redshift ($z \sim 0.06$), luminous ($\sim 10^{45}$ erg s$^{-1}$) quasars with each matched to a different star-forming galaxy, having similar redshift, stellar mass, and star-formation rate. We detected CO(2-1) emission from all quasars, which show diverse morphologies. Contrary to expectations, $Σ_{\rm mol}$ of the quasar sample, computed from the CO(2-1) luminosity, tends to be smaller than the comparison sample at $r < 500$ pc; there is no systematic enhancement of $Σ_{\rm mol}$ in our quasars. We discuss four possible scenarios that would explain the lower molecular gas content (or CO(2-1) luminosity as an actual observable) at the CND-scale of quasars, i.e., AGN-driven outflows, gas-rich minor mergers, time-delay between the onsets of a starburst-phase and a quasar-phase, and X-ray-dominated region (XDR) effects on the gas chemical abundance and excitation. While not extensively discussed in the literature, XDR effects can have an impact on molecular mass measurements particularly in the vicinity of luminous quasar nuclei; therefore higher resolution molecular gas observations, which are now viable using ALMA, need to be considered.

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CIV emission line properties and uncertainties in black hole mass estimates of z ~ 3.5 quasars

Using a high luminosity ($L_{\rm bol} \sim 10^{47.5} - 10^{48.3}$ erg s$^{-1}$), high redshift ($3.2 < z < 3.8$) quasar sample of 19 quasars with optical and near-infrared spectroscopy, we investigate the reliability of the CIV-based black hole mass estimates ($M_{\rm BH}$). The median logarithm of the CIV- and H$β$-based $M_{\rm BH}$ ratios is 0.110 dex with the scatter of 0.647 dex. The CIV-to-H$β$ BH mass differences are significantly correlated with the CIV FWHMs, blueshifts and asymmetries. Corrections of the CIV FWHM using the blueshift and asymmetry reduce the scatter of the mass differences by $\sim$ 0.04-0.2 dex. Quasars in our sample accrete at the Eddington ratio $R_{\rm EDD}>0.3$ and cover a considerable range of blueshifts, with 18/19 of the quasars showing CIV blueshifts (with the median value of 1126 km s$^{-1}$) and 14/19 of the quasars showing CIV blueshifts larger than 500 km s$^{-1}$. It suggests that not all quasars with high Eddington ratios show large blueshifts. The Baldwin effect between the CIV rest-frame equivalent width (REW) and the continuum luminosity at 1350 $\overset{\lower.5em\circ}{\mathrm{A}}$ is not seen, likely due to the limited luminosity range of our sample. We find a lack of flux in the red wing of the composite spectrum with larger CIV blueshift, and detect a higher ratio of [OIII] quasars with REW$_{\rm [OIII]}>5$ $\overset{\lower.5em\circ}{\mathrm{A}}$ in the subsample with lower CIV blueshift. It is more likely that they are caused by the combination of the Eddington ratio and the orientation effect.

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The mass relations between supermassive black holes and their host galaxies at 1<z<2 with HST-WFC3

Correlations between the mass of a supermassive black hole and the properties of its host galaxy (e.g., total stellar mass (M*), luminosity (Lhost)) suggest an evolutionary connection. A powerful test of a co-evolution scenario is to measure the relations MBH-Lhost and MBH-M* at high redshift and compare with local estimates. For this purpose, we acquired HST imaging with WFC3 of 32 X-ray-selected broad-line AGN at 1.2<z<1.7 in deep survey fields. By applying state-of-the-art tools to decompose the HST images including available ACS data, we measured the host galaxy luminosity and stellar mass along with other properties through the 2D model fitting. The black hole mass was determined using the broad Halpha line, detected in the near-infrared with Subaru/FMOS, which potentially minimizes systematic effects using other indicators. We find that the observed ratio of MBH to total M* is 2.7 times larger at z~1.5 than in the local universe, while the scatter is equivalent between the two epochs. A non-evolving mass ratio is consistent with the data at the 2-3 sigma confidence level when accounting for selection effects and their uncertainties. The relationship between MBH-Lhost paints a similar picture. Therefore, our results cannot distinguish whether SMBHs and their total M* and Lhost proceed in lockstep or whether the growth of the former somewhat overshoots the latter, given the uncertainties. Based on a statistical estimate of the bulge-to-total mass fraction, the ratio MBH/M* is offset from the local value by a factor of ~7 which is significant even accounting for selection effects. Taken together, these observations are consistent with a scenario in which stellar mass is subsequently transferred from an angular momentum supported component of the galaxy to the pressure supported one through secular processes or minor mergers at a faster rate than mass accretion onto the SMBH.

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Where do quasar hosts lie with respect to the size-mass relation of galaxies?

The evolution of the galaxy size - stellar mass (Mstellar) relation has been a puzzle for over a decade. High redshift galaxies are significantly more compact than galaxies observed today, at an equivalent mass, but how much of this apparent growth is driven by progenitor bias, minor mergers, secular processes, or feedback from AGN is unclear. To help disentangle the physical mechanisms at work by addressing the latter, we study the galaxy size - Mstellar relation of 32 carefully-selected broad-line AGN hosts at 1.2 < z < 1.7 (7.5 < log M_BH < 8.5; L_bol/L_Edd > 0.1). Using HST with multi-band photometry and state-of-the-art modeling techniques, we measure half-light radii while accounting for uncertainties from subtracting bright central point sources. We find AGN hosts to have sizes ranging from 1 to 6 kpc at Mstellar ~ 0.3 - 1 x 10^11 Msun. Thus, many hosts have intermediate sizes as compared to equal-mass star-forming and quiescent galaxies. While inconsistent with the idea that AGN feedback may induce an increase in galaxy sizes, this finding is consistent with hypotheses in which AGNs preferentially occur in systems with prior concentrated gas reservoirs, or are involved in secular compaction processes perhaps responsible for simultaneously building bulges and shutting down star formation. If driven by minor mergers, which do not grow central black holes as fast as they do bulge-like stellar structures, such a process would explain both the galaxy size - mass relation observed here and the evolution in the black hole, bulge mass relation described in a companion paper.

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Subaru High-z Exploration of Low-Luminosity Quasars (SHELLQs). X. Discovery of 35 Quasars and Luminous Galaxies at 5.7 $\le$ z $\le$ 7.0

We report the discovery of 28 quasars and 7 luminous galaxies at 5.7 $\le$ z $\le$ 7.0. This is the tenth in a series of papers from the Subaru High-z Exploration of Low-Luminosity Quasars (SHELLQs) project, which exploits the deep multi-band imaging data produced by the Hyper Suprime-Cam (HSC) Subaru Strategic Program survey. The total number of spectroscopically identified objects in SHELLQs has now grown to 93 high-z quasars, 31 high-z luminous galaxies, 16 [O III] emitters at z ~ 0.8, and 65 Galactic cool dwarfs (low-mass stars and brown dwarfs). These objects were found over 900 deg2, surveyed by HSC between 2014 March and 2018 January. The full quasar sample includes 18 objects with very strong and narrow Ly alpha emission, whose stacked spectrum is clearly different from that of other quasars or galaxies. While the stacked spectrum shows N V 1240 emission and resembles that of lower-z narrow-line quasars, the small Ly alpha width may suggest a significant contribution from the host galaxies. Thus these objects may be composites of quasars and star-forming galaxies.

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SDSS-IV/SPIDERS: A Catalogue of X-Ray Selected AGN Properties; Spectral Properties and Black Hole Mass Estimates for SPIDERS SDSS DR14 Type 1 AGN

This work presents the catalogue of optical spectral properties for all X-ray selected SPIDERS active galactic nuclei (AGN) up to SDSS DR14. SPIDERS (SPectroscopic IDentification of eROSITA Sources) is an SDSS-IV programme that is currently conducting optical spectroscopy of the counterparts to the X-ray selected sources detected in the ROSAT all-sky survey and the XMM-Newton slew survey in the footprint of the Extended Baryon Oscillation Spectroscopic Survey (eBOSS). The SPIDERS DR14 sample is the largest sample of X-ray selected AGN with optical spectroscopic follow-up to date. The catalogue presented here is based on a clean sample of 7344 2RXS ($\rm \bar{z}$ = 0.5) and 1157 XMM-Newton slew survey ($\rm \bar{z}$ = 0.4) type 1 AGN with spectroscopic coverage of the H$\rm β$ and/or MgII emission lines. Visual inspection results for each object in this sample are available from a combination of literature sources and the SPIDERS group, which provide both reliable redshifts and source classifications. The spectral regions around the H$\rm β$ and MgII emission lines have been fit in order to measure both line and continuum properties, estimate bolometric luminosities, and provide black hole mass estimates using the single-epoch (or photoionisation) method. The use of both H$\rm β$ and MgII allows black hole masses to be estimated up to z $\rm \simeq$ 2.5. A comparison is made between the spectral properties and black hole mass estimates derived from H$\rm β$ and MgII using the subsample of objects which have coverage of both lines in their spectrum. These results have been made publicly available as an SDSS-IV DR14 value added catalogue.

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Multi-wavelength properties of Type 1 and Type 2 AGN Host Galaxies in the Chandra-COSMOS Legacy Survey

We investigate the multi-wavelength properties of host galaxies of 3701 X-ray-selected active galactic nuclei (AGNs) out to z~5 in the Chandra-COSMOS Legacy Survey. Thanks to the extensive multi-wavelength photometry available in the COSMOS field, we derive AGN luminosities, host stellar masses, and star formation rates (SFRs) via a multi-component SED fitting technique. Type 1 and Type 2 AGNs follow the same intrinsic Lx-L6um relation, suggesting that mid-infrared emission is a reasonably good measure of the AGN accretion power regardless of obscuration. We find that there is a strong increase in Type 1 AGN fraction toward higher AGN luminosity, possibly due to the fact that Type 1 AGNs tend to be hosted by more massive galaxies. The AGN luminosity and SFR are consistent with an increase toward high stellar mass, while both the Mstellar-dependence is weaker towards the high-mass end, which could be interpreted as a consequence of quenching both star formation and AGN activity in massive galaxies. AGN host galaxies tend to have SFRs that are consistent with normal star-forming galaxies, independent of AGN luminosities. We confirm that black hole accretion rate and SFR are correlated up to z~5, when forming stars. The majority (~73%) of our AGN sample are faint in the far-infrared, implying that the moderate-luminosity AGNs seem to be still active after the star formation is suppressed. It is not certain whether AGN activity plays a role in quenching the star formation. We conclude that both AGN activity and star formation might be more fundamentally related to host stellar mass.

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Discovery of the First Low-Luminosity Quasar at z > 7

We report the discovery of a quasar at z = 7.07, which was selected from the deep multi-band imaging data collected by the Hyper Suprime-Cam (HSC) Subaru Strategic Program survey. This quasar, HSC J124353.93+010038.5, has an order of magnitude lower luminosity than do the other known quasars at z > 7. The rest-frame ultraviolet absolute magnitude is M1450 = -24.13 +/- 0.08 mag and the bolometric luminosity is Lbol = (1.4 +/- 0.1) x 10^{46} erg/s. Its spectrum in the optical to near-infrared shows strong emission lines, and shows evidence for a fast gas outflow, as the C IV line is blueshifted and there is indication of broad absorption lines. The Mg II-based black hole mass is Mbh = (3.3 +/- 2.0) x 10^8 Msun, thus indicating a moderate mass accretion rate with an Eddington ratio 0.34 +/- 0.20. It is the first z > 7 quasar with sub-Eddington accretion, besides being the third most distant quasar, known to date. The luminosity and black hole mass are comparable to, or even lower than, those measured for the majority of low-z quasars discovered by the Sloan Digital Sky Survey, and thus this quasar likely represents a z > 7 counterpart to quasars commonly observed in the low-z universe.

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Subaru High-z Exploration of Low-Luminosity Quasars (SHELLQs). V. Quasar Luminosity Function and Contribution to Cosmic Reionization at z = 6

We present new measurements of the quasar luminosity function (LF) at $z \sim 6$, over an unprecedentedly wide range of the rest-frame ultraviolet luminosity $M_{1450}$ from $-30$ to $-22$ mag. This is the fifth in a series of publications from the Subaru High-$z$ Exploration of Low-Luminosity Quasars (SHELLQs) project, which exploits the deep multi-band imaging data produced by the Hyper Suprime-Cam (HSC) Subaru Strategic Program survey. The LF was calculated with a complete sample of 110 quasars at $5.7 \le z \le 6.5$, which includes 48 SHELLQs quasars discovered over 650 deg$^2$, and 63 brighter quasars discovered by the Sloan Digital Sky Survey and the Canada-France-Hawaii Quasar Survey (including one overlapping object). This is the largest sample of $z \sim 6$ quasars with a well-defined selection function constructed to date, and has allowed us to detect significant flattening of the LF at its faint end. A double power-law function fit to the sample yields a faint-end slope $α= -1.23^{+0.44}_{-0.34}$, a bright-end slope $β= -2.73^{+0.23}_{-0.31}$, a break magnitude $M_{1450}^* = -24.90^{+0.75}_{-0.90}$, and a characteristic space density $Φ^* = 10.9^{+10.0}_{-6.8}$ Gpc$^{-3}$ mag$^{-1}$. Integrating this best-fit model over the range $-18 < M_{1450} < -30$ mag, quasars emit ionizing photons at the rate of $\dot{n}_{\rm ion} = 10^{48.8 \pm 0.1}$ s$^{-1}$ Mpc$^{-3}$ at $z = 6.0$. This is less than 10 % of the critical rate necessary to keep the intergalactic medium ionized, which indicates that quasars are not a major contributor to cosmic reionization.

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Discovery of strong Balmer line absorption in two luminous LoBAL quasars at z~1.5

We present the discovery of strong Balmer line absorption in H$α$ to H$γ$ in two luminous low-ionization broad absorption line quasars (LoBAL QSOs) at z~1.5, with black hole masses around $10^{10}$ $M_\odot$ from near-IR spectroscopy. There are only two previously known quasars at z>1 showing Balmer line absorption. SDSS J1019+0225 shows blueshifted absorption by ~1400 km/s with an H$α$ rest-frame equivalent width of 13 Å. In SDSS J0859+4239 we find redshifted absorption by ~500 km/s with an H$α$ rest-frame equivalent width of 7 Å. The redshifted absorption could indicate an inflow of high density gas onto the black hole, though we cannot rule out alternative interpretations. The Balmer line absorption in both objects appears to be saturated, indicating partial coverage of the background source by the absorber. We estimate the covering fractions and optical depth of the absorber and derive neutral hydrogen column densities, $N_{\rm{H\,I}}\sim1.3\times 10^{18}$ cm$^{-2}$ for SDSS J1019+0225 and $N_{\rm{H\,I}}\sim9\times 10^{17}$ cm$^{-2}$ for SDSS J0859+4239, respectively. In addition, the optical spectra reveal also absorption troughs in HeI* $\lambda3889$ and $\lambda3189$ in both objects.

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Near-IR spectroscopy of luminous LoBAL quasars at 1<z<2.5

We present near-IR spectroscopy of 22 luminous low-ionization broad absorption line quasars (LoBAL QSOs) at redshift 1.3 1 there is no clear difference in their optical emission line properties. We do not see particularly weak [OIII] or strong FeII emission. The LoBAL QSOs do not show a stronger prevalence of ionized gas outflows as traced by the [OIII] line, compared to normal QSOs of similar luminosity. We conclude that the optical-MIR properties of LoBAL QSOs are consistent with the general quasar population and do not support them to constitute a special phase of active galactic nucleus evolution.

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Evidence for higher black hole spin in radio-loud quasars

One of the major unsolved questions on the understanding of the AGN population is the origin of the dichotomy between radio-quiet and radio-loud quasars. The most promising explanation is provided by the spin paradigm, which suggests radio-loud quasars have higher black hole spin. However, the measurement of black hole spin remains extremely challenging. We here aim at comparing the mean radiative efficiencies of carefully matched samples of radio-loud and radio-quiet SDSS quasars at 0.3<z<0.8. We use the [OIII] luminosity as an indirect average tracer of the ionizing continuum in the extreme-UV regime where differences in the SED due to black hole spin are most pronounced. We find that the radio-loud sample shows an enhancement in [OIII] line strength by a factor of at least 1.5 compared to a radio-quiet sample matched in redshift, black hole mass and optical continuum luminosity or accretion rate. We argue that this enhancement is caused by differences in the SED, suggesting higher average bolometric luminosities at fixed accretion rate in the radio-loud population. This suggests that the radio-loud quasar population has on average systematically larger radiative efficiencies and therefore higher black hole spin than the radio-quiet population, providing observational support for the black hole spin paradigm.

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Subaru High-z Exploration of Low-Luminosity Quasars (SHELLQs). II. Discovery of 32 Quasars and Luminous Galaxies at 5.7 < z < 6.8

We present spectroscopic identification of 32 new quasars and luminous galaxies discovered at 5.7 < z < 6.8. This is the second in a series of papers presenting the results of the Subaru High-z Exploration of Low-Luminosity Quasars (SHELLQs) project, which exploits the deep multi-band imaging data produced by the Hyper Suprime-Cam (HSC) Subaru Strategic Program survey. The photometric candidates were selected by a Bayesian probabilistic algorithm, and then observed with spectrographs on the Gran Telescopio Canarias and the Subaru Telescope. Combined with the sample presented in the previous paper, we have now identified 64 HSC sources over about 430 deg2, which include 33 high-z quasars, 14 high-z luminous galaxies, 2 [O III] emitters at z ~ 0.8, and 15 Galactic brown dwarfs. The new quasars have considerably lower luminosity (M1450 ~ -25 to -22 mag) than most of the previously known high-z quasars. Several of these quasars have luminous (> 10^(43) erg/s) and narrow (< 500 km/s) Ly alpha lines, and also a possible mini broad absorption line system of N V 1240 in the composite spectrum, which clearly separate them from typical quasars. On the other hand, the high-z galaxies have extremely high luminosity (M1450 ~ -24 to -22 mag) compared to other galaxies found at similar redshift. With the discovery of these new classes of objects, we are opening up new parameter spaces in the high-z Universe. Further survey observations and follow-up studies of the identified objects, including the construction of the quasar luminosity function at z ~ 6, are ongoing.

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Clustering of quasars in a wide luminosity range at redshift 4 with Subaru Hyper Suprime-Cam wide field imaging

We examine the clustering of quasars over a wide luminosity range, by utilizing 901 quasars at $\overline{z}_{\rm phot}\sim3.8$ with $-24.73<M_{\rm 1450}<-22.23$ photometrically selected from the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) S16A Wide2 date release and 342 more luminous quasars at $3.4<z_{\rm spec}<4.6$ having $-28.0<M_{\rm 1450}<-23.95$ from the Sloan Digital Sky Survey (SDSS) that fall in the HSC survey fields. We measure the bias factors of two quasar samples by evaluating the cross-correlation functions (CCFs) between the quasar samples and 25790 bright $z\sim4$ Lyman Break Galaxies (LBGs) in $M_{\rm 1450}<-21.25$ photometrically selected from the HSC dataset. Over an angular scale of \timeform{10.0"} to \timeform{1000.0"}, the bias factors are $5.93^{+1.34}_{-1.43}$ and $2.73^{+2.44}_{-2.55}$ for the low and high luminosity quasars, respectively, indicating no luminosity dependence of quasar clustering at $z\sim4$. It is noted that the bias factor of the luminous quasars estimated by the CCF is smaller than that estimated by the auto-correlation function (ACF) over a similar redshift range, especially on scales below \timeform{40.0"}. Moreover, the bias factor of the less-luminous quasars implies the minimal mass of their host dark matter halos (DMHs) is $0.3$-$2\times10^{12}h^{-1}M_{\odot}$, corresponding to a quasar duty cycle of $0.001$-$0.06$.

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