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A&A
Volume 669, January 2023
Article Number A127
Number of page(s) 15
Section Extragalactic astronomy
DOI https://doi.org/10.1051/0004-6361/202244688
Published online 20 January 2023

© The Authors 2023

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This article is published in open access under the Subscribe-to-Open model.

Open Access funding provided by Max Planck Society.

1. Introduction

Over the last 20 yr, quasars have been discovered at ever-increasing redshifts and well into the epoch of re-ionisation (e.g. Fan et al. 2001; Willott et al. 2009; Mortlock et al. 2012; Wu et al. 2015; Jiang et al. 2016; Matsuoka et al. 2018a; Bañados et al. 2016; Wang et al. 2021). These objects signpost accretion onto super-massive black holes (SMBHs) through cosmic time. The mere existence of > 109 M⊙ black holes in the first gigayear of the Universe (z >  5.7, Onoue et al. 2019; Yang et al. 2021) challenges SMBH seeding and growth models, requiring sustained Eddington-limited or even super-Eddington accretion (Volonteri & Rees 2005). The nature of the seeds themselves is still being investigated (for reviews, see Volonteri 2010; Haiman et al. 2013; Johnson & Haardt 2016; Latif & Ferrara 2016; Volonteri et al. 2021). While the bulk of active galaxies discovered at z >  5.7 host black holes with masses of 1–10 billion solar masses, there must be a population of less massive (108 M⊙), super-Eddington-accreting SMBHs caught in an earlier evolutionary state. Some of these less massive, strongly accreting black holes have been found at the centre of high-redshift quasars that display optical properties similar to local narrow-line Seyfert 1 galaxies (NLS1s; e.g. Koptelova et al. 2017, 2019; Onoue et al. 2019). NLS1s are a special class of active galaxies that are defined by their narrow Hβ emission lines (FWHM <  2000 km s−1) and the weakness of their [O III] narrow-line emission relative to Hβ, [O III]/Hβ < 3 (Osterbrock & Dahari 1983; Goodrich 1989). They show strong FeII emission (Osterbrock & Pogge 1985), typically host SMBHs with lower black hole masses (MBH <  108 M⊙), and accrete at a significant fraction of their Eddington limit (10 − 100%; e.g. Pounds et al. 1995; Grupe et al. 2010; Rakshit et al. 2017; Waddell & Gallo 2020), as expected from young and strongly accreting black holes. Large amplitude, short timescale flaring behaviour in the UV continuum has been observed for this class of source (Collier et al. 2001). Rapid, high amplitude variability is also seen at shorter wavelengths, in X-rays (e.g. Turner et al. 2001; Romano et al. 2002). NLS1s usually have steeper X-ray spectra (i.e. larger power-law photon indices). than typical broad-line Seyfert 1 galaxies (Nandra & Pounds 1994; Boller et al. 1996).

Beyond the end of the epoch of re-ionisation, hard X-ray photons unhindered by dust and gas are collectable by sensitive soft X-ray telescopes at observer-frame energies, ∼2 keV. To date, ∼50 quasars at z >  5.7 have been observed in X-rays, mostly via pointed observations with Chandra and XMM-Newton (Brandt et al. 2002; Vignali et al. 2003; Nanni et al. 2017; Vito et al. 2019) following their discovery with optical telescopes. Recently, Barlow-Hall et al. (2022) reported the blind detection of a quasar spectroscopically confirmed at z = 6.31 in the Extragalactic Serendipitous Swift Survey (ExSeSS). The first unbiased, blind X-ray detections of quasars at z >  5.7 in the performance verification fields and all-sky maps of the extended ROentgen Survey with an Imaging Telescope Array (eROSITA; Predehl et al. 2021; Sunyaev et al. 2021) were reported by Medvedev et al. (2020) and Wolf et al. (2021). Khorunzhev et al. (2021) present the discovery with eROSITA of the most X-ray-luminous quasar beyond z ≳ 5.5 with logL2 − 10 keV = 3 × 1046 erg s−1. In addition to being among the most X-ray-luminous quasars at the end of re-ionisation, all of the eROSITA-detected high-redshift quasars are radio detected and radio loud (according to the radio-loudness definition R = fν,5 GHz/fν,4400 Å > 10 defined by Kellermann et al. 1989). However, the z = 5.81 quasar detected in the eROSITA Final Equatorial Depth Survey (eFEDS; Brunner et al. 2022) does not show evidence of any jet contribution in its X-ray output, making it a secure probe of coronal activity and hence black hole accretion history (Wolf et al. 2021). The direct X-ray selection of this spectroscopically confirmed quasar in a contiguous field of uniform exposure imposes constraints on the X-ray luminosity function (XLF) just after the epoch of re-ionisation (z ∼ 6). Wolf et al. (2021) show that an exponential decline at high redshift cannot be excluded. However, models that show a shallower slope at the bright end of the XLF are preferred in the probed high-redshift bin.

Here we present the eROSITA X-ray detection of a second high-redshift quasar in the eFEDS field: the z = 6.56 quasar J0921+0007, initially discovered in a dedicated survey based on the Hyper Suprime Cam (HSC) Subaru Strategic Program (SSP; Aihara et al. 2022): the Subaru High-z Exploration of Low-luminosity Quasars (SHELLQs; Matsuoka et al. 2018a). The source is optically faint but X-ray bright. Its optical and near-infrared (NIR) spectral properties potentially make it a high-redshift NLS1. We present the eROSITA detection of this optically faint source with a 21 ks Chandra ACIS-S follow-up observation and derive its X-ray properties in Sect. 2. We derive the black hole mass of the source and Eddington ratio with a new Ks-band spectrum that covers the MgII region in Sect. 3. We connect the global optical and X-ray emission in Sect. 4 and show that J0921+0007 is X-ray loud. It is the highest-redshift blindly detected X-ray source to date, and its detection further supports a flattening of the XLF beyond the break luminosity, L*. We present its contribution to the global accretion density in Sect. 5.

We have assumed a standard Λ cold dark matter cosmology with parameters from Planck Collaboration VI (2020). Throughout this work, uncertainties are quoted at the 68% confidence level (1σ).

2. HSC J092120.56+000722.9: An X-ray-luminous quasar

2.1. eROSITA detection

The eFEDS was executed during the eROSITA performance verification phase and covers approximately 140 deg2 to a nominal exposure of 2.2 ks. In eFEDS, sources were detected in the 0.2 − 2.3 keV band with the erbox task of the eROSITA Science Analysis Software System (eSASS; Brunner et al. 2022). A detection likelihood threshold DET_LIKE ≥ 6 was applied. A supplementary catalogue1 of 4774 eROSITA/eFEDS sources detected just below this threshold (5 <  DET_LIKE <  6) was also made available. It is expected to contain a high fraction of spurious sources, but it also gives access to interesting faint objects. Using simulations, Brunner et al. (2022) show that reducing the source detection likelihood threshold from DET_LIKE = 6 to DET_LIKE = 5 results in an increase in the number of detections of the simulated point-sources. They report an increase 1% (94% instead of 93%) of detected simulated point-sources brighter than F0.5 − 2 keV = 1 × 10−14 erg s−1 cm−2 and 4% (63% instead of 59%) of sources brighter than F0.5 − 2 keV = 4 × 10−15 erg s−1 cm−2. Similarly, Liu et al. (2022b), performing a standard single-band (0.2–2.3 keV) detection run on a simulated eFEDS field, show that reducing the DET_LIKE threshold from 6 to 5 results in an overall increase in completeness from ∼79% to ∼82% and an increase in the spurious fraction from ∼7% to ∼12%. For the supplementary sample, we identified optical counterparts in the eighth data release of the Dark Energy Spectroscopic Instrument Legacy Imaging Surveys (hereafter LS8; Dey et al. 2019) using the Bayesian cross-matching algorithm NWAY (Salvato et al. 2018). It computes posterior cross-match probabilities, accounting for the surface densities of the matched catalogues, astrometric distances, and uncertainties, as well as independent photometric information. For the latter, we applied the random-forest-generated ‘photometric prior’ presented by Salvato et al. (2022), a model trained on an independent 3XMM point-source population and its optical LS8 properties.

The resulting best optical counterpart solutions were positionally cross-matched to a complete list of spectroscopically confirmed z >  5.5 quasars in the eFEDS footprint compiled from literature (31 sources, Fan et al. 2001; Venemans et al. 2015; Matsuoka et al. 2016, 2018a,b; Matsuoka et al. 2022) within 1″. This exercise returned one match. The eFEDS source J092120.6+000725.9, hereafter J0921+0007, has a LS8 match within 3.11″ of its centroid, which coincides spatially with the spectroscopically confirmed SHELLQs quasar J0921+0007 (z = 6.56, Matsuoka et al. 2018a) within 0.08″. The spectroscopic redshift of this quasar was securely measured by Matsuoka et al. (2018a), using the Lyα emission line. It was subsequently confirmed by Onoue et al. (in prep.) using MgII and Yang et al. (2022) who found z = 6.5646 ± 0.0003 using [CII]. There were 22 possible LS8 counterpart candidates within 30″ of the X-ray source J0921+0007. The individual probability for the chosen LS8 counterpart of being the correct one amongst the candidates is unequivocally high p_i = 0.82 (other candidates have p_i <  0.13). A summary of the NWAY match is presented in Table 1.

Table 1.

Basic source and counterpart information.

While the detection likelihood is at a low level where a large spurious fraction is expected, the alignment with a high-redshift quasar strengthens the detection. At an X-ray detection likelihood of 5, 12% of sources in the eFEDS field are expected to be spurious (Liu et al. 2022b). We estimated the probability of a chance alignment of any spectroscopically confirmed high-redshift quasar in the eFEDS footprint with a spurious detection (i.e. a background fluctuation detected as catalogue source). For this we first observe that, in the eFEDS footprint excluding the borders with lower exposure, higher background and stronger vignetting (90% of the total area; see Liu et al. 2022a) there are 29 482 sources detected in the 0.2–2.3 keV band above the detection likelihood of the quasar DET_LIKE >  5.04. Among these sources, 3277.6 are expected to be spurious from simulations. We thus obtained the probability of a chance alignment as a function of the separating distance R of a quasar and a spurious source as: 31 × 3277.6πR2/area90. Here area90 is the area of the ‘90%’ region: 1640219392 arcsec2. The evolution of the probability of a spurious chance alignment with radius is shown in Fig. 1. Accounting for the eFEDS bi-variate positional error ( σ = RADec _ ERR / 2 = 3.87 ″ $ \sigma=\mathrm{RADec\_ERR} / \sqrt{2}=3.87^{{\prime\prime}} $), within the maximum separation between J0921+0007 and the eROSITA source, the probability of a chance alignment of the quasar with a spurious source is less than 1%.

thumbnail Fig. 1.

Probability of finding any of the 31 spectroscopically confirmed quasars in the eFEDS footprint within a distance R of a spurious X-ray source. The solid (dashed) red line shows the minimum (maximum) distance between the eROSITA source and J0921+0007, accounting for the positional uncertainty of the X-ray source.

In order to confirm the eROSITA detection, we obtained a 21 ks Chandra follow-up observation (GTO proposal, cycle 22, ObsID 24738) pointed at the optical position of the quasar.

2.2. Confirmation with a Chandra pointed observation

On October 26, 2021, the quasar was observed with Chandra ACIS-S with a total exposure time of 21.47 ks (PI: Predehl, Observer: Wolf). On the 0.5–7 keV band Chandra image, sources were detected with the mexican-hat wavelet algorithm wavdetect from the CIAO software package. The default detection parameters for the pixel radii (scales) as well as the significance thresholds (sighthresh and bkgsigthresh) have been used (respectively 2 and 4 pixels, 10−6 and 0.001). We confirm the significant detection of an X-ray source whose centroid lies within 0.78″ of the optical coordinates of the quasar. The positional counts-weighted variances in pixels are X_ERR = 0.45 and Y_ERR = 0.28 (RA_ERR = 0.22″ and Dec_ERR = 0.14″), for a point-spread function (PSF) size of 0.46″.

No other source was detected within 30″ of the optical quasar coordinates in the 0.5–7 keV band. A high-resolution broadband image and the wavdetect 3σ elliptical source detection region are presented in the right panel of Fig. 2. In parallel to this automated detection procedure, we performed forced photometry at the quasar position on the 0.5–7 keV Chandra images. We extracted source counts in a circular region of 2″ radius centred on the coordinates of the quasar. Background counts were extracted in a ring with inner and outer radii of 4″ and 20″. As shown in the right panel of Fig. 2, no other bright source is present in the background region. We computed the binomial no-source probability (e.g. Weisskopf et al. 2007; Vito et al. 2019) as

thumbnail Fig. 2.

X-ray image cutouts in the region of J0921+0007. Left: 4′ × 4′ eROSITA/eFEDS image in the 0.2 − 2.3 keV band, smoothed with a Gaussian kernel. The image is centred on the optical position of the quasar J0921+0007. The concentric circles have radii of 30″ (dotted) and 60″ (dashed). Right: 30″ × 30″ high-resolution Chandra image in the energy range 0.5–7 keV. The ellipse shows a wavdetect-detected source at the optical position of the quasar (marked by a red cross).

P B ( i ≥ s ) = ∑ i = s s + b ( s + b ) ! i ! ( i − s − b ) ! ( 1 1 + r ) i ( 2 + r 1 + r ) s + b − i . $$ \begin{aligned} P_{\rm B}(i\ge s) = \sum _{i=s}^{s+b} \frac{(s+b)!}{i!(i-s-b)!} \left( \frac{1}{1+r} \right)^i\left(\frac{2+r}{1+r}\right)^{s+b-i} .\end{aligned} $$(1)

Here s and b are counts in the source and background region, while r is given by the ratio of areas of these two extraction regions. In the 0.5–7 keV band, we extracted 7 counts in the source region and 52 counts in the background region. We obtained PB, 0.5 − 7 keV ∼ 3 × 10−6; in other words, the source detection is highly significant. The binomial no source probabilities in the narrower energy bands 0.5–1.2 keV and 1.2–2 keV are PB,  0.5 − 1.2 keV ∼ 3 × 10−4 and PB,  1.2 − 2 keV ∼ 6 × 10−4.

2.3. X-ray properties

The forced PSF-fitting photometry results in the supplementary eFEDS catalogue impose that J0921+0007 was significantly detected in the 0.5–1 keV band (DET_LIKE = 6.2). This band samples the rest-frame hard X-ray emission (λ(0.5 − 1 keV)∼3.8 − 7.6 keV). In this band, there are 4.74 ± 2.74 source net counts (as measured from the rate). The background at the source position is 2.42 counts/arcmin2. The measured count rate is r0.5 − 1 keV = (3.86 ± 2.23) × 10−3 cts s−1. We converted the count-rate to an observed frame flux of F0.5 − 1 keV = (2.8 ± 1.6) × 10−15 erg cm−2 s−1 assuming a power law with photon index Γ = 2 and Galactic foreground absorption NH = 2.65 × 1020 cm−2 from HI4PI Collaboration (2016) 2. This corresponds to a rest-frame 2 − 10 keV luminosity of L2−10 keV = (2.96 ± 1.71) × 1045 erg s−1. We also computed count rates and fluxes from the Chandra follow-up data using the srcflux script of the CIAO software package. We manually selected source and background regions centred at the optical coordinates of the quasar. The circular source region has a radius of 2″, while the annulus describing the background region has radii (4″, 13″). Counts were extracted in the 0.5–2 keV band. For the PSF model, we opted for the arfcorr method. We obtained the net count rate: r 0.5 − 2 keV = ( 2 . 8 − 1.6 + 2.5 ) × 10 − 4 cts s − 1 $ r_{0.5{-}2\,\mathrm{keV}}= (2.8^{+2.5}_{-1.6})\times 10^{-4}\,{\mathrm{cts}\,\mathrm{s}^{-1}} $. Once again assuming a nominal absorbed power law with Γ = 2 and NH = 2.65 × 1020 cm−2, we obtained the absorption-corrected energy flux F 0.5 − 2.0 keV = ( 3 . 5 − 2.0 + 3.1 ) × 10 − 15 erg cm − 2 s − 1 $ F_{0.5{-}2.0\,\mathrm{keV}}= (3.5^{+3.1}_{-2.0}) \times 10^{-15}\,\mathrm{erg}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1} $ and the 2–10 keV luminosity L 2 − 10 keV = ( 2 . 1 − 1.2 + 1.9 ) × 10 45 erg s − 1 $ L_{2{-}10\,\mathrm{keV}} = (2.1^{+1.9}_{-1.2}) \times 10^{45}\,\mathrm{erg}\,\mathrm{s}^{-1} $. The luminosity derived from the Chandra data is consistent with the eROSITA results within the 1σ measurement uncertainties. The large error bars are driven by the low-count statistics. Within these uncertainties, no flux variability is detected between the eROSITA observations and Chandra (i.e. Δt ∼ 95 days) in the quasars rest frame.

In addition, we obtained a tentative spectral fit of the counts extracted from the manually defined source and background regions. We used the Bayesian analysis software BXA (Buchner et al. 2014) coupled to the X-ray fitting library XSPEC (Arnaud et al. 1996) and the nested sampling algorithm ultranest (Buchner 2021). We restricted the fitting region to the 0.1–8.5 keV band. Given the low number of counts, we adopt an absorbed, redshifted power-law model: tbabs*zpowerlw, with photoelectric absorption fixed to the Galactic absorbing column density NH. The normalisation and the photon index Γ were allowed to vary in the fit, assuming uninformative, wide priors (Γ = 1.5 − 5). The redshift of zpowerlw was fixed to the redshift of the quasar, z = 6.56. We used the C-statistic for the spectral analysis (Cash 1979). The marginal posterior distributions of the photon index and L2 − 10 keV are presented in Fig. 3. We obtained a steep power-law photon index Γ = 3 . 2 − 0.6 + 0.7 $ \Gamma=3.2^{+0.7}_{-0.6} $. Even assuming no intrinsic absorption, the photon index is higher than typical quasars in this redshift regime (Γ = 2.20, Vito et al. 2019). However, we cannot exclude that the steepness of the photon index is due to the presence of a high-energy cutoff, redshifted into the observed Chandra waveband. The high energy cut-off corresponds to the temperature of the corona, beyond which electrons are no longer able to give energy to the incident photons. Typically this cut-off is two to three times larger than the coronal electron temperature (Petrucci et al. 2001), and is often of the order of a few hundred keV, but has been measured as low as a few tens of keV (e.g. Kara et al. 2017), which is within the observed-frame for this source. Another possible explanation for this steep soft spectrum is the presence of a soft-excess (Arnaud et al. 1985; Boller et al. 1996; Magdziarz et al. 1998; Gierliński & Done 2004; Ross & Fabian 2005; Crummy et al. 2006; Walton et al. 2013). We derived absorbed fluxes and luminosities, accounting for the posterior samples of Γ and the power-law normalisation (see Table 2). We adopted Γ = 3.2 for the spectral shape of J0921+0007 throughout this work.

thumbnail Fig. 3.

Marginal posterior distributions of the photon index, Γ, and the hard X-ray luminosity from the BXA fit to the Chandra spectrum.

Table 2.

X-ray properties of J0921+0007.

Table 2 summarises the X-ray photometry derived from the eROSITA and Chandra data. Figure 4 presents the 2–10 keV luminosity-redshift plane for an up-to-date sample of X-ray-detected quasars (Nanni et al. 2017; Vito et al. 2019; Pons et al. 2020; Belladitta et al. 2020; Medvedev et al. 2021; Khorunzhev et al. 2021; Wolf et al. 2021). It also displays the eFEDS normalised sensitive area. The area sensitivity curves are obtained with the eSASS task apetool. apetool returns the sensitive area in square degrees as a function of source count-rates. We converted count-rates to L2 − 10 keV assuming an absorbed power-law model with Γ = 3 and NH = 3 × 1020 cm−2. The luminosity of J0921+0007 derived from the spectral analysis is shown. The quasar lies at the sensitivity limit of the survey.

thumbnail Fig. 4.

Hard X-ray luminosities of X-ray-detected high-redshift quasars. All eROSITA-detected quasars are marked by a red square. The normalised area of eFEDS that is sensitive to sources modelled by a fiducial absorbed power law (Γ = 3!!!! and NH = 3 × 1020 cm−2) is represented by the background colour map. J0921+0007, shown here as a pink square, lies at the detection limit of the eFEDS survey, as expected from the low eROSITA detection likelihood.

3. Physical properties and active galactic nucleus type from a Ks-band spectrum

J0921+0007 was discovered by Matsuoka et al. (2018a) in the dedicated HSC high-redshift quasar survey SHELLQs. It was selected as quasar candidate based on its red i − z colour and retained by a Bayesian selection method detailed by Matsuoka et al. (2016). The photometry of this quasar resembles that of Galactic brown dwarfs and could only be disentangled from stellar contaminants due to an unusually strong Lyα + NV complex, which steepens the z − Y slope (Matsuoka et al. 2018a). Indeed, J0921+0007 possesses the second most luminous Lyman α line of the entire SHELLQs z >  5.8 quasar sample with log (LLyα/(erg s−1)) = 45 ± 0.01 (Matsuoka et al. 2016, 2018a). Matsuoka et al. (2018a) further report a relatively moderate line width FWHMLyα = 1400 ± 100 km s−1. We present a new NIR observation of this source, derive its black hole properties and determine its AGN type.

3.1. Black hole mass and accretion rate

We estimated the black hole mass from infrared spectroscopy. The MgIIλ2798 emission line, which can be used as a virial black hole mass estimator (Vestergaard & Osmer 2009) is redshifted outside the optical discovery spectrum, which ends at 1.02 μm (1330 Å in the rest frame). Thus, we obtained NIR spectroscopy of J0921+0007. We note that this spectrum was obtained prior to the eROSITA detection of the source.

The Ks-band spectrum of J0921+0007 was obtained by MOIRCS (Ichikawa et al. 2006; Suzuki et al. 2008), a Cassegrain instrument mounted on the Subaru Telescope, on April 22, 2019. The observation was performed in the multi-object spectroscopy mode for secure target acquisition. The VPH-K grism (Ebizuka et al. 2011) was used to cover 2.0–2.4 μm at a spectral resolution of R = 1700 for a 0.8″ slit width. J0921+0007 was observed for 72 min with mean airmass 1.1 and K-band seeing size 0.8 arcsecond. More details of the observations and data analysis will be presented in Onoue et al. (in prep.).

The raw data were reduced and 1D-extracted in the standard manner based on the software system Image Reduction and Analysis Facility (IRAF). To correct for the telluric absorption an A0-type star was observed just before the exposures of J0921+0007. The telluric-corrected 1D spectrum was then scaled to the Ks-band magnitude of J0921+0007 (=20.691 ± 0.052 AB mag) that was obtained by the same run with MOIRCS. Observations in the Ks band are preferable since it covers MgII, the emission line of interest. This 10 min imaging observation enables us to flux-calibrate the observed K-band spectrum accurately without being affected by potential variability of the quasar. The spectrum was scaled to correct for the Galactic extinction in the K band.

Figure 5 shows the obtained Ks-band spectrum, where a strong MgII emission line is clearly detected. We model the spectrum with three components: power-law continuum, FeII pseudo-continuum, and MgII. Since the MOIRCS spectrum covers a narrow wavelength range, the continuum power-law slope (αλ = −1.052; Fλ ∝ λαλ) was estimated by the photometric colour of the optical HSC y band and MOIRCS Ks band. The monochromatic luminosity at rest frame 3000 ÅL3000 = (4.8 ± 0.2) × 1042 erg s−1 s−1 Å−1 was derived by the scaled power-law continuum model with αλ = −1.021. The 3000 Å luminosity was then converted to the bolometric luminosity Lbol = (7.4 ± 0.3) × 1046 erg s−1 assuming a bolometric factor of 5.5 (Richards et al. 2006). For FeII emission lines, the empirical template of a local narrow-line Seyfert galaxy, 1 Zw 1 (Tsuzuki et al. 2006) was convolved with a Gaussian kernel and fitted to the observed continuum together with the power-law continuum. A single Gaussian profile was fitted to the residual to measure the MgII line shape. The derived MgII redshift of 6 . 5634 − 0.0012 + 0.0013 $ 6.5634^{+0.0013}_{-0.0012} $ is consistent with the Lyα redshift reported by Matsuoka et al. (2018a, z = 6.56). The redshift measurement is also consistent with the recent [CII] redshift reported by Yang et al. (2021) for this object (z = 6.5646 ± 0.0003).

thumbnail Fig. 5.

Ks-band MOIRCS spectrum of J0921+0007. The combined fit to the continuum and MgII line is shown by the solid red curve. The decomposition in continuum (blue), the Fe II pseudo continuum (green), and the Gaussian line fit (yellow) are also shown.

The BH mass and Eddington ratio were derived based on the MgII single-epoch method (Vestergaard & Osmer 2009). From the MgII line full width half maximum ( F W H M = 1699 − 110 + 99 $ FWHM =1699^{+99}_{-110} $ km s−1) and the 3000 Å luminosity, we measured the virial black hole mass M BH = ( 2 . 48 − 0.29 + 0.31 ) × 10 8 M ⊙ $ M_{\mathrm{BH}} = (2.48^{+0.31}_{-0.29}) \times 10^8\,M_\odot $ and an Eddington ratio λ = L bol / L Edd = L bol / ( 4 π c G M BH m p / σ T ) = 2 . 29 − 0.29 + 0.30 $ \lambda=L_{\mathrm{bol}}/L_{\mathrm{Edd}}=L_{\mathrm{bol}}/(4\pi\, c \, G \, M_{\mathrm{BH}} m_{\mathrm{p}}/\sigma_{\mathrm{T}})=2.29^{+0.30}_{-0.29} $. J0921+0007 shows a high Eddington ratio, as expected from its steep photon index.

We note that J0921+0007 was also observed with Gemini/GNIRS by Yang et al. (2021). Their continuum and MgII measurements are mostly consistent with ours, while they report a slightly fainter 3000 Å luminosity (L3000 = (3.9 ± 0.4) × 1042 erg s−1). This difference is likely attributed to the different absolute flux calibration between the GNIRS and MOIRCS spectra. For the calibration of their spectrum, Yang et al. (2021) used a J-band magnitude measurement with a relatively large error (J = 21.21 ± 0.28) for their calibration.

3.2. NLS1 classification

Following Osterbrock & Dahari (1983) and Goodrich (1989), a quasar is required to show a narrow Hβ line (FWHMHβ < 2000 km s−1) and a small narrow-line to broad-line flux ratio ([O III]/Hβ < 3) in order to be classified as NLS1s. At z >  6, however, Hβ is shifted out to mid-infrared wavelengths, making the direct classification of high-z quasars as NLS1s by this definition impossible. Using the correlation between MgII and Hβ widths in a sample of Sloan Digital Sky Survey DR14 quasars, Rakshit et al. (2021) proposed selecting NLS1s using FWHMMg II < 2000 km s−1. With an MgII width F W H M Mg I I = 1699 − 110 + 99 $ {FWHM_{\mathrm{Mg{\textsc{ii}}}}}=1699^{+99}_{-110} $ km s−1, J0921+0007 can be classified according to this selection criterion. Rakshit et al. (2021) propose a UV proxy measurement of the ratio of FeII and Hβ equivalent widths rFe II (Boroson & Green 1992) as rFe II,UV = EW(Fe II)/EW(Mg II). Together with the FWHM of Hβ, rFe II is one of the parameters defining the quasar main sequence (e.g. see Marziani et al. 2018b, and references therein). rFe II has been shown to correlate tightly with the Eddington ratio (e.g. Rakshit et al. 2017). We computed the equivalent width of the fitted FeII template in the rest-frame wavelength interval 2200−3090 Å. We note that this measurement is based on an extrapolation of the iron template, since the spectrum only covers rest frame ∼2700−3150 Å. We obtained rFe II,UV ∼ 3.77, a value locating the source at the strongly accreting end of the quasar main sequence (Population A see Marziani et al. 2018a,b).

4. Relative X-ray and optical/UV output

4.1. X-ray loudness

The relative output of the hot corona and the UV disc emission is characterised by the ratio of monochromatic luminosities at 2 keV and 2500 Å:

α OX = 0.384 × log ( L 2 keV / L 2500 ) , $$ \begin{aligned} \alpha _{\mathrm{OX} } = 0.384 \times \mathrm{log} \, (L_{2\,\mathrm {keV}}/L_{2500}), \end{aligned} $$(2)

where L2 keV and L2500 are the rest-frame monochromatic luminosities at 2 keV and 2500 Å, respectively. There is a well-known anti-correlation between αOX and the 2500 Å monochromatic luminosity (e.g. Steffen et al. 2006; Just et al. 2007; Lusso & Risaliti 2016), which signifies that more UV luminous quasars tend to show a stronger UV contribution to their total emission (with respect to the coronal emission). This relation does not show evolution with redshift (e.g. Steffen et al. 2006; Just et al. 2007; Lusso & Risaliti 2016; Nanni et al. 2017; Vito et al. 2019). We computed the αOX by deriving L2500 from the monochromatic luminosity of 3000 Å and the spectral slope reported in Sect. 3.1. The UV luminosity is L2500 = (1.74 ± 0.07) × 1031 erg s−1 Hz−1. We further obtained an estimate of L2 keV from the hard broadband X-ray luminosity obtained from the spectral analysis of the Chandra data, taking into account the posterior distribution of Γ. We obtained αOX = −1.21 ± 0.09. In Fig. 6, we show how this X-ray to UV power-law slope compares to other X-ray-detected high-redshift quasars from Nanni et al. (2017), Vito et al. (2019), Pons et al. (2020), Medvedev et al. (2021) and Wolf et al. (2021). The αOX relation derived for z >  5.7 sources by Nanni et al. (2017) is shown. The eFEDS normalised sensitive area to a fiducial source modelled by an absorbed power law with Γ = 3 and NH = 3 × 1020 cm−2, is represented as background colour gradient. J0921+0007 shows a significantly flatter αOX slope than other high-redshift quasars with comparable UV luminosities. Accounting for the 1σ confidence interval for the αOX − L2500 relation of Nanni et al. (2017), the nominal αOX of J0921+0007 is a > 3σ outlier. With respect to the more conservative relation of Just et al. (2007), J0921+0007 is a > 1.5σ outlier. This indicates that the X-ray contribution to the total emission in this quasar is higher. The eFEDS sensitivity map corroborates the outlier nature in terms of relative X-ray to UV output of J0921+0007: at L2500, we could not have detected this source in eFEDS if it followed the typical αOX − L2500 relation. J0921+0007 is X-ray loud with respect to the bulk of X-ray-detected high-redshift quasars. We note that this result relies on the assumption that the steep photon index measured in the rest-frame hard band of J0921+0007, Γ = 3.2, is not due to any non-coronal components (e.g. soft excess). The object of Medvedev et al. (2020) shows a similarly strong deviation from the αOX − L2500 relation, which is due to non-coronal X-ray emission from the jet. J0921+0007 in contrast is radio-quiet. The significant αOX outlier from the Vito et al. (2019) sample at αOX = −1.28 and logL2500 ∼ 31 is the radio-quiet quasar CFHQS J1641+3755 at z = 6.04. This source shows remarkable similarities to J0921+0007 in terms of black hole properties and its X-ray emission (see discussion).

thumbnail Fig. 6.

X-ray to UV slope αOX as a function of L2500 for quasars at z >  5.7. Because of its strong X-ray emission, J0921+0007 (pink square) deviates significantly from the αOX-L2500 relation, the 1σ confidence interval of which is delimited by the dotted red lines (Nanni et al. 2017). The sensitivity of eFEDS to sources modelled by a steep absorbed power law (Γ = 3 and NH = 3 × 1020 cm−2) is traced by the colour map. The hexagonal pattern represents a sample of XMM-detected SDSS quasars presented by Lusso & Risaliti (2016).

4.2. An increased coronal contribution to the bolometric luminosity

In the previous section we demonstrate that the quasar shows a stronger X-ray emission than typical quasars of similar rest-frame UV luminosity L2500. This implies that the total active galactic nucleus (AGN) emission may be affected by the increased coronal contribution at shorter wavelengths. To account for this, we estimated a corrected AGN bolometric luminosity Lbol, corr by performing an SED fit with the tool Code Investigating GALaxy Emission (CIGALE; Boquien et al. 2019) and its X-ray module X-CIGALE, (Yang et al. 2020). We obtained photometry from the third public data release of the HSC-SSP, LS8, the VISTA Kilo-degree Infrared Galaxy Survey (VIKING; Arnaboldi et al. 2007), the UKIRT Infrared Deep Sky Survey (UKIDSS; Lawrence et al. 2007), and CatWISE2020 (Marocco et al. 2021), by cross-matching the optical position of the quasar to these catalogues and selecting the nearest detection within 1″. Each of the above surveys yielded a detection within 1″. We did not make use of photometry in the absorbed region of the spectrum at λ <  1215 @@@, since transmitted flux, for example from the quasar proximity zone, can negatively affect the fitted (see the red squares Fig. 7). In addition we used the 0.5–2 keV flux from the spectral fit to the Chandra data (Γ ∼ 3.2; see ChandraBXA in Table 2).

thumbnail Fig. 7.

X-CIGALE fit to the quasar optical, infrared, and X-ray photometry. Photometric points from HSC, LS8, UKIDSS, VIKING, and unWISE are marked by squares. The photometry that has been ignored for the SED fit is shown as red squares. The solid black line is the best-fitting model. The dashed blue line shows the fitted disc model and the dashed brown line the unconstrained torus emission. We also show the LDSS3 spectrum presented in Appendix A. The upper panel shows corresponding photometric filters.

We fitted an AGN disc model as defined in the AGN SKIRTOR module, which uses a disc spectral energy distribution (SED) adapted from Feltre et al. (2012, see also Duras et al. 2017; Yang et al. 2020). We fixed the viewing angle with respect to the AGN axis to i = 30deg and probed a grid of E(B − V) values for extinction in the polar direction. The AGN fraction was set to 0.999, as the host galaxy emission is completely dominated by the AGN emission in luminous, distant quasars. We further allowed a large dispersion in the αOX-L2500 relation: ΔαOX = |αOX − αOX(L2500)| = 1.0, where αOX(L2500) was determined using the relation measured by Just et al. (2007). We fixed the power-law photon index of the xray module to Γ = 3.2, a value supported by our X-ray spectral fitting results. We used fiducial galaxy population parameters set in the modules sfhdelayed (delayed star-formation history) and bc03 (single stellar populations, Bruzual & Charlot 2003). Galactic dust attenuation was accounted for via dustatt_calzleit (Calzetti et al. 2000; Leitherer et al. 2002). The redshift was fixed to z = 6.56. The best-fitting model has a reduced χ2 of 0.72. The AGN disc dominates the rest-frame optical/UV part of the SED. The AGN dust emission remains unconstrained. The SED as well as the total model are presented in Fig. 7.

We performed sanity checks by comparing the 2–10 X-ray luminosity L2 − 10 keV, XCIG and the αOX, XCIG from the X-CIGALE output to the measurements from Sects. 2.3 and 3.1. The values are : L2 − 10 keV, XCIG = (3.04 ± 2.72) × 1045 erg s−1 and αOX, XCIG = −1.2. These results are consistent within 1σ with the more precise measurements from the X-ray and infrared spectral analysis.

The corrected bolometric AGN luminosity was obtained by summing the intrinsic AGN disc luminosity averaged over all directions (agn.accretion_power) and the total X-ray luminosity (0.2–100 keV): Lbol, corr = Ldisc + LX, tot = (9.9 ± 4.0) × 1046 erg s−1. We did not include the dust emission in this calculation since it arises from re-processed nuclear UV and X-ray photons (e.g. Lusso et al. 2012; Duras et al. 2020).

We compared the resulting 2 − 10 keV bolometric correction, Kbol = Lbol/L2 − 10 keV, to typical type 1 AGN values from literature. J0921+0007 follows a bolometric correction K bol = 23 − 13 + 29 $ K_{\mathrm{bol}}=23^{+29}_{-13} $, about a factor of 4 smaller than the prediction from the general Kbol − Lbol relation of Duras et al. (2020) and the one for type 1 AGN by Lusso et al. (2012), as can be seen in Fig. 8. These findings further confirm the unusual X-ray loudness of the quasar. Using the same method, we also derived a bolometric correction for the second high-redshift quasar detected in eFEDS, SDSS J0836+0054, from the photometry presented in Wolf et al. (2021). This source also shows X-ray emission excess.

thumbnail Fig. 8.

Bolometric correction for J0921+0007 (pink error bars) compared to predictions from Duras et al. (2020) for the full AGN population (solid blue line) and Lusso et al. (2012) for type 1 AGN (solid brown line). The dispersions are quoted at the 68% level (blue shaded area and brown shaded area). The strong X-ray emission of J0921+0007 with respect to its disc emission causes it to deviate at the > 1σ level from the typical AGN Kbol − Lbol. The green error bars show the bolometric correction for the second eFEDS high-z quasar (Wolf et al. 2021). We note that the bolometric correction of Lusso et al. (2012) is only valid up to log Lbol = 13; the extrapolation (light-shaded area) is shown for visualisation purposes only.

5. AGN demographics in the first gigayear of the Universe

5.1. Comparison to XLF models

X-ray-selected quasars can be used to trace black hole accretion through cosmic time via the XLF. The AGN XLF has been studied in detail over a variety of population in deep or wide surveys (Hasinger et al. 2005; Barger et al. 2005; Vito et al. 2014; Ueda et al. 2014; Buchner et al. 2015; Aird et al. 2015; Georgakakis et al. 2015; Fotopoulou et al. 2016; Ananna et al. 2019). In these works, the space density of X-ray-detected AGN has been investigated up to z = 5 and has been shown to decline exponentially with redshift beyond the luminosity at the knee of the XLF log L* ∼ 44 (Brusa et al. 2009; Civano et al. 2011). Selecting high-redshift AGN in the Chandra Deep Fields, Vito et al. (2018) extended the analysis out to z = 6, with a sample of sources with photometric redshifts beyond z ≥ 5.5. Wolf et al. (2021) showed that the eROSITA detection of a spectroscopically confirmed z = 5.81 quasar in the eFEDS field imposes new constraints on the AGN XLF at its bright end. The detection of SDSS J0836+0054 is consistent with extrapolated models of the XLF from literature. Models with a milder decline in AGN space density in the highest X-ray luminosity bins are favoured by this detection. These findings are corroborated by an analysis of a sample of X-ray-detected high-redshift AGN in the ExSeSS by Barlow-Hall et al. (2022). We note that Barlow-Hall et al. (2022) report the detection of ATLAS J025.6821-33.4627, a spectroscopically confirmed quasar at z = 6.31, which had been, until now, the highest-redshift, blindly X-ray-detected AGN. J0921+0007 was blindly detected in eFEDS, albeit with a low detection-likelihood, and is therefore the highest-redshift, X-ray-selected AGN.

Wolf et al. (2021) show evidence against the steepest declines of the space density of luminous X-ray-detected AGN with increasing redshift. Here we go beyond this claim and show that the detection of J0921+0007 in the field is not supported by predictions of current XLF models over all luminosities extrapolated to higher redshifts. We compare the number count predictions from the best-fitting, extrapolated XLF models presented by Ueda et al. (2014, luminosity-dependent density evolution), Vito et al. (2014, pure density evolution), Georgakakis et al. (2015, pure density evolution), Miyaji et al. (2015, luminosity-dependent density evolution) and Aird et al. (2015, flexible double power law), to the eFEDS detection. We stress that these models were evaluated on AGN samples at z <  5 and that our comparison assumes that the parametric form of the XLF derived by these authors does not strongly evolve from z = 5 to z ∼ 6. We obtained number counts beyond a given redshift and luminosity threshold, zmin and Lmin, from the XLF models by computing

N = ∫ log L min ∞ ∫ z min z = 10 A Γ ( log L X , z ) d V d z ϕ m ( θ ) d z d log L X . $$ \begin{aligned} N= \int _{\mathrm{log} \, L_{\rm min}}^{\infty } \int _{z_{\rm min}}^{z=10} A_\Gamma (\log \, L_\mathrm{X} , z)\frac{\mathrm{d} V}{\mathrm{d} z} \phi _m(\theta ) \, \mathrm{d} \,z \, \mathrm{d} \, \mathrm{log} \ L_\mathrm{X} .\end{aligned} $$(3)

AΓ(log LX, z) is the normalised sensitive area of the survey to a source of luminosity LX and redshift z, d V d z $ \frac{\mathrm{d}V}{\mathrm{d}z} $ the differential comoving volume and ϕm(θ) the model XLF (in units of Mpc−3). As in Wolf et al. (2021), the sensitive area was obtained by converting the apetool (Georgakakis et al. 2008) count-rate based area curve to a luminosity-based area curve with an X-ray spectral model. Here, we assumed a redshifted power law under Galactic absorption, (tbabs*zpowerlw). Following this methodology, redshift-luminosity configurations as a function of the photon index were converted into soft band counts (and thereby to a normalised sensitive area) by generating X-ray spectra using the convolutional XSPEC component clumin. This conversion was fitted with logistic regression. A novelty is that we fitted the luminosity-counts relation over a grid of Γ. Slices of the resulting fitted surface are shown in Fig. 9. In Eq. (3), we can now evaluate the model-dependent sensitivity using this function. We integrated over all luminosities by setting log Lmin = 42.

thumbnail Fig. 9.

Slices of the simulated eFEDS sensitive area cube. Left: sensitive area for fixed Γ = 2 as a function of L2 − 10 keV and z. Right: sensitive area as a function of Γ and L2 − 10 keV for fixed redshift z = 6. The dotted white (solid black) line shows the parameter configurations at 50% (5%) of the normalised sensitive area.

For each of the XLF models, we evaluated Eq. (3) over the range zmin = 5.5 − 7. We accounted for two spectral models by estimating the sensitive survey area A(log LX, z) for Γ = 2.2 (Vito et al. 2019) and Γ = 3.2, the median value derived from the Chandra observation of J0921+0007. This effectively yields the expected number counts over all luminosities beyond an increasing redshift threshold zmin. For each model and each zmin we computed the 15.9th and 84.1th percentile of the count expectations to estimate their 1σ confidence intervals. The resulting inverse cumulative distribution of predicted counts is presented in Fig. 10. We obtained 1σ confidence intervals by sampling from the parameter uncertainties of the models. As the covariance matrix of these parameters was not accounted for, the uncertainty may have been over-estimated. The model predictions are compared to the source counts detected in eFEDS (Fig. 10). We can conclude that over all luminosities, none of the extrapolated XLF models supports two detections in the eFEDS field at high redshift, regardless of the X-ray spectral model. At z >  5.81, the models from Vito et al. (2014), Ueda et al. (2014), Miyaji et al. (2015) and Georgakakis et al. (2015) are consistent with one detection to within 1σ. No model supports a detection at z = 6.56. This is further shown in the 2 lower panels of Fig. 10, where we present for each lower-redshift interval edge, zmin, the Poisson probability for each XLF model of supporting at least one (Pλ(≥1, z)) or two counts (Pλ(≥2, z))in the eFEDS field. Even for the model with the highest number count prediction at z ≥ 5.81 (Vito et al. 2014) the Poisson probability of detecting two sources in eFEDS is less than 0.4. For all models, the probability of generating 1 count at z ≥ 6.56 is less than 0.5. As expected for sources with steeper photon indices, the count expectations are lower. In particular, a detection at z ≥ 6.56 is unlikely with Pλ(≥1, z ≥ 6.56)< 0.25. As discussed in Wolf et al. (2021), the volume probed by the eFEDS survey at z = 5.81 − 6.56 is such that the uncertainty due to cosmic variance in the expected source counts is negligible with respect to the Poisson error. We conclude that the current extrapolated XLF models under-predict the number of high-redshift quasars that we detect in eFEDS.

thumbnail Fig. 10.

Inverse cumulative source count predictions in eFEDS from extrapolated XLF models from Vito et al. (2014), Ueda et al. (2014), Aird et al. (2015), Miyaji et al. (2015) and Georgakakis et al. (2015) integrated over all luminosities. The shaded and hashed areas show the 1σ confidence intervals derived from the model parameter uncertainties. These count predictions depend on the sensitive eFEDS area (Eq. (3)) and therefore on the assumed spectral model for the AGN. We show the predictions for two different photon indices, Γ = 2.2 and Γ = 3.2, respectively in the left and right panels. The black line shows the inverse cumulative distribution of detection in eFEDS. No model supports two detections in eFEDS for the chosen photon indices. At Γ = 2.2, the Vito et al. (2014), Ueda et al. (2014), Miyaji et al. (2015) and Georgakakis et al. (2015) models support the unique detection at z ≥ 5.81. The central and lower panels present the Poisson probabilities of the XLF models supporting respectively one and two detections in eFEDS beyond a given redshift threshold. These probabilities are overall low and demonstrate the discrepancy between the eFEDS counts and the model predictions. With Γ = 3.2 the detection probabilities are lower than with Γ = 2.2.

5.2. Contribution of X-ray-luminous quasars to accretion density at z ∼ 6

The total black hole mass accretion rate per unit volume can be traced through cosmic time via the black hole accretion rate density (BHAD), Ψbhar(z), which is related to the AGN bolometric luminosity function ϕ(Lbol, z), as

Ψ bhar ( z ) = ∫ 1 − ϵ ϵ c 2 L bol ϕ ( L bol , z ) d log L bol , $$ \begin{aligned} \Psi _{\rm bhar}(z) = \int \frac{1-\epsilon }{\epsilon c^2} L_{\rm bol} \, \phi (L_{\rm bol},z) \mathrm{d} \, \mathrm{log} \ L_{\rm bol}, \end{aligned} $$(4)

where Lbol is the bolometric luminosity and ϵ the radiative efficiency. The radiative efficiency ϵ is related to accretion efficiency η and the physics governing the accretion flow. We assume that the X-ray-luminous eFEDS quasars accrete above the critical rate, which delimits a radiatively efficient accretion disc from an inefficient one. We adopted a standard thin disc estimate ϵ = η = 0.1 (e.g. Soltan 1982; Fabian & Iwasawa 1999; Merloni & Heinz 2008; Delvecchio et al. 2014), that is, the radiative efficiency is set equal to the accretion efficiency. We note that the value of ϵ only affects the normalisation of Ψbhar. At higher redshifts, the evolution of the BHAD has been derived from X-ray-detected (Aird et al. 2015; Vito et al. 2018) and X-ray-undetected, stacked AGN (Vito et al. 2016). To estimate the total contribution of the eFEDS-detected quasars, we first note that

Ψ bhar ( z ) = 1 − ϵ K bol ϵ c 2 ∫ L 2 − 10 keV ϕ X ( L 2 − 10 keV , z ) d log L 2 − 10 keV , $$ \begin{aligned} \Psi _{\rm bhar}(z) = \frac{1-\epsilon K_{\rm bol}}{\epsilon c^2} \int L_{\rm 2{-}10\,keV} \, \phi _X (L_{\rm 2{-}10\,keV},z) \mathrm{d} \, \mathrm{log} \ L_{2{-}10\,\mathrm{keV} }, \end{aligned} $$(5)

where L2 − 10 keV is the 2–10 keV luminosity, ϕX(L2 − 10 keV, z) the hard XLF and Kbol the bolometric correction from the 2–10 keV band. The integral is the total AGN emissivity per unit volume. Therefore, we can rewrite Eq. (5) as

Ψ bhar ( z ) ≈ 1 − ϵ ϵ c 2 × ∑ Δ z L bol , AGN V eFEDS , Γ , $$ \begin{aligned} \Psi _{\rm bhar}(z) \approx \frac{1-\epsilon }{\epsilon c^2} \times \sum _{\Delta z} \frac{L_{\rm bol,AGN}}{V_{\rm eFEDS, \Gamma }}, \end{aligned} $$(6)

where Lbol, AGN the bolometric AGN luminosity of sources detected in the Δz bin and VeFEDS, Γ the sensitive comoving volume of the eFEDS survey. The sum is taken over all detections in Δz. We computed this estimator for the redshift interval z = [5.81−6.56], the redshift interval spanned by the two quasars. The contribution of the eFEDS high-z quasars to black hole accretion in this redshift bin can be obtained by summing up the ratio of accretion luminosities obtained in the SED fits presented in Sect. 4.2 (agn.accretion_power) to the corresponding eFEDS sensitive volume (Vito et al. 2016). We obtained this volume by accounting for the sensitivity to sources that have 2–10 keV luminosities of the quasars detected in eFEDS (see Fig. 9). We assumed Γ = 2.2 for the sensitive survey area of J0836+0054 (Wolf et al. 2021) and Γ = 3.2 for J0921+0007 (as derived from the spectral fit in Sect. 2.3). The resulting accretion density is Ψ z = 5.81 − 6.56 = ( 1 . 36 − 0.62 + 3.58 ) × 10 − 7 M ⊙ yr − 1 Mpc − 3 $ \Psi_{z=5.81-6.56}=(1.36^{+3.58}_{-0.62}) \times 10^{-7}\,M_\odot\,\mathrm{yr}^{-1}\,\mathrm{Mpc}^{-3} $. We note that this total AGN emissivity per unit comoving volume only accounts for the un-extincted disc luminosity and not the disc photons reprocessed by the torus and the corona.

We compare this result to lower-redshift measurements and theoretical predictions in Fig. 11. The theoretical predictions shown in this figure assume different seeding masses and growth modes. We show results across the entire halo mass scale (Sijacki et al. 2015; Volonteri et al. 2016; Weinberger et al. 2018; Ni et al. 2022) and results restricted to sub-samples at the high-mass and high-luminosity end (Volonteri et al. 2016; Ni et al. 2022). The departure from co-evolution of black hole accretion rate and the star formation rate at z >  3 is in general difficult to achieve with a cosmological model.

thumbnail Fig. 11.

Black hole accretion rate density (BHAD) for various XLF models and growth simulations. XLF models from Vito et al. (2014), Ueda et al. (2014), Miyaji et al. (2015) and Georgakakis et al. (2015) are extrapolated beyond z = 5 (pale continuation of the red BHAD curves), and the prediction from Buchner et al. (2015) is given over the full z = 4 − 7 range. We include observational results from Vito et al. (2018) from the Chandra Deep Fields. The measurement derived from the high-redshift quasar detections in eFEDS is shown as a yellow square. Our result is consistent with theoretical predictions restricted to the highest halo (and black hole) masses (Volonteri et al. 2016; Ni et al. 2022). For comparison, a scaled version of the star formation rate density from Bouwens et al. (2015) is shown as beige-shaded and dashed area.

It has been suggested that good agreement between observations and simulations is only warranted when only including large black hole or halo masses, while using all masses causes simulations to over-predict the black hole accretion density (Sijacki et al. 2015; Volonteri et al. 2016). For example, the results from the Horizon-AGN simulations (Volonteri et al. 2016) are presented for the total mass range (solid dark green) and for halos with a halo hole mass of > 5 × 1011 M⊙ (dashed dark green). Volonteri et al. (2016) proposed that supernova feedback could be the reason why observational results only agree with simulations when applying a high-mass threshold. Indeed supernovae feedback is expected to deplete the AGN core, effectively stopping black hole growth in low-mass galaxies (Dubois et al. 2015; Habouzit et al. 2017). As the galaxy grows in mass its deeper gravitational potential allows it to more efficiently confine the gas in the nucleus. The black hole accretion density derived from the X-ray-luminous eFEDS detections is in perfect agreement with the predictions from Volonteri et al. (2016) at Mhalo >  5 × 1011 M⊙. Similarly, in their ASTRID simulations Ni et al. (2022) present their BHAD for various X-ray luminosity thresholds. At high luminosities (log LX >  44) the predictions of the steeper falling BHAD curves and the value derived from eFEDS are in excellent agreement. However, we stress again that the eFEDS survey is not sensitive to 44 <  log LX <  45 in the probed redshift regime. We are therefore missing contributions to accretion rate density from quasars accounted for in the Ni et al. (2022) BHAD curve. Because of its sensitivity limit, eFEDS becomes highly incomplete at log LX <  45 at z ∼ 6 (see Fig. 9). The sample of Vito et al. (2018) is extracted from the Chandra Deep Fields. These surveys are smaller in area but deeper than eFEDS and can sample AGN efficiently down to luminosities log LX >  42.5. This difference in sensitivity explains the discrepancy seen at z ∼ 6 between the results of Vito et al. (2018) and the lower boundary obtained in this work: eFEDS misses quasars in the range 42.5 <  LX <  45, which still significantly contribute to black hole accretion. We also point out that the main and supplementary eFEDS catalogues are not spectroscopically complete. In this regard, the data point we derived should be considered a lower limit on the BHAD. Another source of discrepancy between the BHAD derived from various X-ray surveys is the use of photometric redshifts, which can potentially populate the z >  5 bin with interlopers. For our study, we only used X-ray sources with clear multi-wavelength identifications and spectroscopic redshifts. Following Volonteri et al. (2016), our results suggest that, assuming supernova-feedback-regulated black hole growth, most black hole accretion is dominated by extremely luminous AGN. Alternatively, the agreement with the prediction of Ni et al. (2022) indicates that at log LX >  44, black hole accretion is truly dominated by the most X-ray-luminous quasars at log LX >  45.

We have shown that the extrapolated XLF models by Vito et al. (2014), Ueda et al. (2014), Aird et al. (2015), Miyaji et al. (2015) and Georgakakis et al. (2015) underestimate the number of high-z quasar detections in eFEDS (see Fig. 10); however, it can be seen in Fig. 11 that the black hole accretion density derived from these models appears to be consistent with the one resulting from the eFEDS detections. This can be explained by the high X-ray to optical flux ratio for both eFEDS quasars, which results in significantly smaller bolometric corrections (see Fig. 8). The bolometric correction assumed for the conversion of XLFs to BHAD (Eq. (5)) from Duras et al. (2020) causes a higher extrapolated BHAD, despite the underprediction of actual luminous high-z sources in the field. In addition, the black hole accretion density is calculated in Eq. (6) as the efficiency-scaled total emissivity of the quasars detected in the z = 5.81 − 6.56 interval and is therefore inversely proportional to the sensitive volume probed by eFEDS at the luminosities and redshifts of these quasars. The X-ray luminosity-redshift configurations of the quasars detected in eFEDS, in particular that of SDSS J0836+0054, result in a larger sensitive volume (see Fig. 4) and therefore a lower contribution to the black hole accretion density.

6. Discussion and conclusions

We have characterised a z >  6 super-Eddington-accreting NLS1 with low black hole mass based on archival photometry and a new NIR spectrum. We discuss how our findings support the idea that z >  6 NLS1s potentially show physical properties that resemble those of their lower-redshift counterparts. At z = 6.56, J0921+0007 is the most distant X-ray-selected AGN to date and can therefore be used to impose constraints on the high-z XLF.

We derived a comparatively low black hole mass (for a sample of high-redshift quasars with comparable optical/UV luminosity, see e.g. Onoue et al. 2019), which implies that the source is accreting at a super-Eddington rate. The values reported in this work (MBH = (2.5 ± 0.3) × 108 M⊙ and λ = 2 . 3 − 0.3 + 0.4 $ \lambda = 2.3^{+0.4}_{-0.3} $) are consistent with the typical properties of local NLS1s (e.g. Sulentic et al. 2000; Collin & Kawaguchi 2004; Rakshit et al. 2017). We obtained a relatively steep power-law fit to the X-ray spectrum of the source: Γ = 3.2. Such a high value is usually found in the rest-frame soft band of archetypal low-z NLS1s (e.g. Boller et al. 1996; Brandt et al. 1997; Ojha et al. 2020). In the rest-frame hard band, NLS1s typically show photon indices below this value (∼2; e.g. Zhou & Zhang 2010). The steeper photon index found here can be driven by either the large accretion rate (Shemmer et al. 2006) or the presence of unresolved non-coronal components. Similar sources, in terms of rest-frame optical properties, have been discovered by Koptelova et al. (2017) and Bañados et al. (2021). The quasar CFHQS J1641+3755 at z = 6.04 was initially discovered by Willott et al. (2007). Willott et al. (2010) obtained NIR spectroscopy for this source with the NIRI instrument on the Gemini-North Telescope. It shows an MgII profile (FWHMMg II = 1740 ± 190 km s−1) that is very similar to the one observed in the MOIRCS spectrum of J0921+0007 presented in our work. According to the Rakshit et al. (2021) classification criterion, this makes it a high-z NLS1. The derived black hole mass and Eddington ratio are Mbh = 2.4 × 108 M⊙ and λ = 2.3, indicating that CFHQS J1641+3755 may be powered by a low-mass, strongly accreting black hole. Vito et al. (2019) report the X-ray observation of this quasar with Chandra. While it has a relatively modest bolometric luminosity, it is the second-most X-ray-luminous source in their sample, making it deviate from the αOX − LUV by 1.8σ with respect to the best-fitting relation of Steffen et al. (2006). Vito et al. (2019) also derive a steep photon index for this source (Γ = 2.56). We conclude that CFHQS J1641+3755 is another archetypal NLS1 at high redshift. To further support the NLS1 classification of J0921+0007, we measured the extent of the quasar proximity zone and present these results in Appendix A.

In Sect. 5.1 we show that the number of high-z source detections in the eFEDS field, combining the present work with the results from Wolf et al. (2021), is significantly higher than predictions from a large range of XLF models in the literature extrapolated out to z ∼ 6. eFEDS is the largest contiguous public X-ray survey to date with sufficient depth to investigate z ∼ 6 AGN demographics. It probes a cosmological volume that is sufficiently large to contain rare rare log LX >  45 quasars at high redshift, including the unexpected class of high-z NLS1s discussed in this work. The discrepancy between previous XLF models obtained using smaller pencil-beam or non-contiguous surveys underlines the necessity for wide surveys to obtain a realistic census of the rare, powerful sources at the bright end of the XLF (see e.g. Barlow-Hall et al. 2022).

Stacking the Chandra Deep Field South data from a sample of 3.5 <  z <  6.5 galaxies, Vito et al. (2016) show that the contribution of detected luminous quasars at z ∼ 6 to the black hole accretion density is higher than the one from stacked undetected sources by an order of magnitude. These findings corroborate the results of Volonteri et al. (2016), who concluded that most of the black hole growth is supplemented by luminous quasars (Lbol >  1043 erg s−1) in massive halos (> 5 × 1011 M⊙). The accretion density derived from the two detected quasars in eFEDS is consistent with these previous results. At the flux limit of eFEDS, it is only possible to sample the ultra-luminous population, L2 − 10 keV >  1045 erg s−1. Despite this sensitivity limit, our results are already consistent with the predictions from Volonteri et al. (2016) and Ni et al. (2022), indicating that most of the black hole growth is in fact driven by X-ray-ultra-luminous quasars, above the eROSITA sensitivity limit. J0921+0007 is an unexpected member of this category of extreme quasars. Its X-ray luminosity is significantly higher than the value extrapolated from the αOX − LUV relation. In order to quantify how much of the accretion density is in fact driven by young, super-Eddington black holes, a wider survey area will be required at this depth to obtain a more informative sample. This will be made possible in the cumulative eROSITA All-Sky Survey (Merloni et al. 2012, see also Seppi et al. 2022).

2

At this stage the choice of the spectral shape is arbitrary. The aim here is a consistent comparison of the eFEDS and Chandra data.

3

Assuming a steeper power-law slope of α = −1.5, Ishimoto et al. (2020) adopted a brighter value M1450 = −26.16 ± 0.29.

Acknowledgments

JW acknowledges support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy - EXC-2094 - 390783311. He would also like to thank Peter Predehl for his help with the observation presented in this work. MO acknowledges support by the Natural Science Foundation of China (12150410307). MB is supported by the European Innovative Training Network (ITN) “BiD4BEST” funded by the Marie Sklodowska-Curie Actions in Horizon 2020 (GA 860744). This work is based on data from eROSITA, the primary instrument aboard SRG, a joint Russian-German science mission supported by the Russian Space Agency (Roskosmos), in the interests of the Russian Academy of Sciences represented by its Space Research Institute (IKI), and the Deutsches Zentrum für Luft- und Raumfahrt (DLR). The SRG spacecraft was built by Lavochkin Association (NPOL) and its subcontractors, and is operated by NPOL with support from the Max Planck Institute for Extraterrestrial Physics (MPE). The development and construction of the eROSITA X-ray instrument was led by MPE, with contributions from the Dr. Karl Remeis Observatory Bamberg & ECAP (FAU Erlangen-Nuernberg), the University of Hamburg Observatory, the Leibniz Institute for Astrophysics Potsdam (AIP), and the Institute for Astronomy and Astrophysics of the University of Tübingen, with the support of DLR and the Max Planck Society. The Argelander Institute for Astronomy of the University of Bonn and the Ludwig Maximilians Universität Munich also participated in the science preparation for eROSITA. The eROSITA data shown here were processed using the eSASS software system developed by the German eROSITA consortium. The scientific results reported in this article are based to a significant degree on observations made by the Chandra X-ray Observatory. This research is based on data collected at the Subaru Telescope, which is operated by the National Astronomical Observatory of Japan. We are honored and grateful for the opportunity of observing the Universe from Maunakea, which has the cultural, historical, and natural significance in Hawaii. The Legacy Surveys consist of three individual and complementary projects: the Dark Energy Camera Legacy Survey (DECaLS; NOAO Proposal ID # 2014B-0404; PIs: David Schlegel and Arjun Dey), the Beijing-Arizona Sky Survey (BASS; NOAO Proposal ID # 2015A-0801; PIs: Zhou Xu and Xiaohui Fan), and the Mayall z-band Legacy Survey (MzLS; NOAO Proposal ID # 2016A-0453; PI: Arjun Dey). DECaLS, BASS and MzLS together include data obtained, respectively, at the Blanco telescope, Cerro Tololo Inter-American Observatory, National Optical Astronomy Observatory (NOAO); the Bok telescope, Steward Observatory, University of Arizona; and the Mayall telescope, Kitt Peak National Observatory, NOAO. The Legacy Surveys project is honored to be permitted to conduct astronomical research on Iolkam Du’ag (Kitt Peak), a mountain with particular significance to the Tohono O’odham Nation. NOAO is operated by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation. This project used data obtained with the Dark Energy Camera (DECam), which was constructed by the Dark Energy Survey (DES) collaboration. Funding for the DES Projects has been provided by the U.S. Department of Energy, the U.S. National Science Foundation, the Ministry of Science and Education of Spain, the Science and Technology Facilities Council of the United Kingdom, the Higher Education Funding Council for England, the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign, the Kavli Institute of Cosmological Physics at the University of Chicago, Center for Cosmology and Astro-Particle Physics at the Ohio State University, the Mitchell Institute for Fundamental Physics and Astronomy at Texas A&M University, Financiadora de Estudos e Projetos, Fundacao Carlos Chagas Filho de Amparo, Financiadora de Estudos e Projetos, Fundacao Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de Desenvolvimento Cientifico e Tecnologico and the Ministerio da Ciencia, Tecnologia e Inovacao, the Deutsche Forschungsgemeinschaft and the Collaborating Institutions in the Dark Energy Survey. The Collaborating Institutions are Argonne National Laboratory, the University of California at Santa Cruz, the University of Cambridge, Centro de Investigaciones Energeticas, Medioambientales y Tecnologicas-Madrid, the University of Chicago, University College London, the DES-Brazil Consortium, the University of Edinburgh, the Eidgenossische Technische Hochschule (ETH) Zurich, Fermi National Accelerator Laboratory, the University of Illinois at Urbana-Champaign, the Institut de Ciencies de l’Espai (IEEC/CSIC), the Institut de Fisica d’Altes Energies, Lawrence Berkeley National Laboratory, the Ludwig-Maximilians Universitat Munchen and the associated Excellence Cluster Universe, the University of Michigan, the National Optical Astronomy Observatory, the University of Nottingham, the Ohio State University, the University of Pennsylvania, the University of Portsmouth, SLAC National Accelerator Laboratory, Stanford University, the University of Sussex, and Texas A&M University. BASS is a key project of the Telescope Access Program (TAP), which has been funded by the National Astronomical Observatories of China, the Chinese Academy of Sciences (the Strategic Priority Research Program “The Emergence of Cosmological Structures” Grant # XDB09000000), and the Special Fund for Astronomy from the Ministry of Finance. The BASS is also supported by the External Cooperation Program of Chinese Academy of Sciences (Grant # 114A11KYSB20160057), and Chinese National Natural Science Foundation (Grant # 11433005). The Legacy Survey team makes use of data products from the Near-Earth Object Wide-field Infrared Survey Explorer (NEOWISE), which is a project of the Jet Propulsion Laboratory/California Institute of Technology. NEOWISE is funded by the National Aeronautics and Space Administration. The Legacy Surveys imaging of the DESI footprint is supported by the Director, Office of Science, Office of High Energy Physics of the U.S. Department of Energy under Contract No. DE-AC02-05CH1123, by the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility under the same contract; and by the U.S. National Science Foundation, Division of Astronomical Sciences under Contract No. AST-0950945 to NOAO. The Hyper Suprime-Cam (HSC) collaboration includes the astronomical communities of Japan and Taiwan, and Princeton University. The HSC instrumentation and software were developed by the National Astronomical Observatory of Japan (NAOJ), the Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), the University of Tokyo, the High Energy Accelerator Research Organization (KEK), the Academia Sinica Institute for Astronomy and Astrophysics in Taiwan (ASIAA), and Princeton University. Funding was contributed by the FIRST program from Japanese Cabinet Office, the Ministry of Education, Culture, Sports, Science and Technology (MEXT), the Japan Society for the Promotion of Science (JSPS), Japan Science and Technology Agency (JST), the Toray Science Foundation, NAOJ, Kavli IPMU, KEK, ASIAA, and Princeton University. This research made use of Astropy (http://www.astropy.org) a community-developed core Python package for Astronomy (Astropy Collaboration 2013, 2018). This research has made use of software provided by the Chandra X-ray Center (CXC) in the application packages CIAO and Sherpa. In addition this research made use of BXA (https://johannesbuchner.github.io/BXA/) and the corner package (Foreman-Mackey 2016).

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Appendix A: Measuring the size of the proximity zone with an optical spectrum

Lyα proximity zones are ionised regions along the line of sight that are transparent to the quasar flux bluewards of the Lyα line. The surrounding inter-galactic medium (IGM) is thought to have been ionised by the UV radiation emitted by the quasar at the centre. Considering a discrete ionised HII region expanding in a neutral and uniform IGM, Haiman et al. (2001) related the radius of the quasar proximity zone (or Stromgren spheres) to the emission rate of ionising photons, N ˙ ion $ \dot{N}_{\mathrm{ion}} $, the mean neutral hydrogen density in the IGM, nH I, and the lifetime of the quasar, tq:

R H i i = ( 3 N ˙ ion t q 4 π n H i ) 1 / 3 . $$ \begin{aligned} R_{\mathrm{H}ii } = \left( \frac{3\dot{N}_{\rm ion} \, t_{\rm q}}{4\pi n_{\mathrm{H}i }} \right)^{1/3} .\end{aligned} $$(A.1)

The radius of the proximity zone of J0921+0007 has already been measured to be Rp = 3.05 ± 0.45 pMpc by Ishimoto et al. (2020) in the context of the SHELLQs survey (proper distance in Mpc). They used the low signal-to-noise ratio (S/N) discovery spectrum of the quasar taken with the Optical System for Imaging and low-Intermediate Resolution Integrated Spectroscopy (OSIRIS) at the 10.4 m Gran Telescopio Canarias (GTC; 0.9 ks Matsuoka et al. 2018a). With the availability of precise [CII] redshift measurements from Yang et al. (2021), z = 6.5646 ± 0.0003, we could improve upon this measurement. We re-observed J0921+0007 on February 28, 2022, with the LDSS3-C spectrograph mounted at the Magellan-Clay Telescope of the Las Campanas Observatory (Chile). A long-slit spectrum was obtained with the VPH-Red grism, which covers a range of about 6000–10500 Å with a dispersion of about 1.16 Å/px. A 1″ slit was used, which allowed a spectral resolution of about 4.7 Å to be reached. An exposure time of 3 ×1200 s was applied to effectively remove cosmic rays. The seeing was around 0.6–0.7″. We reduced the spectra with IRAF following the classic procedure of overscan subtraction, flat-field correction, and wavelength calibration. The standard star LTT3864 was observed with the same aperture slit to perform the flux calibration. Finally, the three exposures were sky-subtracted and averaged.

The radius of the proximity zone was measured following the methodology of Fan et al. (2006). The spectrum was normalised by a model for the continuum and smoothed by convolving a boxcar function of size 20 Å with the signal. The edge of the proximity zone was then set to be the wavelength at which the continuum-normalised flux bluewards of Lyman α first drops below 10% of the extrapolated model. In practice, the wavelength λedge is found as the wavelength at which the first of three consecutive pixels of the smoothed spectrum are below this threshold (Eilers et al. 2017).

The continuum bluewards of the Lyman α line is strongly affected by absorption and needs to be reconstructed. This can be achieved by performing a principal component analysis on the continua of lower-redshift quasars (Francis et al. 1992; Suzuki et al. 2005; Pâris et al. 2011). Following this method, quasar spectra qmod were modelled as the sum of an average spectrum and projections along principal components as

q mod ( λ ) ∼ μ ( λ ) + ∑ j = 1 m c j ξ j ( λ ) , $$ \begin{aligned} q_{\rm mod}(\lambda ) \sim \mu (\lambda ) + \sum _{j=1}^{m} c_j \xi _j(\lambda ) ,\end{aligned} $$(A.2)

where μ is an average quasar spectrum , ξj is the j-th principal component and cj a weight specific to this quasar. In order to reconstruct the blue side of the spectrum (λ < 1216 Å) from the red side (λ > 1216 Å) for high-redshift quasars, two sets of principal components and associated weights were derived from lower-redshift training samples, one for the full probed wavelength range (e.g. 1020−2000 Å) and one only for the red range. Projections from red-range weights to full-range weights were then derived.

While Eilers et al. (2017) use a mean quasar spectrum and principal component projections derived by Pâris et al. (2011), Ishimoto et al. (2020) used results by Suzuki et al. (2005), since their principal components are derived from fainter quasars, which better represent the SHELLQs quasars. We refer to these work for more details on the continuum reconstruction technique. For our quasar spectrum, we measured the proximity zone using projections from Pâris et al. (2011). The radius of the proximity zone is then: Rp = (dq − dedge)/(1 + zq), where zq is the quasar redshift, dq and dedge are the comoving distances derived from zq and the redshift of the edge of the proximity zone: zedge = λedge/1215.67@@@−1. Accounting solely for the uncertainty in the [CII] redshift reported by Yang et al. (2021), we obtained Rp = 3.05 ± 0.01 Mpc, a result consistent with the measurement of Ishimoto et al. (2020). In addition, we can account for systematic uncertainties on the [CII] redshift by applying a conservative offset δv = 100 km s−1 in quadrature (Eilers et al. 2020). At z = 6.56, such a velocity offset results in an additional redshift systematic of σz, syst = 0.0025. We obtained Rp = 3.05 ± 0.13 pMpc.

Since the size of the proximity zone is expected to depend on the quasar luminosity, tracing the redshift evolution of Rp usually requires its measurements to be corrected to a common scale, that is, normalised to the same absolute magnitude at 1450 Å, M1450. Following the relation by Eilers et al. (2017),

R p , corr = R p × 10 0.4 ( 27 + M 1450 ) / 2.35 , $$ \begin{aligned} R_{\rm p,corr}=R_{\rm p} \times 10^{0.4(27+M_ {1450})/2.35}, \end{aligned} $$(A.3)

we obtained Rp, corr = 5.48 ± 0.72pMpc. Here we have used M1450 = −25.55 ± 0.23, as derived from the NIR spectral slope (see Sect. 3.1)3. The evolution of the size of quasar proximity zones with redshift has been extensively investigated (e.g. Carilli et al. 2010; Venemans et al. 2015; Mazzucchelli et al. 2017; Eilers et al. 2017; Davies et al. 2020). From a sample of z <  6.6 quasars, Eilers et al. (2017) recover a relatively shallow redshift evolution:

R p , corr ≈ 4.86 pMpc × ( 1 + z 7 ) − 1.44 . $$ \begin{aligned} R_{\rm p,corr} \approx 4.86 \, \mathrm{pMpc} \times \left( \frac{1+z}{7}\right) ^{-1.44} .\end{aligned} $$(A.4)

At z = 6.56, the average luminosity-corrected proximity zone radius is Rp, corr ≈ 4.34 pMpc. Similarly, using the luminosity scaling of Ishimoto et al. (2020),

R p , corr , − 25 = R p × 10 0.4 ( 25 + M 1450 ) / 1.80 , $$ \begin{aligned} R_{\rm p,corr,-25}=R_{\rm p} \times 10^{0.4(25+M_ {1450})/1.80}, \end{aligned} $$(A.5)

we obtained a corrected proximity zone radius Rp, corr, −25 = 2.36 ± 0.40 pMpc, which is larger than their prediction of the best-fit Rp, corr, −25 − z relation: R p , corr , − 25 ¯ = 1.37 ± 0.23 pMpc $ \bar{R_{\mathrm{p,corr,-25}}}=1.37 \pm 0.23 \, \mathrm{pMpc} $.

The luminosity-scaled proximity zone radius of J0921+0007 is thus relatively large with respect to the bulk of the high-redshift quasar population. Indeed, as can be seen from the unsmoothed spectrum presented in Fig. A.1, the profile of the strong Lyman α line appears double-peaked with a sharp absorption feature at the exact wavelength of Lyman α. The strong transmission bluewards of the absorption edge indicates that the quasar is embedded in a large and completely ionised region of the IGM. The unabsorbed blue wing of the Lyman α drives the overall line luminosity reported by Matsuoka et al. (2018a).

thumbnail Fig. A.1.

Continuum-normalised LDSS3 spectrum of J0921+0007. The size of the proximity zone is defined here as the proper distance between the rest-frame wavelength of Lyα (dashed orange line) and the wavelength where the smoothed continuum normalised flux (solid red line) first drops below 0.1% of its extrapolated value, marked here by a solid green line. The unsmoothed continuum-normalised spectrum is shown in black.

Uncertainty on the absorbed quasar continuum can significantly affect the measurement of the proximity zone. Performing Monte Carlo simulations, Ishimoto et al. (2020) show that the low S/N causes an uncertainty (0.71 pMpc) in their Rp measurement that is larger than the uncertainty due to the redshift error. We estimated the uncertainty in Rp imprinted by the uncertainty on the flux measurement in the red part of the spectrum. For this, we generated 1000 spectra by perturbing the red part of the LDSS3 spectrum, at wavelengths in the observed frame at < 1216@@@×(1 + z). We applied Gaussian random noise accounting for the RMS of the spectrum at 9000 Å, σ = 2.285 × 10−18 erg s−1cm−2. This is a conservative estimate of the spectral noise since the higher transmission close to the Lyman break is expected to yield lower flux uncertainties. For each of these simulated spectra, we computed the radius of the proximity zone and obtained R p = ( 3 . 00 − 0.58 + 0.49 ) pMpc $ R_{\mathrm{p}}=(3.00^{+0.49}_{-0.58}) \, \mathrm{pMpc} $. The error related to the uncertainties bluewards of the Lyman α line therefore dominates uncertainties due to the redshift estimate. We stress the necessity of a higher S/N spectrum to confirm the large size of the proximity zone. We note that the LDSS3 spectrum shows no evolution in the spectral shape of Lyα with respect to the OSIRIS discovery spectrum presented by Matsuoka et al. (2018a). We repeated the measurement of the proximity zone radius of J0921+0007, using the OSIRIS discovery spectrum, accounting for the flux uncertainties redwards of the Lyα emission line. We obtained R p = 3 . 63 − 0.44 + 1.00 pMpc $ R_{\mathrm{p}}=3.63^{+1.00}_{-0.44} \, \mathrm{pMpc} $. While this result shows larger uncertainties, it is consistent within 1σ with the measurement on our new LDSS3 spectrum.

The relatively large proximity zone can have two origins. The first hypothesis is that the active phase of the quasar exceeds the typical lifetime of quasars tq ∼ 106 yr (e.g. Khrykin et al. 2016; Davies et al. 2019; Khrykin et al. 2021; Eilers et al. 2021). This interpretation is inconsistent with the idea that the low black hole mass of J0921+0007 is indicative of a young SMBH. The luminosity-scaled proximity zone radius Rp, corr, −25 = 2.36 ± 0.40 pMpc is relatively large for the black hole mass measured in this work (Ishimoto et al. 2020, see their Fig. 8). Alternatively the quasar has alternated between highly luminous phases and quiescent phases. The proximity zone could have grown during extremely luminous phases of the AGN. Such large amplitude variability in the ionising continuum emission is indeed expected in NLS1s (Collier et al. 2001; Romano et al. 2002). The SED of NLS1s is also potentially quite different to that of broad-line quasars, which can further affect the ionisation balance in the proximity zone. J0921+0007 is the second most Lyman α luminous quasar of the SHELLQs survey (Matsuoka et al. 2016, 2018a, 2019; Matsuoka et al. 2022), which implies that the broad-line region gas is exposed to strong ionising radiation. This is also confirmed by its unusually high X-ray luminosity (Fig. 4 and 6). We therefore propose that the quasar is currently undergoing a super-Eddington accretion phase that generates powerful UV/X-ray radiation, which in turn ionises the surrounding IGM efficiently. It is in such phases that the proximity zone grows to relatively large radii. The ionising continuum radiation of NLS1s is, however, expected to show large amplitude short-term variability. The response of non-equilibrium blinking light-bulb quasar models has been studied by Davies et al. (2020); however, the timescales on which NLS1s are expected to show X-ray/UV variability (hours to days) are much smaller than the shortest timescales explored in this work (100 yr). Capturing X-ray variability on timescales of days for this quasar would require a long monitoring campaign (> 180 ks; e.g. Nanni et al. 2018; Yang et al. 2022). The confirmation of short timescale X-ray variability could explain the relatively large proximity zone of J0921+0007. This could imply phases of even more extreme X-ray loudness. In addition, a long exposure would put more stringent constraints on the spectral shape of the source.

All Tables

Table 1.

Basic source and counterpart information.

In the text
Table 2.

X-ray properties of J0921+0007.

In the text

All Figures

thumbnail Fig. 1.

Probability of finding any of the 31 spectroscopically confirmed quasars in the eFEDS footprint within a distance R of a spurious X-ray source. The solid (dashed) red line shows the minimum (maximum) distance between the eROSITA source and J0921+0007, accounting for the positional uncertainty of the X-ray source.
In the text
thumbnail Fig. 2.

X-ray image cutouts in the region of J0921+0007. Left: 4′ × 4′ eROSITA/eFEDS image in the 0.2 − 2.3 keV band, smoothed with a Gaussian kernel. The image is centred on the optical position of the quasar J0921+0007. The concentric circles have radii of 30″ (dotted) and 60″ (dashed). Right: 30″ × 30″ high-resolution Chandra image in the energy range 0.5–7 keV. The ellipse shows a wavdetect-detected source at the optical position of the quasar (marked by a red cross).
In the text
thumbnail Fig. 3.

Marginal posterior distributions of the photon index, Γ, and the hard X-ray luminosity from the BXA fit to the Chandra spectrum.
In the text
thumbnail Fig. 4.

Hard X-ray luminosities of X-ray-detected high-redshift quasars. All eROSITA-detected quasars are marked by a red square. The normalised area of eFEDS that is sensitive to sources modelled by a fiducial absorbed power law (Γ = 3!!!! and NH = 3 × 1020 cm−2) is represented by the background colour map. J0921+0007, shown here as a pink square, lies at the detection limit of the eFEDS survey, as expected from the low eROSITA detection likelihood.
In the text
thumbnail Fig. 5.

Ks-band MOIRCS spectrum of J0921+0007. The combined fit to the continuum and MgII line is shown by the solid red curve. The decomposition in continuum (blue), the Fe II pseudo continuum (green), and the Gaussian line fit (yellow) are also shown.
In the text
thumbnail Fig. 6.

X-ray to UV slope αOX as a function of L2500 for quasars at z >  5.7. Because of its strong X-ray emission, J0921+0007 (pink square) deviates significantly from the αOX-L2500 relation, the 1σ confidence interval of which is delimited by the dotted red lines (Nanni et al. 2017). The sensitivity of eFEDS to sources modelled by a steep absorbed power law (Γ = 3 and NH = 3 × 1020 cm−2) is traced by the colour map. The hexagonal pattern represents a sample of XMM-detected SDSS quasars presented by Lusso & Risaliti (2016).
In the text
thumbnail Fig. 7.

X-CIGALE fit to the quasar optical, infrared, and X-ray photometry. Photometric points from HSC, LS8, UKIDSS, VIKING, and unWISE are marked by squares. The photometry that has been ignored for the SED fit is shown as red squares. The solid black line is the best-fitting model. The dashed blue line shows the fitted disc model and the dashed brown line the unconstrained torus emission. We also show the LDSS3 spectrum presented in Appendix A. The upper panel shows corresponding photometric filters.
In the text
thumbnail Fig. 8.

Bolometric correction for J0921+0007 (pink error bars) compared to predictions from Duras et al. (2020) for the full AGN population (solid blue line) and Lusso et al. (2012) for type 1 AGN (solid brown line). The dispersions are quoted at the 68% level (blue shaded area and brown shaded area). The strong X-ray emission of J0921+0007 with respect to its disc emission causes it to deviate at the > 1σ level from the typical AGN Kbol − Lbol. The green error bars show the bolometric correction for the second eFEDS high-z quasar (Wolf et al. 2021). We note that the bolometric correction of Lusso et al. (2012) is only valid up to log Lbol = 13; the extrapolation (light-shaded area) is shown for visualisation purposes only.
In the text
thumbnail Fig. 9.

Slices of the simulated eFEDS sensitive area cube. Left: sensitive area for fixed Γ = 2 as a function of L2 − 10 keV and z. Right: sensitive area as a function of Γ and L2 − 10 keV for fixed redshift z = 6. The dotted white (solid black) line shows the parameter configurations at 50% (5%) of the normalised sensitive area.
In the text
thumbnail Fig. 10.

Inverse cumulative source count predictions in eFEDS from extrapolated XLF models from Vito et al. (2014), Ueda et al. (2014), Aird et al. (2015), Miyaji et al. (2015) and Georgakakis et al. (2015) integrated over all luminosities. The shaded and hashed areas show the 1σ confidence intervals derived from the model parameter uncertainties. These count predictions depend on the sensitive eFEDS area (Eq. (3)) and therefore on the assumed spectral model for the AGN. We show the predictions for two different photon indices, Γ = 2.2 and Γ = 3.2, respectively in the left and right panels. The black line shows the inverse cumulative distribution of detection in eFEDS. No model supports two detections in eFEDS for the chosen photon indices. At Γ = 2.2, the Vito et al. (2014), Ueda et al. (2014), Miyaji et al. (2015) and Georgakakis et al. (2015) models support the unique detection at z ≥ 5.81. The central and lower panels present the Poisson probabilities of the XLF models supporting respectively one and two detections in eFEDS beyond a given redshift threshold. These probabilities are overall low and demonstrate the discrepancy between the eFEDS counts and the model predictions. With Γ = 3.2 the detection probabilities are lower than with Γ = 2.2.
In the text
thumbnail Fig. 11.

Black hole accretion rate density (BHAD) for various XLF models and growth simulations. XLF models from Vito et al. (2014), Ueda et al. (2014), Miyaji et al. (2015) and Georgakakis et al. (2015) are extrapolated beyond z = 5 (pale continuation of the red BHAD curves), and the prediction from Buchner et al. (2015) is given over the full z = 4 − 7 range. We include observational results from Vito et al. (2018) from the Chandra Deep Fields. The measurement derived from the high-redshift quasar detections in eFEDS is shown as a yellow square. Our result is consistent with theoretical predictions restricted to the highest halo (and black hole) masses (Volonteri et al. 2016; Ni et al. 2022). For comparison, a scaled version of the star formation rate density from Bouwens et al. (2015) is shown as beige-shaded and dashed area.
In the text
thumbnail Fig. A.1.

Continuum-normalised LDSS3 spectrum of J0921+0007. The size of the proximity zone is defined here as the proper distance between the rest-frame wavelength of Lyα (dashed orange line) and the wavelength where the smoothed continuum normalised flux (solid red line) first drops below 0.1% of its extrapolated value, marked here by a solid green line. The unsmoothed continuum-normalised spectrum is shown in black.
In the text

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