Discovery of a hyperluminous quasar at $z$ = 1.62 with Eddington ratio $>$ 3 in the eFEDS field confirmed by KOOLS-IFU on Seimei Telescope

The target (eFEDSJ0828–0139) was selected from the HyLIRG candidate sample provided by Toba et al. (2022b). A full description of HyLIRG candidate selection is presented by Y. Toba et al. (in preparation). Hence, we present a summary. Toba et al. (2022b) performed the spectral energy distribution (SED) analysis for Wide-field Infrared Survey Explorer (WISE: Wright et al. (2010)) 22 $\mu$m-selected sources in the eROSITA Final Equatorial Depth Survey (eFEDS: Brunner et al. (2022)), According to their $L_{\rm IR}$, 150 HyLIRG candidates were left, more than half of which have spectroscopic redshift ($z_{\rm spec}$) through the follow-up campaign, such as the Sloan Digital Sky Survey (SDSS; York et al. (2000)) V/eFRDS observations (Almeida et al., 2023).

Our target is the brightest source in the optical ($r$-mag = 16.78) among our HyLIRG candidate sample with photometric redshift ($z_{\rm phot}$). eFEDSJ0828–0139 is classified as an unobscured AGN (i.e., quasar) with a hydrogen column density of $\log\,N_{\rm H}\sim 20.8$ cm^-2 through an eROSITA spectral analysis (Liu et al., 2022). This object has also been selected as an AGN/quasar candidate from a multi-wavelength photometric perspective, such as WISE (Secrest et al., 2015; Assef et al., 2018) and Gaia (Bailer-Jones et al., 2019; Wu et al., 2023). Its $z_{\rm phot}$ is estimated by some studies, for instance, $z_{\rm phot}=2.825^{+0.405}_{-0.215}$ (Richards et al., 2015), $1.321\pm 0.611$ (Duncan, 2022) and $1.367^{+0.192}_{-0.126}$ (Salvato et al., 2022), indicating a large redshift uncertainty.

To derive AGN properties such as AGN bolometric luminosity ($L^{\rm AGN}_{\rm bol}$), $M_{\rm BH}$, and $\lambda_{\rm Edd}$ of our quasar, spectral fitting to KOOLS-IFU spectrum was conducted using the Quasar Spectral Fitting package (QSFit v1.3.0⁶⁶6https://qsfit.inaf.it: Calderone et al. (2017)). We fitted the KOOLS-IFU spectrum as a combination of (i) an AGN continuum with a single power-law, (ii) a Balmer continuum modeled by Grandi (1982) and Dietrich et al. (2002), (iii) iron-blended emission lines with UV-optical templates (Véron-Cetty et al., 2004; Vestergaard & Wilkes, 2001), and (iv) emission lines with Gaussian components. QSFit fits all the components simultaneously following a Levenberg-Marquardt least-squares minimization algorithm with MPFIT (Markwardt, 2009) procedure. Spectral fitting was executed after correcting for the galactic extinction provided by Schlegel et al. (1998) with the Milky Way attenuation curve (O’Donnell, 1994).

The main purpose of this spectral fitting is to measure the full width at half maximum (FWHM) of Mg ii $\lambda$2798 and continuum luminosity at 3000 Å, $\lambda\,L_{\lambda}{\rm(3000\,\AA)}$, that are ingredients for $M_{\rm BH}$ estimates. Based on outputs from QSFit, we estimated $M_{\rm BH}$ through a single-epoch recipe provided by Vestergaard & Osmer (2009);

$L^{\rm AGN}_{\rm bol}$ was converted from BC${}_{\rm 3000}\times\lambda L_{\lambda}\,{\rm(3000\,\AA)}$ where BC₃₀₀₀ = $5.2\pm 0.2$ is the bolometric correction (Runnoe et al., 2012). Following Toba et al. (2021a), the uncertainty in $M_{\rm BH}$ is calculated through the error propagation of Equation 1 while the uncertainty in $L^{\rm AGN}_{\rm bol}$ is propagated from 1$\sigma$ errors of $\lambda L_{\lambda}\,{\rm(3000\,\AA)}$ and BC₃₀₀₀.

We collected the multi-wavelength data from X-ray to FIR in the same manner as Toba et al. (2022b). We refer the reader to that paper for details, but in short, we used GALEX (Martin et al., 2005) for ultraviolet (UV) data, SDSS for optical data, UKIDSS (Lawrence et al., 2007) for near-IR (NIR) data, WISE for mid-IR (MIR) data, and AKARI (Murakami et al., 2007) for FIR data. UV-to-MIR photometry is corrected for Galactic extinction (Schlegel et al., 1998). In addition, we have added photometry obtained from SCUBA-2 observation (section 2.2.2). Because our target was not detected at 450 and 850 $\mu$m, we input their 3$\sigma$ upper limits for the SED fitting, which is crucial to pin down the FIR SED of eFEDSJ0828$-$0139.

We employed the Code Investigating GALaxy Emission (CIGALE ver.2022.1⁷⁷7https://cigale.lam.fr/2022/07/04/version-2022-1/; Burgarella et al. (2005); Noll et al. (2009); Boquien et al. (2019); Yang et al. (2020, 2022)). This code allows us to include values for many parameters related to, e.g., the star formation (SF) history (SFH), single stellar population (SSP), attenuation law, AGN emissions, and dust emissions by considering the energy balance between the UV/optical and IR (see, e.g., Hashiguchi et al. (2023); Toba et al. (2024)). Table 2.4 summarizes the parameter ranges used in the SED fitting with CIGALE. These parameter sets are the same as presented in Toba et al. (2021b) optimized for HyLIRG candidates. A full description of the assumed models is provided by Toba et al. (2021b); hence, we provide a summary. We assume a delayed SFH with recent starburst (Ciesla et al., 2017) with parameterizing e-folding time of the main stellar population model ($\tau_{\rm main}$), the age of the main stellar population in the galaxy, the age of the burst, and the ratio of the SF rate (SFR) after and before the burst (R_sfr). A starburst attenuation curve (Calzetti et al., 2000; Leitherer et al., 2002) is used for dust attenuation, in which we parameterize the color excess of the nebular emission lines, $E(B-V)_{\rm lines}$. We chose the SSP model (Bruzual & Charlot, 2003), assuming the initial mass function (IMF) of Chabrier (2003), and the standard nebular emission model with the implementation of the new CLOUDY HII-region model (Villa-Vélez et al., 2021) is included in CIGALE (Inoue, 2011). AGN emission is modeled by using the SKIRTOR (Stalevski et al., 2016). This torus model consists of seven parameters: torus optical depth at 9.7 $\mu$m ($\tau_{\rm 9.7}$), torus density radial parameter ($p$), torus density angular parameter ($q$), the angle between the equatorial plane and edge of the torus ($\Delta$), the ratio of the maximum to minimum radii of the torus ($R_{\rm max}/R_{\rm min}$), viewing angle ($\theta$), and AGN fraction in total IR luminosity ($f_{\rm AGN}$). Dust grain emission is modeled by Draine et al. (2014) in which we parameterize the mass fraction of PAHs ($q_{\rm PAH}$), the minimum radiation field ($U_{\rm min}$), the power-low slope of the radiation field distribution ($\alpha$), and the fraction illuminated with a variable radiation field ranging from $U_{\rm min}$ to $U_{\rm max}$ ($\gamma$). X-ray emission is modeled with a fixed power-law photon index of AGN (Liu et al., 2022), and only $\alpha_{\rm OX}$ is parameterized.

Figure 1 shows the optical spectrum of eFEDSJ0828$-$0139 taken by the KOOLS-IFU, where several emission lines such as Al iii$\lambda$1860, Si iii]$\lambda$1892, C iii]$\lambda$1909 and Mg ii are clearly detected. The result of the spectral fitting with QSFit is also shown in Figure 1. The spectroscopic redshift of eFEDSJ0828$-$0139 measured from Mg ii is $z_{\rm spec}=1.6224\pm 0.0007$. The FWHM of Mg ii and the continuum luminosity at 3000 Å  are FWHM (Mg ii) = $(1.9\pm 0.2)\times 10^{3}$ km s^-1 and $\lambda L_{\lambda}\,{\rm(3000\,\AA)}=(56.1\pm 0.4)\times 10^{45}$ erg s^-1, respectively, which results in the black hole mass of $M_{\rm BH}=(6.2\pm 1.2)\times 10^{8}$ $M_{\odot}$. We note that Buendia-Rios et al. (2023) recently provided a recipe for virial BH mass based on Al iii line. We find that the BH mass using their recipe is $\log\,(M^{\rm AlIII}_{\rm BH}/M_{\odot})\sim 8.5$, which is roughly consistent with Mg ii-based $M_{\rm BH}$. Eddington luminosity is $L_{\rm Edd}=(8.0\pm 0.2)\times 10^{46}$ erg s^-1. The AGN bolometric luminosity is $L^{\rm AGN}_{\rm bol}=(2.9\pm 0.1)\times 10^{47}$ erg s^-1, indicating a hyper-luminous quasar as similar to WISE-SDSS selected, WISSH quasars at $z>2$ (Duras et al., 2017). Consequently, the Eddington ratio of eFEDSJ0828$-$0139 is estimated to be $\lambda_{\rm Edd}=3.6\pm 0.7$, making it a prominent quasar with BH at super-Eddington accretion.

Martínez-Aldama et al. (2018) reported that such quasars with extremely-high $\lambda_{\rm Edd}$ (so-called extreme accretor (xA) quasars: Marziani & Sulentic (2014)) shows relatively strong Al iii and Si iii] emissions compared with C iii] and conspicuous Fe ii lines in their rest UV-to-optical spectra. We find that the line flux ratio for Al iii/Si iii] and C iii]/Si iii] is $0.44\pm 0.18$ and $1.25\pm 0.27$, respectively. These values satisfy the selection criteria of xA quasars (Marziani & Sulentic, 2014), supporting that eFEDSJ0828$-$0139 is an extremely high $\lambda_{\rm Edd}$ quasar.

A caveat is that BH mass estimated by a single-epoch method (i.e., Equation 1) has a sizeable systematic uncertainty up to 0.4 dex (see, e.g., Shen (2013)), which has also been supported by the recent reverberation mapping with the SDSS (Shen et al., 2024). This means that the estimated Eddington ratio also potentially has a large uncertainty. We confirm the estimated BH mass is consistent with that using another emission line (albeit a single epoch) and obtain evidence of a high Eddington ratio inferred from emission line ratios. However, our $M_{\rm BH}$ and $\lambda_{\rm Edd}$ do not include the systematic errors mentioned above, which should be kept in mind for the following discussion.

Figure 2 shows the best-fit SED of eFEDSJ0828$-$0139, demonstrating that the observed SED is moderately well-fitted by the stellar, nebular, AGN, and SF components with a reduced $\chi^{2}$ of 4.9. The derived total IR luminosity is $L_{\rm IR}=(6.8\pm 1.8)\times 10^{13}$ $L_{\odot}$, which confirms that our target is an HyLIRG. The stellar mass ($M_{*}$) and star formation rate (SFR) are $M_{*}=(3.9\pm 2.0)\times 10^{11}$ $M_{\odot}$ and SFR = $(1.3\pm 0.5)\times 10^{3}$ $M_{\odot}$ yr^-1, respectively. These are typical values of HyLIRGs reported in previous works (e.g., Gao et al. (2021)). The BH mass and stellar mass ratio of eFEDSJ0828$-$0139 is $\log(M_{\rm BH}/M_{*})$ = $-$2.8 $\pm$ 0.2, which agrees with the results reported in Suh et al. (2020).

A potential issue caused by the SED fitting with upper limits of AKARI and SCUBA-2 data is about SF (i.e., dust emission from host galaxy) contribution to the total SED, which is also relevant to the accuracy of IR luminosity and SFR. The CIGALE takes into account energy conservation of the amount of UV/optical radiation from SF and AGN absorbed by a dust and the amount of IR radiation re-emitted by the dust when the SED fitting. Hence, FIR SED is expected to be constrained reasonably. Nevertheless, the lack of deep FIR data around the peak of the FIR SED would affect the results. To test the requirement to add an SF component to the SED fitting, we employ the Bayesian information criterion (BIC; Schwarz (1978)) for two fits that are derived with and without an SF component. The BIC is defined as BIC = $\chi^{2}$ + $k$ $\times$ ln($n$), where $\chi^{2}$ is non-reduced chi-square, $k$ is the number of degrees of freedom (DOF), and $n$ is the number of photometric data points used for the fitting, respectively. We then compare the results of two SED fittings without/with the SF (dust emission) module by using $\Delta$BIC = BIC_woSF – BIC_wSF. The $\Delta$BIC tells whether the SF/dust model is needed to provide a better fit by considering the difference in DOF (e.g., Ciesla et al. (2017); Buat et al. (2019); Aufort et al. (2020); Toba et al. (2020b)). If $\Delta$BIC is larger than two, adding the SF/dust component provides a better fit than not (Liddle, 2004; Stanley et al., 2015). The resultant value for eFEDSJ0828$-$0139 is $\Delta$BIC = 7.3, which suggests that the SF/dust component is required to explain the observed SED.

We also estimate IR luminosity and SFR based on the SED fitting without using SCUBA-2 data to see how even the upper limits of SCUBA-2 data are crucial to constrain those quantities. The resultant values are $L_{\rm IR}=(7.3\pm 1.9)\times 10^{13}$ $L_{\odot}$ and SFR = $(1.6\pm 0.6)\times 10^{3}$ $M_{\odot}$ yr^-1, which suggests that SCUBA-2 data prevents SFR and $L_{\rm IR}$ from being overestimated. In summary, dust emission from the host galaxy requires explaining the observed SED, and SCUBA-2 data are crucial to pin down the FIR SED, even if they are upper limits. Hence, potential uncertainties on IR luminosity and SFR are expected to be small in this work.

Figure 3 shows the Eddington ratio as a function of redshift. We compare the Eddington ratio from a value-added catalog⁸⁸8http://quasar.astro.illinois.edu/paper_data/DR16Q/dr16q_prop_May16_2023.fits.gz (Wu & Shen, 2022) for the SDSS DR16 quasar catalog (Lyke et al., 2020), in which the continuum and emission-line properties for 750,414 broad-line quasars are provided. Note that 25 sources have $\lambda_{\rm Edd}>3$ among the quasars with $1<z<2$. We visually check their spectra and find that the Eddington ratios of the majority of these quasars are poorly constrained with a large uncertainty of $\lambda_{\rm Edd}$ ($\sigma_{\lambda_{\rm Edd}}$) partially due to the low SN of the emission lines (C iv and Mg ii). If we restrict ourselves to $\lambda_{\rm Edd}/\sigma_{\lambda_{\rm Edd}}>5$ (that is similar to eFEDSJ0828$-$0139), only four objects remain. We also compare $\lambda_{\rm Edd}$ of WISSH quasars (Vietri et al., 2018) and extremely red quasars (ERQs: Perrotta et al. (2019)) that are also known as high $\lambda_{\rm Edd}$ quasars.

We find that eFEDSJ0828$-$0139 has the highest $\lambda_{\rm Edd}$ at $z\sim$ 1.6, which is even higher than the ERQs and WISSH quasars at $z>2$. In addition to a high BH accretion rate, this object has an extremely high SFR ($>1000$ $M_{\odot}$ yr^-1) as described in section 3.2. Given the fact that $M_{\rm BH}/M_{*}$ value is consistent with local relation (Suh et al., 2020), we may be witnessing the growing phase of both SMBH and its host galaxy in the course of the galaxy–SMBH co-evolution, as expected by the numerical simulation.