Multiwavelength Spectral Energy Distribution Analysis of X-Ray Selected Active Galactic Nuclei at z = 0.2–0.8 in the Stripe 82 Region

We perform a systematic, multiwavelength spectral energy distribution (SED) analysis of X-ray detected active galactic nuclei (AGNs) at z = 0.2–0.8 with Sloan Digital Sky Survey (SDSS) counterparts in the Stripe 82 region, consisting of 60 type 1 and 137 type 2 AGNs covering a 2–10 keV luminosity range of 41.6<logLx<44.7 . The latest CIGALE code, where dusty polar components are included, is employed. To obtain reliable host and AGN parameters in type 1 AGNs, we utilize the image-decomposed optical SEDs of host galaxies by Li et al. based on the Subaru Hyper-Suprime Cam images. The mean ratio of black hole masses (M BH) and stellar masses (M stellar) of our X-ray detected type 1 AGN sample, log(MBH/Mstellar)=−2.7±0.5 , is close to the local relation between BH and stellar masses as reported by Li et al. for SDSS quasars. This ratio is slightly lower than that found for more luminous ( logLbol>45 ) type 1 AGNs at z ∼ 1.5. This can be explained by the AGN luminosity dependence of log(MBH/Mstellar) , which little evolves with redshift. We confirm the trend that the UV-to-X-ray slope (α OX) or X-ray-to-bolometric correction factor (κ 2–10) increases with AGN luminosity or Eddington ratio. We find that type 1 and type 2 AGNs with the same luminosity ranges share similar host stellar mass distributions, whereas type 2s tend to show smaller AGN luminosities than type 1s. This supports the luminosity-dependent (or Eddington-ratio-dependent) unified scheme.


Introduction
The cosmological evolution of galaxies and supermassive black holes (SMBHs) in their centers has been a mainstream subject of astronomical research.Many studies report a tight correlation between the SMBH mass (M BH ) and the galactic classical bulge mass (M bulge ) or the stellar velocity dispersion in the local Universe (z ∼ 0; e.g., Magorrian et al. 1998;Ferrarese & Merritt 2000;Gebhardt et al. 2000;Marconi & Hunt 2003;Häring & Rix 2004;Gültekin et al. 2009;Kormendy & Ho 2013).This indicates that SMBHs and their host galaxies have co-evolved by their growths affecting one another (e.g., Kormendy & Ho 2013).Active galactic nuclei (AGNs) represent the processes where the SMBH grows by mass accretion.A straightforward approach to witnessing the site of SMBH-galaxy coevolution is to study the properties of the host galaxies of AGNs (e.g., their stellar mass) and their relations to basic AGN parameters (e.g., the BH mass, luminosity, and obscuration).
X-ray observations are a powerful tool for searching for AGNs with high completeness, thanks to their strong penetrating power against gas and dust, particularly at high photon energies above 2 keV.They also provide clean AGN samples because of the small contamination by the host galaxy emission.Thus, a useful, widely used technique for tackling the issue is multiwavelength spectral energy distribution (SED) analysis of X-ray selected AGNs, which enables one to simultaneously constrain both AGNs and their host properties.
To reveal all the processes of SMBH growth, it is important to study various populations of AGNs.In general, AGNs are classified into two types by their optical spectral features: "type 1" AGNs, which show both broad emission lines and narrow ones, with typical velocities of ∼2000-20,000 km s −1 and <1000 km s −1 , respectively, and "type 2" AGNs, which show only narrow emission lines.They can also be classified by X-ray absorption by line-of-sight material: "unabsorbed" AGNs with typical hydrogen column densities of N H < 10 22 cm −2 and "absorbed" AGNs with N H > 10 22 cm −2 .The unified scheme of AGNs (Antonucci 1993) explains the differences between these AGN properties by the viewing angle with respect to the dusty torus.When intervening in the line of sight, the torus obscures the broadline region and absorbs direct X-ray emission from the hot corona located close to the SMBH.Generally, the optical and X-ray classifications of an AGN agree with each other (i.e., type 1 and type 2 AGNs correspond to unabsorbed and absorbed AGNs, respectively).A fraction of AGNs show mismatched classifications, however; for instance, Garcet et al. (2007) found that 12% of X-ray selected AGNs had intrinsically differing X-ray and optical classifications.The origins of the mismatches are still under debate (e.g., see Ogawa et al. 2021).Verification of the AGN unified scheme has been one of the fundamental issues in understanding AGN phenomena.

Goals of This Work
There are two main focuses of this paper.The first immediate objective is to establish the relation of the SMBH mass and the host stellar mass of X-ray selected AGNs as a function of AGN luminosity and redshift.For this purpose, we systematically analyze the SEDs of X-ray selected AGNs at redshifts z < 0.8 in the Sloan Digital Sky Survey (SDSS) Stripe 82 region (see Section 1.2), one of the best-studied multiwavelength fields covering a large area (31.3 deg 2 ), and combine the results with those obtained at z ∼ 1.5 from the Subaru/XMM-Newton Deep Field (SXDF; Furusawa et al. 2008;Ueda et al. 2008;Akiyama et al. 2015;Setoguchi et al. 2021), a deeper multiwavelength field covering an area of ∼1 deg 2 .The ultimate goal of this study is to reveal the origin of the cosmological evolution of the AGN luminosity function, as explained in the next subsubsection.The second objective is to test if the "AGN unified scheme" is valid in X-ray AGNs.The unified scheme assumes that all AGNs belong to intrinsically the same population, meaning that their host galaxies should be the same among different AGN types.This can be checked by comparing the host properties of type 1 and type 2 AGNs with similar AGN properties.

Relation between SMBH Mass and Stellar Mass
Past X-ray surveys of AGNs have revealed that the comoving spatial number density of lower-luminosity AGNs show a peaks at a lower redshift than that of higher-luminosity ones.This is often referred to as a "cosmic downsizing" phenomenon.A similar downsizing trend has also been found for galaxy evolution (e.g., Cowie et al. 1996;Kodama et al. 2004;Fontanot et al. 2009), supporting an SMBH-galaxy coevolution scenario.The origin of SMBH downsizing is still under debate (e.g., Draper & Ballantyne 2012;Fanidakis et al. 2012;Enoki et al. 2014;Shirakata et al. 2019).Some authors (e.g., Draper & Ballantyne 2012) suggest that there are two channels of SMBH growth, via major galaxy mergers and secular processes within a single galaxy, which are responsible for activating more luminous AGNs at higher redshifts and less luminous ones at lower redshifts, respectively.Thus, it is of great interest to investigate the host/AGN properties of lowluminosity AGNs (log L x < 43.5) at z < 1, where their number density is peaked, and to compare them with those of higherluminosity AGNs at z > 1.
The relation between SMBH mass and host stellar mass gives us an important clue to test whether the underlying mechanisms of coevolution are the same or not among AGNs at different redshift and luminosity ranges.Type 1 AGNs are ideal objects for this study, because M BH can be directly determined through measurements of broadline widths and continuum luminosities by single-epoch optical spectroscopy (e.g., Vestergaard & Peterson 2006;Jahnke et al. 2009;Merloni et al. 2010;Assef et al. 2011;Rakshit et al. 2020).Since it is difficult to spatially separate the bulge and disk components in the distant Universe, the relation between M BH and the total stellar mass (M stellar ) has been intensively investigated to discuss the coevolution in broadline AGNs (e.g., Shields et al. 2003;Matsuoka et al. 2015;Reines & Volonteri 2015;Sun et al. 2015;Yue et al. 2018;Ding et al. 2020;Ishino et al. 2020;Suh et al. 2020;Mountrichas 2023).It has been an issue to reliably estimate the total stellar mass or SMBH mass in a type 1 AGN, however, because it is often difficult to separate the contributions from the host galaxy and nucleus in the SED analysis.In a very luminous AGN, it is challenging to accurately extract the spectrum of the host galaxy, because the AGN dominates the IR-optical-UV emission, which could cause a large uncertainty in M stellar (e.g., Toba et al. 2018Toba et al. , 2022)).In a lower-luminosity AGN, the AGN spectrum can be significantly affected by contamination from the host galaxy lights, making it difficult to accurately estimate AGN parameters (e.g., M BH , bolometric luminosity (L bol ), and the UV/optical-to-X-ray spectral index (α ox )). 8  To overcome these problems, high-resolution optical images that allow one to spatially decomposite the nucleus and host components are useful.Ishino et al. (2020) investigated 862 type 1 SDSS quasars and their host galaxy properties at z < 1 using Subaru Hyper-Suprime Cam (HSC; Miyazaki et al. 2018) data (HSC Subaru Strategic Program;Aihara et al. 2018) and 1D profile fitting.Li et al. (2021a) carried out a 2D profile fitting to 4887 type 1 SDSS quasars and measured the host galaxy flux, effective radius (r e ), and Sérsic index (n).Then, by performing SED fitting to the optical photometries of the host galaxies, Li et al. (2021a) investigated the evolution of the M BH -M stellar relation of type 1 SDSS quasars at 0.2 < z < 0.8.In this paper, we basically follow their approach to separating the contributions from the host galaxy and the AGN in the SED analysis, which enables us to best estimate both M BH and M stellar for our X-ray selected type 1 AGN sample (Section 2).
1.1.2.Testing the AGN Unified Scheme X-ray surveys performed at energies above 2 keV also provide a large number of obscured (type 2) AGNs, which constitute the dominant AGN population at low to moderate luminosity ranges (Toba et al. 2013;Ueda et al. 2014).As mentioned earlier, comparing the basic properties of host galaxies among type 1 and type 2 AGNs is always important, to test the AGN unified scheme (Antonucci 1993) and the possible AGN type dependence on environment.Bornancini & García Lambas (2018) find no significant difference of the M stellar distribution in type 1 and type 2 AGNs at z = 0.3-1.1,consistent with the prediction from the unified scheme.By contrast, Zhuang & Ho (2020) concluded that type 2 AGNs show stronger star formation activity than type 1 AGNs at z < 0.3, regardless of their M stellar , λ Edd , and molecular gas mass.Zou et al. (2019) and Mountrichas et al. (2021) suggest that type 1 and type 2 AGNs reside in hosts with similar star formation rates (SFRs), but with smaller and larger stellar masses, respectively.

Survey Field: Stripe 82 Region
The SDSS Stripe 82 region is one of the most intensively studied, wide-area multiwavelength survey fields, on which medium-depth X-ray surveys with XMM-Newton and Chandra have been performed.with multiwavelength photometries over the radio, IR, optical, UV, and X-ray bands.The catalog covers an area of 31.3 deg 2 .The optical spectroscopic completeness of the total X-ray sources is 43%.The Stripe 82X catalog is useful not only for studies of X-ray selected AGNs (LaMassa et al. 2016a(LaMassa et al. , 2017(LaMassa et al. , 2019)), but also for other AGN populations, such as mid-IR-selected AGNs (Glikman et al. 2018).The BH masses of type 1 AGNs were available in the catalogs of Pâris et al. (2018) and Rakshit et al. (2020), which were calculated from the line widths of the Mg II, Hβ, or C IV lines and monochromatic luminosities at 5100 Å (L λ5100 ), by analyzing the SDSS spectra.The large X-ray source catalog with multiwavelength data sets, reliably decomposed host galaxy SEDs by the HSC images at z = 0.2-0.8, and M BH values in type 1 AGNs offer us an ideal opportunity to investigate the AGN and host connection at the low-redshift ranges where low to moderate AGNs have number density peaks.

Outline of This Paper
In this paper, we perform a systematic multiwavelength SED analysis of X-ray AGNs matched to the SDSS spectroscopic catalog in the Stripe 82 region.We utilize the latest CIGALE code (Yang et al. 2022), where polar dusty components are included in the AGN template.Thus, our sample contains X-ray detected optical type 1 AGNs whose host photometries are decomposed from the HSC images by Li et al. (2021a) and X-ray detected type 2 AGNs.For the type 1 AGNs, we fix the host galaxy parameters as determined by Li et al. (2021a) to reliably separate the AGN emission.Below is the outline of this paper.In Section 2, we provide a detailed description of the sample selection and the technique utilized for SED fitting.In Section 3, we statistically study the relations among AGN parameters and host stellar mass and compare them between type 1 and type 2 AGNs.We also discuss the multiwavelength SED of AGNs in terms of α OX or the 2-10 keV to bolometric correction factor (κ 2-10 ).Section 4 summarizes the conclusions drawn from our research.We adopt cosmological parameters of H 0 = 70.4km s −1 Mpc −1 , Ω M = 0.272, and Ω Λ = 0.728 (the Wilkinson Microwave Anisotropy Probe 7 cosmology: Komatsu et al. 2011).

Sample Selection
Li et al. (2021a) performed a 2D image decomposition analysis for 4887 host galaxies of SDSS-detected type 1 quasars at z = 0.2-0.8,including those in the Stripe 82 region.The point-source component (corresponding to the quasar) and the host galaxy component were fitted with a model consisting of the point-spread function (PSF) model and a 2D Sérsic profile, respectively.They determined the host galaxy parameters, e.g., the host galaxy fluxes of the HSC g, r, i, z, and y (hereinafter called grizy) filters, the effective radius r e , the Sérsic index n, and the ellipticity ò. 2424 out of 4887 objects are classified as a final sample whose selection criteria are defined by Li et al. (2021a).The selection criteria relevant to our study are as follows: 1. z < 0.8. 2. The derived M stellar meets the stellar-mass-cut criteria: log M stellar,cut < log M stellar < 11.5, where log M stellar,cut is 9.3 (z = 0.2-0.4),9.8 (z = 0.4-0.6), and 10.3 (z = 0.6-0.8).
3. The reduced χ 2 of the SED fitting is smaller than 10.Li et al. (2021a) cataloged 371 optical type 1 AGNs at z = 0.2-0.8within the Stripe 82X region.Among them, we selected 111 objects detected with XMM-Newton and/or Chandra that have SDSS Data Release 14 (DR14) spectroscopic redshifts and multiwavelength counterparts in Ananna et al. (2017) andLaMassa et al. (2016b).To guarantee the reliability of M BH and counterpart matching, we chose 81 objects with an M BH Quality Flag (QF) = 0 in the SDSS DR14Q catalog and QF = 1-2 in the Stripe 82X catalog.The former QF condition ensures the quality of host galaxy decomposition by a principal component analysis (PCA; Yip et al. 2004aYip et al. , 2004b) ) in estimating the continuum luminosities and widths of broad emission lines.The latter corresponds to reliable multiwavelength identification, by excluding the cases where different counterparts are found in multiple bands with comparable likelihood ratios or there is a counterpart in only one band (see Ananna et al. 2017;Rakshit et al. 2020).
To correct the systematic biases, Li et al. (2021a) calibrated host galaxy fluxes of the grizy bands using simulated galaxy and AGN data sets.To minimize any possible calibration uncertainties, we selected the objects with small differences between the fitted and calibrated fluxes in the HSC i band.The criterion we adopted was |F fit − F cal |/F cal < 0.3, where F fit and F cal are the fitted flux (before calibration) and the calibrated flux (after calibration), respectively.Li et al. (2021a) decomposed the HSC images to derive the host galaxy parameters including F fit .However, galaxy structural measurements can have significant biases, like underestimating the size of large galaxies, due to various effects such as PSF blurring, limited signal-to-noise ratios, and reduced surface brightness.To address these biases, Li et al. (2021a) employed two calibration methods: inserting model galaxies into empty areas of real HSC images and adding unresolved quasars, using model PSFs, to real HSC images of galaxies in the CANDELS field.After these calibrations, F cal is calculated.Finally, 66 objects whose fluxes are decomposed in all grizy bands were chosen.
We also selected X-ray selected, optical type 2 AGNs at z = 0.2-0.8 from the Stripe 82X catalog.In addition to the QF criterion regarding crossmatching, we imposed the selection criteria as follows: 1.No counterparts are found in SDSS DR14Q (Pâris et al. 2018) within 1″ of the position.2. No broad lines are observed in the optical spectrum.(In the SDSS catalog, if emission lines are detected at the >10σ level with a width of >200 km s −1 at the 5σ level, objects are classified as "BROADLINE" in their subclasses.)3. Spectroscopic redshifts are determined with no warning flags (i.e., ZWARNING = 0 in the SDSS catalog).4. The spectral type is classified as a galaxy by the PCA in the SDSS optical spectroscopy pipeline (see Section 3.2 of Pâris et al. 2018 for more details).5.The "morphology" column in the Stripe 82X catalog is not assigned to type 1 AGNs or QSOs.In Ananna et al. (2017), first an object is classified as a point-like or extended source on the basis of optical and near-IR morphology obtained by Jiang et al. (2014), Fliri & Trujillo (2016), and/or McMahon et al. (2013).Second, according to the photometries and the image classification (point-like or extended), a limited set of SED templates is selected from those for stars, elliptical/spiral/starburst galaxies, type 1/type 2 AGNs, and QSOs (Ilbert et al. 2009;Salvato et al. 2009;Hsu et al. 2014), and the "morphology" is finally determined via template fitting (see Sections 3.1, 3.3, and Table 5 in Ananna et al. 2017 for details).
This selection left 158 type 2 AGNs.

SED Fitting with CIGALE
We performed X-ray to radio SED modeling for a sample of 224 AGNs (type 1: 66 sources; type 2: 158 sources) utilizing a new version of CIGALE (Code Investigating GALaxy Emission, version 2022.0;Burgarella et al. 2005;Noll et al. 2009;Boquien et al. 2019;Yang et al. 2020Yang et al. , 2022)).CIGALE assumes the energy balance between UV/optical absorption and far-IR emission, which enables us to model a multiwavelength SED in a self-consistent way.This code is designed to calculate the likelihoods of all the models on a user-defined grid and return the likelihood-weighted mean of a physical quantity by Bayesian estimation.It is noteworthy that CIGALE is able to take into account upper limits in the photometric data, using the method of Sawicki (2012), as described in Section 4.3 of Boquien et al. (2019).
CIGALE offers several options for the SED templates of each component.In this work, we adopted the same module selection as in Toba et al. (2021) and Setoguchi et al. (2021).We employed a delayed star formation history (SFH) model, where τ main represents the e-folding time of the main stellar population.The simple stellar population (SSP) was modeled by the stellar templates of Bruzual & Charlot (2003) and the Chabrier initial mass function (IMF; Chabrier 2003).We utilized the default template by Inoue (2011) for the nebular emission.In order to consider the dust attenuation to the stellar components, we adopted the extinction curve by Calzetti et al. (2000) and Leitherer et al. (2002), which is characterized by the color excess (E(B − V ) * ).The reprocessed IR dust emission of UV/optical stellar radiation is modeled with the templates by Dale et al. (2014).For the optical to IR emission of an AGN, we used the two-phase torus model named SKIRTOR (Stalevski et al. 2016), incorporating polar dust emission with a single modified blackbody.This model takes into account the extinction and re-emission of the direct AGN component by the torus and polar dust.In the following subsection, we show the details of the SED modeling of type 1 and type 2 AGNs separately.

Type 1 AGN Sample
As described in Section 1, in a type 1 AGN, the host component can be largely contaminated by the AGN component in the optical band, because the nuclear emission is not obscured by the dusty torus and hence is much brighter than in a type 2 AGN.To obtain reliable host and AGN parameters by separating the two components in type 1 AGNs, we analyzed their SEDs in two steps: (1) the optical SEDs of the host galaxies decomposed by Li et al. (2021a); and (2) the IR, optical, UV, and X-ray SEDs of the total emission including host and AGN components.
In the first step, we analyzed the optical host SEDs based on the fitted fluxes in Li et al. (2021a), utilizing the same SED modules as adopted by Li et al. (2021a).At this stage, dust reemission components were ignored.Table 1 details the free parameter ranges of the host SED analysis.We obtain reasonable fits with reduced χ 2 values less than 10 for all 66 objects.The obtained stellar masses are confirmed to be fully consistent with those reported in Li et al. (2021a).
In the second step, we performed a multicomponent SED fitting to 19 photometries in the radio (Very Large Array or VLA), far-IR (Herschel/SPIRE), mid-IR (Spitzer/IRAC and Wide-field Infrared Survey Explorer or WISE), near-IR (VISTA), optical (Subaru), ultraviolet (GALEX), and X-ray (XMM-Newton or/and Chandra) bands for each object (see Ananna et al. 2017 andLaMassa et al. 2016b for details).The photometries, except for the optical bands, were taken from the Stripe 82X catalog.To obtain the nondecomposed optical photometries from the Subaru data, we performed a nearestneighbor matching between the Subaru/HSC images and the Stripe 82X catalog within 1″.We assigned an upper flux limit if the object was observed but not detected in that band (see Section 2.2.3 for the mid-IR and far-IR photometries).We corrected the X-ray fluxes for absorption, if any, according to the recipe described in Section 2.3.
Here we considered dust re-emission and AGN components, which were not considered in the first step.As mentioned earlier, we utilized the SKIRTOR model for the AGN emission, which has seven parameters: the torus optical depth at 9.7 μm (τ 9.7 ), the torus density radial parameter (p), the torus density angular parameter (q), the angle between the equatorial plane and the edge of the torus (Δ), the maximum to minimum radii ratio of the torus (R R max min ), the viewing angle (θ), and the fraction of AGN contribution to the total IR luminosity ( f AGN ).We fixed R R max min and θ at values typically observed in type 1 AGNs, following Yang et al. (2020).When we performed a total SED analysis for the type 1 AGNs, the normalization factor in CIGALE was set to be unity to fix the host galaxy component to that obtained from the host SED analysis.Table 2 summarizes the free parameters in the total SED model.We obtain reasonable fits with reduced χ 2 < 10 (the same threshold as adopted in Setoguchi et al. 2021) for 60 out of the 66 objects.The worse fits for the remaining objects could be

Type 2 AGNs
For type 2 AGNs, we only perform the second step (i.e., analysis of the IR-to-X-ray SED of the total emission) without fixing the host parameters.This is because, due to the extinction of the AGN component, the optical SED is dominated by the host galaxy and hence the stellar mass is reliably constrained.We confirmed that the SEDs of 137 objects out of 158 are reproduced with reduced χ 2 < 10 and satisfy the stellar-mass-cut criteria imposed by Li et al. (2021a; see Section 2.1).Hereafter, we refer to these 137 AGNs as the "type 2 AGN" sample.The estimated L bol and M stellar are listed in Table 3.The ranges of the free parameters are listed in Table 4.

Notes on Mid-IR and Far-IR Data
In this subsubsection, we discuss the mid-IR-to-far-IR data quality of our sample.The mid-IR photometries of our sample are given by the all-sky WISE (AllWISE) mission, the Spitzer-HETDEX Exploratory Large Area Survey This relatively low detection rate can be attributed to the limited depth of HerS.The flux limit of HerS is 31 mJy at 250 μm (3σ), which corresponds to SFR = 15-115 M e yr −1 at z = 0.2-0.8.9This may provide the upper limit of the SFRs of our sample.Here we note that the SFRs of our sample are not well constrained due to the limited far-IR photometries.However, the stellar masses are reliably constrained from the optical to near-IR SEDs (Conroy 2013).

X-Ray Luminosities
Figure 2(a) plots the observed (absorption-uncorrected) restframe 2-10 keV luminosity versus redshift for our type 1 and type 2 AGN samples, consisting of 60 and 137 objects, respectively.We also plot the intrinsic (absorption-corrected) luminosity (L X ) versus redshift for the same samples in Figure 2(b).We calculated L X by correcting for absorption if present, using the hardness ratio between the 0.5-2 and 2-10 keV (for XMM-Newton) or 2-7 keV (for Chandra) fluxes available in the Stripe 82X catalog.Following the recipe in Ueda et al. (2003), we assume a power-law photon index of 1.9 and take into account a reflection component from cold matter covering a solid angle of 2π.As noticed from the figure, the luminosity range spans L 41.6 log 44.7 X < < , covering the low-luminosity range (log L X < 43.5) we are particularly interested in (see Section 1).The mean and standard deviation of log L X are 43.38 ± 0.43 for the type 1 AGNs and 42.94 ± 0.56 for the type 2 AGNs.

New BH Mass Estimation in Type 1 AGNs Based on Image Decomposition
To reliably estimate the SMBH mass of a type 1 AGN by using the broadline width and continuum luminosity (L 5100 ), it is critical to properly subtract the host contribution at rest-frame 5100 Å, particularly at a low AGN luminosity.To decompose the host galaxy contribution in the optical spectrum, Rakshit et al. (2020) performed the PCA using solely spectral information.In our work, we are able to accurately separate the AGN and host components at 5100 Å on the basis of image decomposition and multiwavelength SED fitting.Figure 3(a) plots the fraction of AGN contribution to the total rest-frame 5100 Å luminosity as a function of AGN bolometric luminosity, showing that the host contamination becomes more significant toward lower AGN luminosities.We compare the SMBH masses obtained with our method and those by Rakshit et al. (2020) in Figure 3(b).It is seen that we obtain slightly smaller SMBH masses than those in Rakshit et al. (2020).Throughout this work, we adopt the SMBH masses estimated by our method, which are also listed in Table 5.The Eddington ratio is calculated as λ Edd = L bol /L Edd , where L Edd = 1.3 × 10 38 M BH /M e .The median, mean, and standard deviation of these parameters in type 1 AGNs are listed in Table 6.Our sample covers 68% (±1σ) regions of log M BH /M e = 7.83 ± 0.64, log L bol /erg s −1 = 44.52 ± 0.45, and log M stellar /M e = 10.61 ± 0.35.This is one of the largest X-ray selected type 1 AGN samples with reliable stellar mass estimates covering a low to medium luminosity range of log L bol < 45 at z = 0.2-0.8.We discuss the differences between the type 1 and type 2 samples in Section 3.3.We plot constant Eddington ratio lines corresponding to log λ Edd = -2.0,-1.0, and 0.0.As noticed, most of our objects are distributed between log λ Edd = -2.5 and -0.5, with a mean value of -1.5 (Table 6).Since the scatter in M BH is larger than that in λ Edd (Figures 4(a) and (c)), we may regard the bolometric luminosity, which is the product of M BH and τ 9.7 3, 5, 9 p 0.0, 1.0, 1.5 q 0.0, 1.0, 1.5 Δ 10, 30, 50°R R Edd l ~-, is similar to that found in the local hard X-ray selected type 1 AGN sample (Koss et al. 2017), implying that the ERDF of type 1 AGNs little evolves from z < 0.2 to z = 0.2-0.8.

Type 1 AGNs
Figure 5(b) plots the relation between M stellar and M BH .We perform a correlation analysis with the method of Kelly (2007), which allows us to take into account the parameter errors.We obtain a correlation coefficient of r = 0.64 ± 0.12, indicating a positive correlation.This supports M stellar being used as a proxy of M BH , at least for type 1 AGNs, albeit with a 1σ scatter of 0.5 dex (Table 6).The relation between L bol and M stellar is shown in Figure 5(c).A similar positive correlation as found between L bol and M BH in Figure 5(a) is noticed.This is expected because M stellar and M BH are correlated.In Figure 5(b), we display the local M BH -M bulge relations obtained by Kormendy & Ho (2013) and by Ding et al. (2020).The mean value of log (M BH /M stellar ) is found to be −2.7 ± 0.5 (Table 6).This result is consistent with the earlier report by Li et al. (2021b) for SDSS type 1 quasars.This is expected, because our X-ray selected type 1 AGN sample is a subsample of the Li et al. (2021b) one and X-ray detection causes no significant selection biases between them (see Appendix A).
This mean value of M BH /M stellar in our sample is similar to the local SMBH-to-bulge mass ratio, log (M BH /M bulge ) = − 2.4.We find that all of our host galaxies have a Sérsic index n < 2.5 in the Li et al. (2021a) catalog, and hence are likely to have disk-dominant morphologies.Since M stellar includes M bulge and the galactic disk mass, it is suggested that the M BH -M bulge ratio in our sample should be larger than the local value-that is, our objects have overmassive BHs relative to galactic bulges.As discussed in, e.g., Dekel & Burkert (2014), Shangguan et al. (2020), andLi et al. (2021a), at a later stage of the AGN phase currently observed in our sample, the concentration of gas through reservoirs or gas compaction mechanisms (e.g., minor mergers or disk instabilities) must  take place to enhance the star formation in classical bulges and cause it to overtake the M BH evolution.As we mention in Section 1, in order to investigate the origin of the cosmic downsizing of SMBH evolution, it is quite interesting to compare our results with those obtained for more luminous AGNs at higher redshifts.(This table is available in its entirety in machine-readable form.) A key question is which is the more important parameter-z or L bol -that primarily determines the mean M BH /M stellar ratio?Generally, it is difficult to separate the dependences because of the inevitable coupling between luminosity and redshift in a single flux-limited sample.The combination of multiple surveys with different depths and widths is useful for better constraining it, by expanding the coverage in the luminosity versus redshift plane.
Figure 6 plots M M log BH stellar ( ) against L log bol , color-coded by redshift, for our type 1 AGN sample at z = 0.2-0.8(Stripe 82) and type 1 AGNs at z ∼ 1.4 in the Subaru/XMM-Newton Deep Survey (SXDS) region (Setoguchi et al. 2021).The averaged values of M M log BH stellar ( ) in different luminosity bins for the two samples are plotted.This shows that M M log BH stellar ( ) increases with L log bol , as already reported by Setoguchi et al. (2021), for the SXDS sample, whereas its redshift dependence is weaker.To confirm the above result, we perform a multiple linear regression analysis among M M log BH stellar ( ), z, and L log bol for the combined (Stripe 82 + SXDS) sample by utilizing the Python module statsmodels (Seabold & Perktold 2010).We obtain the following The best-fit lines in Equation (1) at two z values (z = 0.5 and 1.5) are plotted in Figure 6.As Maji et al. (2022) pointed out, to evaluate which variable of the function has a stronger dependence, one must perform the "standardization" of each parameter-that is, subtracting the mean value and dividing the difference by the standard deviation.Then we obtain the coefficients of 0.11 ± 0.11 and 0.41 ± 0.11 for standardized values of z and L log bol , respectively.The larger coefficient in the latter term indicates that the relation between M M log BH stellar ( ) and L log bol is the primary one.The positive luminosity dependence of M M log BH stellar ( ) may be a natural consequence that objects with larger M M log BH stellar ( ) ratios tend to show larger luminosities at a given stellar mass when the M M log BH stellar ( ) distribution has an intrinsic scatter.In fact, Li et al. (2021b) performed detailed simulations and found that the observed M BH -M stellar ratios were biased toward higher values at higher redshifts in a flux-limited sample (i.e., a luminosity-limited sample at a given redshift) due to this effect.Our result suggests that M M log BH stellar ( ) at given L log bol little evolves with redshift, supporting the conclusion by Li et al. (2021b).Caution must be taken in interpreting the above bestfit relation, however, because selection biases are complicated.The weak redshift dependence is likely affected by the sample selection bias in a flux-limited sample (i.e., a luminositylimited sample at a given redshift).In fact, Li et al. (2021b) performed detailed simulations and found that the observed M BH -M stellar ratios are biased toward higher values at higher redshifts by assuming the ERDF by Schulze et al. (2015).
To summarize, we infer that the difference in the mean  7 that the majority of X-ray selected type 1 AGNs at z = 0.2-0.8(this work), z = 0.5-1.1 (Schramm & Silverman 2013), and z = 1.2-1.7 (Ding et al. 2020) 10 have disk-like morphologies, although a minor but significant fraction may have bulge-like ones.All these results suggest that, at least for the majority of type 1 AGNs, there are no distinct differences between the lowluminosity, low-redshift AGNs and the high-luminosity, highredshift ones.This provides no evidence for two distinct channels for SMBH growth to explain the downsizing behavior and seems to be more consistent with theoretical models that  consider common AGN triggering mechanisms over a wide redshift range (e.g., Shirakata et al. 2019).
We would like to make caveats here, however, that the tentative conclusion above is based purely on X-ray selected type 1 AGNs and does not include absorbed AGNs, the dominant X-ray AGN population at the low-luminosity range.In addition, there are mid-IR-selected, high-luminosity AGN populations that are not considered in our study, such as "reddened type 1 quasars" (Glikman et al. 2018).These AGNs are known to be relatively X-ray weak (Ricci et al. 2017;Goulding et al. 2018;Toba et al. 2019) and some of them (obscured ones) show evidence for the merger channel of SMBH growth (e.g., Treister et al. 2012;Donley et al. 2018).To reach firm conclusions on the trigger mechanisms for all AGNs, it is crucial to investigate the nature of these populations that are not included in this work.
The relations between κ 2-10 and λ Edd or L bol are shown in Figure 8.We find the trend that κ 2-10 increases with λ Edd or L bol in our objects.We also plot the mean values of κ < , but the small number of objects satisfied log 2 Edd l < -.Our result confirms that the correlation continues to even lower Eddington rates of log 2 Edd l < -.This may be consistent with the disk truncation scenario, as suggested in changing-look AGNs (e.g., Noda & Done 2018).Thus, κ 2-10 may be used as a beacon of the mass accretion rates normalized by the BH mass, as previously pointed out (e.g., Vasudevan & Fabian 2007;Lusso et al. 2010), over a wider range of log Edd l .

Comparison of X-Ray Detected Type 1 and Type 2 AGNs
We compare the AGN and host properties between the X-ray detected type 1 and type 2 AGN samples.In Figure 4, we display the histograms of M stellar , L bol , and L bol /M stellar for the type 2 AGN sample (red) to be compared with those for the type 2 AGN sample (blue).The median, mean, and standard deviation of these parameters are summarized in Table 6. Figure 5(c) shows the L bol versus M stellar plot.As is evident in this figure, type 2 AGNs are more abundant in the low-L bol region.A Kolmogorov-Smirnov (KS) test for the L bol distribution gives p = 3.2 × 10 −4 , indicating a significant difference between the type 1 and type 2 AGN samples.In other words, the observed fraction of type 2 AGNs in the total AGNs decreases with bolometric luminosity.To derive the intrinsic type 2 AGN fraction as a function of L bol is beyond the scope of this paper, because our samples are not complete and complex selection biases must be corrected.
To test the AGN unified scheme, it is important to check whether the host stellar mass distributions of type 1 and type 2 AGNs with given AGN properties are the same or not.Recalling the fact that L bol is more correlated with M BH than with λ Edd in type 1 AGNs (see Section 3.1.2),it is not fair to directly compare the M stellar distributions using the whole type 1 and type 2 AGN samples, given that type 2 AGNs tend to have lower luminosities (i.e., biased toward lower SMBH masses).Thus, we divide the samples by L bol -those with L log 44.5 bol > and with L log 44.5 bol < for each AGN type.We find that the M stellar distribution of type 2 AGNs is similar to that of type 1 AGNs in both luminosity regions; KS tests yield p = 5.1 × 10 −2 ( L log 44.5 bol > ) and p = 2.9 × 10 −1 ( L log 44.5 bol < ).Thus, type 1 and type 2 AGNs with common luminosity (likely SMBH mass) ranges share similar host properties in terms of stellar mass.This is quite important, because it helps to justify the use of the host stellar mass, in place of the BH mass, to roughly estimate Eddington ratios, commonly in type 1 and type 2 AGNs, as has been done in many studies.Our results support the "luminosity-dependent" unified scheme (Ueda et al. 2003;La Franca et al. 2004;Simpson 2005;Hasinger 2008;Toba et al. 2014;Ueda et al. 2014) or probably the "Eddingtonratio-dependent" unified scheme (Ricci et al. 2017); that is, type 1 and type 2 AGNs belong to the same population of host galaxies with obscuring AGN tori whose covering fraction decreases with luminosity (or Eddington ratio).

Conclusion
In this study, we have conducted a comprehensive analysis of X-ray detected AGNs with multiwavelength counterparts in the Stripe 82 region at z = 0.2-0.8.The sample consisted of 60 type 1 AGNs and 137 type 2 AGNs, spanning an X-ray luminosity range of L log 41.6 44.7 X -

=
. We utilized the latest CIGALE code, which includes dusty polar components, to carry out the analysis.To obtain accurate parameters of both the AGN and the host galaxy in type 1 AGNs, we utilized the image-decomposed optical SEDs obtained by Li et al. (2021a) based on Subaru HSC images.We estimated reliable BH masses using the host and total SEDs by subtracting the host galaxy contribution in the continuum luminosity at 5100 Å.
Our conclusions are summarized as follows.
1.The mean value of log (M BH /M stellar ) in our type 1 AGN sample is found to be −2.7 ± 0.5, which is similar to the local mass ratio between BHs and bulges.2. Performing a multilinear regression analysis on a combined sample of type 1 AGNs in the Stripe 82 region and SXDF (Setoguchi et al. 2021), we find that M M log BH stellar ( ) depends primarily on the AGN luminosity, not on redshift.The offset in M M log BH stellar ( ) between our type 1 AGN sample and more luminous ( L log 45 bol > ) type 1 AGNs at z ∼ 1.5 can be attributed to its luminosity dependence.3. We find anticorrelations between the UV-to-X-ray slope (α OX ) and AGN luminosity or Eddington ratio, which are consistent with previous studies.We confirm the trend that the X-ray-to-bolometric correction factor (κ 2-10 ) increases with Eddington ratio by covering a range of log 2 Edd l < -. 4. Our type 1 and type 2 AGNs with the same luminosity ranges share similar distributions of M stellar , whereas type 2 AGNs exhibit smaller L bol on average than type 1 AGNs.This supports the luminosity-dependent (or Eddington-ratio-dependent) unified scheme.13 The Astrophysical Journal, 961:246 (15pp), 2024 February 1 Setoguchi et al.
the X-ray detected and undetected type 1 AGN samples.By performing KS tests, we find no significant differences in these distributions between the two samples.The M BH -M stellar relation is displayed in Figure 9(g), again showing no significant difference between the two samples.These results suggest that X-ray detection does not cause any biases in selecting type 1 AGNs.Most probably, X-ray detection or nondetection is determined by time variability, which is faster in X-ray bands (through the Comptonizing corona) than in the optical band (accretion disk).
LaMassa et al. (2016a) investigated the optical to mid-IR colors of 552 X-ray selected AGNs with WISE and UKIDSS detections, based on the previous version of the Stripe 82X catalog utilizing the XMM-Newton AO10 data.Their sample contains 24 type 1 and three type 2 AGNs in our sample.LaMassa et al. (2019) listed 4847 AGN candidates based on the X-ray and WISE data.The overlap with our is 36 out of the 60 type 1 AGNs and 25 out of the 137 type 2 AGNs.We have confirmed that the luminosity ranges of the overlapping objects are similar to those of our samples.LaMassa et al. (2017) andGlikman et al. (2018) studied the properties of 12 "red quasar" candidates and 147 WISEselected AGNs, respectively.None of these are included in our samples.This point will be discussed in Section 3.1.3.

Figure 1 .
Figure 1.(a) and (b) Examples of the total (host+AGN) SED fittings for type 1 AGNs dominated by host galaxy emission (left; 010618.71-002204.0) and by AGN emission (right; 232640.01-003041.4) in the optical bands.The black solid lines show the best-fit SEDs.
Figure 4 plots the histograms of the best-fit parameters of the CIGALE SED fitting for our type 1 AGN sample: (a) M BH ; (b) L bol ; (c) λ Edd ; (d) M stellar ; (e) M BH /M stellar ; and (f) L bol /M stellar .The median, mean, and standard deviation of these parameters in type 1 AGNs are listed in Table6.Our sample covers 68% (±1σ) regions of log M BH /M e = 7.83 ± 0.64, log L bol /erg s −1 = 44.52 ± 0.45, and log M stellar /M e = 10.61 ± 0.35.This is one of the largest X-ray selected type 1 AGN samples with reliable stellar mass estimates covering a low to medium luminosity range of log L bol < 45 at z = 0.2-0.8.We discuss the differences between the type 1 and type 2 samples in Section 3.3.
Figure5(a) plots the relation between the M BH and L bol of our sample.We plot constant Eddington ratio lines corresponding to log λ Edd = -2.0,-1.0, and 0.0.As noticed, most of our objects are distributed between log λ Edd = -2.5 and -0.5, with a mean value of -1.5 (Table6).Since the scatter in M BH is larger than that in λ Edd(Figures 4(a)  and (c)), we may regard the bolometric luminosity, which is the product of M BH and

λ
Edd , as mainly being determined by the M BH in our sample.It is beyond the scope of this paper to derive the intrinsic Eddington ratio distribution function (ERDF) by correcting for all sample selection biases.Nevertheless, the peak in the observed distribution, log 1.5

Figure 3 .
Figure 3. (a) Fractional AGN contribution to the total continuum luminosity at 5100 Å as a function of L bol .(b) The comparison of M BH between our new estimates and those by Rakshit et al. (2020).The black solid line shows the one-to-one relation.The blue triangles represent X-ray detected type 1 AGNs.

Figure 5 .
Figure 5. Relations between (a) M stellar and M BH ; (b) L bol and M BH ; and (c) M stellar and L bol .(a) The black solid and dashed lines show the Eddington ratio (λ Edd ) = 0, − 1, and − 2. (b) The black solid and dashed lines represent the local BH-to-bulge mass relations from Kormendy & Ho (2013) and from Ding et al. (2020), respectively.

Figure 6 .
Figure 6.log (M BH /M stellar ) as a function of log L bol .The data points are colorcoded by redshift.The triangles correspond to X-ray detected type 1 AGNs in the Stripe 82 (this work) and SXDS regions (Setoguchi et al. 2021).The green inverse triangles and cyan squares represent bins of objects in the Stripe 82 and SXDS regions, respectively.The vertical position and the error bar show a mean and a standard deviation of log (M BH /M stellar ) in each bin.The black solid and dashed lines display the best-fit multiple linear regression in Equation (1) at z = 0.5 and z = 1.5, respectively.

Figure 7 .
Figure 7. α ox plotted against (a) L 2500 Å [erg s −1 Hz −1 ] and (b) λ Edd .The black solid and dashed lines in (a) represent the best-fit linear regression in Equation (2) and the relation of α OX -L 2500 Å by Lusso et al. (2010) and by Just et al. (2007), respectively.The black solid and dashed lines in (b) show the best-fit linear regression in Equation (3) and the α OX -λ Edd relation by Lusso et al. (2010), respectively.

Figure 8 .
Figure 8. κ 2-10 vs. (a) L bol or (b) λ Edd .The black diamonds display binned results.The vertical position and the error bar show the mean value and the standard deviation of κ 2-10 in each bin, respectively.The gray squares represent AGNs fromVasudevan & Fabian (2007).The X-ray weak object, PG 1011-040, is removed.

Table 1
Grid of Parameters Used for the Host SED Fitting in Type 1 AGNs with CIGALE SKIRTOR, enables us to estimate "agn.accretionpower," which is the intrinsic AGN disk luminosity averaged over all directions.In this work, we adopt this parameter as L bol in both type 1 and type 2 AGNs.Table5lists the best-fit parameters of M stellar and L bol for each object derived from the SED fitting, together with the basic source information.Examples of the total SED fittings in type 1 AGNs are represented in Figure1.

Table 2
Grid of Parameters Used for the Total (Host+AGN) SED Fitting with CIGALE

Table 3
Summary of Properties of X-Ray Detected Type 1 AGNs and Hosts Grid of Parameters Used for the Total SEDs of Type 2 AGNs with CIGALE Notes.Column (1): unique identifier in the SDSS DR14Q catalog.Column (2): unique spectrum identifier in SDSS DR14.Column (3): redshift from the SDSS spectra.Column (4): logarithmic bolometric AGN luminosity derived by CIGALE, for which we adopt the output parameter "agn.accretionpower."Column(5):newly estimated logarithmic BH mass and its 1σ error.Column (6): logarithmic stellar mass derived by CIGALE and its 1σ error.(Thistable is available in its entirety in machine-readable form.)Table 4 Table7summarizes major previous studies investigating M BH -M stellar relations for X-ray selected type 1 AGNs at various luminosity and redshift ranges.It also provides information on galaxy morphologies whenever available.As noticed, high-luminosity AGNs (typically with log L bol  45) at z  1.2 have larger BH-to-stellar mass ratios,

Table 5
Summary of Properties of X-Ray Detected Type 2 AGNs and Hosts

Table 6
Statistical Properties of Key Parameters in Our Type 1 and Type 2 AGN Samples Notes.Column (1): key AGN and host parameters in our type 1 and type 2 AGN samples.Statistical properties are summarized in terms of: column (2): median; column (3): mean; and column (4): σ (standard deviation).

Table 7
Summary of Previous Studies on the M BH -M stellar Relation in Broadline AGNs Column (1): references that studied the M BH -M stellar relation in broadline AGNs (ordered by publication date)-n and B/T mean the Sérsic index and the bulge-to-total luminosity ratio, respectively.Column (2): the redshift range.Column (3): the log L bol range.Column (4): the mean value of log (M BH /M stellar ).Column (5): morphologies of the host galaxies.Column (6): the number of objects.Column (7): if the objects are X-ray selected, this column contains "Yes." Just et al. 2007;Lusso et al. 2010together with those derived byJust et al. (2007)andLusso et al. (2010).The full sample ofJust et al. (2007)is composed of luminous quasars (log L 2500 Å  32) and the samples fromSteffen et al. (2006)and fromShemmer et al. (2006), covering a range of log L 2500 Å = 27.7-32.5outtoz=4.5.Lusso et al. (2010)selected 545 type 1 AGNs at z = 0.04-4.25 with log L 2500 Å = 25.7-31.4,detected in the XMM-COSMOS survey.As noticed, our results are well consistent with the results byJust et al. (2007).We note that the mean value of α OX of our sample is ∼0.05 smaller than the bestfit relations byLusso et al. (2010)at the same L 2500 Å or λ Edd ranges.We infer that the differences are attributable to sample selection effects; the sample ofLusso et al. (2010)contains many AGNs at z > 1 for which the detection limit of the X-ray luminosity is higher than ours, so may miss X-ray faint AGNs, whereas our sample may miss optically/UV faint AGNs because of the magnitude limits in SDSS.The scatter in α OX around the best-fit relation is found to be ±0.35,which is consistent with previous studies (e.g.,Just et al. 2007;Lusso et al. 2010).