The eROSITA Final Equatorial-Depth Survey (eFEDS): Host-galaxy Demographics of X-ray AGNs with Subaru Hyper Suprime-Cam

X-ray surveys of the extragalactic sky, primarily with Chandra and XMM-Newton, have made remarkable progress in the study of accretion onto supermassive black holes (SMBHs) across our observable universe (see Brandt & Hasinger, 2005, for a review). We now have a clearer understanding of the cosmic evolution of Active Galactic Nuclei (AGNs) from $z\sim 6$ to the present with the inclusion of the obscured population (e.g., Merloni et al., 2014). Remarkably, the average accretion rate density of SMBHs mirrors that of the cosmic star formation rate (SFR) density lending evidence for a connection between the growth of SMBHs and their host galaxies (e.g., Silverman et al., 2008; Madau & Dickinson, 2014; Aird et al., 2015; Yang et al., 2018). With an assumption on the accretion efficiency, the integral of the mass growth rate of SMBHs with cosmic time broadly agrees with the local mass density of inactive SMBHs (Soltan, 1982; Shankar et al., 2013).

Over the past decade or more, large observational efforts from both the ground and space have accelerated investigations into the properties of the host galaxies of distant X-ray detected AGNs motivated by the possible links mentioned above, the local SMBH-bulge scaling relations (Kormendy & Ho, 2013), and the need for energy injection from SMBHs (i.e., AGN feedback) to produce realistic massive galaxies in cosmological simulations (e.g., Silk & Rees, 1998; Sijacki et al., 2007; Weinberger et al., 2018). It is well known that X-ray selection of AGNs results in cases that are underluminous in the optical thus facilitating the views of their underlying host galaxy. However, challenges with disentangling the AGN and galaxy emission are always an issue at most wavelengths with the likely exception of the FIR. Based on these efforts, we firmly understand that the bulk of X-ray AGNs prefer to reside in massive star-forming galaxies (e.g., Silverman et al., 2009; Brusa et al., 2009; Suh et al., 2017; Li et al., 2019; Zou et al., 2019; Florez et al., 2020) and within dark matter halos near the peak efficiency in converting baryons to stars (e.g., Gilli et al., 2009; Allevato et al., 2011; Georgakakis et al., 2019). Their hosts show signs of having a light profile descriptive of disk galaxies (e.g., Schawinski et al., 2011; Cisternas et al., 2011a) and more compact emission (e.g., Kocevski et al., 2017; Silverman et al., 2019; Ni et al., 2021; Li et al., 2021b) that may indicate the emergence of a central stellar concentration (i.e., bulge). At $z<1$, galaxy mergers can effectively trigger AGN accretion but do not appear to be the dominant mechanism (e.g., Cisternas et al. 2011a; Silverman et al. 2011; Kocevski et al. 2012; Goulding et al. 2018; Ellison et al. 2019; Tang et al. submitted), while in the gas-rich universe at higher redshifts, the picture is less clear (e.g., Mechtley et al., 2016; Shah et al., 2020; Silva et al., 2021). Even with such progress, we have not yet demonstrated a causal link between the galaxies, their evolution, and the activation and feedback of their central SMBHs.

Some limitations may be due to the fact that current X-ray selected AGN samples, sufficient in depth to probe the higher redshift universe and faint obscured population (e.g., Hasinger et al., 2007; Elvis et al., 2009; Luo et al., 2017), do not reach the level of statistical significance comparable to wide-field studies of AGNs in the low-redshift universe as accomplished with the Sloan Digital Sky Survey (e.g., Kauffmann et al., 2003; Heckman & Kauffmann, 2006; Lyke et al., 2020). We now have a better understanding that large number statistics ($>10^{3}$ per redshift interval $dz\sim 0.1$) are required to break degeneracies between parameters (e.g., redshift, stellar mass, environment, galaxy structure, galaxy color) inherent in studies of the connection between SMBHs and galaxies. Wide-area X-ray imaging is needed to fully exploit the rich optical and near-infrared imaging currently being amassed by Subaru Hyper Suprime-Cam (Aihara et al., 2022), the Dark Energy Survey and future efforts with the Vera Rubin Observatory (LSST), Euclid, and the Nancy Grace Roman Space Telescope (NGRST). With the successful launch of eROSITA (Merloni et al., 2020; Predehl et al., 2021) which uniquely combines a higher sensitivity than its predecessor ROSAT survey, a large field of view ($\approx 1$ degree in diameter) and a large collecting area designed for deep all-sky survey, large samples of X-ray detected AGNs across cosmic time are now being amassed.

Here, we use the wide and deep optical imaging of the HSC Subaru Strategic Program to report on the properties of the host galaxies of X-ray AGNs detected by eROSITA. The joint effort between the eROSITA and Subaru/HSC teams focuses on a 140 deg² region of the sky observed during the SRG/eROSITA Performance Verification (PV) phase, i.e., the eROSITA Final Equatorial Depth Survey (eFEDS), where the deep five-band ($grizy$) imaging from HSC can be exploited for a range of science from eROSITA. Here, we implement 2D image analysis tools to decompose the AGN and host galaxy optical emissions (while considering the point-spread function; PSF) for 3796 AGNs at $0.2<z<0.8$ to study the properties of their host galaxies including stellar mass, disk vs. bulge nature, rest-frame color (indicative of the SFR or age of the underlying population), and obscuration. We attempt to place X-ray AGNs in the broader context of galaxy evolution by comparing to a large sample of inactive (comparison) galaxies available from the HSC-SSP with the equivalent intrinsic measurements (Kawinwanichakij et al. 2021; hereafter K21). Furthermore, we compare to a recent study on the hosts of optically-selected quasars from SDSS using the HSC imaging and tools used in this study (Li et al. 2021b; hereafter L21). This paper is structured as follows. Section 2 describes the X-ray AGN selection and their optical counterparts. Section 3 introduces our image decomposition method. The physical properties of AGNs and their host galaxies are presented in Section 4. The implications of our results in the broader context of AGN-galaxy connection are discussed in Section 5. In Section 6 we summarize our main findings. Throughout, we assume $\Omega_{\Lambda}$ = 0.7, $\Omega_{\rm m}$ = 0.3, and $H_{0}=70\rm\ km\ s^{-1}\ Mpc^{-1}$. Magnitudes are given in the AB system.

The eFEDS point source catalog (Brunner et al., 2022) enables us to construct a large sample of AGNs for studies of their host galaxies. In total, the catalog contains 27910 primary X-ray point sources with a detection likelihood (i.e., signal-to-noise) greater than 6 in the 0.2–2.3 keV band. The spurious detection rate has been assessed at the level of 1.8%. The X-ray flux limit of the eFEDS survey is $\sim 6.5\times 10^{-15}\ \rm erg\ s^{-1}\ cm^{-2}$ in the soft (0.5–2 keV) band, for a completeness level of $\sim 80\%$.

Optical-to-mid-IR counterparts of X-ray point sources are identified in Salvato et al. (2022) through the Bayesian-based NWAY method and the maximum likelihood ratio-based astromatch method using the data taken from the DESI Legacy Imaging Surveys Data Release 8 (Dey et al., 2019). A high fraction ($90.5\%$) of X-ray sources have reliable optical associations, with each object being assigned a counterpart reliability flag (CTP_quality). The contamination is primarily due to uncertainties on the centroid of the X-ray emission which is typically around $3^{\prime\prime}-5^{\prime\prime}$ dependent on the X-ray source significance and off-axis angle (Brunner et al., 2022). About 80% of the X-ray point sources have CTP_quality $\geq 2$, meaning that the counterpart has been identified as the best association by at least one method, and are classified as "Likely" or "Secure" extragalactic by assessing their X-ray, optical, and IR properties. Spectroscopic redshifts ($z_{\rm spec}$) are available for 6591 sources from past spectroscopic surveys (mainly from SDSS; Ahumada et al. 2020; Abdurro’uf et al. 2022). Photometric redshifts ($z_{\rm phot}$) for eFEDS sources are available in Salvato et al. (2022), which are measured from multi-wavelength SED fitting using LePHARE.

Liu et al. (2022) performed X-ray spectral fitting for eFEDS sources to characterize their properties. The X-ray spectral fitting is performed with BXA (Buchner et al., 2014), which connects XSPEC (Arnaud, 1996) with the UltraNest nested sampling algorithm (Buchner, 2017). The fitting starts from a single absorbed powerlaw model (TBabs*zTBabs*powerlaw), as most of the X-ray sources are expected to be AGNs. A second soft powerlaw or a blackbody component is added for sources with at least 20 net counts to account for the possible existence of a soft-excess component. As some of the X-ray sources might be stars or compact galaxy clusters, the collisionally-ionized gas emission model apec is also performed. The outcome of this X-ray spectral analysis is an eFEDS AGN catalog which comprises 22079 eFEDS point sources, as well as the intrinsic AGN properties such as absorption corrected rest-frame 0.5–2 keV luminosity (LumiIntr_Med_s; $L_{\rm X}$) and the hydrogen column density (lognH_s_m1; $N_{\rm H}$) from a single-powerlaw fit.

We build our AGN sample from the Liu et al. (2022) catalog at $0.2<z<0.8$ since the AGN-host decomposition with HSC imaging is most reliable in this redshift range (L21). The selected sources automatically satisfy CTP_quality $\geq 2$ and "Likely" or "Secure" extragalactic as required in Liu et al. (2022). We exclude 691 sources that lie outside the inner 90% area of the eFEDS footprint (inArea90 = True) as the data quality significantly drops due to higher background, stronger vignetting, and shorter exposure. To ensure reliable $z_{\rm phot}$, we only include sources with a level-4 reliability, which means the $z_{\rm phot}$ in Salvato et al. (2022) is consistent with those derived from the deep neural network technique of Nishizawa et al. (in prep) for sources in common. This leads to 4975 X-ray AGNs as our parent sample. We then cross-match their optical counterparts with the HSC S20A wide layer data using a 1″ matching radius to identify eROSITA AGNs that have clean HSC images in the five optical bands based on the following criteria:

1. 1.

   isprimary = True

2. 2.

   nchild = 0

3. 3.

   pixelflags_edge = False

4. 4.

   pixelflags_bad = False

5. 5.

   pixelflags_crcenter = False

6. 6.

   mask_brightstar_halo, ghost, blooming = False

7. 7.

   pixelflags_saturatedcenter = False

The redshift and $L_{\rm X}$ distributions for 3796 matched sources are shown in Figure 1. Over 95% of our sample have $L_{\rm X}$ larger than $10^{42}\ \rm erg\ s^{-1}$, thus are expected to be bona-fide X-ray AGNs. Adopting the bolometric correction in the 0.5–2 keV band given in Lusso et al. (2012), the bolometric luminosity of our sample spans from $10^{43}\,\textit{$\rm erg\ s^{-1}$}$ to $10^{46}\,\textit{$\rm erg\ s^{-1}$}$ with a mean (median) of $8\times 10^{44}\,\textit{$\rm erg\ s^{-1}$}$ ($3\times 10^{44}\,\textit{$\rm erg\ s^{-1}$}$). Most (3509/3796) of them have $\textit{$N_{\rm H}$}<10^{22}\,\textit{$\rm cm^{-2}$}$ due to that eROSITA is most sensitive to the soft X-ray emissions.

We conduct a 2D decomposition of the total optical emission into the AGN and host galaxy contribution separately using the HSC imaging data in five bands ($grizy$) as fully presented in L21, which has been successfully implemented to measure the host galaxy properties of $\sim 5000$ SDSS quasars. We refer the readers to Sections 3 and 4 in L21 for the details of our decomposition method and reliability checks through extensive image simulations (based on $\sim 1$ million simulated model galaxies and $\sim 5000$ real CANDELS galaxies plus model AGNs with realistic noise added) which include dependencies on host-to-total emission, magnitude, galaxy structural properties, and resolution (seeing conditions). Here, we briefly summarize the concept of our method.

We generate background-subtracted co-added HSC images ($60\times 60^{\prime\prime}$) in $grizy$ bands (Kawanomoto et al., 2018), together with the variance images and PSF models for each source using the HSC pipeline hscpipe v8.4  (Bosch et al., 2018). The size of the cut-out image used for decomposition is chosen automatically to be between $41\texttimes\times 41$ ($7^{\prime\prime}\times 7^{\prime\prime}$) and $131\times 131$ ($22^{\prime\prime}\times 22^{\prime\prime}$) pixels to ensure that the flux from the target AGN and close companions are fully included. We then implement an automated fitting routine using the image modeling tool Lenstronomy (Birrer et al., 2015; Birrer & Amara, 2018) to decompose the cut-out images for the target AGN into a point source and an underlying host galaxy, assuming that the point source can be described by a PSF model. A 2D $\rm S\acute{e}rsic$ profile convolved with the PSF is used to model the host-galaxy component. If present, companion objects, brighter than 25 mag in each cutout image, are simultaneously modeled with a $\rm S\acute{e}rsic$ profile. We first fit each source using the $i$-band image since it was observed under the best seeing conditions (typically 0.6″) and that the host-galaxy contribution in the $i$-band is relatively high. Then sources are fit in the other bands by fixing the structural parameters to the $i$-band results. The outputs of our fitting routine include the model AGN and galaxy magnitude in all optical bands, and the structural properties of the host galaxy in the $i$-band, i.e., $\rm S\acute{e}rsic$ index ($0.3<n<7.0$), galaxy size (half-light radius of the semi-major axis $0.1^{\prime\prime}<\textit{$R_{\rm e}$}<5.0^{\prime\prime}$), ellipticity ($0<\epsilon<0.8$) and position angle. Motivated by L21, we further fix the $\rm S\acute{e}rsic$ index to $n=0.7$ and $n=2.0$ for those hit the lower and upper boundaries, respectively, as such objects are most likely to have moderate $\rm S\acute{e}rsic$ indices but the model degeneracy or/and the PSF mismatch led to very low/high $\rm S\acute{e}rsic$ indices. In Figure 2 we show results from the image decomposition for three representative AGNs with varying host-to-total flux ratio ($f_{\rm gal}$) in the $i$-band.

We then adopt the image simulation result in L21 to correct for systematic measurement biases on the decomposed galaxy magnitude which arises from the fact that the structure parameters are wavelength dependent but are fixed to the $i$-band values. The uncertainties of our decomposition results are evaluated by examining the scatter between the input and output parameters in the image simulations at a given host galaxy magnitude and host-to-total flux ratio for each source. In Figure 3 we show the estimated uncertainties for the three main parameters: galaxy size, $\rm S\acute{e}rsic$ index, and decomposed galaxy magnitudes. The uncertainties on the galaxy size are significantly higher for the most compact galaxies whose sizes are smaller than the HSC PSF, and the most extended galaxies whose outskirts are indistinguishable from the background light. The uncertainties on the $\rm S\acute{e}rsic$ index increase when galaxies moving from disk-dominated to bulge-dominated due to the difficulty of separating the point source from a centrally concentrated bulge. The host galaxy magnitudes are well constrained for bright objects ($i\lesssim 23.0$), while the faint objects only contribute to a small fraction of our sample. Note that these uncertainties are estimated under a certain model, thus they could be underestimated due to model mismatch (e.g., PSF mismatch, existence of complex galaxy structures).

Spectral energy distribution (SED) fitting is then performed on the decomposed galaxy flux (corrected for measurement bias and galactic extinction) to infer the stellar population properties for AGN host galaxies such as stellar mass and rest-frame colors using CIGALE (Boquien et al., 2019; Yang et al., 2020). A Chabrier (2003) initial mass function, a Bruzual & Charlot (2003) stellar population model, a delayed star-formation history and a Calzetti et al. (2000) extinction law are assumed. In the fitting, we add an additional 10% flux error in quadrature to account for the unknown uncertainties in the decomposition due to model mismatch. This results in a typical uncertainty on ${\rm log}\,\mathcal{M}_{\star}$ of 0.25 dex. We refer the readers to Sections 3.2 and 4.2 in L21 for a full description of our method and the evaluation of the robustness of the SED fitting results through simulations.

Following L21, we set a stellar-mass cut ($\mathcal{M}_{\star,\rm cut}$) to construct a relatively mass-complete sample, which is chosen to correspond to the 90% completeness limit at an $i$-band magnitude of 23 mag using the method described in Pozzetti et al. (2010). This is to avoid problematic decomposition and stellar mass measurements for faint host galaxies. Mass limits at $z=0.3$, 0.5, and 0.7 are $10^{9.2}\,M_{\odot}$, $10^{9.8}\,M_{\odot}$, and $10^{10.3}\,M_{\odot}$, respectively. This leaves 3414 sources for the following analysis.

The physical properties of AGN host galaxies provide key clues on the triggering mechanism of AGN activity and how BHs and galaxies coevolve. To this end, we have measured the structure, star formation and obscuration properties for a large sample of eROSITA-detected AGNs. We find that the host galaxies of low-$\mathcal{M}_{\star}$ AGNs show a preference of disk-dominated star-forming galaxies and are on average more compact than inactive star-forming disks, while they become increasingly bulge-dominated and quiescent as $\mathcal{M}_{\star}$ increases; although we caution that the star-forming disk fraction may be underestimated at the massive end due to the host galaxy contribution to nuclear obscuration. The statistical difference between low-$\mathcal{M}_{\star}$ ($10.0<\textit{${\rm log}\,\mathcal{M}_{\star}$}<11.0$) and high-$\mathcal{M}_{\star}$ ($\textit{${\rm log}\,\mathcal{M}_{\star}$}>11.0$) AGNs points to an evolution sequence in which the BH and galaxy grow in mass while transform in structure and star-forming activity, as desired to establish the BH – bulge correlation seen in the local universe. In fact, Li et al. (2021c) found that the intrinsic (corrected for selection bias and measurement uncertainties) $\textit{$\mathcal{M}_{\rm BH}$}-\textit{$\mathcal{M}_{\star}$}$ relation for massive systems ($\textit{${\rm log}\,\mathcal{M}_{\star}$}\gtrsim 10.0$ and $\textit{${\rm log}\,\mathcal{M}_{\rm BH}$}\gtrsim 7.0$) does not evolve with redshift since $z\sim 0.8$ and tightly follows the local $\textit{$\mathcal{M}_{\rm BH}$}-\textit{$\mathcal{M}_{\rm bulge}$}$ relation for early type galaxies. This led them to conclude that a structural transition event is required to transform the tight $\textit{$\mathcal{M}_{\rm BH}$}-\textit{$\mathcal{M}_{\star}$}$ relation (probed by mostly disk-dominated broad-line AGNs) at high redshifts to the local $\textit{$\mathcal{M}_{\rm BH}$}-\textit{$\mathcal{M}_{\rm bulge}$}$ relation where $\textit{$\mathcal{M}_{\rm bulge}$}\approx\textit{$\mathcal{M}_{\star}$}$ for massive galaxies (see also Jahnke et al. 2009; Cisternas et al. 2011b; Schramm & Silverman 2013). Such a result is further complemented by the analysis of the $\textit{$\mathcal{M}_{\rm BH}$}-\sigma_{\star}$ (stellar velocity dispersion) relation in Silverman et al. (2022) where compact/quiescent AGNs are more closely aligned with the local relation. Given the bolometric luminosity of our sample (90% have $43.5<\textit{${\rm log}\,L_{\rm bol}$}<45.5$) and their unobscured nature, their $\mathcal{M}_{\rm BH}$ are expected to be $\sim 10^{6.5}-10^{8.5}\,\textit{$M_{\odot}$}$ assuming an Eddington ratio of 0.1, thus they should generally follow the mass relation of broad-line AGNs. The correlations between $\rm S\acute{e}rsic$ index, galaxy size, and quiescent fraction with stellar mass found in this work provide supportive evidence of such an evolutionary sequence to establish the local scaling relations.

Even so, we notice that the majority of relatively low-$\mathcal{M}_{\star}$ AGNs are still actively forming stars and have significant stellar disks. This is not necessarily in tension with the negative feedback scenario given the common dependence on the cold gas reservoirs for growing both BHs and galaxies. In fact, Ward et al. (2022) demonstrated that cosmological simulations (illustrisTNG, EAGLE, SIMBA) that incorporate strong BH feedback to quench massive galaxies also predict that AGNs with similar luminosities as this work tend to reside in gas-rich, star-forming galaxies. Nevertheless, for these AGNs to align with the scaling relations defined by early type galaxies, a transformation in their morphology and star-forming activity is still indispensable in the next few Gyrs.

In the classical picture, major mergers and the subsequent AGN feedback are responsible to drive such a transformation (e.g., Di Matteo et al., 2005; Hopkins et al., 2008). However, although it remains controversial on whether AGNs show an excess in the merger rate compared to inactive galaxies, the overall major merger fractions among X-ray selected AGNs are low (a few percent up to $\sim 30\%$; e.g., Schawinski et al. 2011; Kocevski et al. 2015; Gao et al. 2020). The prevalence of stellar disks in our sample is also at odds with the major merger scenario, but instead favors that internal disk instabilities or minor mergers are the dominant mechanisms in triggering AGN activity. Besides, most of the bulge growth seems to be not dominated by major mergers either, with simulations and observations demonstrating a greater role of violent disk instabilities in building classical bulges through a coalescence of massive disk clumps (e.g., Elmegreen et al., 2008; Martig et al., 2012; Bell et al., 2017; Du et al., 2021). This raises the question of whether the subsequent quenching (if any) is related with the AGN triggering and bulge formation process.

The lack of direct evidence of negative feedback in luminous AGNs can be reconciled with a significant time delay or if the cumulative energy injected by BHs in their low-accretion rate but long-lasting phase is more relevant in quenching star formation (e.g., Weinberger et al., 2018; Piotrowska et al., 2022). The latter scenario is supported by the observational evidence that the integrated BH mass appears to be the strongest predictor of galaxy quiescence in the local universe (e.g., Terrazas et al., 2016; Piotrowska et al., 2022). However, it is unclear how such a less violent feedback scenario is accompanied by a structural transformation given that quiescence is also well-correlated with galaxy compactness (e.g., Whitaker et al., 2017). It should also be realized that a prerequisite for a massive BH to quench a massive galaxy is that the system must have been gas rich and efficient in forming stars and fueling the BHs in order to accumulate such a large mass. One possible scenario is that the onset of quenching and structural transformation are both triggered by a dissipative compaction event which grows the bulge and rapidly consume the gas reservoirs in a few hundred million years through a central starburst (e.g., Barro et al., 2016; Tacchella et al., 2016; Lapiner et al., 2021). The feedback from BHs during or/and after the compaction event serves to further reduce the SFR and maintain the quiescence by preventing gas cooling and accretion. Given that the feeding of the central BHs is efficient during the compact star-forming phase (e.g., Kocevski et al., 2017; Ni et al., 2021), we can expect to see a high incidence of luminous AGNs in compact star-forming disks with concentrated molecular gas reservoirs (e.g., Chang et al., 2020; Molina et al., 2021; Stacey et al., 2021), a transformation of galaxy structure and star-forming activity along the growth of BHs and galaxies, and eventually a correlation between the integrated $\mathcal{M}_{\rm BH}$, the galaxy’s central mass concentration and quiescence. A schematic view of this evolution pathway is presented in Figure 13 (Path A).

While the above scenario can explain the statistical trends found in large AGN samples studied here and previous efforts based on HSC imaging (Li et al., 2021b, c; Nagele et al., 2022; Silverman et al., 2022), it is crucial to emphasize that there could be significant variation in the evolution pathways of individual AGNs. Some galaxies may never undergo such transition events given the large dispersion in the size and $\rm S\acute{e}rsic$ index distributions. This is most likely to be the case for low luminosity AGNs ($\textit{${\rm log}\,L_{\rm bol}$}\lesssim 44.0$) which on average hosting low-mass BHs ($\textit{${\rm log}\,\mathcal{M}_{\rm BH}$}\lesssim 7.0$) where the small $\mathcal{M}_{\rm BH}$ indicates that there may not have been much gas flowing into the nuclear region in the past. The structure transformation and feedback from BHs are likely inefficient in such systems and they will continue to grow the stellar disk (Path B). As a result, such AGNs will follow the mass relation of late type galaxies at $z=0$ that has a different normalization compared to early type galaxies (Reines & Volonteri, 2015). Alternatively, since the existing local dynamical $\mathcal{M}_{\rm BH}$ measurements are biased to the most compact early-type galaxies (Shankar et al., 2016), the structure transformation of some AGNs, especially for high-$\mathcal{M}_{\star}$ objects that are still hosted by pure disks at $z\sim 0.2$, may not be necessary if massive BHs in disk galaxies exist in the local universe but their $\mathcal{M}_{\rm BH}$ are yet to be measured. A detailed discussion on how this bias may affect our evolutionary picture is beyond the scope of this paper.

In this work, we investigate the physical properties of X-ray selected AGNs and their host galaxies in the eFEDS field at $0.2<z<0.8$. Thanks to the wide area of eFEDS, a large sample of 3796 AGNs can be detected and analyzed. Using wide and deep optical imaging in the $grizy$ bands from the HSC-SSP survey, we decompose the AGN images into an underlying host galaxy (modeled by a 2D $\rm S\acute{e}rsic$ profile) and a point source component (modeled by a PSF), allowing us to measure the structural parameters for AGN host galaxies. SED fitting is performed on the decomposed host galaxy emission to estimate stellar population properties such as stellar mass and rest-frame colors. Combined with the X-ray spectral fitting result, we extensively investigated the properties of AGN host galaxies including star-forming activity, disk vs. bulge nature, galaxy size, and obscuration. Our main conclusions are the following:

1. 1.

   The AGN contribution to the total optical light is broadly distributed at a given $L_{\rm X}$ over all luminosities considered ($42.0<\textit{${\rm log}\,L_{\rm X}$}/\textit{$\rm erg\ s^{-1}$}<44.5$), and can be significant down to $\textit{${\rm log}\,L_{\rm X}$}\sim 42.5\,\textit{$\rm erg\ s^{-1}$}$. Ignoring the point source component can significantly bias the structural measurements of AGN host galaxies even at the lowest X-ray luminosities. This highlights the importance of AGN-host decomposition for the study of AGNs and their host galaxies in the optical bands (Section 4.1).

2. 2.

   AGN host galaxies with low to moderate stellar masses ($\textit{${\rm log}\,\mathcal{M}_{\star}$}<11.3\,\textit{$M_{\odot}$}$) are predominately star-forming systems. The star-forming fraction drops at the high mass end while still showing an excess ($\sim 20\%$) compared to inactive control galaxies (Section 4.2).

3. 3.

   The $\rm S\acute{e}rsic\ index$ distribution is consistent with the bulk of AGNs ($64\%$) residing in galaxies with significant stellar disks ($n<2$), while its relationship with stellar mass suggests that AGN hosts become increasingly bulge dominated and quiescent when approaching $\textit{${\rm log}\,\mathcal{M}_{\star}$}>11.0\,\textit{$M_{\odot}$}$ (Section 4.3).

4. 4.

   The size of AGN hosts, and for those classified as star-forming AGNs, tend to be more compact than inactive star-forming galaxies at a given stellar mass. This result is in agreement with studies of optically-selected SDSS quasars (Li et al., 2021b) and suggests that the physical mechanism responsible for building the central mass concentration can also efficiently trigger AGN activity (Section 4.4).

5. 5.

   The host galaxies of X-ray unobscured ($\textit{$N_{\rm H}$}<10^{22}\,\textit{$\rm cm^{-2}$}$) AGNs are biased towards face-on systems, while X-ray obscured AGNs ($\textit{$N_{\rm H}$}>10^{22}\,\textit{$\rm cm^{-2}$}$) reside in both face-on and edge-on galaxies, indicating that the host galaxy can produce X-ray obscuration up to $10^{22}\,\textit{$\rm cm^{-2}$}$. The average $E(B-V)/\textit{$N_{\rm H}$}$ for the nuclei is similar to the galactic dust-to-gas ratio, lending further support that part of the obscuration could come from galaxy-scale gas and dust. This host galaxy contribution to the X-ray obscuration may cause a bias against the detection of massive star-forming disks as AGN host galaxies since such AGNs would appear X-ray obscured thus missed by eROSITA. The missing star-forming host fraction is negligible at $\textit{${\rm log}\,\mathcal{M}_{\star}$}<10.5\,\textit{$M_{\odot}$}$ but can be significant (up to $30\%$) at the high mass end (Section 4.5).

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/NRTA software system developed by the German eROSITA consortium.

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 the 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. JS is supported by JSPS KAKENHI Grant Number JP18H01251 and JP22H01262, and the World Premier International Research Center Initiative (WPI Initiative (WPI), MEXT, Japan. This paper makes use of software developed for the Large Synoptic Survey Telescope. We thank the LSST Project for making their code available as free software at http://dm.lsst.org This paper is based [in part] on data collected at the Subaru Telescope and retrieved from the HSC data archive system, which is operated by Subaru Telescope and Astronomy Data Center (ADC) at NAOJ. Data analysis was in part carried out with the cooperation of Center for Computational Astrophysics (CfCA), NAOJ.

The image decomposition and SED fitting results will be publicly available after the paper is accepted.