The link among X-ray spectral properties, AGN structure and the host galaxy

In this work, we compare the SMBH and host galaxy properties of X-ray obscured and unobscured AGN. For that purpose, we use $\sim 35 000$ X-ray detected AGN in the 4XMM-DR11 catalogue for which there are available measurements for their X-ray spectral parameters, from the XMM2Athena Horizon 2020 European project. We calculate the host galaxy properties via SED fitting analysis. Our final sample consists of 1 443 AGN. In the first part of our analysis, we use different N$_H$ thresholds (10$^{23}$ cm$^{-2}$ or 10$^{22}$ cm$^{-2}$), taking also into account the uncertainties associated with the N$_H$ measurements, to classify these sources into obscured and unobscured. We find that obscured AGN tend to live in more massive systems that have lower SFR compared to their unobscured counterparts. However, only the difference in stellar mass, M$_*$, appears statistically significant ($>2\sigma$). The results do not depend on the N$_H$ threshold used to classify AGN. The differences in M$_*$ and SFR are not statistically significant for luminous AGN ($\rm log (L_{X,2-10 KeV}/erg s^{-1})>44$). Our findings also show that unobscured AGN have, on average, higher specific black hole accretion rates compared to their obscured counterparts. In the second part of our analysis, we cross-match the 1 443 X-ray AGN with the SDSS DR16 quasar catalogue to obtain information on the SMBH properties of our sources. This results in 271 type 1 AGN, at $\rm z<1.9$. Our findings show that type 1 AGN with increased N$_H$ ($>10^{22}$ cm$^{-2}$) tend to have higher M$_{BH}$ compared to AGN with lower N$_H$ values, at similar M$_*$. The M$_{BH}$/M$_*$ ratio remains consistent for N$_H$ values below 10$^{22}$ cm$^{-2}$, but it exhibits signs of an increase at higher N$_H$ values. Finally, we detect a correlation between $\Gamma$ and Eddington ratio, but only for type 1 sources with N$_H<10^{22}$ cm$^{-2}$.


Introduction
Active galactic nuclei (AGN) are powered by accretion onto the supermassive black hole (SMBH) that is located in the centre of most, if not all, galaxies.It is well known that AGN and their host galaxies co-evolve.This coeval growth is manifested in a number of ways.For instance, strong correlations have been found between the mass of the SMBH, M BH , and various galaxy properties, such as the bulge, or stellar mass (M * ), and the stellar velocity dispersion of galaxies (e.g.Magorrian et al. 1998;Ferrarese & Merritt 2000;Häring & Rix 2004).Moreover, both the AGN activity and the star formation are fed by the same material (cold gas) and peak at similar cosmic times (z ∼ 2; e.g.Boyle et al. 2000;Sobral et al. 2013).Thus, for the purposes of understanding galaxy evolution, it is important to shed light on the structure of AGN in order to elucidate the physical mechanism(s) that feed the central SMBH and to study the AGN feedback.
One important aspect of this pursuit is to decipher the physical difference between obscured and unobscured AGN.
According to the unification model (e.g.Urry & Padovani 1995;Nenkova et al. 2002;Netzer 2015), AGN are surrounded by a dusty gas torus structure that absorbs radiation emitted from the SMBH and the accretion disc around it.This absorbed radiation is then re-emitted at longer (infrared) wavelengths.In the context of this model, an AGN is classified as obscured or unobscured depending on the inclination of the line of sight with respect to the symmetry axis of the accretion disc and torus.When the AGN is observed edge-on, the source is characterised as obscured, while it is classified as unobscured when the AGN is viewed face-on.Recent investigations have proposed a more intricate structure for AGN to account for the diverse classifications observed at different wavelengths, such as X-ray versus optical classifications (e.g.Ogawa et al. 2021;Esparza-Arredondo et al. 2021).Advanced techniques such as infrared interferometry have enabled detailed examination of the inner regions of AGN, unveiling complexities within the torus and challenging the conventional notion of a simple, smooth toroidal model (e.g.Tristram et al. 2007).Studies focusing on short timescale variability in X-ray column density have identified fluctuations, indicating dynamic changes in the distribution of obscuring material (e.g.Marinucci et al. 2016).While the presence of clumps in the torus contributes to the diversity of observed AGN types and offers valuable insights into the accretion processes around SMBHs, according to the unification model, the inclination angle remains the pivotal factor for distinguishing between obscured and unobscured AGN.
An alternative interpretation of the AGN obscuration comes from the class of the evolutionary models.In this case, the different AGN types are attributed to SMBH and their host galaxies being observed at different phases.The main idea of these models is that obscured AGN are observed at an early phase, when the energetic output from the accretion disc around the SMBH is not strong enough and incapable of expelling the gas that surrounds it.As material is accreted onto the SMBH, its energetic output becomes more powerful and eventually pushes away the obscuring material (e.g.Ciotti & Ostriker 1997;Hopkins et al. 2006;Somerville et al. 2008).
Studying the two AGN populations can shed light on many different aspects of the AGN-galaxy interplay.An important step towards this direction is to first understand the nature of obscured and unobscured AGN.A popular approach to uncover their features and behaviours is to compare the host galaxy properties of the two AGN types.If the different AGN populations live in similar environments, this would provide support to the unification model, whereas if they reside in galaxies of different properties, it would suggest that they are observed at different evolutionary phases.
Previous studies that compared the host galaxy properties of obscured and unobscured AGN found conflicting results, depending on the wavelengths used to identify AGN (optical, infrared, X-rays) and the obscuration criteria applied to classify sources.For X-ray-selected AGN, when the source classification is based on optical criteria, for instance, using optical spectra to identify broad and narrow emission lines, most studies have found that obscured AGN (type 2) tend to live in more massive galaxies compared to their unobscured (type 1) counterparts.However, both AGN types live in systems with similar levels of star formation (e.g.Zou et al. 2019;Mountrichas et al. 2021a).When the classification is based on X-ray criteria, though, for instance on the value of the hydrogen column density, N H , some studies have not observed significant differences in the host galaxy properties of obscured and unobscured AGN (e.g.Masoura et al. 2021;Mountrichas et al. 2021c), while other studies have found an increase of M * with N H (Lanzuisi et al. 2017).Differences regarding both the M * and the stellar populations of the two AGN classes have also been reported (Georgantopoulos et al. 2023).
Another important aspect that can shed light on the structure of AGN is the study of the possible correlation between the X-ray spectral index, Γ, and the Eddington ratio, n Edd .The Eddington ratio is defined as the ratio of the AGN bolometric luminosity, L bol , and the Eddington luminosity, L Edd (L Edd = 1.26 × 10 38 M BH /M erg s −1 , where M BH is the mass of the SMBH).The relation between Γ and n Edd has been interpreted as the link between the accretion efficiency in the accretion disc and the physical status of the corona.Due to the larger amount of optical and UV photons produced by the accretion disc, the X-ray emitting plasma is more efficiently cooled at a higher n Edd (e.g.Vasudevan & Fabian 2007;Davis & Laor 2011).Alternatively, a correlation between Γ and n Edd could be explained by the significant dependence of the cutoff energy on the n Edd (for more details see Ricci et al. 2018).Apart from the physical interpretation of a possible correla-tion between Γ and n Edd , it is still not clear whether such a correlation is robust or universal, since relevant studies have found conflicting results (e.g.Shemmer et al. 2008;Risaliti et al. 2009;Sobolewska & Papadakis 2009;Brightman et al. 2013;Trakhtenbrot et al. 2017;Kamraj et al. 2022).
In this work, we utilised X-ray AGN from the 4XMM-DR11 catalogue, for which there are available measurements for their X-ray spectral parameters, within the framework of the XMM2Athena 1 project.The 4XMM-DR11 dataset proved advantageous for our investigations due to its extensive collection of X-ray sources detected by the XMM-Newton observatory.The utilisation of XMM-Newton is particularly beneficial due to its high sensitivity and spatial resolution, allowing for the identification of faint and distant sources.Furthermore, the dataset demonstrates homogeneity, as the processed data within it adhere to a consistent processing methodology.Using the calculations for the spectral parameters, we classified sources into X-ray obscured and unobscured and compared their host galaxy properties.We then cross-matched the X-ray dataset with the Wu & Shen (2022) catalogue, which provides calculations for SMBH properties, such as black hole mass, M BH , and bolometric luminosity, L bol , for SDSS quasars.This enabled us to compare the SMBH properties of the two AGN populations.
The paper is structured as follows.In Sect.2, the two aforementioned catalogues are described.Section 3 presents the spectral energy distribution (SED) fitting analysis followed to measure the host galaxy properties.The selection criteria and the final samples are described in Sect. 4. Our results and conclusions are presented in Sect. 5.In Sect.6, we summarise the main findings of this work.

Data
In this work, we used X-ray AGN included in the 4XMM-DR11 catalogue (Webb et al. 2020).The 4XMM-DR11 is the fourth generation catalogue of serendipitous X-ray sources from the European Space Agency's (ESA) XMM-Newton observatory.It has been created by the XMM-Newton Survey Science Centre (SSC) on behalf of ESA.The catalogue contains 319 565 detections with spectra in 11 907 observations.There are 100 237 (31.4%) detections that were made in both detectors, 135 342 (45.5%) detections that come solely from the pn detector, and 73 986 (23.2%) detections that are only from the MOS cameras.
There are 210 444 sources that have available spectrum from one or more detections.The process followed for the classification and fitting of these sources has been done within the framework of the XMM2Athena project and is described in detail in Viitanen et al. (in prep.).In brief, the Tranin et al. (2022) catalogue was used to classify the sources.In Tranin et al. (2022), they used a reference sample constructed by cross-matching the Swift-XRT (2SXPS; Evans et al. 2020) sample and the tenth data release of the XMM-Newton serendipitous dataset (4XMM-DR10) with catalogues of identified AGN, stars, and other X-ray source types (for more details, see their For the X-ray sources classified as AGN, we calculated photometric redshifts for those with a reliable optical counterpart in SDSS or PanSTARRS following the methodology pre-sented in Ruiz et al. (2018).In the case of SDSS sources with spectroscopic observations, the corresponding redshift was used instead.There are 35 538 AGN with available redshift (8467 of them have spectroscopic redshift).A detailed presentation of this photometric redshift catalogue is presented in Ruiz et al. (in prep.).
The X-ray spectral analysis of these AGN was conducted within the framework of the XMM2Athena project (Webb et al. 2023).Details of this analysis can be found in Viitanen et al. (in prep.).In summary, a Bayesian spectral fit is performed with the BXA tool (Buchner et al. 2014) that facilitates the connection between XSPEC, which is used for the analysis of the X-ray spectral data (Arnaud 1996), and the nested sampling package UltraNest (Buchner et al. 2021).An uninformative prior was assigned to each parameter within the model, and the exploration of the entire parameter space with equal-weighted sampling points was carried out using the MLFriends algorithm (Buchner 2019), implemented within UltraNest.UltraNest is a Bayesian inference library designed for high-dimensional parameter estimation and model selection.UltraNest employs a nested sampling algorithm that works by enclosing high likelihood regions within a set of nested iso-likelihood contours.The algorithm then successively samples from the prior within these contours, effectively exploring the parameter space in a way that efficiently allocates computational resources to regions of higher likelihood.This makes nested sampling particularly effective for problems with multiple modes, as it naturally discovers and characterises these modes.As part of the fitting process, the empirical background model in the bxa.sherpa.backgroundmodule was utilised.This model has two parts.One part models the detector background and contains the contribution of lines and is not folded through the instrumental response.The second part accounts for emission of the cosmic X-ray background and Xray emission of the local hot bubble and Galactic halo.The background model, which is made up of a mixture of power laws, Gaussian lines, and thermal emission components, is fitted in a multi-step process to the background spectrum with the model increasing in complexity in each step and with the parameters of the previous steps constrained within a narrow range of the best-fit value obtained in the previous step.An χ 2 test was used to estimate the goodness of fit of the background spectra, and p-values were then obtained based on the χ 2 values and the number of effective parameters.
For the fitting of the source X-ray spectrum, a power law with two absorbing media was used: the local Galactic absorption with the column density fixed to the total column density in that line of sight plus in situ absorption at the AGN redshift with a free column density.For the free parameters of the model, the following priors were applied: log f X ∈ −17, −7 (erg s −1 cm −2 ); Γ ∈ 0, 6, log NH ∈ 20, 26 (cm −2 ); and IIN (normalisation) ∈ 0, 5, where f X and IIN are the X-ray flux and the inter-instrument normalisation (in the case of PN and MOS detections).To quantify the goodness of fit, a p-value is provided in the catalogue.Its calculation is described in detail in Viitanen et al. (in prep.).For each free parameter the catalogue includes the median and mode values, the 5 and 95 percentiles as well as the values that encompass the narrowest 90% interval (taken as the uncertainty of the mode).The parameters used in our analysis are the mode values of N H , Γ, and the fluxes (calculated in the 2-10 keV energy band).Using these estimated parameters, the X-ray luminosities, L X , were calculated after correcting for the fitted intrinsic absorption.We opted for mode values because they are the most probable values of the distribution, and they capture the cases that are closer to the edges of the sampled interval better than the median values.It is important to highlight that this selection, however, does not impact the overall results and conclusions of our study.An example of a source spectrum and model fit including the background modelling is presented in Fig. 1.
One goal of this study is to compare the SMBH properties of X-ray obscured and unobscured AGN.To add this information to our sources, we cross-matched the 35 538 AGN with the Wu & Shen (2022) catalogue.This catalogue includes the continuum and emission line properties for 750 414 broadline quasars from the data release 16 of SDSS (DR16Q) measured through optical spectroscopy.The quasars span a range of 0.1 ≤ z ≤ 6 and 44 ≤ log (L bol /erg s −1 ) ≤ 48, and the L bol were calculated using the measured continuum luminosity at rest-frame wavelengths of 5100 Å, 3000 Å and 1350 Å, depending on the redshift of the source (for more details see Sect.4.1 in Wu & Shen 2022).The catalogue also includes single-epoch virial M BH .The M BH have been calculated adopting the fiducial recipes on H β (for sources with z < 0.7) or the Mg ii (for sources with 0.7 ≤ z < 1.9) lines.At higher redshifts, the C iv line was measured.These M BH and L bol were used to calculate the n Edd .
The default redshifts in DR16Q are mostly based on the redshifts derived by the SDSS pipeline (Bolton et al. 2012).Lyke et al. (2020) also visually inspected a small fraction of quasars and updated their default redshift in DR16Q with visual redshifts.In the catalogue provided by Wu & Shen (2022), they presented improved systemic redshifts using the measured line peaks and correcting for velocity shifts of various lines with respect to the systemic velocity (for more details, see their Sect.4.2).

Calculation of the host galaxy properties
For the calculation of the star-formation rate, SFR, and stellar mass, M * , of the AGN host galaxies, we applied SED fitting using the CIGALE algorithm (Boquien et al. 2019;Yang et al. 2020Yang et al. , 2022)).CIGALE allows for the inclusion of the X-ray flux in the fitting process and has the ability to account for the extinction of the UV and optical emission in the poles of AGN (Yang et al. 2020;Mountrichas et al. 2021b,a;Buat et al. 2021).
A172, page 3 of 14 3.0, 7.0 Torus density radial parameter p (ρ ∝ r −p e −q| cos(θ)| ) 1.0 Torus density angular parameter q (ρ ∝ r −p e −q| cos(θ)| ) 1.0 Angle between the equatorial plan and edge of the torus 40 We used the same templates and parametric grid in the SED fitting process as those used in recent works (Mountrichas et al. 2021c(Mountrichas et al. , 2022c(Mountrichas et al. ,a, 2023;;Mountrichas & Shankar 2023).In brief, the galaxy component was modelled using a delayed starformation history, SFH, model with a function form SFR ∝ t × exp(−t/τ).A star formation burst was included (Małek et al. 2018;Buat et al. 2019) as a constant ongoing period of star formation of 50 Myr.Stellar emission was modelled using the single stellar population templates of Bruzual & Charlot (2003) and was attenuated following the Charlot & Fall (2000) attenuation law.To model the nebular emission, CIGALE adopts the nebular templates based on Villa-Velez et al. (2021).The emission of the dust heated by stars was modelled based on Dale et al. (2014), without any AGN contribution.The AGN emission was included using the SKIRTOR models of Stalevski et al. (2012Stalevski et al. ( , 2016)).CIGALE has the ability to model the X-ray emission of galaxies.In the SED fitting process, the intrinsic L X in the 2−10 keV band were used.The parameter space used in the SED fitting process is shown in Table 1.

Selection criteria and final samples
From the 35 538 AGN available in our catalogue, we used those with flag = 0, provided by the catalogue produced by the XMM2Athena.A detailed description of the flag numbering is given in Viitanen et al. (in prep.).In brief, sources with flag = 0 have background and source fits with a pvalue > 0.01, which is the threshold used to classify a fit as acceptable.There were 29 509 AGN that met this criterion.In our analysis, we needed reliable estimates of the host galaxy properties via SED fitting measurements.Therefore, we required all our X-ray AGN to have available photometry from SDSS or Pan-STARRS, 2MASS, and WISE in the following bands: (u), g, r, i, z, (y), J, H, K, W1, W2, and W4 (e.g.Mountrichas et al. 2021aMountrichas et al. ,c, 2022c,a;,a;Buat et al. 2021).There were 2,501 AGN that fulfilled these requirements.We note that, although we did not require it, all of these AGN also have W3 measurements available.For these sources, we applied an SED fitting using the templates and parameter space described in Sect.3.
To restrict our analysis of sources to those with the most reliable host galaxy measurements, we excluded badly fitted SEDs.For that purpose, we considered only sources for which the reduced χ 2 , χ 2 r < 5.This value has been used in previous studies (e.g.Masoura et al. 2018;Buat et al. 2021;Mountrichas et al. 2022c,a;Koutoulidis et al. 2022;Pouliasis et al. 2022) and is based on visual inspection of the SEDs.This requirement was met by 78% of the sources.To further exclude systems with unreliable measurements of the host galaxy properties, we applied the same method presented in previous studies (e.g.Mountrichas et al. 2021cMountrichas et al. ,a, 2023;;Buat et al. 2021;Koutoulidis et al. 2022).This method is based on a comparison between the value of the best model and the A172, page 4 of 14 likelihood-weighted mean value calculated by CIGALE.Specifically in our analysis, we only considered sources with 1 5 ≤ SFR best SFR bayes ≤ 5 and 1 5 ≤ M * ,best M * ,bayes ≤ 5, where SFR best and M * ,best are the best-fit values of SFR and M * , respectively, and SFR bayes and M * ,bayes are the Bayesian values estimated by CIGALE.The SFR and M * criteria were met by 88% and 97% of the sources.Previous studies have employed these ranges for the selection of reliable SFR and M * estimations while leveraging the CIGALE code (e.g.Mountrichas et al. 2021aMountrichas et al. ,c, 2022cMountrichas et al. ,a,b, 2023;;Mountrichas & Shankar 2023;Buat et al. 2021;Koutoulidis et al. 2022;Pouliasis et al. 2022).Mountrichas et al. (2021c) explored variations in the range, considering 0.1−0.33 for the lower limit and 3−10 for the upper limit.They affirmed that the outcomes remained insensitive to the specific choice of these limits.In our study, we validate this observation by investigating the impact of varying these boundaries within the specified limits.Our findings indicate that such variations result in a dataset size change of less than 5%, underscoring that they do not introduce significant alterations to our overall results and conclusions.
We also restricted the sample used in our analysis to sources with z < 1.9.The reason is twofold: our dataset does not include obscured sources at higher redshifts, and M BH measurements available in the Wu & Shen (2022) catalogue are not reliable at z > 1.9 (i.e.M BH calculated using the C iv broad line are considered less reliable).Finally, we excluded sources for which their redshift in the XMM dataset differs more than 0.1 compared to the redshift quoted in the Wu & Shen (2022) catalogue (16 AGN were excluded from this criterion).This threshold was determined by considering that during the process of SED fitting, redshift values are rounded to the nearest tenth decimal place.We note that no filtering has been applied regarding the uncertainties associated with the photometric redshifts available in our catalogue.The vast majority of sources with erroneous photometric redshifts would result in poor SED fits and consequently be excluded by the SED quality criteria previously described.Furthermore, we conducted an investigation to determine whether our results were impacted when restricting the analysis solely to AGN with spectroscopic redshifts, which is discussed in the following section.
There were 1443 X-ray AGN that fulfilled these criteria.Of these sources, 1231 lie at z < 0.7 and 212 at 0.7 ≤ z < 1.9.This sample was used in the analysis presented in Sects.5.1 and 5.2.Of the 1443 AGN, 344 are also included in the Wu & Shen (2022) catalogue.Out of them, 271 are at z < 1.9.These 271 AGN were used in our analysis presented in Sect.5.3.

Results and discussion
In this section, we compare the properties of host galaxies (SFR, M * ) and SMBHs (n Edd ) X-ray obscured and unobscured AGN.We also study the L bol −M BH and M BH −M * relations as a function of X-ray obscuration (N H ). Finally, we investigate the relation between the powerlaw slope (Γ) of the X-ray spectral model with n Edd .

Host galaxy properties of X-ray obscured and unobscured active galactic nuclei
In our analysis, we used the 1 443 AGN that met the criteria described in Sect. 4. Their distribution in the L X -redshift plane is presented in Fig. 2. We first split the sources into X-ray obscured and unobscured (or mildly obscured) AGN using  an N H limit of 10 23 cm −2 .Specifically, we used the lower and upper limits of the 90% confidence interval on the N H mode from the spectral fitting analysis.An AGN was classified as obscured if the lower limit of their N H value was higher than 10 23 cm −2 .Similarly, an AGN was identified as unobscured (or moderately obscured) if the upper limit of its N H value was lower than 10 23 cm −2 .Table 2 presents the number of sources classified.Then, we compared the SFR and M * of the host galaxies of the two AGN populations.The selection of classification criteria served a dual purpose.Firstly, it relied on recent research findings (Georgantopoulos et al. 2023) that highlight that distinctions in the properties of SMBHs and their host galaxies between obscured and unobscured AGN tend to diminish when the N H value falls below the threshold of N H < 23 cm −2 .Secondly, by taking into account the uncertainties associated with N H , the classification ensured that only firmly obscured and unobscured sources were categorised as such, enhancing the reliability of the classification process.
The results are presented in Fig. 3.In the figure, we have restricted both datasets to z < 0.7.This is because there are no AGN classified as obscured using the criteria described above, at z > 0.7, in our dataset.We also note that the distributions have been weighted to account for the different L X and redshift of obscured and unobscured AGN.For that purpose, each source was assigned a weight based on its L X and A172, page 5 of 14  2021), Koutoulidis et al. (2022).Specifically, the weight was calculated by measuring the joint L X distributions of the two populations (i.e.we added the number of obscured and unobscured AGN in each L X bin in bins of 0.1 dex) and then normalising the L X distributions by the total number of sources in each bin.The same procedure was followed for the redshift distributions.The total weight that was assigned in each source was the product of the two weights.We made use of these weights in all distributions presented in the remainder of this section.
Figure 3 shows the distributions of unobscured (blue shaded histograms) and obscured AGN (red dashed line histograms).The top panel presents the SFR distributions of the two AGN classes.The (weighted) median log SFR of the unobscured and obscured AGN is 0.82 and 0.57, respectively (Table 2).Applying a Kolmogorov-Smirnov (KS) test yielded a p-value of 0.10 (also shown in the legend of the plot).Similar pvalue were obtained by applying a Mann-Whitney test (MW; p-value = 0.14) and a Kuiper (p-value = 0.32) test.Therefore, the difference of 0.25 dex does not appear statistically significant (two distributions differ with a statistical significance of ∼2σ for a p-value of 0.05).
The bottom panel of Fig. 3 shows the M * distributions of obscured (blue shaded histogram) and unobscured (red dashed line) AGN.The weighted median of the log M * is 10.86 and 10.95 for unobscured and obscured AGN, respectively.Although the difference is small, it appears to be statistically significant (Table 2).Specifically, the p-value derived from the KS test was 0.02.Similar p-value were also obtained by applying MW and Kuiper tests (<0.05).We note that the (weighted) standard deviations (SDs) of the two populations are 11.22 (obscured) and 11.13 (unobscured).The (weighted) 95% confidence intervals (CI) are 10.91−11.30and 10.99−11.07 for the obscured and unobscured AGN, respectively.Therefore, based on our results, obscured AGN tend to live in more massive systems, and their hosts have a lower SFR compared to their unobscured counterparts.However, only the M * difference appears to be statistically significant.
Furthermore, we explored whether our outcomes are influenced by potential redshift evolution within the z < 0.7 redshift range encompassed by our dataset.For that purpose, we split the AGN sample into two redshift bins using the median value of the z < 0.7 dataset (i.e. at z = 0.21).The results do not appear redshift dependent since similar trends and p-values were obtained.Additionally, we examined whether our findings might be sensitive to uncertainties associated with photometric redshift estimates.To address this concern, we narrowed down our analysis to include only sources with spectroscopic redshifts.We obtained similar results in this restricted subset.
Most previous studies that examined the host galaxy properties of X-ray obscured and unobscured AGN did not find (significant) differences for the SFR and M * of the hosts of the two AGN populations.Specifically, Masoura et al. (2021) and Mountrichas et al. (2021c) studied the SFR and M * of X-ray obscured and unobscured AGN at 0 < z < 3.5 using data from the XMM-XXL and the Boötes fields, respectively, and concluded that both AGN classes live in galaxies with similar properties (see also Merloni et al. 2014).We note that the aforementioned studies did not account for the uncertainties in the N H values and applied a lower N H threshold (N H = 10 21.5 cm −2 ) to classify their AGN.However, Lanzuisi et al. (2017) studied AGN at 0.1 < z < 4 in the COSMOS field and found that the average N H shows a clear positive correlation with M * but not with the SFR.Studies that used optical criteria (e.g.optical spectra) to classify the AGN into type 1 and type 2 found that the two AGN types live in galaxies with similar SFR, but type 2 sources tend to reside in more massive systems, by ∼0.3 dex, both at low redshift (z < 1; Mountrichas et al. 2021c) and at high redshift (z < 3.5; Zou et al. 2019).
More recently, Georgantopoulos et al. ( 2023) compared the stellar populations and M * , among others, of X-ray obscured and unobscured AGN host galaxies in the COSMOS field at z ∼ 1 using N H = 10 23 cm −2 to classify their sources.Their analysis showed that the distribution of M * of obscured AGN is skewed to a higher M * compared to unobscured AGN.Specifically, they found that heavily obscured AGN live in galaxies that have a higher M * by 0.13 dex compared to unobscured sources.Although the difference was small, it was statistically significant (p-value = 1.3 × 10 −3 ).Notably, their results are in excellent agreement with our findings.They also found that heavily A172, page 6 of 14 obscured AGN tend to live in systems with older stars compared to unobscured AGN.This is consistent with our finding of a lower SFR for heavily obscured AGN hosts compared to those that are unobscured, although in our measurements the difference did not appear statistically significant.Georgantopoulos et al. (2023) suggested that a possible cause for the discrepant results among previous studies could be the different N H thresholds that were used.Indeed, when they lowered the N H value used to classify their AGN, the statistical significance of the differences detected in the host galaxy properties of the two AGN classes was lower (see their Fig.13).
To verify this hypothesis, we lowered the N H threshold utilised for our AGN classification to N H = 10 22 cm −2 using the lower and upper limits of N H specified at the outset of this section and repeated the analysis.The findings are showcased in Fig. 4 and Table 2. Results similar to those presented in Fig. 3 emerged.Specifically, obscured AGN tend to inhabit more massive systems (by 0.12 dex) and have a lower SFR (by 0.26 dex) compared to unobscured AGN.However, among these differences, only the variation in M * demonstrates statistical significance.It is observed that the (weighted) standard deviation of the two populations is 11.54 for the obscured AGN and 11.29 for the unobscured AGN.The (weighted) 95% confidence intervals are 11.10−11.40for the obscured AGN and 11.00−11.10for the unobscured AGN.Nonetheless, if we ignore the errors of the N H measurements, effectively classifying AGN based solely on their N H values without considering the limits of the measurements and implement a threshold at N H = 10 22 cm −2 , similar to what most prior studies have used for AGN classification, we uncover a marginally statistically significant difference in the M * distributions of the two AGN types (p-value = 0.052) and no statistically significant difference in terms of the SFR distributions of the obscured and unobscured AGN.
An alternative hypothesis proposed by Georgantopoulos et al. ( 2023) is that the variations in results across different studies could be attributed to the diverse luminosity ranges covered by the respective samples.For instance, AGN in the Boötes and XXM-XXL fields (Masoura et al. 2021;Mountrichas et al. 2021c) probe higher luminosities compared to those probed by sources in the COSMOS field (Lanzuisi et al. 2017;Georgantopoulos et al. 2023).This is also true when we compare the results between studies that used X-ray and optical criteria to classify the AGN.The latter have either used sources in the COSMOS field (e.g.Zou et al. 2019) that mainly probe low to intermediate L X AGN, or they have restricted their analysis to low luminosity systems at low redshift (e.g.Mountrichas et al. 2021c).To examine this hypothesis, we restricted our X-ray dataset to luminous sources by applying a luminosity cut at log [L X (erg s −1 ) > 44] (at z < 0.7), and we classified the AGN using an N H value of 10 22 (using the lower and upper limits of N H ) and repeated the analysis.There are 17 luminous and obscured AGN and 223 luminous and unobscured AGN.We detected a difference of 0.35 dex (based on the weighted median values) in the SFR of the two AGN populations.The obscured AGN appear to live in more massive systems compared to unobscured AGN (by 0.06 dex).However, none of these differences appeared to be statistically significant (p-value = 0.52 and 0.17 for the SFR and M * , respectively).

Eddington ratio of X-ray obscured and unobscured active galactic nuclei
The difference with the highest statistical significance that Georgantopoulos et al. (2023) reported was between the n Edd of obscured and unobscured sources (see e.g.their Table 3).Prompted by their results, we examined this difference in our dataset.For the dataset used in this part of our analysis, we did not have any available M BH , and therefore there were no n Edd measurements for our sources.Cross-matching our sample with the Wu & Shen (2022) catalogue (see Sect. 2) in which there are available n Edd measurements would constrain our dataset to only broad-line sources and exclude narrow-line AGN.In the next section, we examine whether n Edd depends on N H (for broad-line AGN).In order to include both broad-and narrowline sources in our investigation, in place of n Edd , we examined the specific black hole accretion rate, λ sBHAR , of obscured and unobscured AGN.We note that λ sBHAR is the rate of the accretion onto the SMBH relative to the M * of the host galaxy.It is often used as a proxy of n Edd , particularly when M BH measurements are not available (e.g.Georgakakis et al. 2017;Aird et al. 2018;Mountrichas et al. 2021c;Pouliasis et al. 2022).For the calculation of λ sBHAR , the following expression was used (e.g.Aird et al. 2018): A172, page 7 of 14 for the source classification.The bottom panel presents the results using N H = 10 22 cm −2 to characterise sources.In both cases, the errors of the N H measurements have been taken into account (see text for more details).Distributions are also weighted based on the redshift and L X of the sources.
where k bol is a bolometric correction factor that converts the X-ray luminosity to AGN bolometric luminosity.We adopted the value of k bol = 25 (e.g.Georgakakis et al. 2017;Aird et al. 2018;Mountrichas et al. 2021cMountrichas et al. , 2022c)). Figure 5 presents the λ sBHAR distributions of obscured and unobscured AGN using different N H thresholds to classify sources, as indicated at the top of each panel (taking into account the errors on the N H measurements).All distributions are weighted based on the L X and redshift of the sources.Table 2 presents the (weighted) median log λ sBHAR of the obscured and unobscured AGN for N H = 10 23 cm −2 and N H = 10 22 cm −2 .We found a difference of ∼0.1−0.2 dex in the λ sBHAR values of the two populations.Specifically, we found obscured sources tend to have, on average, a lower λ sBHAR compared to unobscured sources.. Based on the p-values derived using a KS test, this difference has a high statistical significance, regardless of the N H limit used.Similar p-values were found by applying MW and Kuiper tests.
Our results are in agreement with those reported in Georgantopoulos et al. (2023).We note that the difference we found appears smaller compared to the difference presented in the aforementioned study (∼0.3 dex).As we have already pointed out, we used stricter criteria in our analysis for the classification of AGN as obscured and unobscured compared to what was used in Georgantopoulos et al. (2023).Moreover, in Georgantopoulos et al. (2023), for the calculation of n Edd , they applied the same bolometric correction on L X to infer L bol as in this study.However, they used M BH measurements derived by stellar velocity dispersions, σ; that is, they utilised a different scaling relation compared to our work.
We concluded that the obscured AGN tend to live in more massive systems compared to unobscured AGN at z < 0.7.The difference in M * is small (≈0.1 dex), but it appears to be statistically significant.Obscured sources also live in hosts that have a lower SFR, by ≈0.25 dex, than unobscured AGN; however, this difference is not statistically significant (< 2σ).Moreover, neither of these differences appears to be statistically significant for luminous AGN (log [L X (erg s −1 ) > 44] and/or when less strict criteria are used for the source classification (i.e.errors on N H are ignored).Based on our analysis, the difference between the two AGN populations with the highest statistical significance is that regarding the λ sBHAR , which is a proxy of the n Edd .

Comparative analysis of super massive black hole characteristics, X-ray spectral attributes, and host galaxy properties
In the second part of our analysis, we examined the relationships among L bol , M BH , and M * as a function of the X-ray obscuration (N H ). We also investigated the correlation between the powerlaw slope, Γ, of the spectral model with the n Edd .For that purpose, we used the 271 X-ray AGN that are in common between the XMM catalogue and the Wu & Shen (2022) catalogue (see Sect. 4).
Here and in the following (sub-) sections, we characterise as AGN with high N H those sources with log N H ≥ 10 22 cm −2 using the mode value of N H that is available in our catalogue (i.e.without using the lower and upper limits of N H ).There are 23 AGN with high N H values and 248 AGN with low N H values in our dataset.The reason for using this threshold is that it facilitates a better comparison with previous studies.Furthermore, we note that characterising an AGN with high N H based on requiring the lower limit of N H to be higher than 10 23 cm −2 (10 22 cm −2 ) would result in zero (seven) sources.
Figures 6-8 present the distributions of L X , M * , and M BH as a function of redshift, respectively, for the 271 X-ray AGN.All three properties increase with redshift regardless of the N H value of the source.A Spearman correlation analysis revealed that there is a significant correlation between L X , M * , and M BH with redshift, albeit these correlations appear higher in the case of sources with N H < 10 22 cm −2 (Table 3).We note that in this part of our analysis, only broad-line (type 1) sources were included (see Sect. 2).

Bolometric luminosity versus black hole mass
In Fig. 9, we plot the L bol as a function of M BH .We chose to plot the L bol measurements that are available in the Wu & Shen (2022) catalogue.We note that their L bol calculations are in excellent agreement with the L bol measurements from CIGALE.Specifically, the mean difference of the two calculations is 0.04 dex (with a dispersion of 0.36), and thus this choice does not affect our results and conclusions.The lines correspond to A172, page 8 of 14  L bol = L Edd (black long-dashed line), L bol = 0.1 L Edd (green solid line), and L bol = 0.01 L Edd (red dotted line).The vast majority of our AGN lie between Eddington ratios of 0.01 and 1, with a median value of n Edd = 0.14), in agreement with previous studies (e.g.Trump et al. 2009;Lusso et al. 2012;Sun et al. 2015;Suh et al. 2020;Mountrichas 2023).Different symbols correspond to different redshift intervals, as indicated in the legend of the plot.The median value of n Edd is 0.09 and 0.24 at z < 0.7 and 0.7 < z < 1.9, respectively.The measurements in Fig. 9 are colour-coded based on the N H of the sources.Although the AGN sample used in this part of our analysis consists of type 1 sources, there are a few AGN that present low levels of X-ray obscuration (N H ∼ 10 22 cm −2 ).It is known that X-ray and optical obscuration do not necessarily coincide and several instances have been documented in the literature where type 1 AGN exhibit X-ray obscuration (e.g.Mateos et al. 2005Mateos et al. , 2010;;Scott et al. 2011;Shimizu et al. 2018;Kamraj et al. 2019;Masoura et al. 2020).Regarding the n Edd    The p-values obtained by applying a Spearman correlation analysis for the full redshift range (z < 1.9) as well as at low redshift (z < 0.7) and high redshift (0.7 < z < 1.9) are also shown.Measurements are colour-coded based on the N H of each source.

Black hole mass versus stellar mass
Next in our analysis, we examined the correlation between M BH and M * .The results are presented in Fig. 10.A strong correlation was detected between the two parameters.Applying a Spearman correlation analysis yielded a p-value of 3.5 × 10 −29 .A similar value was found using a Kendall correlation analysis (pvalue = 8.1 × 10 −26 ).Strong correlations between M BH and M * were also found when we split the dataset into two redshift intervals.The p-values are shown in the legend of Fig. 10.In this case the correlations, although strong, were weaker compared to the correlation found for our full sample.This can be attributed to the narrower range of M BH and M * probed by the sources within distinct redshift intervals compared to the sources encompassing the entire redshift range (see Figs. 7 and 8).To validate this conjecture, we employed the AGN dataset spanning the complete redshift range (z ≤ 1.9); we restricted the (log of) M * and M BH ranges within 11.0−13.0and 8.5−10, respectively (resembling the intervals embraced by AGN residing within 0.7 ≤ z ≤ 1.9); and we carried out a Spearman correlation analysis.This procedure resulted in a p-value of 0.008.Similarly, we obtained a p-value of 6 × 10 −4 by limiting the M * and M BH ranges to 10.0−11.5 and 7.0−9.5 (akin to the intervals pertinent to AGN existing within z < 0.7).
Prompted by the results of Sarria et al. (2010), who examined three X-ray AGN at z = 1−2, with N H = 10 22.5−23.0cm −2 and observed that they were consistent with the local M BH − M * relation, we colour coded the symbols in Fig. 10 based on the N H values of the sources.We noticed that sources with increased N H have a higher M BH for similar M * compared to sources with a lower N H .This is better illustrated in Fig. 11, where we mark AGN with N H values above and below 10 22 cm −2 differently, as indicated in the legend of the plot.The different lines in Fig. 11 indicate the best fits for the various subsets acquired through the application of a least-squares analysis.As mentioned above, AGN with higher N H values tend to have more massive black holes compared to AGN with lower N H values at similar M * , at least up to log [M * (M )] = 12.We also examined the ratio of M BH /M * as a function of redshift.Based on the results presented in the top panel of Fig. 12, the M BH /M * does not evolve with cosmic time up z < 2. The median log(M BH /M * ) value was found at −2.63.This value is in agreement with most previous studies that measured the M BH /M * ratio in the local Universe (e.g.−2.85; Häring & Rix 2004) as well as at high redshifts (e.g.Suh et al. 2020;Mountrichas 2023).The bottom panel of Fig. 12 presents the distributions of the M BH /M * ratio at different redshift intervals.The median value of the M BH /M * ratio at z < 0.7 is −2.69, and at 0.7 < z < 1.9, it is −2.55.The application of KS tests confirmed that the distributions are similar (p-values > 0.9 among all redshift intervals).
The results that appear in the top panel of Fig. 12 are colourcoded based on the N H of the sources.Sources with higher N H values seem to have a higher M BH /M * ratio.To examine this further, in Fig. 13, we plot the M BH /M * ratio as a function of N H .The blue line shows the best fit of the M BH M * − log N H relation for log N H < 22 cm −2 , whereas the red line shows the best fit for log N H > 22 cm −2 .The blue line is nearly flat, with a slope of 0.014 (standard error 0.079), which indicates that the M BH /M * ratio is almost constant for AGN with log N H < 22 cm −2 .However, the best fit for AGN with log N H > 22 cm −2 has a slope of 0.69 (standard error 0.24), which indicates that the M BH /M * ratio increases with N H for X-ray AGN with high N H values.A Spearman correlation analysis revealed a p-value = 0.06 for the correlation between M BH M * −log N H for sources with log N H > 22 cm −2 , which indicates a statistical significance of ∼2σ.The median value of the log M BH /M * ratio is -2.40 and -2.66 for AGN with N H > 10 22 cm −2 and N H < 10 22 cm −2 , respectively.We note, though, that a larger number of sources with N H > 10 22 cm −2 is required to formulate robust conclusions.
In the preceding sections, we observed that obscured AGN live, on average, in galaxies with a higher M * compared to unobscured AGN.Moreover, obscured AGN tend to have a higher M BH compared to their unobscured counterparts at similar M * .When combined with the higher M BH /M * ratio within the AGN population displaying elevated N H values, assuming this holds true, it implies that the SMBH growth in the obscured phase is higher than the galaxy growth.This may suggest that the growth A172, page 10 of 14 of the M BH occurs first, while the early stellar mass assembly may not be so efficient (Mountrichas et al. 2023).

Powerlaw slope versus Eddington ratio
We also investigated if there is a correlation between the powerlaw slope, Γ, of the X-ray spectral model and the n Edd .The results are shown in the top panel of Fig. 14.A strong correlation was found between Γ and n Edd (p-value = 8.1 × 10 −7 , applying both a Spearman and a Kendall correlation analysis).However, the correlation between the two parameters was also strong when we split the dataset into two redshift intervals; at 0.7 < z < 1.9, the p-value appears higher compared to the p-value obtained at z < 0.7 (see legend in the top panel of Fig. 14).This is most probably due to the different lines used for the calculation of the M BH and not a result of cosmic evolution.Risaliti et al. (2009) reported a strong correlation between the two parameters when the M BH was calculated using the H β line, while the authors reported a weaker correlation when the M BH was measured using the Mg ii line.There are only 12 sources in our dataset with 0.7 < z < 1.9 that have M BH calculations from both lines; there- (blue line; Γ = 0.306× n Edd + 2.303)), and for AGN with N H > 10 22 cm −2 (red line; Γ = 0.083× n Edd + 1.565)).Similar results were obtained when we split the two AGN populations into two redshift intervals at z = 0.7.Furthermore, our observations hold when considering the associated uncertainties of Γ and n Edd .This was verified, by utilising the linmix module (Kelly 2007), which performs a linear regression between two parameters by repeatedly perturbing the datapoints within their uncertainties.
We find it worth pointing out that in Fig. 14 there are some sources with non-physical values (Γ > 2.5 or Γ < 1.5).Although their occurrence is relatively low among AGN with N H < 10 22 cm −2 (15%), it becomes more pronounced (57%) for AGN with higher N H values.To examine whether this might influence the absence of a correlation between Γ and n Edd for AGN with N H > 10 22 cm −2 , we opted to exclude these sources and repeated the correlation analysis.However, even after this exclusion, we still did not observe a significant correlation between the two parameters for sources with elevated N H values.We find it essential to note, however, that this refinement in the analysis left us with a considerably reduced sample size, comprising only ten AGN with N H > 10 22 cm −2 .
The X-ray spectral index is sensitive to the properties of the accretion disc, such as temperature and ionisation state.Therefore, a correlation between the X-ray spectral index and n Edd for AGN with N H < 10 22 cm −2 may imply that changes in the A172, page 11 of 14 accretion rate can alter the structure and properties of the accretion disc, influencing the X-ray emission.The X-ray emission is also associated with a hot, optically thin corona of electrons above the accretion disc.The properties of the corona, such as its temperature and optical depth, can impact the X-ray spectral index.Thus, changes in the n Edd may lead to variations in the corona properties, affecting the X-ray spectrum.The AGN with N H < 10 22 cm −2 allow for a clearer view of the inner regions of the accretion disc and the corona.Furthermore, in AGN with low N H , a more direct view of the accretion disc may allow for a better determination of the Eddington ratio.Additionally, we investigated if this lack of correlation between the two parameters for the AGN population with N H > 10 22 cm −2 is due to the small number of available sources.For that purpose, we randomly selected an equal number of AGN with N H < 10 22 cm −2 to that with N H > 10 22 cm −2 , and we measured the correlation between Γ and n Edd .After 500 repetitions of this process, we obtained a median p-value of 0.047 from Spearman analysis (Kendall's correlation analysis yielded p-value = 0.091).The p-value obtained for the simulated AGN with N H < 10 22 cm −2 is about an order of magnitude lower compared to that obtained from the AGN with N H > 10 22 cm −2 .This indicates that the lack of correlation between Γ and n Edd for AGN with N H > 10 22 cm −2 is intrinsic and not due to their smaller sample size.This result aligns with the Comptonisation models, wherein variations in the accretion rate have a more pronounced impact on the soft spectral component (which gets lost in absorbed sources) compared to the hard powerlaw photon index.
As already noted, λ sBHAR is often used as a proxy of n Edd .Lopez et al. ( 2023) used X-ray selected AGN in the miniJ-PAS footprint and found, among other things, that the n Edd and λ sBHAR have a difference of 0.6 dex.They attributed this difference to the scatter on the M BH −M * relation of their sources.A difference between n Edd and λ sBHAR was also reported by Mountrichas & Buat (2023), albeit lower (∼0.25 dex), using AGN in the XMM-XXL field.Figure 15 presents a comparison between the two parameters for the 271 X-ray AGN that are in common between the XMM catalogue and the Wu & Shen (2022) catalogue.We found that, overall, there is good agreement between n Edd and λ sBHAR , with a median difference of 0.10 dex.We stress that this comparison includes only broadline AGN.We also confirm that this difference does not depend on N H , at least up to N H = 10 22.5−23 cm −2 , as probed by our dataset.
Since the n Edd measurements are in agreement with the λ sBHAR calculations, we then examined the correlation between Γ and λ sBHAR .We found similar results as those between Γ and n Edd .Specifically, a strong correlation was found between the two parameters for AGN with N H < 10 22 cm −2 (pvalue = 2.8 × 10 −3 ), but no correlation was detected for sources with N H > 10 22 cm −2 (p-value = 0.95).Prompted by these results, we utilised the larger AGN dataset used in Sect.5.1 (i.e.before matching the XMM sources with the Wu & Shen 2022, catalogue) to examine the correlation between Γ and λ sBHAR for the two AGN populations.This allowed us to investigate the Γ − λ sBHAR relation using a significantly larger sample of obscured sources (130 AGN) that has been defined with stricter A172, page 12 of 14 criteria (i.e.taking into account the uncertainties associated with N H ) and, more importantly, to include narrow-line (type 2) AGN in our investigation.A Spearman correlation analysis yielded a p-value of 1.8 × 10 −11 for AGN with N H < 10 22 cm −2 and 0.31 for AGN with N H > 10 22 cm −2 .We conclude that Γ and n Edd are correlated at all redshift and L X probed by our dataset.However, we did not detect such a correlation for AGN with increased N H values (N H > 10 22 cm −2 ).
Previous studies have found contradictory results regarding whether there is a correlation between Γ and n Edd .Shemmer et al. (2008) used 35 unabsorbed type 1 radio quiet (RQ) AGN at z < 3.2 (25 out of the 35 sources were at z < 0.5) and found a significant correlation between Γ and n Edd .They concluded that a measurement of Γ and L X can provide an estimate of n Edd and M BH with a mean uncertainty of a factor less than or equal to three.Brightman et al. (2013) used 69 RQ AGN in the COSMOS and ECDFS fields at z < 2 and found a significant correlation between the X-ray spectral index and n Edd .However, based on their analysis, the scatter of the Γ − n Edd relation is large, and thus the relation is only suitable for large samples and not for individual sources.We note, though, that the L bol of their sources was calculated following a mix of different methods (SED fitting and bolometric correction to the L X ), and this may contribute to the scatter.Trakhtenbrot et al. (2017) used 228 hard X-ray-selected AGN from the Swift/Bat AGN Spectroscopic Survey (BASS) and found a very weak but statistically significant correlation between Γ and n Edd .Nonetheless, their M BH measurements come from several different methods (see their Sect.2.3), and they reported that the correlation was weaker or even absent within their different subsets.More recently, Kamraj et al. (2022) used 195 Seyfert 1 AGN in the local Universe (z < 0.2) with NuSTAR and Swift/XRT or XMM observations.They studied the correlation between the X-ray spectral index and n Edd using three models to fit the Xray spectra of their sources.They found considerable scatter and no strong trend between Γ and n Edd for all the spectral models they applied.They concluded that the Γ−n Edd may not be universal nor robust and could vary with the choice of the sample, the luminosity range probed, and the energy range of X-ray data used in the analysis.We note that their M BH estimates come from the second data release of the optical measurements from the BASS survey and were inferred using a compilation of different techniques (e.g.broad-line measurements from optical spectra, stellar velocity dispersions, reverberation mapping), which could increase the scatter in the Γ − n Edd and weaken any possible correlation.
Combining the results of our analysis with those from previous works, we conclude that caution has to be taken when compiling results from different studies that have used different methods to measure the M BH and the L bol .Furthermore, the correlation between Γ and n Edd may not be universal and could (also) depend on the level of the X-ray obscuration of the sources.

Conclusions
The parent sample of this work includes ∼35 000 X-ray AGN included in the 4XMM-DR11 catalogue for which there are available X-ray spectra fitting measurements.To measure the host galaxy properties of these sources, we matched them with multiwavelength datasets and constructed their SEDs.Using the CIGALE SED fitting algorithm, we calculated the SFR and M * of the AGN.Our analysis demanded stringent selection criteria to ensure that only AGN with dependable X-ray spectral and SED fitting measurements were incorporated in our investigation.There were 1443 AGN that fulfilled these requirements.We then applied strict criteria using the N H values and their associated uncertainties to classify sources into obscured and unobscured AGN and compared their SMBH and host galaxy properties.Our main findings are the following: -Obscured AGN tend to live in more massive systems (by ∼0.1 dex) compared to unobscured AGN.The difference, although small, appears to be statistically significant.
Obscured sources also tend to live in galaxies with a lower SFR (by ∼0.25 dex) compared to their unobscured counterparts; however, this difference is not statistically significant.The results do not depend on the N H threshold used to classify AGN (N H = 10 23 cm −2 or N H = 10 22 cm −2 ), and the differences are not statistically significant at high L X (log [L X (ergs −1 )] > 44) nor if we disregard the errors associated with the N H measurements. -Unobscured AGN have, on average, higher specific black hole accretion rates (a proxy of the Eddington ratio) compared to unobscured sources.The difference is 0.1−0.2dex and appears to have a high statistical significance.Furthermore, we cross-matched our dataset with the catalogue of Wu & Shen (2022), which includes measurements for the M BH , L bol , and Eddington ratio, among others, for ∼750 000 QSOs from SDSS.There are 271 type 1 AGN in common between the two datasets up to a redshift of 1.9.We studied the n Edd and M BH /M * ratio of the two AGN populations, and we examined if there is a correlation between Γ and n Edd .Our main results are summarised as follows: -Type 1 AGN with N H > 10 22 cm −2 tend to have a higher M BH compared to type 1 sources with lower N H values at similar M * .-For type 1 AGN, the M BH /M * ratio is nearly constant, with N H up to N H = 10 22 cm −2 .However, our results suggest that the M BH /M * ratio increases at higher N H values. -A correlation was found between the spectral photon index, Γ, and the Eddington ratio, n Edd , for type 1 AGN with N H < 10 22 cm −2 .The findings of our work indicate that the inconsistent results among previous studies regarding the host galaxy properties of obscured and unobscured AGN could mainly be due to the different luminosities probed.Additionally, our analysis indicates that during the obscured phase, SMBH growth exceeds that of the host galaxies, potentially implying a sequential growth pattern where M BH develops first, while early stellar mass assembly might not be as efficient.Furthermore, the disparities in previous research regarding the correlation between Γ and n Edd may also be partly attributed to differences in the fraction of obscured and unobscured AGN within the samples used in those studies.
fur Astronomie (MPIA Heidelberg), Max-Planck-Institut fur Extraterrestrische Physik (MPE), Nanjing University, National Astronomical Observatories of China (NAOC), New Mexico State University, The Ohio State University, Pennsylvania State University, Smithsonian Astrophysical Observatory, Space Telescope Science Institute (STScI), the Stellar Astrophysics Participation Group, Universidad Nacional Autónoma de México, University of Arizona, University of Colorado Boulder, University of Illinois at Urbana-Champaign, University of Toronto, University of Utah, University of Virginia, Yale University, and Yunnan University.The Pan-STARRS1 Surveys (PS1) and the PS1 public science archive have been made possible through contributions by the Institute for Astronomy, the University of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society and its participating institutes, the Max Planck Institute for Astronomy, Heidelberg and the Max Planck Institute for Extraterrestrial Physics, Garching, The Johns Hopkins University, Durham University, the University of Edinburgh, the Queen's University Belfast, the Harvard-Smithsonian Center for Astrophysics, the Las Cumbres Observatory Global Telescope Network Incorporated, the National Central University of Taiwan, the Space Telescope Science Institute, the National Aeronautics and Space Administration under Grant No. NNX08AR22G issued through the Planetary Science Division of the NASA Science Mission Directorate, the National Science Foundation Grant No. AST-1238877, the University of Maryland, Eotvos Lorand University (ELTE), the Los Alamos National Laboratory, and the Gordon and Betty Moore Foundation.This publication makes use of data products from the Wide-field Infrared Survey Explorer, which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration.This research has made use of TOPCAT version 4.8 (Taylor 2005) and Astropy (Astropy Collaboration 2022).

Fig. 1 .
Fig. 1.Example of a source spectrum and model fit (left panels), including the background modelling (right panels) for the PN (top panels) and MOS (bottom panels).

Fig. 2 .
Fig. 2. Distribution of the 1443 X-ray AGN in the L X -redshift plane.

Fig. 3 .
Fig.3.Host galaxy properties of X-ray obscured (red dashed line histograms) and unobscured AGN (blue shaded histograms).Sources are classified as obscured when the lower limit of their N H value is higher than 10 23 cm −2 .We classified AGN as unobscured if the upper limit of their N H value is below 10 23 cm −2 .The top panel presents the SFR distributions of the two AGN populations.The bottom panel shows their M * distributions.The number of sources and the p-values obtained by applying a KS test are shown in the legend of the plots.Distributions are weighted based on the redshift and L X of the sources.

Fig. 4 .
Fig. 4. Similar to Fig. 3 but using a limit of N H = 10 22 cm −2 to classify AGN (taking into account the errors of the N H measurements).

Fig. 5 .
Fig.5.Distributions of λ sBHAR for obscured and unobscured AGN.The top panel presents the distributions using an N H threshold of 10 23 cm −2 for the source classification.The bottom panel presents the results using N H = 10 22 cm −2 to characterise sources.In both cases, the errors of the N H measurements have been taken into account (see text for more details).Distributions are also weighted based on the redshift and L X of the sources.

Fig. 6 .
Fig.6.X-ray luminosity, L X , as a function of redshift.AGN with log N H > 10 22 cm −2 are marked with red circles, whereas sources with log N H < 10 22 cm −2 are marked with blue triangles.

Fig. 7 .
Fig. 7. Stellar mass, M * , as a function of redshift.AGN with log N H > 10 22 cm −2 are marked with red circles, whereas sources with N H < 10 22 cm −2 are marked with blue triangles.

Fig. 8 .
Fig.8.Black hole mass, M BH , as a function of redshift.AGN with log N H > 10 22 cm −2 are marked with red circles, whereas sources with N H < 10 22 cm −2 are marked with blue triangles.

NFig. 9 .Fig. 10 .
Fig. 9. Bolometric luminosity, L bol , as a function of M BH .Different symbols correspond to different redshift intervals, as indicated in the legend.The lines correspond to L bol = L Edd (black dashed line), L bol = 0.1 L Edd (green solid line) and L bol = 0.01 L Edd (red dotted line).Measurements are colour-coded based on the N H of each source.

Fig. 11 .
Fig. 11.Black hole mass, M BH , as a function of M * for sources with log N H > 10 22 cm −2 (red circles) and sources with log N H < 10 22 cm −2 (blue triangles).Different lines represent the best fits of the different subsets, as indicated in the legend.

Fig. 12 .
Fig. 12. Ratio of M BH to M * .The top panel presents the M BH − M * ratio as a function of redshift, and the bottom panel shows the distributions of the M BH − M * ratio at different redshift intervals.

Fig. 13 .
Fig. 13. of M BH to M * as a function of N H .

22 Fig. 14 .
Fig. 14.Spectral photon index, Γ, as a function of n Edd .In the top panel, different symbols correspond to different redshift intervals, as indicated in the legend.The results are colour-coded based on the N H values of the sources.The p-values obtained by applying a Spearman correlation analysis are shown in the legend.The bottom panel shows the same relation but for X-ray AGN with N H > 10 22 cm −2 (red circles) and AGN with N H < 10 22 cm −2 (blue triangles).The p-values for the Γ − n Edd correlation for each AGN population are presented in the legend of the plot.The different lines correspond to the best fits using the total AGN sample (black dashed line), AGN with N H > 10 22 cm −2 (red solid line), and AGN with N H < 10 22 cm −2 (blue line).

Table 1 .
Models and the values for their free parameters used by CIGALE for the SED fitting.

Table 2 .
Weighted median values of SFR, M * , and λ sBHAR for obscured and unobscured AGN.N H = 10 23 cm −2 N H = 10 22 cm −2 Notes.We used different N H thresholds for the source classification.The number of sources and the p-values yielded by applying KS tests are also presented.

Table 3 .
p-values obtained from Spearman correlation analysis, assessing the correlations among L X , M * , M BH , and redshift.