© ESO 2021

1. Introduction

Active galactic nuclei (AGNs) are some of the most powerful objects in the sky because of the extreme accretion process of the super-massive black holes (SMBHs) in the center of galaxies (Soltan 1982; Richstone et al. 1998). The material (gas and dust) surrounding the SMBH not only feeds the central monster but is the origin of the obscuration of the AGN (see Hickox & Alexander 2018, for a recent review). Studying the properties of this obscuring material in AGNs is key to understanding the growth of SMBHs. The AGN unified model (Antonucci 1993; Urry & Padovani 1995) suggests that the obscuring material in the AGNs is shaped as an optically thick torus-like structure. The obscuring torus was initially thought to be smooth. However, many recent observations show that the material within the torus is clumpy rather than uniformly distributed (see Netzer 2015, for a recent review). For example, the rapid variable sources and eclipse events found in X-ray observations (e.g., Risaliti et al. 2002; Markowitz et al. 2014; Laha et al. 2020) and the observed 10 μm silicate features in the infrared (IR) spectra cannot be explained by a smooth torus (e.g., Nenkova et al. 2002; Mason et al. 2009).

Based on the obscuration of the torus, AGNs can be categorized into unobscured when the column density along the line of sight is N_H,los < 10²² cm⁻², and obscured when N_H,los > 10²² cm⁻². The most obscured sources are called Compton thick (CT-) AGNs when N_H,los > 10²⁴ cm⁻². Moreover, AGNs with different levels of obscuration are the main contributors to the cosmic X-ray background (CXB; the diffuse X-ray emission in the universe; e.g., Maccacaro 1991; Madau et al. 1994; Comastri et al. 1995). Hard X-ray surveys are more efficient in detecting obscured AGNs because high-energy photons can more easily penetrate the dense material surrounding the SMBH. However, only a small number of CT-AGNs have been discovered so far (e.g., Risaliti et al. 1999; Burlon et al. 2011; Ricci et al. 2015; Lanzuisi et al. 2018) because of their large obscuration, which makes it difficult to both detect them and properly measure their column density. Consequently, the uncertainties on the measurement of the intrinsic distribution of the column density of AGNs are still significant. The fraction of CT-AGNs predicted by AGN population synthesis models (∼30–50%; Gilli et al. 2007; Ueda et al. 2014; Buchner et al. 2015; Ananna et al. 2019) is much higher than what has been observed so far (∼10–30%; Burlon et al. 2011; Ricci et al. 2015; Lansbury et al. 2017; Masini et al. 2018; Zappacosta et al. 2018). Therefore, the intrinsic column density distribution of AGNs is still controversial.

In this work, we perform a broadband X-ray spectral analysis of high-quality (soft and hard) data available for a large, unbiased sample of obscured AGNs in the local universe (z < 0.15). In Sect. 2, we introduce the criteria that are used to select the unbiased AGN sample and describe the X-ray spectral analysis technique. In Sect. 3, we report the spectral analysis results. In Sect. 4, we develop a new method to calculate the intrinsic line-of-sight column density distribution of the AGNs in the local Universe. We also compare our derived distribution with the results obtained in previous observations and the constraints from different population synthesis models. All reported uncertainties are at 90% confidence level unless otherwise stated. Standard cosmological parameters are adopted as follows: ⟨H₀⟩ = 70 km s⁻¹ Mpc⁻¹, ⟨q₀⟩ = 0.0, and ⟨Ω_Λ⟩ = 0.73.

2. Sample selection and spectral analysis

2.1. Selection criteria

The sources presented in this work are selected from the 100-month Palermo Swift-BAT catalog¹ (Marchesi et al., in prep.), which covers 50% of the sky at the 15–150 keV flux limit of ∼5.4×10⁻¹² erg cm⁻² s⁻¹. The selection criteria are as follows:

1. Sources with line-of-sight column density² (N_H,los) between 10²³ and 10²⁴ cm⁻². To characterize the physical and geometrical properties of the obscuring material around the SMBH, a clear signal is needed from the reprocessed component of the obscuring torus to overcome the line-of-sight component. Though ideal for studying the obscuring torus, when sampling, there is significant bias against CT-AGNs. Therefore, here we select heavily obscured Compton-thin AGNs, against which there is less bias when studying the obscuring torus. In sources with N_H,los < 10²³ cm⁻², the contribution of the reprocessed component to the overall AGN emission is negligible (< 5% at 2–10 keV; Baloković et al. 2018), which makes the derivation of the torus properties a difficult process in those sources. We therefore select Compton-thin sources with N_H,los > 10²³ cm⁻² in our study of the AGN torus. We analyzed the nearby CT-AGNs selected from the Swift-BAT catalog in a separate set of papers (Marchesi et al. 2018, 2019, and in prep., Zhao et al. 2019a,b).

2. Available NuSTAR data. NuSTAR data are instrumental in properly characterizing the properties of heavily obscured AGNs in the local universe because of the significant suppression of their spectra at soft X-rays (see, e.g., Civano et al. 2015; Marchesi et al. 2018).

The obscuring material that reprocesses the X-ray emissions from the “hot corona” is mainly related to the dusty torus (< 10 pc) proposed by the AGN unified model and to the interstellar medium (ISM; > kpc) of the host galaxy (see, Netzer 2015; Almeida & Ricci 2017; Hickox & Alexander 2018, for recent reviews). The typical column density N_H toward the nucleus decreases with size scale as R⁻² (where R is the distance from the central SMBH). Thus, the N_H from the galaxy-wide scale is thought to be N_H < 10²³ cm⁻², except for galaxy mergers (e.g., Di Matteo et al. 2005) and high-redshift quasars where the galaxies are rich in gas (Circosta et al. 2019). The dusty gas in the compact torus can produce obscuration up to N_H ≈ 10²⁵ cm⁻². Our selected sources are heavily obscured (N_H > 10²³ cm⁻²) and are in the local Universe (z < 0.15), and no evidence has been found for merger events. Therefore, we assume that the obscuring material that reprocesses the X-ray emission in our sources is mainly from the AGN torus.

A total of 93 out of ∼1000 AGNs in the BAT catalog have been selected and analyzed in this work. The information about the observations used when analyzing each source is listed in the Appendix. The median redshift of the sources in our finalized sample is ⟨z⟩ = 0.02776 (i.e., the median distance is ⟨d⟩∼122 Mpc).

2.2. Spectral analysis

We perform a broadband (1–78 keV) X-ray spectral analysis of all 93 sources in our sample. NuSTAR (3–78 keV) data provide coverage in the hard X-rays. For the soft-X-ray band, we use archival XMM-Newton data when they are available (1–10 keV; 48 sources); otherwise we use archival Chandra data (1–7 keV; 19 sources). We use Swift-XRT data (1–10 keV; 26 sources) when neither XMM-Newton nor Chandra data are available. The details of the data reduction are listed and described in Appendix A.

The spectra are fitted using XSPEC (Arnaud 1996) version 12.10.0c. The photoelectric cross-section is from Verner et al. (1996); the element abundance is from Anders & Grevesse (1989) and metal abundance is fixed to solar; the Galactic absorption column density is obtained using the nh task (Kalberla et al. 2005) in HEAsoft for each source. The χ² statistic is adopted when XMM-Newton data and Chandra data are used, while the C statistic (Cash 1979) is used when Swift-XRT data are applied due to the low quality of the Swift-XRT spectra and the limited number of counts in each bin.

The spectra of heavily obscured AGNs are complicated by the emergence of the reprocessed component, including the Compton scattering and fluorescent emission lines, which are buried by the line-of-sight component in the unobscured AGN spectra. However, despite the additional difficulty of characterizing the spectra, this reprocessed component becomes a perfect tool to estimate the physical and geometrical properties of the obscuring material surrounding the central SMBH. In this work, following Zhao et al. (2020), we analyze the spectra of the sources in our sample using the self-consistent Borus model (Baloković et al. 2018), which optimizes the exploration of the parameter space and has been intensively used to characterize heavily obscured AGNs.

The complete Borus model used in the spectral analysis consists of three components:

(A) A reprocessed component produced by the obscuring material near the SMBH, including the Compton-scattered continuum and fluorescent lines, characterized by borus02. borus02 assumes a sphere with conical cutouts at both poles (Baloković et al. 2018), approximating a torus with an opening angle that can vary in the range of θ_Tor = [0 − 84]°, corresponding to a torus covering factor of c_f = cos(θ_Tor) = [1 − 0.1]. The inclination angle, which is the angle between the axis of the AGN and the observer’s line of sight, is also a free parameter ranging from θ_inc = [18 − 87]°, where θ_obs = 18° is when the AGN is observed face-on and θ_obs = 87° is observed edge-on. The average column density of the obscuring torus can vary in the range of log(N_H,tor) = [22.0–25.5].

(B) A line-of-sight component or the absorbed intrinsic continuum, described by a cut-off power law, denoted by cutoffpl in XSPEC, multiplied by an obscuring component, including both the photoelectric absorption (zphabs) and the Compton-scattering (cabs) effects. It is worth noting that the torus column density in the reprocessed component is decoupled from the line-of-sight column density: the torus column density is an average property of the obscuring torus. In contrast, the line-of-sight column density represents a quantity that is along our line of sight and could vary when observed at different epochs.

The line-of-sight column density N_H,los can be significantly different from N_H,tor, which can be used as an approximation of the nonuniform (clumpy) distribution of matter surrounding the SMBH (see discussion in Sect. 4.2 of Baloković et al. 2018). Buchner et al. (2019), Tanimoto et al. (2019), who assume a clumpy torus scenario, provide a more realistic description of the obscuring material surrounding the accreting SMBH. However, these authors do not provide information about the global average properties of the torus, such as for example its average column density, which is a significant focus of this paper. Moreover, the Tanimoto et al. (2019) model has not yet been made publicly available.

(C) A scattered component modeling the fractional AGN emission that is scattered rather than absorbed by the obscuring material. The scattered component is characterized by an unabsorbed cut-off power law multiplied by a constant. The fractional unabsorbed continuum is usually less than 5–10% of the intrinsic continuum (see, e.g., Noguchi et al. 2010; Marchesi et al. 2016) and accounts for the AGN emission at low-energy below a few keV.

In the process of modeling the spectra, we tie the photon indices, Γ, the cut-off energy, E_cut, and the normalization, norm, of the intrinsic continuum, the reprocessed component, and the fractional unabsorbed continuum together, assuming that the three components have the same origin. The photon index in borus02 ranges in [1.4–2.6], and therefore the photon index in the cut-off power law varies between 1.4 and 2.6 as well.

The Borus model is used in the following XSPEC configuration:

(1)

where constant₁ is the cross-calibration between NuSTAR and the soft-X-ray observatories, that is, XMM-Newton, Chandra, and Swift-XRT; phabs models the Galactic absorption from our Galaxy; and constant₂ is the fraction of the unabsorbed continuum in the scattered component.

The cut-off energy is fixed at E_cut = 500 keV for all sources, except for ESO 383-18, whose cut-off energy is found to be E_cut < 20 keV. The spectra of nine sources (ESO 263-13, Mrk 3, NGC 835, NGC 2655, NGC 4102, NGC 4258, NGC 4507, NGC 5728 and NGC 7319) all show strong nonAGN thermal emission around 1 keV, which may be caused by the star formation process and/or diffuse gas emission. We use mekal (Mewe et al. 1985) to model this nonAGN thermal contribution: the temperature and the relative metal abundance in mekal are both left free to vary. To better constrain the parameters of the mekal model, we fit the spectra of these sources down to 0.3 keV. When analyzing the spectra of 3C 445, we add a few Gaussian lines to model different emission lines. The relative iron abundance of the reprocessed component, A_Fe, is fixed to 1 (the solar value), except for three sources (3C 445, 3C 452 and ESO 383-18), where a significant improvement in spectral fit (> 3σ using ftest in XSPEC) has been found when A_Fe is free to vary. The best-fit iron abundances are , , and .

We note that the obscuring material in the AGNs might also originate from the polar dust outflow as revealed by IR observations (e.g., Tristram et al. 2007). However, the X-ray observations are less affected by the polar outflow because the gas density in the polar outflow is much less than that in the torus (Wada et al. 2016). Indeed, the covering factors measured in X-ray are systematically smaller than those measured in IR (see, Fig. 2 in Tanimoto et al. 2019). This suggests that the typical size of the X-ray obscuring material is much smaller (i.e., the torus) than the typical sizes of the IR emission (i.e., torus + polar dust). Therefore, in the following discussion, we assume that absorption measured in the X-ray spectra of the sources in our sample is mainly due to the obscuring material in the torus, except for a few cases discussed in Sect. 3.

3. Results

The spectra of 93 sources and their best-fit models can be found online³. The best-fit results of the spectral analysis, that is, line-of-sight column density, N_H,los, torus average column density, N_H,tor, cosine of the inclination angle, cos(θ_inc), torus covering factors, c_f, 2–10 keV flux, Flux_2 − 10, and 2–10 keV intrinsic (absorption-corrected) luminosity, L_{int, 2 − 10}, are reported in Tables A.2–A.4 when XMM-Newton, Chandra, and Swift-XRT data are used, respectively. For 15 sources in our sample, the contributions of their reprocessed emission to the overall spectra are marginal, such that the parameters of the reprocessed component, for example the torus average column density, inclination angle, and torus covering factor, cannot be constrained at all. Therefore we analyze their spectra using only the line-of-sight component and the scattered component for those sources. Eight sources in our sample are found to have line-of-sight column density N_H,los < 10²³ cm⁻² or N_H,los > 10²⁴ cm⁻², and therefore these sources are excluded from our sample. The spectra and best-fit model predictions of four representative sources have been plotted in Fig. A.1.

Flux variations are commonly found in the X-ray spectra of AGNs, especially when multiple observations are taken over timescales that vary from weeks to years (e.g., Guainazzi 2002; Risaliti 2002; Markowitz et al. 2014). Such variabilities are commonly explained by either the fluctuation of the AGN intrinsic emission (e.g., Nandra 2001) or the variation in the absorbing column density along the line of sight (see, e.g., Risaliti et al. 2002; Bianchi et al. 2012). Within the 93 sources in our sample, 20 sources are semi-simultaneously observed by NuSTAR and the soft-X-ray observatories. In the remaining 73 sources, 43 (∼59%) are measured with significant flux variations between the soft- and hard-X-ray observations (2–10 keV flux variation > 20 percent). Within these 43 sources, 16 mainly show intrinsic emission variation; 15 sources show N_H,los variation; and the flux variabilities of 12 sources can be explained only by considering both intrinsic emission and N_H,los variations. The details of the variability analysis are reported in Appendix B. The best-fit results of the sources with flux variability are summarized in Table B.1. It is worth noting that if a source had multiple soft-X-ray observations, we chose the one taken closest to their NuSTAR observation time. Therefore, the fraction of the sources in our sample that experienced flux variabilities might be even higher if all soft-X-ray observations are taken into account; however, we cannot exclude the possibility that the N_H,los measured with different instruments may have different values (apparent variability) due to different bandpasses, energy resolution, and effective areas. The N_H,los reported in Tables A.2–A.4 are those measured in the NuSTAR observing epoch, and we use them in the following discussions.

Marchesi et al. (2019, hereafter M19) reported the CT-AGNs in the nearby Universe, which are also selected from the BAT 100-month catalog and are covered by NuSTAR data. The sources were analyzed using the borus02 model as well, with the distinction that the inclination angle is fixed in the edge-on direction when fitting the spectra. We re-analyze these CT sources using the same model presented in Sect. 2.2 and leave the inclination angle free to vary when fitting the spectra. Thus, we were able to compare the properties of the obscuring torus of CT sources with those of the Compton-thin sources in our sample. The best-fit re-analysis results of the CT sources in the M19 sample are reported in Table A.5. Four CT sources in the M19 sample are found to be Compton thin in our re-analysis. Therefore, we add those four sources to our Compton-thin sample, which now includes 89 sources in total⁴.

Although CT-AGNs are an ideal sample with which to study the obscuring torus – because of their significantly suppressed line-of-sight emission, which allows clear visualization of the reprocessed emission from the torus–, we need to keep in mind the strong bias against the detection of CT-AGNs, which means that the observed CT sample is likely incomplete. Indeed, the detected fraction of CT-AGNs (f_CT) in the BAT sample decreases significantly as the distance (redshift) increases (f_CT ≈ 31% at 10 Mpc and f_CT ≈ 4% at 100 Mpc; Ricci et al. 2015), suggesting that the detection of CT-AGNs is significantly biased, especially for low-luminosity CT-AGNs at large distance. Therefore, the torus properties derived from the CT sample in this work may not represent the torus properties of the whole CT-AGN population.

The main results of the spectral analysis are as follows:

• The Compton-thin sources in our sample are evenly observed in every direction considering the uncertainties as shown in Fig. 1 (upper left), suggesting that our BAT-selected Compton-thin AGN sample is an unbiased sample. In contrast, most of the CT sources in the M19 sample are observed edge-on, which is in agreement with the material distribution formalism used in the clumpy torus model which assumes that the obscuring clumps are populated in the edge-on direction (e.g., Nenkova et al. 2008; Buchner et al. 2019; Tanimoto et al. 2019).

• The torus column densities of the majority of Compton-thin sources and CT-AGNs are in the > 10²⁴ cm⁻² range as presented in Fig. 1 (upper right), suggesting that CT reflectors are commonly found in both Compton-thin AGNs and CT-AGNs. A similar result was also reported by Buchner et al. (2019), for example.

• The average torus column density is similar for both Compton-thin AGNs and CT-AGNs, namely log(N_{H, tor, ave}) ∼ 24.15 (see left panel of Fig. 2), independent of the observing angle.

• We notice that the average column densities of the tori of Compton-thin sources are generally larger than their line-of-sight column densities, suggesting that Compton-thin AGNs are usually observed through an under-dense region in their tori. Conversely, the average column densities of the tori of CT-AGNs are always smaller than their line-of-sight column densities, suggesting that CT-AGNs are observed through an over-dense region in their tori; although we cannot exclude the possibility that the additional obscuration along the line of sight of sources (especially when observed face-on) with N_H,tor < N_H,los is due to polar outflows (Hönig et al. 2013).

• Compton-thin AGNs and CT-AGNs have (statistically) different covering factors, with the former having larger (c_f > 0.5) covering factors than the latter (c_f < 0.5), as shown in Fig. 1 (bottom left). Interestingly, the average torus covering factor of Compton-thin AGNs is c_f, ave ∼ 0.67. In contrast, the average torus covering factor decreases significantly when the line-of-sight column density reaches the CT regime, as shown in Fig. 2 (right). The low-c_f found in the CT sample might reflect the fact that the CT sample is significantly biased. The detected CT-AGNs in the BAT sample are the intrinsically most luminous sources, which typically have a lower c_f compared with the intrinsically fainter AGNs (Burlon et al. 2011; Ricci et al. 2017b; Marchesi et al. 2019), suggesting that BAT samples only the low-c_f CT-AGNs even in the nearby Universe. Indeed, Ricci et al. (2015) measured a c_f ≈ 0.70 for AGNs in the local Universe using a statistical method (the fraction of the absorbed AGNs is used as a proxy for the mean torus covering factor of the AGNs in the sample). Their result is in good agreement with the average covering factor measured in our unbiased Compton-thin sample.

• The obscuring material in the torus of AGNs is significantly inhomogeneous. The torus average column densities of the majority of Compton-thin AGNs and CT-AGNs are at least three times smaller or larger than their line-of-sight column densities, as shown in Fig. 1 (bottom right). Moreover, for ∼30% of sources in the sample, their torus average column densities are different from their line-of-sight column densities by more than a factor of ten. A similarly inhomogeneous torus result was found by Laha et al. (2020), who studied a sample of 20 Compton-thin AGNs.

• The distributions of the torus column density contrast ratio (CR = N_H,tor/N_H,los which shows how inhomogeneous the torus is) observed in Compton-thin AGNs and CT-AGNs are different (see, Fig. 1 bottom right). We consider that the overall distribution of the torus column density contrast ratio of different AGN types should be a combination of the CR distribution of both Compton-thin AGNs and CT-AGNs. To combine the two distributions, we rescale the torus column density contrast ratio distribution of CT-AGNs before producing the overall distribution because we are biased against the detection of CT-AGNs, that is, we need to consider the intrinsic number of Compton-thin AGNs and CT-AGNs. Here, we assume that the numbers of Compton-thin AGNs and CT-AGNs are similar, which is in agreement with the results of previous works and those found here, as discussed further in Sect. 4. After rescaling, we find that the torus column density contrast ratio is rather flat over CR = [0.03,30] (Fig. 1 bottom right), suggesting that for a given torus column density, an AGN can be observed with different line-of-sight column densities with equal probabilities.

Fig. 1. Left to right in the first row and second row: number of sources with a specific range of inclination angles, cos(θinc), torus column densities, log(NH,tor), torus covering factors, cf, and torus column density contrast ratios, NH,tor/NH,los, from the Compton-thin sources in our sample (gray histogram) and CT sources from M19 (orange histogram), respectively. cos(θinc)∼0.05 is when the AGN is observed edge-on and cos(θinc)∼0.95 is when the AGN is observed face-on. The error bar is at 90% confidence level. The overall distribution of the torus column density contrast ratio after rescaling is plotted in yellow. We do not include the 15 sources fitted with only a line-of-sight component and a scattered component here.

Fig. 2. Torus column density log(NH,tor) (left) and torus covering factor cf (right) as a function of line-of-sight column density, log(NH,los). Compton-thin sources are plotted in light gray points, while CT sources are plotted in light red squares. The average and 1σ standard error of the torus column densities and torus covering factors in different line-of-sight column density bins are plotted in black points for Compton-thin sources and red squares for CT sources, respectively. Left panel: NH,tor = NH,los is plotted as a light-gray dashed line. The low covering factors of the CT sources are due to the bias explained in Sect. 3.

In the Compton-thin sample, the effect of the biases discussed above are much weaker than in the CT sample, because the reprocessed component does not dominate the hard band emission of Compton-thin AGNs. Therefore, there is less bias in the sampling method against the tori properties measured in the Compton-thin sample. We use only these measurements to derive the intrinsic N_H,los distribution of AGNs in the local Universe in Sect. 4.

4. Intrinsic line-of-sight column density distribution of AGNs

The line-of-sight column density distribution of AGNs in the local Universe has been measured in recent years (e.g., Burlon et al. 2011; Ricci et al. 2015). However, the observed line-of-sight column density distribution is significantly affected by selection bias. Therefore, the intrinsic distribution of the AGN line-of-sight column density depends heavily on the absorption correction used, particularly for N_H,los > 10^23.5 cm⁻². To investigate the actual intrinsic line-of-sight column density distribution of AGNs in the local Universe, we developed a Monte Carlo method based on the measured properties of the obscuring tori in our unbiased sample from Sect. 3. Here we assume that different types of AGNs possess tori with similar properties (Antonucci 1993; Urry & Padovani 1995). The details of our method are as follows:

1. We randomly draw a torus average column density N_H,tor from the distribution shown in Fig. 3.

2. We then assign a random contrast ratio in the range of [0.03–30] to each N_H,tor (only a small fraction of sources have extremely inhomogeneous torus with a contrast ratio outside of this range), and therefore the line-of-sight column density of each torus is N_H,los = N_H,tor/CR;

3. We assume a 33% fraction of unobscured AGNs because the average covering factor of the torus in our sample is c_f, ave ∼ 0.67, and therefore the lines of sight of 33% of the AGNs do not intersect their torus. We presume that the distribution of N_H,los between 10²⁰ cm⁻² and 10²² cm⁻² is flat.

Fig. 3. Distribution of the average column density of the tori of the sources in our unbiased Compton-thin AGN sample. The histogram describes the same sample as in the upper right panel of Fig. 1 but with different grouping bins.

A discrepancy in the intrinsic line-of-sight column density distribution between the previous observational results obtained using Swift-BAT (e.g., Burlon et al. 2011; Ricci et al. 2015) and constraints from different population synthesis models (e.g., Gilli et al. 2007; Ueda et al. 2014; Buchner et al. 2015; Ananna et al. 2019) still exists. We compare our derived intrinsic line-of-sight column density distribution with the results of these authors⁵ in Table 1 and Fig. 4.

Fig. 4. Comparison between the distributions of intrinsic line-of-sight column density derived from our new developed method with previous observational results (left) and those used in different population synthesis models (right). The extremely obscured sources with log(NH,los) > 26 are included in the 25 < log(NH,los) < 26 bin.

When comparing to the Swift-BAT observed column density distributions (Burlon et al. 2011; Ricci et al. 2015), our method predicts a larger fraction of CT-AGNs (see, Table 1), which is likely because of the difficulty that Swift-BAT has in detecting extremely heavily obscured AGNs. Our predictions are in good agreement with the column density distribution used in the population synthesis model in Ueda et al. (2014), which is also based on a low-redshift Swift-BAT-selected sample. It is worth noting that the column density distribution is luminosity (and redshift) dependent (see, e.g., Buchner et al. 2015). Different works adopt different samples of AGNs with different luminosity and redshift ranges when deriving the column density distribution. In particular, our work provides a constraint on the line-of-sight column density distribution of AGNs with a median 2–10 keV intrinsic luminosity of ⟨L_{int, 2 − 10}⟩ = 1.20 × 10⁴³ erg s⁻¹ in the local Universe (z < 0.15). The listed column density distributions of each of the studies in Table 1 are the values at z ∼ 0. We note that the fraction of unobscured AGNs derived in our work at z ∼ 0 is larger than those obtained in Gilli et al. (2007), Buchner et al. (2015), Ananna et al. (2019). Therefore, an overestimation of the CXB at the soft X-ray band might occur if the fraction of unobscured AGNs is consistent at different redshifts, suggesting that the unobscured AGN fraction should significantly decrease, moving towards higher redshifts, as discovered in observations (e.g., Lanzuisi et al. 2018).

Figure 5 shows a comparison of the average torus properties obtained from our unbiased sample (left side) and the intrinsic line-of-sight column density distribution derived from our method.

Fig. 5. Average torus properties of our unbiased Compton-thin sample (left) and intrinsic line-of-sight column density distribution derived from our new developed method (right).

5. Conclusions

We study the obscuring tori of AGNs by analyzing the broadband X-ray spectra of a large and unbiased sample of heavily obscured AGNs in the local Universe. We find that Compton-thin AGNs and CT-AGNs may possess similar tori, whose average column density is Compton thick (N_{H, tor, ave}  ≈  1.4 × 10²⁴ cm⁻²), but that they are observed through different (under-dense or over-dense) regions of the tori. The average torus covering factor of the Compton-thin sample is c_f = 0.67, suggesting that the fraction of unobscured AGNs is ∼33%. We also find that the obscuring tori of most AGNs are significantly inhomogeneous. Using the obtained properties of the obscuring torus and a Monte Carlo method, we calculate the intrinsic line-of-sight column density distribution of AGNs in the nearby Universe, finding good agreement with recent AGN population synthesis models. Our results may help understand the properties of the obscuring materials surrounding the SMBH in the local Universe and help to constrain the future population synthesis study of the CXB. In the future, new X-ray missions such as Athena and the proposed Lynx and AXIS facilities will detect a large sample of obscured AGNs at high redshift (see, e.g., Marchesi et al. 2020), which could help us to further constrain the evolution of AGN obscuration and SMBH growth over cosmic time.

Acknowledgments

X.Z. thanks the anonymous referee for their detailed and useful comments, which helped improve the paper significantly. X.Z., M.A. and S.M. acknowledge NASA funding under contract 80NSSC17K0635 and 80NSSC19K0531. X.Z. also acknowledges NASA funding under contract 80NSSC20K0043. This research has made use of the Palermo BAT Catalogue and database operated at INAF-IASF Palermo. We thank the NuSTAR Operations, Software and Calibrations teams for support with these observations. This research has made use of data and/or software provided by the High Energy Astrophysics Science Archive Research Center (HEASARC), which is a service of the Astrophysics Science Division at NASA/GSFC and the High Energy Astrophysics Division of the Smithsonian Astrophysical Observatory. This work is based on observations obtained with XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA. The scientific results reported in this article are based in part on observations made by data obtained from the Chandra Data Archive. This work made use of data supplied by the UK Swift Science Data Centre at the University of Leicester.

References

Appendix A: Data reduction and spectral analysis results

Information about the observations adopted when analyzing each source is listed in Tables A.1. The redshift of each source is adopted from NED⁶ and SIMBAD⁷, except for 2MASX J00502684+8229000, for which there is no redshift record; we therefore let the redshift of this source free to vary when fitting its spectra obtain a best-fit redshift of z ∼ 0.03817.

The NuSTAR data of both FPMA and FPMB are calibrated, cleaned, and screened using the nupipeline script version 0.4.6 and calibration database (CALDB) version 20181030. The sources spectra, ancillary response files (ARF), and response matrix files (RMF) are obtained using the nuproducts script version 0.3.0. The source spectra are extracted from a 75″ circular region, and the background spectra are extracted using a 75″ circular region near the source but avoiding contamination from the source.

The XMM-Newton data from two MOS cameras (Turner et al. 2001) and one EPIC CCD camera (pn; Strüder et al. 2001) onboard XMM-Newton are utilized in the spectral analysis. The XMM-Newton data are reduced using the Science Analysis System (SAS; Jansen et al. 2001) version 17.0.0 following standard procedures. The flares are removed by visually inspecting the high-energy light curve (10–12 keV) when the count rates exceed 0.35 cts s⁻¹ for MOS and 0.4 cts s⁻¹ for pn. The source spectra are extracted from a circular region with a radius of 15″; the background spectra are extracted from a circle nearby the source with the same radius as the source spectra but avoiding contamination from sources.

Chandra data, focused on the 0.3–7 keV energy band, are used in our spectral analysis when XMM-Newton data are not available. We reduced the Chandra data using the Chandra’s data analysis system, CIAO software package (Fruscione et al. 2006) version 4.11 and Chandra CALDB version 4.8.2. The level = 1 data are reprocessed using the CIAO chandra_repro script. The source spectrum is extracted from a circular region with a radius of 5″; the background spectrum is extracted from a circular region near the source with a radius of 10″. The CIAO specextract tool is used to extract both source and background spectra, ARF, and RMF files following standard procedures.

Given the smaller effective area in soft X-ray band (eight times smaller than XMM-Newton pn and four times smaller than Chandra at 3 keV), Swift-XRT data are used only when neither XMM-Newton nor Chandra data are available. The spectra are obtained from the online Swift product generator⁸ (see also Evans et al. 2009). In the case of variability, we did not stack multiple observations of the same source. The Swift-XRT spectra are rebinned with a minimum of 5 counts per bin because of the limited number of counts using the HEAsoft task grppha, while the NuSTAR, XMM-Newton, and Chandra spectra are rebinned with a minimum of 20 counts per bin.

Fig. A.1. Spectra and ratio (between the data and model predictions) of ESO 263-13 (XMM-Newton+NuSTAR), UCG 3995B (Chandra+NuSTAR), LEDA 549777 (Swift-XRT+NuSTAR) and NGC 7212 (in M19 sample). NuSTAR and soft X-ray data are plotted in blue and red, respectively. The total best-fit model predictions and different components of the models of are plotted in cyan and black, respectively. The reprocessed component, line-of-sight component, and scattered (and Mekal) component are plotted in dashed, solid, and dotted lines, respectively. Significant flux variabilities are found in ESO 263-13 and UGC 3995B.

Appendix B: Variability analysis

To properly characterize the spectra of the sources observed with flux variation between the NuSTAR observations and soft X-ray observations (2–10 keV flux variation > 20 percent), we fit them three times: 1. First we allow the cross-calibration factor between the soft X-rays spectra and NuSTAR spectra, C_soft/NuS, free to vary, assuming the flux variability is caused by the intrinsic emission variation. The sources whose flux variabilities are thought to be caused by intrinsic emission variations are those with C_soft/NuS different from unity at 90% confidence level. 2. Second, we fix C_soft/NuS = 1, and disentangling the line-of-sight column densities of the soft-X-ray observations, N_{H,los, soft} and NuSTAR observations, N_H,los, NuS, assuming the flux variability is caused by N_H,los variations. The sources whose flux variabilities are caused by N_H,los variations are those whose N_H,los, NuS are different from their N_{H,los, soft} at 90% confidence level. 3. Finally, we allow C_soft/NuS free to vary and disentangling the N_{H,los, soft} and N_H,los, NuS, assuming the flux variability is caused by both the intrinsic emission and N_H,los variations. If the improvement in the fit is > 90% confidence level using the ftest in XSPEC with respect to the previous two scenarios the first two scenarios, we assume that the flux variability of this source is the result of both intrinsic emission and N_H,los variations. Otherwise, the cause of the flux variation of this source is determined by comparing the reduced statistics (χ²/d.o.f or cstat/d.o.f) of the best-fit of the first two scenarios. For sources whose flux variabilities are caused by the N_H,los variations only, we fix their cross-calibration factors at C_soft/NuS = 1 to better constrain the other parameters. Here, we assume a consistent reprocessed component and scattered component between different observing epochs, considering that the global structure and properties of the obscuring torus is stable over a timescale of a few years. We summarize the best-fit results of the sources with observed flux variability (including four variable sources from M19 sample) in Table B.1.

All Tables

All Figures

Fig. 1. Left to right in the first row and second row: number of sources with a specific range of inclination angles, cos(θinc), torus column densities, log(NH,tor), torus covering factors, cf, and torus column density contrast ratios, NH,tor/NH,los, from the Compton-thin sources in our sample (gray histogram) and CT sources from M19 (orange histogram), respectively. cos(θinc)∼0.05 is when the AGN is observed edge-on and cos(θinc)∼0.95 is when the AGN is observed face-on. The error bar is at 90% confidence level. The overall distribution of the torus column density contrast ratio after rescaling is plotted in yellow. We do not include the 15 sources fitted with only a line-of-sight component and a scattered component here.

In the text

Fig. 2. Torus column density log(NH,tor) (left) and torus covering factor cf (right) as a function of line-of-sight column density, log(NH,los). Compton-thin sources are plotted in light gray points, while CT sources are plotted in light red squares. The average and 1σ standard error of the torus column densities and torus covering factors in different line-of-sight column density bins are plotted in black points for Compton-thin sources and red squares for CT sources, respectively. Left panel: NH,tor = NH,los is plotted as a light-gray dashed line. The low covering factors of the CT sources are due to the bias explained in Sect. 3.

In the text

	Fig. 3. Distribution of the average column density of the tori of the sources in our unbiased Compton-thin AGN sample. The histogram describes the same sample as in the upper right panel of Fig. 1 but with different grouping bins.
In the text

	Fig. 4. Comparison between the distributions of intrinsic line-of-sight column density derived from our new developed method with previous observational results (left) and those used in different population synthesis models (right). The extremely obscured sources with log(NH,los) > 26 are included in the 25 < log(NH,los) < 26 bin.
In the text

	Fig. 5. Average torus properties of our unbiased Compton-thin sample (left) and intrinsic line-of-sight column density distribution derived from our new developed method (right).
In the text

Fig. A.1. Spectra and ratio (between the data and model predictions) of ESO 263-13 (XMM-Newton+NuSTAR), UCG 3995B (Chandra+NuSTAR), LEDA 549777 (Swift-XRT+NuSTAR) and NGC 7212 (in M19 sample). NuSTAR and soft X-ray data are plotted in blue and red, respectively. The total best-fit model predictions and different components of the models of are plotted in cyan and black, respectively. The reprocessed component, line-of-sight component, and scattered (and Mekal) component are plotted in dashed, solid, and dotted lines, respectively. Significant flux variabilities are found in ESO 263-13 and UGC 3995B.

In the text