Systematic Study of AGN Clumpy Tori with Broadband X-Ray Spectroscopy: Updated Unified Picture of AGN Structure

Suzaku carried four X-ray CCD cameras called the XIS, which covered an energy band below ≈10 keV. The XIS 0, XIS 2, and XIS 3 are front side–illuminated CCDs (XIS-FI), and XIS 1 is a backside-illuminated one (XIS-BI). Suzaku also carried a collimated-type instrument called the HXD, which was sensitive to photons above ≈10 keV. The HXD consisted of the PIN (10–70 keV) and GSO (40–600 keV) detectors. We did not analyze any GSO data in this paper, because most of our targets were too faint to be detected with the GSO.

We reduced Suzaku data in a standard way, utilizing HEAsoft version 6.26.1 and CALDB released on 2018 October 10 (XIS) and 2011 September 13 (HXD). We reprocessed the unfiltered XIS event data with the aepipeline script. The XIS source events were extracted from a circular region with a radius of 3'–4' (depending on the source flux) centered at the source position, and the background was taken from a source-free circular region with a radius of 2'–3'. For NGC 4388, we utilized the same background spectrum as used in Shirai et al. (2008), which was produced from the data of Arp 220 observed on 2006 January 7–9, because there was a largely extended emission around the nucleus of NGC 4388. We generated the response matrix file (RMF) with xisrmfgen and ancillary response file (ARF) with xissimarfgen (Ishisaki et al. 2007). The spectra of XIS-FIs were coadded in order to improve the statistics. We utilized only the data of XIS-FIs, whose effective area in the iron K band was larger than that of XIS-BI.

The unfiltered HXD-PIN data were also reprocessed by using aepipeline. We made the spectrum of the non-X-ray background (NXB) using the "tuned" background event files (Fukazawa et al. 2009).⁵ We added a simulated spectrum of the cosmic X-ray background to the spectrum of the NXB. In the spectral analysis, only the 16–40 keV range was utilized, where the source flux is sure to be brighter than 3% of the NXB level (the maximum systematic error in the 15–70 keV range; Fukazawa et al. 2009).

There are three X-ray CCD cameras on XMM-Newton: one EPIC/pn and two EPIC/MOS. We did not use the data of the MOS cameras, which have a much smaller effective area than the pn camera. We analyzed the pn data using the Science Analysis Software (SAS) version 17.0.0 and calibration file (CCF) released on 2018 June 22. We reprocessed the data with the epproc script. The source spectra were extracted from a circular region with a radius of 40'' centered on the source peak and the background from a source-free circular region with a 50'' radius in the same CCD chip. The RMF and ARF were generated with rmfgen and arfgen, respectively.

NuSTAR carries two FPMs (FPMA and FPMB), which cover an energy range of 3–79 keV. The FPM data were analyzed with HEAsoft v6.26.1 and CALDB released on 2019 October 12. The spectra were extracted from a circular region with a 50''–75'' radius (depending on the source flux) centered at the source peak, and the background was taken from a nearby source-free circular region with a 60''–75'' radius. The source spectra, background spectra, RMF, and ARF of the two FPMs are combined with addascaspec.

A typical broadband X-ray spectrum of an unobscured AGN consists of (1) a direct component from the nucleus, which is well represented by a power law with an exponential high energy cutoff; (2) reflection components from the accretion disk (if any) and torus accompanied by fluorescence emission lines; and (3) a soft excess component. The spectrum is often subject to absorption by ionized (warm) and/or cold gas in the line of sight. To explain a hump structure peaked around 30 keV and an apparently broad iron K emission line feature, two major distinct models have been proposed: one invoking a strong relativistic reflection component from the inner accretion disk (e.g., Tanaka et al. 1995) and the other invoking variable partial absorbers (e.g., Miyakawa et al. 2012). The discussion of which model is physically correct has long been controversial. This paper does not aim to answer this long-standing question because our main goal is to constrain the torus structure. In fact, Ogawa et al. (2019) obtained similar results on the torus parameters by adopting either of the two models.

For simplicity, in this paper, we adopt the latter model (partial covering model). The whole model for unobscured AGNs is expressed in the XSPEC (Arnaud 1996) terminology as follows (model 1):

$$\begin{eqnarray}&&\begin{array}{l}\mathrm{Model}\ 1={\mathsf{const}}\ast {\mathsf{phabs}}\\ \quad \ast \,({\mathsf{zphabs}}\ast {\mathsf{cabs}}\ast {\mathsf{WA}}\ast {\mathsf{WA}}\ast {\mathsf{WA}}\\ \quad \ast \,({\mathsf{zcutoffpl}}+{\mathsf{compTT}})\\ \quad +\,{\mathsf{atable}}\{{\mathsf{xclumpy}}\_{\mathsf{R}}.{\mathsf{fits}}\}+{\mathsf{atable}}\{{\mathsf{xclumpy}}\_{\mathsf{L}}.{\mathsf{fits}}\}\\ \quad +\,{\mathsf{zgauss}}).\end{array}\end{eqnarray} \tag{ 2 }$$

• (1)  
  The const and phabs terms represent the cross-calibration constant (C) and the Galactic absorption, respectively. When we analyze NuSTAR data, we set C = 1 for the XIS-FI or EPIC-pn data as the reference and make it free for the NuSTAR/FPMs. That for the Suzaku/HXD-PIN is fixed at 1.16 or 1.18, depending on the target position in the detector coordinates, based on the calibration using the Crab Nebula. We fix the hydrogen column density of the Galactic absorption (${N}_{{\rm{H}}}^{\mathrm{Gal}}$) to the total Galactic H i and H₂ value given by Willingale et al. (2013).
• (2)  
  The zcutoffpl term represents the direct component (cutoff power law), and the compTT term is the soft excess (the thermal Comptonization model by Titarchuk 1994 is adopted). The cutoff energy is fixed at 300 keV, a canonical value for nearby AGNs (Dadina 2008). The photoelectric absorption and Compton scattering are taken into account with the zphabs and cabs models, respectively. Its line-of-sight column density (${N}_{{\rm{H}}}^{\mathrm{LOS}}$) is self-consistently determined by the torus parameters with the equation

  $$\begin{eqnarray}&&{N}_{{\rm{H}}}^{\mathrm{LOS}}={N}_{{\rm{H}}}^{\mathrm{Equ}}\exp \left(-\displaystyle \frac{{\left({i}_{{\rm{X}}}-90^\circ \right)}^{2}}{{\sigma }_{{\rm{X}}}{}^{2}}\right).\end{eqnarray} \tag{ 3 }$$

  Note that this condition was not considered in the analysis of Ogawa et al. (2019). Adopting the model by Iso et al. (2016), we consider three layers of absorption by ionized matter (WA); one is a full absorber, and two are partial absorbers. To model the ionized absorbers, we generate a table model by running XSTAR version 2.54a (Kallman & Bautista 2001; Bautista & Kallman 2001) for different values of the ionization parameter (ξ) and hydrogen column density (N_H). We adopt the same grid as that used by Miyakawa et al. (2012), where ξ and N_H range over $0.1\lt \mathrm{log}\xi /\mathrm{erg}\,\mathrm{cm}\,{{\rm{s}}}^{-1}\lt 5$ and $20\lt \mathrm{log}{N}_{{\rm{H}}}/{\mathrm{cm}}^{-2}\lt 25$ with 20 logarithmic intervals, respectively. We assume that the ionized gas has solar abundances, a temperature of 10⁵ K, a density of 10¹² cm⁻³, and a turbulent velocity of 200 km s⁻¹, and that the incident spectrum is a power law with a photon index of 2.0.
• (3)  
  The table models (atable{xclumpy_R.fits} and atable{xclumpy_L.fits}) correspond to the reflection continuum and fluorescence emission lines from the torus, respectively, based on the XCLUMPY model. The parameters are the power-law normalization at 1 keV, photon index, cutoff energy, equatorial hydrogen column density $({N}_{{\rm{H}}}^{\mathrm{Equ}})$, torus angular width (σ_X), and inclination angle (i_X). We link the photon index, normalization, and cutoff energy to those of the direct component. In unobscured AGNs, the observed equivalent width of the narrow iron Kα line mainly constrains the torus parameters (Ogawa et al. 2019). To avoid degeneracy among them, we fix i_X at 45° for all objects as a typical value of unobscured AGNs (see Appendix B).
• (4)  
  The zgauss term represents an additional emission line feature below 1 keV.

We adopt the same spectral model as in Tanimoto et al. (2020) for obscured AGNs. Compared with model 1, we ignore ionized absorbers because absorption by the torus is dominant. Instead, we consider (1) an unabsorbed scattered component by a surrounding gas of the power-law continuum and (2) optically thin thermal emission from the host galaxy, both of which become unignorable at low energy bands. This model (model 2) is expressed in the XSPEC terminology as follows:

$$\begin{eqnarray}\begin{array}{rcl}\mathrm{Model}\ 2 & = & {\mathsf{const}}{\mathsf{1}}\ast {\mathsf{phabs}}\\ & & \ast \,({\mathsf{const}}{\mathsf{2}}\ast {\mathsf{zphabs}}\ast {\mathsf{cabs}}\ast {\mathsf{zcutoffpl}}\\ & & +\,{\mathsf{const}}{\mathsf{3}}\ast {\mathsf{zcutoffpl}}+{\mathsf{atable}}\{{\mathsf{xclumpy}}\_{\mathsf{R}}.{\mathsf{fits}}\}\\ & & +\,{\mathsf{const}}{\mathsf{4}}\ast {\mathsf{atable}}\{{\mathsf{xclumpy}}\_{\mathsf{L}}.{\mathsf{fits}}\}+{\mathsf{apec}}).\end{array}\end{eqnarray} \tag{ 4 }$$

• (1)  
  The const1 and phabs terms represent the cross-calibration constant and the Galactic absorption, respectively (same as in model 1; see Section 4.1).
• (2)  
  The zcutoffpl term represents the direct component. The const2 factor accounts for its possible time variability between two different observation epochs, which is fixed to unity for Suzaku/XIS. The zphabs * cabs term represents the photoelectric absorption and Compton scattering by the torus, whose line-of-sight column density is determined by Equation (3).
• (3)  
  The const3 factor gives the scattering fraction (f_scat). The parameters of zcutoffpl are linked to those of the direct component.
• (4)  
  The table models of XCLUMPY (atable{xclumpy_R.fits} and const4 * atable{xclumpy_L.fits}) correspond to the reflection continuum and emission line components from the torus, respectively. To account for possible systematic uncertainties (due to the simplified assumption of the geometry and metal abundances), const4 is multiplied to the latter table. The photon index, normalization, and cutoff energy are linked to those of the direct component. The values of ${N}_{{\rm{H}}}^{\mathrm{Equ}}$, σ_X, and i_X are left free.
• (5)  
  The apec term represents optically thin thermal emission from the host galaxy. In NGC 3081 and NGC 4388, two different temperature components are required.

We find that models 1 and 2 give a fairly good description of the broadband spectra of all objects (${\chi }_{\mathrm{red}}^{2}\lt 1.3$). Tables 3 and 4 summarize the best-fit parameters of the unobscured and obscured AGNs, respectively. In the left panels of Figures 1 and 2, we overplot the best-fit models folded with the energy responses and their residuals from the data. The right panels of Figures 1 and 2 plot the best-fit models in units of EI(E) (where I(E) is the energy flux) for unobscured and obscured AGNs, respectively. Table 5 lists the best-estimated intrinsic luminosities and Eddington ratios with adopted black hole masses. Here we define the Eddington luminosity as L_Edd = 1.26 × 10³⁸(M_BH/M_⊙) erg s⁻¹ and convert the 2–10 keV luminosities to bolometric ones with a correction factor of 20.

Table 3.  Best-fit Parameters of Unobscured AGNs

Object	phabs	zcutoffpl	compTT	WA1a	WA2a	WA3a	XCLUMPY	zgauss	const
	${N}_{{\rm{H}}}^{\mathrm{Gal}}$	Γ	kTbb	NH	NH	NH	${N}_{{\rm{H}}}^{\mathrm{Equ}}$	Eline, σline, Kline	CFPMs/XIS	χ2/dof
		KP	kTP	$\mathrm{log}\xi$	$\mathrm{log}\xi$	$\mathrm{log}\xi$	σ		CFPMs/pn	${\chi }_{\mathrm{red}}^{2}$
			τ	Cfrac	Cfrac	Cfrac	i		CHXD/XIS
			KS				${N}_{{\rm{H}}}^{\mathrm{LOS}}$
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
NGC 2992	5.89c	${1.71}_{-0.01}^{+0.01}$	⋯	⋯	${0.61}_{-0.18}^{+0.14}$	${1.58}_{-0.07}^{+0.16}$	${0.97}_{-0.10}^{+0.06}$	⋯	⋯	3140.6/2478
		${19.6}_{-0.3}^{+0.2}$	⋯	⋯	${0.10}_{-0.00}^{+0.09}$ d	${0.15}_{-0.05}^{+0.23}$ d	${19.0}_{-0.1}^{+0.2}$		${1.12}_{-0.01}^{+0.01}$	1.27
			⋯	⋯	${0.53}_{-0.04}^{+0.05}$	0.53b	45c		⋯
			⋯				${36.4}_{-1.4}^{+1.4}$
MCG−5-23-16	12.0c	${1.95}_{-0.01}^{+0.01}$	⋯	${0.11}_{-0.05}^{+0.05}$	${221}_{-8}^{+10}$	⋯	${0.25}_{-0.02}^{+0.02}$	⋯	${1.00}_{-0.01}^{+0.01}$	4096.8/3436
		${63.3}_{-2.1}^{+2.0}$	⋯	${1.66}_{-0.11}^{+0.22}$	${2.65}_{-0.04}^{+0.03}$	⋯	${26.3}_{-0.3}^{+0.3}$		⋯	1.19
			⋯	1c	${0.34}_{-0.01}^{+0.01}$	⋯	45c		⋯
			⋯				${137}_{-1}^{+1}$
NGC 3783	14.1c	${1.64}_{-0.02}^{+0.03}$	${93.8}_{-5.2}^{+4.2}$	${1.72}_{-0.16}^{+0.13}$	${111}_{-17}^{+48}$	${9.27}_{-0.56}^{+0.98}$	${2.08}_{-0.35}^{+1.03}$	${0.60}_{-0.01}^{+0.01}$, 10c, ${3.23}_{-0.41}^{+0.41}$	⋯	1714.0/1391
		${9.68}_{-0.44}^{+0.66}$	${2.02}_{-0.02}^{+7.61}$ d	${1.53}_{-0.05}^{+0.06}$	${3.43}_{-0.05}^{+0.15}$	${1.13}_{-0.06}^{+0.15}$	${16.7}_{-0.4}^{+0.5}$		${1.12}_{-0.01}^{+0.01}$	1.23
			${0.010}_{-0.000}^{+0.427}$ d	1c	${0.68}_{-0.02}^{+0.02}$	0.68b	45c		⋯
			${16.6}_{-6.6}^{+11.1}$				${14.0}_{-1.5}^{+5.2}$
UGC 6728	5.55c	${2.03}_{-0.02}^{+0.01}$	⋯	⋯	${60.8}_{-10.5}^{+10.8}$	⋯	${6.74}_{-3.45}^{+6.14}$	⋯	⋯	668.0/652
		${7.97}_{-0.51}^{+0.67}$	⋯	⋯	${2.54}_{-0.05}^{+0.10}$	⋯	${11.6}_{-1.6}^{+1.3}$ d		⋯	1.02
			⋯	⋯	${0.39}_{-0.04}^{+0.04}$	⋯	45c		1.16c
			⋯				<0.44
NGC 4051	1.20c	${2.01}_{-0.02}^{+0.02}$	${96.7}_{-4.6}^{+5.8}$	⋯	${500}_{-63}^{+0}$ d	${10.5}_{-0.6}^{+0.8}$	${6.01}_{-0.90}^{+1.04}$	⋯	⋯	1522.7/1313
		${8.92}_{-0.56}^{+0.43}$	${2.08}_{-0.08}^{+12.94}$ d	⋯	${1.62}_{-0.85}^{+1.24}$	${2.16}_{-0.02}^{+0.02}$	${12.0}_{-2.0}^{+0.7}$ d		${1.44}_{-0.01}^{+0.01}$	1.16
			${0.85}_{-0.84}^{+0.61}$ d	⋯	${0.43}_{-0.02}^{+0.04}$	0.43b	45c		⋯
			${1.20}_{-0.67}^{+0.08}$				<0.22
NGC 4395	1.93c	${1.50}_{-0.00}^{+0.03}$ d	⋯	⋯	${5.05}_{-0.39}^{+0.56}$	⋯	${7.44}_{-3.53}^{+7.20}$	⋯	⋯	508.5/473
		${0.94}_{-0.02}^{+0.06}$	⋯	⋯	${1.74}_{-0.09}^{+0.10}$	⋯	${14.5}_{-0.7}^{+0.6}$		⋯	1.08
			⋯	⋯	${0.84}_{-0.03}^{+0.03}$	⋯	45c		1.18c
			⋯				${5.15}_{-3.21}^{+3.53}$
MCG−6-30-15	4.74c	${2.16}_{-0.01}^{+0.02}$	${77.8}_{-1.8}^{+1.9}$	${0.24}_{-0.02}^{+0.03}$	${115}_{-8}^{+8}$	${2.54}_{-0.16}^{+0.18}$	${18.8}_{-1.5}^{+7.3}$	${0.59}_{-0.01}^{+0.01}$, 10c, ${15.7}_{-0.8}^{+0.7}$	⋯	2621.4/2083
		${36.2}_{-1.7}^{+2.0}$	${2.00}_{-0.00}^{+2.28}$ d	${0.36}_{-0.02}^{+0.03}$	${2.71}_{-0.02}^{+0.02}$	${0.10}_{-0.00}^{+0.23}$ d	${13.8}_{-0.2}^{+0.1}$	${0.67}_{-0.01}^{+0.01}$, 10c, ${13.9}_{-0.6}^{+0.6}$	${0.91}_{-0.01}^{+0.01}$	1.26
			${0.010}_{-0.000}^{+0.455}$ d	1c	${0.26}_{-0.02}^{+0.02}$	0.26b	45c		⋯
			${29.4}_{-14.6}^{+2.3}$				${4.57}_{-0.74}^{+0.72}$
IC 4329A	5.60c	${1.77}_{-0.01}^{+0.01}$	⋯	${0.073}_{-0.036}^{+0.042}$	${319}_{-23}^{+31}$	⋯	${0.26}_{-0.02}^{+0.02}$	${0.79}_{-0.01}^{+0.01}$, 20c, ${2.21}_{-0.28}^{+0.28}$	${0.98}_{-0.01}^{+0.01}$	1523.2/1248
		${37.6}_{-0.8}^{+0.9}$	⋯	${1.56}_{-0.23}^{+0.19}$	${2.96}_{-0.01}^{+0.01}$	⋯	${22.1}_{-0.2}^{+0.2}$		⋯	1.22
			⋯	1c	${0.21}_{-0.01}^{+0.01}$	⋯	45c		⋯
			⋯				${40.7}_{-1.3}^{+1.0}$
NGC 6814	14.8c	${1.60}_{-0.03}^{+0.05}$	⋯	⋯	${298}_{-170}^{+202}$ d	⋯	${1.44}_{-0.92}^{+4.28}$	⋯	⋯	368.0/332
		${2.54}_{-0.79}^{+1.34}$	⋯	⋯	${2.96}_{-0.35}^{+0.29}$	⋯	${12.1}_{-2.1}^{+3.9}$ d		⋯	1.11
			⋯	⋯	${0.34}_{-0.09}^{+0.22}$	⋯	45c		1.16c
			⋯				<2.2
NGC 7213	1.11c	${1.63}_{-0.05}^{+0.10}$	${123}_{-10.0}^{+8.1}$	⋯	${4.27}_{-0.61}^{+0.46}$	⋯	${1.82}_{-0.36}^{+1.45}$	⋯	⋯	1874.9/1613
		${4.53}_{-0.88}^{+1.33}$	${4.75}_{-2.36}^{+1.10}$	⋯	${1.76}_{-0.05}^{+0.08}$	⋯	${13.8}_{-1.4}^{+0.9}$		⋯	1.16
			${2.69}_{-0.94}^{+7.87}$	⋯	${0.25}_{-0.04}^{+0.05}$	⋯	45c		1.16c
			${0.33}_{-0.17}^{+0.12}$				${0.36}_{-0.33}^{+1.09}$
NGC 7314	1.59c	${1.99}_{-0.01}^{+0.02}$	⋯	${0.33}_{-0.04}^{+0.04}$	${1.10}_{-0.18}^{+0.22}$	${500}_{-8}^{+0}$ d	${0.16}_{-0.02}^{+0.06}$	⋯	⋯	1945.0/1698
		${23.0}_{-0.8}^{+1.4}$	⋯	${0.64}_{-0.10}^{+0.20}$	${0.10}_{-0.00}^{+0.43}$ d	${3.17}_{-0.04}^{+0.03}$	${24.2}_{-1.1}^{+0.6}$		${0.96}_{-0.01}^{+0.01}$	1.15
			⋯	1c	${0.38}_{-0.02}^{+0.02}$	0.38b	45c		⋯
			⋯				${49.5}_{-2.4}^{+2.0}$
NGC 7469	5.39c	${1.86}_{-0.02}^{+0.02}$	${80.6}_{-2.0}^{+2.7}$	${0.16}_{-0.04}^{+0.05}$	${500}_{-13}^{+0}$ d	⋯	${2.06}_{-0.47}^{+1.22}$	⋯	⋯	1696.2/1561
		${10.1}_{-0.5}^{+0.6}$	${2.00}_{-0.00}^{+1.97}$ d	${2.39}_{-0.06}^{+0.07}$	${3.31}_{-0.05}^{+0.06}$	⋯	${12.4}_{-1.3}^{+0.8}$		${1.13}_{-0.01}^{+0.01}$	1.09
			${3.41}_{-0.46}^{+6.86}$	1c	${0.18}_{-0.03}^{+0.03}$	⋯	45c		⋯
			${2.63}_{-2.21}^{+0.13}$				<0.15

Notes. Column (1): galaxy name. Column (2): hydrogen column density of the Galactic absorption in 10²⁰ cm⁻². Column (3): photon index of the direct component and the normalization at 1 keV in 10⁻³ photons keV⁻¹ cm⁻² s⁻¹. Column (4): input soft photon temperature in eV, plasma temperature in keV, plasma optical depth, and normalization of soft excess component at 1 keV in 10⁻² photons keV⁻¹ cm⁻² s⁻¹. Columns (5)–(7): hydrogen column density of an ionized absorber in 10²² cm⁻², its logarithmic ionization parameter (ξ in erg cm s⁻¹), and its covering fraction. Column (8): hydrogen column density along the equatorial plane in 10²⁴ cm⁻², torus angular width in degrees, inclination angle of the observer in degrees, and hydrogen column density along the line of sight in 10²⁰ cm⁻². Column (9): energy of the emission line in keV, its line width in eV, and its normalization at 1 keV in 10⁻⁴ photons keV⁻¹ cm⁻² s⁻¹. Column (10): relative normalization of NuSTAR/FPMs to Suzaku/XIS, NuSTAR to XMM-Newton/EPIC-pn, and Suzaku/HXD to Suzaku/XIS.

^aThe WA1 model is a full absorber, and the WA2 and WA3 models represent partial absorbers. ^bThe value is linked to that of WA2. ^cFixed. ^dThe parameter reaches a limit of its allowed range.

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Table 4.  Best-fit Parameters of Obscured AGNs

Object	phabs	zcutoffpl	apec	XCLUMPY	const3	const4	const(1,2)
	${N}_{{\rm{H}}}^{\mathrm{Gal}}$	Γ	kT1	${N}_{{\rm{H}}}^{\mathrm{Equ}}$	fscat	NLine	CTIME	χ2/dof
		KP	KA1	σ			CFPMs/XIS	${\chi }_{\mathrm{red}}^{2}$
			kT2	i			CHXD/XIS
			KA2	${N}_{{\rm{H}}}^{\mathrm{LOS}}$
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
NGC 3081	4.63a	${1.81}_{-0.25}^{+0.69}$ b	${0.99}_{-0.20}^{+0.27}$	${5.65}_{-4.69}^{+10.20}$	${0.42}_{-0.26}^{+0.40}$	1a	1a	96.9/82
		${0.90}_{-0.45}^{+0.84}$	${2.15}_{-0.41}^{+0.78}$	${23.1}_{-6.3}^{+12.5}$			⋯	1.18
			${0.19}_{-0.03}^{+0.04}$	${57.5}_{-10.0}^{+24.6}$			1.18a
			${19.9}_{-8.5}^{+14.6}$	${7.77}_{-0.76}^{+1.22}$
NGC 4388	2.87a	${1.50}_{-0.00}^{+0.01}$ b	${0.30}_{-0.02}^{+0.02}$	${0.90}_{-0.19}^{+0.14}$	${1.69}_{-0.06}^{+0.05}$	${1.68}_{-0.30}^{+0.34}$	${0.26}_{-0.02}^{+0.02}$	2071.9/1974
		${1.07}_{-0.03}^{+0.03}$	${9.50}_{-1.16}^{+1.15}$	${19.7}_{-3.8}^{+4.0}$			1a	1.05
			${1.21}_{-0.03}^{+0.03}$	${69.5}_{-2.4}^{+2.7}$			⋯
			${13.8}_{-1.0}^{+1.0}$	${3.02}_{-0.05}^{+0.05}$
Centaurus A	11.7a	${1.76}_{-0.01}^{+0.01}$	${0.78}_{-0.07}^{+0.07}$	${0.18}_{-0.03}^{+0.08}$	${0.62}_{-0.05}^{+0.04}$	${0.70}_{-0.08}^{+0.15}$	${1.30}_{-0.01}^{+0.01}$	3095.0/2919
		${17.1}_{-0.2}^{+0.4}$	${31.1}_{-5.2}^{+5.1}$	${49.7}_{-8.5}^{+4.3}$			1a	1.06
			⋯	${51.6}_{-3.1}^{+6.8}$			⋯
			⋯	${0.99}_{-0.01}^{+0.01}$
NGC 6300	10.6a	${1.79}_{-0.06}^{+0.05}$	${0.59}_{-0.33}^{+0.16}$	${9.78}_{-2.88}^{+6.21}$	${0.68}_{-0.08}^{+0.10}$	1a	${0.95}_{-0.03}^{+0.03}$	1128.5/1059
		${1.23}_{-0.14}^{+0.11}$	${2.55}_{-0.70}^{+0.69}$	${19.1}_{-1.6}^{+2.1}$			1a	1.07
			⋯	${52.7}_{-4.7}^{+4.7}$			⋯
			⋯	${2.09}_{-0.06}^{+0.07}$

Notes. Column (1): galaxy name. Column (2): hydrogen column density of the Galactic absorption in 10²⁰ cm⁻². Column (3): photon index of the direct component and the normalization at 1 keV in 10⁻² photons keV⁻¹ cm⁻² s⁻¹. Column (4): temperature of the apec model in keV and normalization of the apec model in 10${}^{-19}/4\pi {[{D}_{{\rm{A}}}(1+z)]}^{2}\int {n}_{{\rm{e}}}{n}_{{\rm{H}}}{dV}$, where D_A is the angular diameter distance to the source in centimeters, and n_e and n_H are the electron and hydrogen densities in cm⁻³. Column (5): hydrogen column density along the equatorial plane in 10²⁴ cm⁻², torus angular width in degrees, inclination angle of the observer in degrees, and hydrogen column density along the line of sight in 10²³ cm⁻². Column (6): scattering fraction in percent. Column (7): relative normalization of the emission lines to the reflection component. Column (8): time variability constant, relative normalization of NuSTAR/FPMs to Suzaku/XIS, and relative normalization of Suzaku/HXD to Suzaku/XIS.

^aFixed. ^bThe parameter reaches a limit of its allowed range.

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Table 5.  X-Ray Luminosity

Object	logL2–10a	$\mathrm{log}{\lambda }_{\mathrm{Edd}}$	$\mathrm{log}{M}_{\mathrm{BH}}/{M}_{\odot }$	Reference
(1)	(2)	(3)	(4)	(5)
NGC 2992	43.0	−1.52	7.72	a
MCG−5–23–16	43.4	−1.34	7.98	b
NGC 3783	42.9	−1.13	7.27	b
UGC 6728	42.3	−0.40	5.85	c
NGC 4051	41.9	−0.48	5.60	d
NGC 4395	40.0	−1.72	4.88	b
MCG−6–30–15	43	−1.24	7.42	b
IC 4329A	43.9	−0.76	7.84	d
NGC 6814	41.8	−1.41	6.46	d
NGC 7213	42.2	−1.99	7.37	e
NGC 7314	42.5	−1.57	7.24	d
NGC 7469	43.3	−0.65	7.11	d
NGC 3081	42.6	−1.87	7.70	f
NGC 4388	43.0	−1.84	8.00	f
Centaurus A	42.0	−2.70	7.94	b
NGC 6300	42.1	−1.99	7.30	f

Note. Column (1): galaxy name. Column (2): logarithmic intrinsic luminosity in the 2–10 keV band. Column (3): logarithmic Eddington ratio (λ_Edd = L_bol/L_Edd). Here we obtained the bolometric luminosity as L_bol = 20L₂₋₁₀ and defined the Eddington luminosity as L_Edd = 1.26 × 10³⁸ M_BH/M_☉. Column (4): logarithmic black hole mass. Column (5): reference for the black hole mass.

^aWe calculate the X-ray luminosities from the redshifts, except for the very nearby objects NGC 4051, NGC 4395, and Centaurus A, for which we adopt distances of 17.6 (Yoshii et al. 2014), 3.85 (Tully et al. 2009), and 3.84 (Rejkuba 2004) Mpc, respectively.

References. (a) Woo & Urry (2002); (b) García-Bernete et al. (2019); (c) Bentz et al. (2016); (d) Koss et al. (2017); (e) Vasudevan et al. (2010); (f) Kawamuro et al. (2016a).

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Since all of our targets are nearby and bright AGNs, they have been extensively studied by many authors. In Appendix A, we compare our results with previous works of broadband X-ray spectroscopy that utilized the same data as used here, when available.

In this subsection, we summarize the torus properties of our sample obtained from the X-ray spectral analysis described in Section 4. On the basis of the unobscured AGN fraction in a hard X-ray selected sample, Ricci et al. (2017a) showed that the Eddington ratio (i.e., the luminosity normalized by the black hole mass) is a key parameter that determines the torus geometry; since radiation pressure works to expel dusty gas, the torus covering fraction rapidly decreases when $\mathrm{log}{\lambda }_{\mathrm{Edd}}\,\gtrsim -1.5$. Thus, it is important to check whether the torus structure we determine for the individual objects through X-ray spectroscopy is consistent with their prediction.

Figure 3(a) plots the torus angular width determined from the X-ray spectra (σ_X) against Eddington ratio. By including the unobscured AGNs, which show higher Eddington ratios than most of the obscured AGNs in our sample, we confirm the trend reported by Tanimoto et al. (2020) that AGNs with high Eddington ratios have smaller σ_X. To be more quantitative, we estimate the covering factor of the torus with N_H > 10²² cm⁻², C_T, that is, the fractional solid angle of torus material whose mean column density exceeds 10²² cm⁻² in the XCLUMPY geometry. In XCLUMPY, the mean hydrogen column density at the elevation angle θ_* (≡90° − i_X) is given by

$$\begin{eqnarray}&&{N}_{{\rm{H}}}\left({\theta }_{* }\right)={N}_{{\rm{H}}}^{\mathrm{Equ}}\exp \left(-{\left(\displaystyle \frac{{\theta }_{* }}{{\sigma }_{{\rm{X}}}}\right)}^{2}\right).\end{eqnarray} \tag{ 5 }$$

Defining θ_c such that ${N}_{{\rm{H}}}\left({\theta }_{{\rm{c}}}\right)={10}^{22}\,{\mathrm{cm}}^{-2}$, C_T can be calculated from the torus parameters as

$$\begin{eqnarray}\begin{array}{rcl}{C}_{{\rm{T}}} & = & \displaystyle \frac{1}{4\pi }{\displaystyle \int }_{0}^{2\pi }{\displaystyle \int }_{\tfrac{\pi }{2}-{\theta }_{{\rm{c}}}}^{\tfrac{\pi }{2}+{\theta }_{{\rm{c}}}}\sin \theta d\theta d\phi \\ & = & \sin \left({\sigma }_{{\rm{X}}}\sqrt{\mathrm{ln}\left(\displaystyle \frac{{N}_{{\rm{H}}}^{\mathrm{Equ}}}{{10}^{22}\,{{\rm{cm}}}^{-2}}\right)}\right).\end{array}\end{eqnarray} \tag{ 6 }$$

Figure 3(b) plots C_T against λ_Edd. As noticed, our results follow the trend of the C_T versus λ_Edd relation by Ricci et al. (2017b) based on the statistical study. The good agreement supports our assumption of i_X = 45° for unobscured AGNs in our sample (see Appendix B for the results with different i_X values).

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Figure 4 compares the torus parameters determined from the X-ray spectra and those from the infrared ones. We recall that the X-ray results trace all material, including gas and dust, whereas the infrared ones trace only dust. Hence, if the spatial distribution of gas and dust is not exactly the same and/or the dust temperature is not spatially uniform, it is possible that they give different solutions.

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As noticed from Figure 4(a), we confirm the finding by Tanimoto et al. (2020) that the torus angular widths obtained from the infrared spectra (σ_IR) become systematically larger than those obtained from the X-ray ones (σ_X), even including unobscured AGNs (Figure 4(a)). Tanimoto et al. (2020) suggested that this apparent discrepancy may be explained by a significant contribution from polar dusty outflows to the observed infrared flux, as found by infrared interferometric observations of nearby AGNs (Tristram et al. 2014; López-Gonzaga et al. 2016; Leftley et al. 2018; Lyu & Rieke 2018). Tanimoto et al. (2020) argued that this effect became most prominent at the highest inclinations because the flux from hot dust in the inner part of the torus was reduced due to extinction by outer cooler dust. Our results suggest that this effect is still present in our unobscured AGNs, which might have inclinations of ∼45°, on average. Although both CLUMPY and XCLUMPY do not include such polar components, the effect is more severe in the infrared spectra than in the X-ray ones. In X-rays, because the total mass in such polar outflows is much smaller than that contained in the torus itself, the reflection component from the polar outflow is weak compared with the torus reflection component at energies above a few keV (Liu et al. 2019).

In Figure 4(b), we compare the inclination angles determined from the X-ray (i_X) and infrared spectra (i_IR) for obscured AGNs by adding four sources to the original Tanimoto et al. (2020) sample. Here only objects whose i_X is determined with an accuracy of <30° are included; unobscured AGNs are not included because we cannot directly constrain their i_X from the spectra. We confirm that i_X is generally larger than i_IR. If σ_IR is overestimated as discussed above, then it could cause i_IR to be underestimated due to its degeneracy (Nenkova et al. 2008b; Ramos Almeida et al. 2014).

Figure 4(c) confirms the results by Tanimoto et al. (2020) that the N_H/A_V ratios along the line of sight in obscured AGNs are similar to the Galactic value (N_H/A_V = 1.87 × 10²¹ cm⁻² mag⁻¹;  Draine 2003), on average, with a scatter of ∼1 dex. By contrast, unobscured AGNs show systematically smaller N_H/A_V values than the Galactic one. In an unobscured AGN, the line-of-sight A_V is not directly determined by extinction along the path toward the central region but is constrained by the infrared emission in the torus region (see next section). If the torus angular width σ_IR is overestimated by a larger factor than that in the elevation angle (90° − i_IR), it would make the line-of-sight A_V larger than the true value (see Equation (3)).

Figure 4(d) also suggests that the N_H/A_V ratios along the equatorial plane are similar to the Galactic value, on average, for both obscured and unobscured AGNs.⁶ It is consistent with the results of ${N}_{{\rm{H}}}^{\mathrm{LOS}}$ obtained for obscured AGNs (Figure 4(c)), which are more directly constrained by the data through X-ray absorption (N_H) and the infrared silicate absorption feature (A_V). Our results imply that the gas-to-dust ratios of AGN tori are similar to the Galactic value, on average, but may be variable object to object with ∼1 dex.

The simultaneous XMM-Newton and NuSTAR data observed in 2019 May are reported here for the first time. We obtain ${\rm{\Gamma }}={1.71}_{-0.01}^{+0.01}$ and ${N}_{{\rm{H}}}^{\mathrm{LOS}}={3.64}_{-0.14}^{+0.14}\times {10}^{21}\,{\mathrm{cm}}^{-2}$.

Jointly analyzing the NuSTAR and Suzaku spectra, we obtain ${\rm{\Gamma }}={1.95}_{-0.01}^{+0.01}$ and ${N}_{{\rm{H}}}^{\mathrm{LOS}}={1.37}_{-0.01}^{+0.01}\times {10}^{22}\,{\mathrm{cm}}^{-2}$. Our results are very similar to those using the same Suzaku data reported by Zoghbi et al. (2017), ${\rm{\Gamma }}={1.90}_{-0.01}^{+0.01}$ and ${N}_{{\rm{H}}}^{\mathrm{LOS}}={1.41}_{-0.01}^{+0.01}\,\times {10}^{22}\,{\mathrm{cm}}^{-2}$, and the NuSTAR results observed in the same epoch (${\rm{\Gamma }}={1.87}_{-0.01}^{+0.01}$ and ${N}_{{\rm{H}}}^{\mathrm{LOS}}={1.39}_{-0.01}^{+0.01}\times {10}^{22}\,{\mathrm{cm}}^{-2}$). They utilized the xillver (García et al. 2013) and relxill models (Dauser et al. 2014; García et al. 2014) to reproduce the distant reflection and relativistic reflection components, respectively.

We obtain ${\rm{\Gamma }}={1.64}_{-0.02}^{+0.03}$, which is smaller than the result by Mao et al. (2019; ${\rm{\Gamma }}={1.75}_{-0.02}^{+0.02}$), using the same NuSTAR and XMM-Newton data. We infer that this is because they adopted a different spectral model. They utilized the REFL model (Magdziarz & Zdziarski 1995; Zycki et al. 1999) in SPEX (Kaastra et al. 1996) for a neutral reflection component and took nine warm absorbers into account.

The photon index ${\rm{\Gamma }}={2.03}_{-0.02}^{+0.01}$ well matches with the result reported by Walton et al. (2013a) using the same Suzaku data (${\rm{\Gamma }}={2.00}_{-0.03}^{+0.04}$) despite the different spectral modeling. They included a relativistic reflection component using the REFLIONX (Ross & Fabian 2005) model convolved with RELCONV (Dauser et al. 2013).

The simultaneous XMM-Newton and NuSTAR data observed in 2018 November are reported here for the first time. We obtain ${\rm{\Gamma }}={2.02}_{-0.01}^{+0.01}$ and ${N}_{{\rm{H}}}^{\mathrm{LOS}}\lt 2.22\times {10}^{19}\,{\mathrm{cm}}^{-2}$. The source was in a high flux state (e.g., Pounds et al. 2004).

We obtain Γ < 1.53 and ${N}_{{\rm{H}}}^{\mathrm{LOS}}={5.15}_{-3.21}^{+3.53}\times {10}^{20}\,{\mathrm{cm}}^{-2}$. The photon index is consistent with that reported by Kawamuro et al. (2016b) using the same Suzaku data (${\rm{\Gamma }}={1.49}_{-0.10}^{+0.15}$). The line-of-sight absorption by the torus is smaller than their result (${N}_{{\rm{H}}}^{\mathrm{LOS}}={1.60}_{-0.19}^{+0.20}\times {10}^{22}\,{\mathrm{cm}}^{-2}$) because Kawamuro et al. (2016b) did not consider an ionized absorber.

We obtain ${\rm{\Gamma }}={2.16}_{-0.01}^{+0.02}$. This is in good agreement with the result reported by Marinucci et al. (2014) using the same XMM-Newton and NuSTAR data (${\rm{\Gamma }}={2.16}_{-0.01}^{+0.01}$). The slight difference comes from the different spectral modeling; Marinucci et al. (2014) considered a distant reflection component from ionized material using the xillver model and five absorbers.

We obtain ${\rm{\Gamma }}={1.60}_{-0.03}^{+0.05}$ and ${N}_{{\rm{H}}}^{\mathrm{LOS}}\lt 2.2\times {10}^{20}\,{\mathrm{cm}}^{-2}$. These are different from the results based on the same Suzaku data reported by Walton et al. (2013b), ${\rm{\Gamma }}={1.53}_{-0.02}^{+0.02}$ and ${N}_{{\rm{H}}}^{\mathrm{LOS}}={3.4}_{-1.5}^{+1.5}\times {10}^{20}\,{\mathrm{cm}}^{-2}$. The difference comes from the different spectral modeling; they used the REFLIONX code for a reflection component and did not consider a partial absorber.

We obtain ${\rm{\Gamma }}={1.63}_{-0.05}^{+0.10}$. Our results are consistent with those reported by Patrick et al. (2012) using the same Suzaku and Swift/BAT data, ${\rm{\Gamma }}={1.74}_{-0.01}^{+0.01}$, within the errors. They used the REFLIONX model for a reflection component.

We obtain ${\rm{\Gamma }}={1.99}_{-0.01}^{+0.02}$ and ${N}_{{\rm{H}}}^{\mathrm{LOS}}={4.95}_{-0.24}^{+0.20}\times {10}^{21}{\mathrm{cm}}^{-2}$. These are slightly different from the NuSTAR results (Panagiotou & Walter 2019), ${\rm{\Gamma }}={2.09}_{-0.02}^{+0.01}$ and ${N}_{{\rm{H}}}^{\mathrm{LOS}}={1.1}_{-0.2}^{+0.2}\,\times {10}^{22}\,{\mathrm{cm}}^{-2}$. We infer that because they analyzed only the NuSTAR data and did not consider ionized absorbers, a larger absorption than ours was obtained.

The model with two apec components well reproduces the broadband X-ray spectra. We obtain Γ > 1.56 and ${N}_{{\rm{H}}}^{\mathrm{LOS}}\,={7.77}_{-0.76}^{+1.22}\times {10}^{23}\,{\mathrm{cm}}^{-2}$. Our results are consistent with the results reported by Kawamuro et al. (2016a) using the same Suzaku data, ${\rm{\Gamma }}={1.73}_{-0.05}^{+0.05}$ and ${N}_{{\rm{H}}}^{\mathrm{LOS}}={8.25}_{-0.38}^{+0.40}\times {10}^{23}\,{\mathrm{cm}}^{-2}$.

The model with two apec components well reproduces the broadband NuSTAR+Suzaku spectrum. Our best-fitting parameters are Γ < 1.51 and ${N}_{{\rm{H}}}^{\mathrm{LOS}}={3.02}_{-0.05}^{+0.05}\times {10}^{23}\,{\mathrm{cm}}^{-2}$. Analyzing the Suzaku XIS+HXD spectra, Kawamuro et al. (2016a) obtained ${\rm{\Gamma }}={1.65}_{-0.01}^{+0.01}$ and ${N}_{{\rm{H}}}^{\mathrm{LOS}}={2.38}_{-0.07}^{+0.07}\,\times {10}^{23}\,{\mathrm{cm}}^{-2}$. Using the NuSTAR data, Masini et al. (2016) obtained ${\rm{\Gamma }}\,={1.65}_{-0.08}^{+0.08}$ and ${N}_{{\rm{H}}}^{\mathrm{LOS}}={4.4}_{-0.6}^{+0.6}\times {10}^{23}\,{\mathrm{cm}}^{-2}$. Kawamuro et al. (2016a) utilized the pexrav model (Magdziarz & Zdziarski 1995), and Masini et al. (2016) utilized the MYTorus model (Murphy & Yaqoob 2009). Our photon index is slightly smaller than these results. We infer that this is because the XCLUMPY model contains a strong unabsorbed (hence soft) reflected continuum escaped through clumps in the near-side torus, which works to make the intrinsic spectrum harder (see the discussion in Tanimoto et al. 2019).

Results utilizing the Suzaku data are reported here for the first time. The model with one apec component well reproduces the broadband NuSTAR+Suzaku spectrum. We obtain ${\rm{\Gamma }}={1.76}_{-0.01}^{+0.01}$ and ${N}_{{\rm{H}}}^{\mathrm{LOS}}={9.87}_{-0.08}^{+0.15}\times {10}^{22}\,{\mathrm{cm}}^{-2}$. Our photon index is slightly smaller from the NuSTAR result; Fürst et al. (2016) obtained ${\rm{\Gamma }}={1.82}_{-0.01}^{+0.01}$ and ${N}_{{\rm{H}}}^{\mathrm{LOS}}={1.11}_{-0.02}^{+0.15}\times {10}^{23}\,{\mathrm{cm}}^{-2}$, utilizing the MYTorus model. This may be explained the same way as for NGC 4388.

The model with one apec component well reproduces the broadband NuSTAR+Suzaku spectrum. We obtain ${\rm{\Gamma }}={1.79}_{-0.06}^{+0.05}$ and ${N}_{{\rm{H}}}^{\mathrm{LOS}}={2.09}_{-0.06}^{+0.07}\times {10}^{23}\,{\mathrm{cm}}^{-2}$, which are in good agreement with the Suzaku results reported by Kawamuro et al. (2016a), ${\rm{\Gamma }}={1.86}_{-0.02}^{+0.02}$ and ${N}_{{\rm{H}}}^{\mathrm{LOS}}={2.22}_{-0.03}^{+0.04}\times {10}^{23}\,{\mathrm{cm}}^{-2}$. Our photon index is slightly smaller than that reported by Panagiotou & Walter (2019) using the NuSTAR data, ${\rm{\Gamma }}={1.90}_{-0.03}^{+0.03}$ and ${N}_{{\rm{H}}}^{\mathrm{LOS}}\,={2.07}_{-0.04}^{+0.05}\,\times {10}^{23}\,{\mathrm{cm}}^{-2}$. Since they used the pexrav model for the reflection component, the discrepancy may also be explained the same way as for NGC 4388.