X-Ray Constraint on the Location of the AGN Torus in the Circinus Galaxy

Here we briefly review the torus geometry of the XCLUMPY model. XCLUMPY assumes a power-law distribution of spherical clumps with a fixed radius R_clump in the radial direction between the inner and outer radii (r_in and r_out), and a normal distribution in the elevation direction. The number density of clumps is expressed in Equation (1) (where we use the spherical coordinate system: r is a radius, θ is a polar angle, ϕ is an azimuthal angle):

$$\begin{eqnarray}&&d(r,\theta ,\phi )\propto {\left(\displaystyle \frac{r}{{r}_{{\rm{i}}{\rm{n}}}}\right)}^{-0.5}\exp \left(\displaystyle \frac{-{\left(\theta -\pi /2\right)}^{2}}{{\sigma }^{2}}\right).\end{eqnarray} \tag{ 1 }$$

This model has three variable torus parameters: equatorial hydrogen column density (${N}_{{\rm{H}}}^{\mathrm{Equ}}$), torus angular width (σ), and inclination angle (i). The number of clumps along the equatorial plane is set to be 10. Tanimoto et al. (2019) assume r_in = 0.05 pc, r_out = 1 pc, and R_clump = 0.002 pc, although only their scale ratios are meaningful because of the geometric similarity (see Section 1).

In the original XCLUMPY model, it was assumed that all clumps were completely at rest. In our updated model, we consider the azimuthal velocity of a clump located at r and θ:

$$\begin{eqnarray}&&{v}_{\phi }=\sqrt{\displaystyle \frac{{GM}}{r}}\sin \theta =c\sqrt{\displaystyle \frac{{r}_{{\rm{g}}}}{r}}\sin \theta ,\end{eqnarray} \tag{ 2 }$$

where G is the gravitational constant, M the black hole mass, c the speed of light, and r_g ≡ GM/c² the gravitational radius. This assumes a balance between the centrifugal force and gravitational force projected onto the equatorial plane (see Figure 1). For simplicity, we ignore any velocity field in the elevation direction, which is not important for the spectra of edge-on sources (like the Circinus galaxy).

To save computation time, we do not repeat Monte Carlo simulations by fully taking into account the motions of clumps in all interactions (e.g., Compton scattering and photoelectric absorption of continuum photons). Instead, as an approximation, we only consider the motion of a clump that emits or scatters a fluorescence line photon at its last interaction. This enables us to perform a post-analysis of the photon event files that were used to make the table models of XCLUMPY. Although Doppler broadening of absorption edge features in the reflection continuum cannot be reproduced with this approximation, it is sufficient for studies focusing on the profile of emission lines. In the simulation of MONACO, the last interaction point and the last direction of each photon are recorded. Then, we correct the energy and weight of each photon for the Doppler and relativistic beaming effects, respectively, to produce a new table model of the fluorescence lines. Since a Keplerian velocity is determined by the ratio of the radius to the gravitational radius, we introduce the parameter $\mathrm{log}({r}_{\mathrm{in}}/{r}_{{\rm{g}}})$, which ranges from 4.0 to 7.0 in steps of 0.5.

In Appendix D, we present examples of the Fe Kα line profiles, together with the spatial distribution of photon-emitting positions, for four different sets of the torus parameters.

Suzaku (Mitsuda et al. 2007), the fifth Japanese X-ray astronomical satellite, observed the Circinus galaxy in 2006 July. Analysis results utilizing these data were published in Yang et al. (2009), Arévalo et al. (2014), and Tanimoto et al. (2019), although Arévalo et al. (2014) did not include them in the spectral fitting. Suzaku carried four X-ray CCD cameras (X-ray Imaging Spectrometer, XIS: Koyama et al. 2007) and a collimated hard X-ray instrument (Hard X-ray Detector, HXD: Takahashi et al. 2007). XIS0, XIS2, and XIS3 are front-side-illuminated CCDs (XIS-FI: 0.4–12.0 keV) and XIS1 is a back-side-illuminated one (XIS-BI: 0.2–12.0 keV). The HXD consists of two types of detectors: a GSO/BGO phoswich counter and PIN silicon diodes (Kokubun et al. 2007). The GSO/BGO counter is sensitive to 40–600 keV and PIN diodes to 10–70 keV. We analyzed the data using HEAsoft v6.27 and the calibration database (CALDB) released on 2018 October 23 (XIS) and 2011 September 15 (HXD).

We reprocessed the unfiltered XIS data with the aepipeline script. Events were extracted from a circular region with a radius of 100'' centered on the source peak. We took the background from a source-free circular region with a radius of 100''. We generated the XIS redistribution matrix files (RMF) and ancillary response files (ARF) by using xisrmfgen and xissimarfgen, respectively. To improve the statistics, we combined the spectra of XIS-FI detectors (XIS0, XIS2, and XIS3) with addascaspec. We binned the XIS spectra to contain at least 100 counts per bin.

The unfiltered HXD data were also reprocessed with the aepipeline script. We generated the PIN and GSO spectra by using hxdpinxbpi and hxdgsoxbpi, respectively. We utilized the tuned background files (Fukazawa et al. 2009) to obtain the non-X-ray background (NXB). The cosmic X-ray background (CXB) was added to the NXB of the PIN spectrum. The CXB in the GSO spectrum was ignored.

XMM-Newton (Jansen et al. 2001), the second ESA X-ray astronomical satellite, observed the Circinus galaxy six times between 2001 and 2018 (Molendi et al. 2003; Massaro et al. 2006; Arévalo et al. 2014; Tanimoto et al. 2019). In this paper, we utilize the data from 2013 February, which were taken simultaneously with NuSTAR (see below). XMM-Newton carries three X-ray CCD cameras: EPIC/pn (Strüder et al. 2001) and two EPIC/MOSs (Turner et al. 2001). We analyzed only the data of pn, which has the largest effective area, using the science analysis software (SAS) v18.0.0 and CALDB released on 2019 November 28.

We reprocessed the unfiltered pn data with the epproc script. Source events were extracted from a circular region with a radius of 100'' centered on the source peak, for consistency with the Suzaku spectra. We subtracted the background taken from a source-free circular region with a radius of 100''. We generated the ARF and RMF by using arfgen and rmfgen, respectively. We binned the pn spectrum to contain at least 100 counts per bin.

NuSTAR (Harrison et al. 2013), the first X-ray astronomical satellite capable of focusing hard X-rays above 10 keV, observed the Circinus galaxy four times in 2013. The results were published in Arévalo et al. (2014), Brightman et al. (2015), and Tanimoto et al. (2019). NuSTAR carries two focal plane modules (FPMs), which are sensitive to 3–79 keV. We utilized the data observed in 2013 January, which are the only data observed on-axis. We used HEAsoft v6.27 and CALDB released on 2020 May 14 for data reduction.

We reprocessed the FPMs' data by using nupipeline and nuproducts. Events were extracted from a circular region with a radius of 100'' centered on the source peak, and we subtracted the background taken from a source-free circular region with a radius of 100''. We binned the FPMs' spectra to contain at least 100 counts per bin.

Chandra (Weisskopf et al. 2002) observed the Circinus galaxy several times since 2000 with the Advanced CCD Imaging Spectrometer (ACIS: Garmire et al. 2003) with or without the High Energy Transmission Grating (HETG: Canizares et al. 2005). Many authors have published papers using some of these data (with HETG: Sambruna et al. 2001; Bianchi et al. 2002; Shu et al. 2010, 2011; Arévalo et al. 2014; Liu 2016a, 2016b; Hikitani et al. 2018; Kawamuro et al. 2019; without HETG: Marinucci et al. 2013; Arévalo et al. 2014; Kawamuro et al. 2019). Its excellent angular resolution (<1'') enables us to separate the AGN from nearby X-ray sources by utilizing the ACIS imaging data. We analyzed 14 observations (13 with HETG and one without). We followed the standard analysis procedures with the Chandra interactive analysis of observations (CIAO v4.12) software and calibration files (CALDB v4.9.1).

3.4.1. HETG Data

3.4.2. ACIS Imaging Data

4.1.1. CGX1

Qiu et al. (2019) showed that CGX1 was a ULX. Here we adopt a spectral model developed by Shidatsu et al. (2017), a physically motivated model that reproduces well the broadband spectra of a ULX covering the hard X-ray band above 10 keV. This model consists of two components: disk blackbody radiation from the accretion disk and Comptonization in the optically thick corona. The seed-photon temperature of the Comptonized component (T₀) is set to be twice that of the innermost temperature of the disk (T_in) (see Shidatsu et al. 2017 for details). The model is represented as follows in the XSPEC terminology:

$$\begin{eqnarray}&&\mathrm{CGX}1={\mathsf{phabs}}* ({\mathsf{diskbb}}+{\mathsf{mscomptt}}),\end{eqnarray} \tag{ 3 }$$

where mscomptt is a local model by Shidatsu et al. (2017). We obtain a good fit with the model (${\chi }_{\mathrm{red}}^{2}=175/161$). Table 2 summarizes the best-fit parameters. Figure 2 shows the X-ray spectrum folded with the energy response and the best-fit model.

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Table 2. Best-fit Parameters of CGX1

NH	kTin	Ndbb a	z	T0/Tin	kTe	τ	Nmscomptt	F2−10	χ2/dof
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
${1.07}_{-0.19}^{+0.21}$	${0.21}_{-0.04}^{+0.04}$	${29.6}_{-20.3}^{+70.4a}$	0.0014 (fixed)	2.0 (fixed)	4.0 (fixed)	${5.03}_{-0.30}^{+0.26}$	$({1.02}_{-0.11}^{+0.16})\times {10}^{-4}$	9.7 × 10−13	175/161

Notes. Columns: (1) hydrogen column density in units of 10²² atoms cm^−2; (2) innermost temperature of the disk; (3) normalization of diskbb; (4) redshift fixed at that of the Circinus galaxy; (5) ratio of the seed-photon temperature (T₀) to the innermost temperature of the disk (T_in); (6) plasma temperature in units of keV; (7) Thomson scattering optical depth; (8) normalization of mscomptt; (9) observed X-ray flux in the 2–10 keV band in units of erg cm⁻² s⁻¹.

^a The parameter reaches a limit of its allowed range.

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4.1.2. CGX2

To model the spectrum of CGX2, an SNR, we use basically the same model as that in Arévalo et al. (2014), which consists of three components of optically thin thermal plasma. The model is represented as follows in the XSPEC terminology:

$$\begin{eqnarray}\begin{array}{rcl}\mathrm{CGX}2 & = & {\mathsf{phabs}}\\ & & * \{{\mathsf{apec}}{\mathsf{1}}+{\mathsf{apec}}{\mathsf{2}}+{\mathsf{gsmooth}}({\mathsf{0}}.{\mathsf{065}}\ {\mathsf{keV}})* {\mathsf{apec}}{\mathsf{3}}\}.\end{array}\end{eqnarray} \tag{ 4 }$$

Here we employ the apec model instead of mekal adopted by Arévalo et al. (2014) because the latter does not cover the energy band above ∼50 keV. We confirm that it successfully reproduces the spectrum (${\chi }_{\mathrm{red}}^{2}=308/270$). Table 3 summarizes the best-fit parameters. Figure 3 shows the folded X-ray spectrum and the best-fit models.

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Table 3. Best-fit Parameters of CGX2

Model	NH	kT	Z	z	Norm.
	(1022)	(keV)
phabs	${1.64}_{-0.05}^{+0.09}$	⋯	⋯	⋯	⋯
apec1	⋯	${0.143}_{-0.012}^{+0.003}$	0.5 (fixed)	$({8.28}_{-1.25}^{+0.20})\times {10}^{-2}$	$({1.75}_{-0.65}^{+1.24})\times {10}^{-1}$
apec2	⋯	${1.15}_{-0.05}^{+0.05}$	${5.0}_{-0.6}^{+0.9}$	$(-{5.65}_{-8.58}^{+0.70})\times {10}^{-3}$	$({2.16}_{-0.10}^{+0.39})\times {10}^{-4}$
apec3	⋯	${9.88}_{-0.73}^{+0.71}$	5.0 (linked)	$(-{2.63}_{-0.44}^{+0.15})\times {10}^{-3}$	$({6.42}_{-0.49}^{+0.15})\times {10}^{-4}$

Note. The metal abundance Z of the lowest-temperature component is fixed at 0.5. Those of the high- and medium-temperature components are linked together.

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4.1.3. Diffuse Emission

The diffuse emission mainly originates from X-ray reflection by gas around the nucleus of the intrinsic AGN emission. Accordingly, we adopt pexmon (Magdziarz & Zdziarski 1995), a Compton reflection model from optically thick matter, and a component scattered by optically thin matter (cutoff power law) to reproduce the spectrum. We also add emission lines reported in Arévalo et al. (2014) that are not included in the pexmon model (Table 5). The model is represented as follows in the XSPEC terminology:

$$\begin{eqnarray}&&{\rm{d}}{\rm{i}}{\rm{f}}{\rm{f}}{\rm{u}}{\rm{s}}{\rm{e}}={\mathsf{p}}{\mathsf{h}}{\mathsf{a}}{\mathsf{b}}{\mathsf{s}}\ast ({\mathsf{p}}{\mathsf{e}}{\mathsf{x}}{\mathsf{m}}{\mathsf{o}}{\mathsf{n}}+{\mathsf{z}}{\mathsf{c}}{\mathsf{u}}{\mathsf{t}}{\mathsf{o}}{\mathsf{f}}{\mathsf{f}}{\mathsf{p}}{\mathsf{l}}+{\mathsf{z}}{\mathsf{g}}{\mathsf{a}}{\mathsf{u}}{\mathsf{s}}{\mathsf{s}}{\mathsf{e}}{\mathsf{s}}).\end{eqnarray} \tag{ 5 }$$

We link the photon index and cutoff energy to those of the intrinsic AGN component in the simultaneous fitting of the broadband spectra (see Section 4.2.1). The inclination angle in the pexmon model is fixed at 60°.

4.2.1. Spectral Models

Earlier works showed that many high-order ionization lines were present in the spectrum of the Circinus galaxy below 3 keV (e.g., Sambruna et al. 2001). This suggests that the soft band is characterized by significant emission from photoionized plasma. To focus on the reflection component from the torus, we ignore the data below 3 keV. We perform simultaneous fits to the spectra observed with Chandra/HETG (HEG first order, 3–8 keV), Chandra/ACIS (imaging, 3–7 keV), Suzaku/XIS-FI (3–10 keV), Suzaku/XIS-BI (3–10 keV), Suzaku/PIN (20–40 keV), Suzaku/GSO (50–100 keV), XMM-Newton/pn (3–10 keV), NuSTAR/FPMA (8–70 keV), and NuSTAR/FPMB (8–70 keV).

The X-ray spectrum of an obscured AGN mainly consists of three components: a transmitted component, a component reflected by the torus, and an unabsorbed scattered component (e.g., Kawamuro et al. 2016; Tanimoto et al. 2018). We accordingly model the emission from the AGN (not including the diffuse component mentioned in Section 4.1) as follows in the XSPEC terminology:

$$\begin{eqnarray}\begin{array}{r}\begin{array}{rcl}{\rm{A}}{\rm{G}}{\rm{N}} & = & {\mathsf{p}}{\mathsf{h}}{\mathsf{a}}{\mathsf{b}}{\mathsf{s}}\\ & & \ast ({\mathsf{z}}{\mathsf{v}}{\mathsf{p}}{\mathsf{h}}{\mathsf{a}}{\mathsf{b}}{\mathsf{s}}\ast {\mathsf{c}}{\mathsf{a}}{\mathsf{b}}{\mathsf{s}}\ast {\mathsf{z}}{\mathsf{c}}{\mathsf{u}}{\mathsf{t}}{\mathsf{o}}{\mathsf{f}}{\mathsf{f}}{\mathsf{p}}{\mathsf{l}}+{\mathsf{c}}{\mathsf{o}}{\mathsf{n}}{\mathsf{s}}{\mathsf{t}}{\mathsf{1}}\ast {\mathsf{z}}{\mathsf{c}}{\mathsf{u}}{\mathsf{t}}{\mathsf{o}}{\mathsf{f}}{\mathsf{f}}{\mathsf{p}}{\mathsf{l}}\\ & & +{\mathsf{a}}{\mathsf{t}}{\mathsf{a}}{\mathsf{b}}{\mathsf{l}}{\mathsf{e}}\{{\mathsf{x}}{\mathsf{c}}{\mathsf{l}}{\mathsf{u}}{\mathsf{m}}{\mathsf{p}}{\mathsf{y}}{\mathsf{v}}{\rm{\_}}{\mathsf{R}}.{\mathsf{f}}{\mathsf{i}}{\mathsf{t}}{\mathsf{s}}\}\\ & & +{\mathsf{c}}{\mathsf{o}}{\mathsf{n}}{\mathsf{s}}{\mathsf{t}}{\mathsf{2}}\ast {\mathsf{a}}{\mathsf{t}}{\mathsf{a}}{\mathsf{b}}{\mathsf{l}}{\mathsf{e}}\{{\mathsf{x}}{\mathsf{c}}{\mathsf{l}}{\mathsf{u}}{\mathsf{m}}{\mathsf{p}}{\mathsf{y}}{\mathsf{v}}{\mathsf{d}}{\rm{\_}}{\mathsf{L}}.{\mathsf{f}}{\mathsf{i}}{\mathsf{t}}{\mathsf{s}}\}\\ & & +{\mathsf{z}}{\mathsf{g}}{\mathsf{a}}{\mathsf{u}}{\mathsf{s}}{\mathsf{s}}{\mathsf{e}}{\mathsf{s}}).\end{array}\end{array}\end{eqnarray} \tag{ 6 }$$

• 1.  
  The first term (phabs) represents the Galactic absorption.
• 2.  
  The first term in the parentheses represents the component transmitted through the torus. The zvphabs and cabs models represent photoelectric absorption and Compton scattering by the torus, respectively.
• 3.  
  The second term in the parentheses represents the unabsorbed scattered component. The parameters of zcutoffpl (photon index, cutoff energy, normalization) are linked to those of the transmitted component. The const1 factor gives the scattering fraction.
• 4.  
  The third and fourth terms in the parentheses represent the reflection continuum and the fluorescence lines from the torus. The metal abundance, photon index, cutoff energy, and normalization are set to those of the transmitted component. We introduce a relative normalization factor of the emission lines to the reflection continuum (const2) to take into account systematic uncertainties due to the simplified assumption of the torus geometry.
• 5.  
  We add the emission lines reported by Arévalo et al. (2014) not included in the XCLUMPY model (Table 5).

The whole model used for the simultaneous fitting is represented as follows:

$$\begin{eqnarray}\quad \begin{array}{ccl}{\rm{m}}{\rm{o}}{\rm{d}}{\rm{e}}{\rm{l}}1 & = & {\mathsf{c}}{\mathsf{o}}{\mathsf{n}}{\mathsf{s}}{\mathsf{t}}{\mathsf{3}}\ast {\rm{A}}{\rm{G}}{\rm{N}}\\ {\rm{m}}{\rm{o}}{\rm{d}}{\rm{e}}{\rm{l}}2 & = & {\mathsf{c}}{\mathsf{o}}{\mathsf{n}}{\mathsf{s}}{\mathsf{t}}{\mathsf{3}}\ast {\rm{d}}{\rm{i}}{\rm{f}}{\rm{f}}{\rm{u}}{\rm{s}}{\rm{e}}\\ {\rm{m}}{\rm{o}}{\rm{d}}{\rm{e}}{\rm{l}}3 & = & {\mathsf{c}}{\mathsf{o}}{\mathsf{n}}{\mathsf{s}}{\mathsf{t}}{\mathsf{3}}\ast ({\rm{A}}{\rm{G}}{\rm{N}}+{\rm{d}}{\rm{i}}{\rm{f}}{\rm{f}}{\rm{u}}{\rm{s}}{\rm{e}}+{\mathsf{c}}{\mathsf{o}}{\mathsf{n}}{\mathsf{s}}{\mathsf{t}}{\mathsf{4}}\ast {\rm{C}}{\rm{G}}{\rm{X}}1\\ & & +{\rm{C}}{\rm{G}}{\rm{X}}2).\end{array}\,\end{eqnarray} \tag{ 7 }$$

• 1.  
  The model forms of "CGX1," "CGX2," "diffuse," and "AGN" are described in Equations (3)-(6), respectively. The parameters of CGX1 and CGX2 were frozen at the best-fit values obtained from the spectral analysis of the Chandra/ACIS imaging data (Section 4.1). As mentioned above, the photon index and cutoff energy of the diffuse component are linked to those of the AGN one.
• 2.  
  We apply model1 to the Chandra/HETG spectrum, model2 to the Chandra/ACIS diffuse spectrum, and model3 to the other spectra.
• 3.  
  const3 is a cross-normalization factor to correct for a possible difference in the absolute flux calibration among different instruments. We fix that of Chandra/HETG at unity as a reference. Those of Suzaku/XIS-FI (C_FI), Suzaku/XIS-BI (C_BI), XMM-Newton/pn (C_pn), NuSTAR/FPMA (C_FPMA), and NuSTAR/FPMB (C_FPMB) are left as free parameters. Those of Suzaku/PIN and Suzaku/GSO are set to be 1.16 × C_FI based on calibration with the Crab Nebula. The cross-normalization of the Chandra/ACIS diffuse spectrum is fixed at unity.
• 4.  
  const4 accounts for time variability of the ULX (CGX1). Those of Suzaku/XIS-FI (T_FI) and XMM-Newton/pn (T_pn) are left as free parameters. Those of Suzaku/XIS-BI, Suzaku/PIN, and Suzaku/GSO are linked to T_FI, whereas those of NuSTAR/FPMA and NuSTAR/FPMB are to T_pn (because the NuSTAR and XMM-Newton observations were simultaneous). We note that the X-ray spectrum of a ULX changes with luminosity; generally, it becomes softer at higher luminosities (e.g., Walton et al. 2014; Shidatsu et al. 2017). Applying the same model adopted here to the spectra of IC 342 X-1 observed in multiple epochs, Shidatsu et al. (2017) obtained ∼20% smaller optical depths (τ) of the Comptonizing corona when the luminosity increased by a factor of 2–3. Accordingly, we repeat our analysis by setting τ = 4 for the CGX1 spectra in the Suzaku and NuSTAR/XMM-Newton data, where its luminosity is estimated to be a factor of ∼2 higher than in the Chandra data (Table 4). We confirm that it has little effect on the result of our broadband spectral fitting of the Circinus galaxy because the luminosity of CGX1 is sufficiently small compared with that of the AGN. Thus, we adopt the result obtained by considering only the change in luminosity of CGX1.

Table 4. Best-fit Parameters of the Broadband Spectra

Region	No.	Parameter	Best-fit Value	Units
AGN	(1)	${N}_{{\rm{H}}}^{\mathrm{Equ}}$	${21.6}_{-1.7}^{+2.4}$	1024 cm−2
	(2)	${N}_{{\rm{H}}}^{\mathrm{LOS}}$	${5.95}_{-0.60}^{+0.76}$	1024 cm−2
	(3)	Z	${1.52}_{-0.06}^{+0.05}$	solar value
	(4)	σ a	${10.3}_{-0.3a}^{+0.8}$	deg
	(5)	i	${78.3}_{-0.9}^{+0.5}$	deg
	(6)	Γ	${1.68}_{-0.09}^{+0.05}$
	(7)	Ecut	${48.0}_{-5.4}^{+5.0}$	keV
	(8)	NLine	${1.08}_{-0.05}^{+0.06}$
	(9)	$\mathrm{log}({r}_{\mathrm{in}}/{r}_{{\rm{g}}})$	${4.84}_{-0.08}^{+0.08}$
	(10)	NDir	${0.80}_{-0.18}^{+0.11}$	photons keV−1 cm−2 s−1
	(11)	fscat	${2.2}_{-1.1}^{+1.8}\times {10}^{-2}$	%
	(12)	L2−10	${6.34}_{-0.64}^{+0.43}$	1042 erg s−1
diffuse	(13)	Z	${0.96}_{-0.11}^{+0.12}$	solar value
	(14)	Npexmon	${6.75}_{-1.22}^{+0.90}\times {10}^{-3}$	photons keV−1 cm−2 s−1
	(15)	Nzcutoffpl	${2.14}_{-0.47}^{+0.47}\times {10}^{-4}$	photons keV−1 cm−2 s−1
	(16)	CFI	${0.85}_{-0.02}^{+0.02}$
	(17)	CBI	${0.90}_{-0.03}^{+0.03}$
	(18)	Cpn	${0.81}_{-0.03}^{+0.03}$
	(19)	CFPMA	${0.80}_{-0.03}^{+0.03}$
	(20)	CFPMB	${0.83}_{-0.03}^{+0.03}$
	(21)	TFI	${1.88}_{-0.30}^{+0.30}$
	(22)	Tpn	${2.29}_{-0.39}^{+0.39}$
	(23)	zHETG	${1.64}_{-0.09}^{+0.10}\times {10}^{-3}$
	(24)	zFI	${0.70}_{-0.22}^{+0.22}\times {10}^{-3}$
	(25)	zBI	$-{0.33}_{-0.41}^{+0.39}\times {10}^{-3}$
	(26)	zpn	$-{1.41}_{-0.47}^{+0.46}\times {10}^{-3}$
	(27)	zACIS	$-{0.72}_{-1.01}^{+0.88}\times {10}^{-3}$
	(28)	F2−10	1.39 × 10−11	erg cm−2 s−1
	(29)	F10−100	2.62 × 10−10	erg cm−2 s−1
		χ2/dof	2275/1991

Note. (1) Hydrogen column density along the equatorial plane. (2) Hydrogen column density along the line of sight. (3) Metal abundance of the torus. (4) Torus angular width. (5) Inclination angle. (6) Photon index. (7) Cutoff energy. (8) Relative normalization of the emission lines to the reflection continuum. (9) Torus inner radius in units of gravitational radius. (10) Normalization of the direct component. (11) Scattering fraction as a percentage. (12) Intrinsic AGN luminosity in the 2–10 keV band. (13) Metal abundance of the diffuse emission. Iron abundance was set to this value. (14) Normalization of the reflection component in the diffuse emission. (15) Normalization of the scattered component in the diffuse emission. (16)–(20) Cross-normalization factors. (21)–(22) Time-variability factors. (23)–(27) Redshift of each spectrum. Those of NuSTAR and Suzaku/HXD are fixed at 0.0014. (28)–(29) Obscured AGN flux in the 2–10 keV and 10–100 keV bands.

^a The parameter reaches a limit of its allowed range.

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All the redshift parameters in the AGN and diffuse components are linked together for the spectrum of each instrument. Since the AGN contains a strong Fe Kα line, the redshift determination based on it depends very sensitively on the precise energy-scale calibration of each instrument; in fact, we find that adopting a common redshift value for all the instruments leads to highly unacceptable fits. (If we fix the redshifts of all instruments to 0.0014, we even obtain a much worse fit with χ²/dof = 2468/1996.) To take into account the possible calibration uncertainties in an approximate way, we allow the linked value of the redshift to vary among different instruments except for the Suzaku/HXD and NuSTAR spectra, for which we fix z = 0.0014. We confirm that the resultant redshift parameters are consistent with z = 0.0014 within the calibration uncertainties (Chandra Calibration Status Summary ⁸ , Koyama et al. (2007), XMM-Newton Calibration Technical Note ⁹ ). Note that, for simplicity, we have ignored these small-scale uncertainties in modeling the CGX1 and CGX2 spectra because they do not affect our results on the AGN component.

4.2.2. Results

We successfully reproduce the broadband (3–100 keV) spectra of the Circinus galaxy with the above model. The best-fit parameters are summarized in Table 4. Figure 4 shows the folded X-ray spectra and best-fit models. We obtain the main torus parameters ${N}_{{\rm{H}}}^{\mathrm{Equ}}={2.16}_{-0.17}^{+0.24}\times {10}^{25}\ {\mathrm{cm}}^{-2}$, $\sigma ={10.3}_{-0.3}^{+0.8}\,{\rm{d}}{\rm{e}}{\rm{g}}$, and $i={78.3}_{-0.9}^{+0.5}\,{\rm{d}}{\rm{e}}{\rm{g}}$. We also find that the supersolar abundance ($Z={1.52}_{-0.06}^{+0.05}$) significantly improve the fit, mainly to reproduce the Compton-shoulder fraction (see Appendix C). The cross-normalization factors of XMM-Newton/pn and Suzaku/XIS are consistent with Madsen et al. (2017) but those of NuSTAR/FPMs are not. ¹⁰ The best-fit value of const2 (the relative normalization factor of line components to the continuum in XCLUMPY), ${1.08}_{-0.05}^{+0.06}$, is slightly over 1.0. Since the torus parameters, such as ${N}_{{\rm{H}}}^{\mathrm{Equ}}$, affect the equivalent width of the Fe Kα line (see Figure 4 in Tanimoto et al. 2019), this may be explained if the actual distribution of clumps in the elevation direction is not perfectly represented by a single-Gaussian model as assumed (e.g., more material exists very close to the equatorial plane). Nevertheless, the result that const2 is close to unity is evidence that the assumed geometry is a good approximation. The bolometric luminosity is estimated to be ${L}_{\mathrm{bol}}={1.27}_{-0.13}^{+0.09}\times {10}^{44}\ \mathrm{erg}\ {{\rm{s}}}^{-1}$ by assuming that X-ray and bolometric luminosities are related by L_bol = 20 × L₂₋₁₀ (Vasudevan & Fabian 2009). ¹¹ We compare these results with previous studies in Section 6.

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Marinucci et al. (2013) analyzed Chandra imaging data of the Circinus galaxy and detected the spatial extent of the Fe Kα line-emitting region. The spatial extent has line-broadening effects in grating spectra, which we have to correct for in order to accurately measure the intrinsic spectral line width. ¹² In this subsection, we confirm the spatial extent of the Fe Kα line-emitting region by comparing the radial profile obtained from a Chandra image with that obtained from simulations. We analyze the zeroth-order image of ObsID = 4771, one of the longest exposure data with HETGs, which is little affected by pile-up thanks to the grating mode.

We perform simulations with the MARX code (Davis et al. 2012), which produces simulated event files based on a Monte Carlo method. The input spectrum is determined from our broadband spectral fitting in Section 4. Since the AspectBlur parameter in MARX is still under calibration, we perform simulations with two different settings, AspectBlur = 0.0'' and 0.25'', referring to Fabbiano et al. (2020) and the latest calibration of the point-spread function by the MARX team ¹³ , respectively. Figure 5 compares the simulated and observed radial profiles of the source. This confirms that the Circinus galaxy has a spatial extent in the 6.0–7.0 keV band regardless of the adopted value of AspectBlur. Note that the extent is not circularly symmetric but has a complex structure (Marinucci et al. 2013). Hence, we cannot refer to this plot to estimate the extent along the dispersion direction of the HEG data in a given observation.

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Since the width of the line-broadening effect due to a spatial extent is inversely proportional to the grating order (Appendix A), we can, in principle, separate the effect by simultaneously analyzing multiple spectra of different grating orders. Thus, we perform a simultaneous fitting to the Chandra/HETG first-, second-, and third-order spectra in the 6.3–6.5 keV band. Considering the small photon statistics, we bin each spectrum to contain at least one count per bin, and use Cash statistics (C-stat; Cash 1979) to determine the best-fit parameters. We use basically the same model as model1 (Equation (7)) but take into account the effect of line broadening by the spatial extent, which is proportional to the inverse of the grating order (see Appendix A). The model is represented as follows in the XSPEC terminology:

$$\begin{eqnarray}\begin{array}{r}\begin{array}{rcl}{\rm{m}}{\rm{o}}{\rm{d}}{\rm{e}}{\rm{l}}4 & = & {\mathsf{c}}{\mathsf{o}}{\mathsf{n}}{\mathsf{s}}{\mathsf{t}}{\mathsf{3}}\ast {\mathsf{p}}{\mathsf{h}}{\mathsf{a}}{\mathsf{b}}{\mathsf{s}}\\ & & \ast ({\mathsf{z}}{\mathsf{v}}{\mathsf{p}}{\mathsf{h}}{\mathsf{a}}{\mathsf{b}}{\mathsf{s}}\ast {\mathsf{c}}{\mathsf{a}}{\mathsf{b}}{\mathsf{s}}\ast {\mathsf{z}}{\mathsf{c}}{\mathsf{u}}{\mathsf{t}}{\mathsf{o}}{\mathsf{f}}{\mathsf{f}}{\mathsf{p}}{\mathsf{l}}+{\mathsf{c}}{\mathsf{o}}{\mathsf{n}}{\mathsf{s}}{\mathsf{t}}{\mathsf{1}}\ast {\mathsf{z}}{\mathsf{c}}{\mathsf{u}}{\mathsf{t}}{\mathsf{o}}{\mathsf{f}}{\mathsf{f}}{\mathsf{p}}{\mathsf{l}}\\ & & +{\mathsf{a}}{\mathsf{t}}{\mathsf{a}}{\mathsf{b}}{\mathsf{l}}{\mathsf{e}}\{{\mathsf{x}}{\mathsf{c}}{\mathsf{l}}{\mathsf{u}}{\mathsf{m}}{\mathsf{p}}{\mathsf{y}}{\mathsf{v}}{\rm{\_}}{\mathsf{R}}.{\mathsf{f}}{\mathsf{i}}{\mathsf{t}}{\mathsf{s}}\}\\ & & +({\mathsf{1}}-{\mathsf{c}}{\mathsf{o}}{\mathsf{n}}{\mathsf{s}}{\mathsf{t}}{\mathsf{5}})\ast {\mathsf{a}}{\mathsf{t}}{\mathsf{a}}{\mathsf{b}}{\mathsf{l}}{\mathsf{e}}\{{\mathsf{x}}{\mathsf{c}}{\mathsf{l}}{\mathsf{u}}{\mathsf{m}}{\mathsf{p}}{\mathsf{y}}{\mathsf{v}}{\mathsf{d}}{\rm{\_}}{\mathsf{L}}.{\mathsf{f}}{\mathsf{i}}{\mathsf{t}}{\mathsf{s}}\}\\ & & +{\mathsf{c}}{\mathsf{o}}{\mathsf{n}}{\mathsf{s}}{\mathsf{t}}{\mathsf{5}}\ast {\mathsf{g}}{\mathsf{s}}{\mathsf{m}}{\mathsf{o}}{\mathsf{o}}{\mathsf{t}}{\mathsf{h}}\ast {\mathsf{a}}{\mathsf{t}}{\mathsf{a}}{\mathsf{b}}{\mathsf{l}}{\mathsf{e}}\{{\mathsf{x}}{\mathsf{c}}{\mathsf{l}}{\mathsf{u}}{\mathsf{m}}{\mathsf{p}}{\mathsf{y}}{\mathsf{v}}{\mathsf{d}}{\rm{\_}}{\mathsf{L}}.{\mathsf{f}}{\mathsf{i}}{\mathsf{t}}{\mathsf{s}}\}\\ & & +{\mathsf{z}}{\mathsf{g}}{\mathsf{a}}{\mathsf{u}}{\mathsf{s}}{\mathsf{s}}{\mathsf{e}}{\mathsf{s}}).\end{array}\end{array}\end{eqnarray} \tag{ 8 }$$

• 1.  
  const5 represents the fraction of the extended emission in the total intensity (f_diff), which is left as a free parameter.
• 2.  
  The fourth and fifth terms correspond to the fluorescence lines from the pointlike and extended regions. The gsmooth model represents the effect of spatial broadening. Its width is left as a free parameter (${\sigma }_{{\rm{E}}}^{\mathrm{diff}}$). The torus inner radius in the fourth term is left free, whereas that in the fifth one is fixed at $\mathrm{log}({r}_{\mathrm{in}}/{r}_{{\rm{g}}})=7.0$ (i.e., effectively no intrinsic spectral broadening).
• 3.  
  The cross-normalization factors (const3) of the second- and third-order spectra are left as free parameters, whereas that of the first-order one is fixed at unity. The normalization of the lines (xclumpyvd_L.fits) and the torus inner radius (r_in/r_g) are set free. The other parameters are fixed to the values in Tables 4 and 5.

Table 5. Emission Lines Added in the Model

Region	Energy	Sigma	Norm.	ID
	(keV)	(eV)	(photons cm−2 s−1)
(1)	(2)	(3)	(4)	(5)
AGN	3.11	5.8	${3.9}_{-1.3}^{+1.4}\times {10}^{-6}$	S xvi Kβ
	3.90	4.8	${1.68}_{-0.87}^{+0.87}\times {10}^{-6}$	Ar xviii
	5.88 a	1.0	${0.89}_{-0.89}^{+1.18}$ a × 10−6	Cr xxiv
	6.50	50.0	${1.41}_{-0.51}^{+0.48}\times {10}^{-5}$	Fe xx
	${6.68}_{-0.01}^{+0.01}$	${50.6}_{-12.9}^{+17.5}$	${2.86}_{-0.40}^{+0.46}\times {10}^{-5}$	Fe xxv
Diffuse	3.11	5.8	${2.8}_{-1.2}^{+1.2}\times {10}^{-6}$	S xvi Kβ
	3.27	1.2	${2.16}_{-1.02}^{+1.02}\times {10}^{-6}$	Ar xviii
	3.69	1.0	${1.44}_{-0.94}^{+0.89}\times {10}^{-6}$	Ca ii−xiv + Ar xvii
	3.90	4.8	${1.57}_{-0.88}^{+0.85}\times {10}^{-6}$	Ar xviii
	5.41	0.1	${1.49}_{-1.01}^{+0.99}\times {10}^{-6}$	Cr i
	6.68 (linked)	10.0	${4.9}_{-2.4}^{+2.4}\times {10}^{-6}$	Fe xxv

Note. Column (1): region. Column (2): line energy. These are fixed at the values reported in Arévalo et al. (2014) except for the Fe xxv line. This is allowed to vary within 50 eV centered on 6.66 keV in the broadband fitting. The energy of the diffuse Fe xxv line is linked to that of the AGN component. Column (3): line width. These are fixed at the values reported in Arévalo et al. (2014) except for the AGN Fe xxv line. The width of the AGN 6.66 keV line is left free in the broadband fitting. Column (4): normalization of the lines. These were also left free in the broadband fitting. Lines whose best-fit normalizations are less than 1.0 × 10⁻¹⁰ were not included. Column (5): line ID.

^a The parameter reaches a limit of its allowed range.

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The best-fit parameters are summarized in Table 6. Figure 6 shows the folded X-ray spectra and the best-fit models. We estimate the inner radius of the torus to be $\mathrm{log}\left({r}_{\mathrm{in}}/{r}_{{\rm{g}}}\right)={5.28}_{-0.23}^{+0.42}$. Since the mass of the SMBH is (1.7 ± 0.3) × 10⁶ M_⊙ (Greenhill et al. 2003), this corresponds to ${r}_{\mathrm{in}}={1.6}_{-0.9}^{+1.5}\times {10}^{-2}\ \mathrm{pc}$. At the same time, the spectral analysis also constrains the spatial extent of Fe Kα in the Circinus galaxy averaged over the dispersion directions of all the HEG data used in our analysis: the fraction of the extended emission is ${0.19}_{-0.09}^{+0.16}$ and the angular width is ${\sigma }_{\mathrm{angl}}^{\mathrm{diff}}\,={0.66}_{-0.21}^{+0.33}\ \mathrm{arcsec}$.

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Table 6. Best-fit Parameters of the Fe Kα Line

C2nd	C3rd	z2nd	z3rd	fdiff	${\sigma }_{{\rm{E}}}^{\mathrm{diff}}$ (eV)	$\mathrm{log}({r}_{\mathrm{in}}/{r}_{{\rm{g}}})$	Norm.	C/dof
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
${0.83}_{-0.10}^{+0.11}$	${0.64}_{-0.08}^{+0.09}$	${1.57}_{-0.25}^{+0.25}\times {10}^{-3}$	${1.53}_{-0.26}^{+0.25}\times {10}^{-3}$	${0.19}_{-0.09}^{+0.16}$	${24.8}_{-7.7}^{+12.4}$	${5.28}_{-0.23}^{+0.42}$	${0.91}_{-0.04}^{+0.04}$	98.8/100

Note. Columns (1) and (2): cross-normalization factors for the second- and third-order spectra, respectively. Columns (3) and (4): redshifts for the second- and third-order spectra, respectively. Column (5): fraction of the extended emission. Column (6): width of the spatial extent. Column (7): torus inner radius in units of the gravitational radius. Column (8): normalization of xclumpyvd_L.fits. Column (9): the maximum likelihood-based statistic for Poisson data given in Cash statistic.

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We confirm the previous results based on broadband X-ray spectroscopy (e.g., Arévalo et al. 2014; Tanimoto et al. 2019), that the AGN torus in the Circinus galaxy is Compton-thick (${N}_{{\rm{H}}}^{\mathrm{Equ}}\,={2.16}_{-0.17}^{+0.24}\times {10}^{25}\ {\mathrm{cm}}^{-2};$ ${N}_{{\rm{H}}}^{\mathrm{LOS}}={5.95}_{-0.60}^{+0.76}\,\times {10}^{24}\ {\mathrm{cm}}^{-2}$), geometrically thin ($\sigma ={10.3}_{-0.3}^{+0.8}\,{\rm{d}}{\rm{e}}{\rm{g}}$), and viewed edge-on ($i\,={78.3}_{-0.9}^{+0.5}\,{\rm{d}}{\rm{e}}{\rm{g}}$). Our results supersede the earlier work by Tanimoto et al. (2019), who first applied XCLUMPY to the broadband spectrum of the Circinus galaxy observed with Suzaku, XMM-Newton, and NuSTAR. They obtained ${N}_{{\rm{H}}}^{\mathrm{Equ}}={9.08}_{-0.08}^{+0.14}\,\times {10}^{24}\ {\mathrm{cm}}^{-2}$ (${N}_{{\rm{H}}}^{\mathrm{LOS}}={4.86}_{-0.04}^{+0.07}\,\times {10}^{24}\ {\mathrm{cm}}^{-2}$), $\sigma ={14.7}_{-0.4}^{+0.5}\,{\rm{d}}{\rm{e}}{\rm{g}}$, $i={78.3}_{-0.2}^{+0.2}\,{\rm{d}}{\rm{e}}{\rm{g}}$. Our inclination angle is consistent with the value of Tanimoto et al. (2019), whereas the hydrogen column density along the equatorial plane and the torus angular width are somewhat larger and smaller than theirs, respectively. We infer that the differences arise because Tanimoto et al. (2019) assumed the solar abundance and did not separately treat the diffuse emission, which contaminates the AGN spectrum in a soft band. In Tanimoto et al. (2019) these effects worked to overestimate the photon index of the intrinsic power-law component (${\rm{\Gamma }}\,={1.80}_{-0.03}^{+0.01}$ compared with our result of ${\rm{\Gamma }}={1.68}_{-0.09}^{+0.05}$) and hence required a larger solid angle of the reflector (i.e., a larger torus angular width) to reproduce the observed reflection spectrum. Since the column density along the line of sight (${N}_{{\rm{H}}}^{\mathrm{LOS}}$) is well constrained by the spectrum, the large torus angular width may have led them to underestimate that along the equatorial plane (${N}_{{\rm{H}}}^{\mathrm{Equ}}$).

Arévalo et al. (2014) analyzed the XMM-Newton and NuSTAR data of the Circinus galaxy observed in 2013 with the MYTorus and Torus models, and obtained ${N}_{{\rm{H}}}^{{\rm{E}}{\rm{q}}{\rm{u}}}=(6.6{\textstyle \text{\unicode{x02013}}}10)\times {10}^{24}\,{{\rm{c}}{\rm{m}}}^{-2}$, Γ = 2.2–2.4. Our hydrogen column density along the equatorial plane (${N}_{{\rm{H}}}^{\mathrm{Equ}}=\ {21.6}_{-1.7}^{+2.4}\times {10}^{24}\ {\mathrm{cm}}^{-2}$) and photon index (${\rm{\Gamma }}\,={1.68}_{-0.09}^{+0.05}$) are larger and smaller than their results, respectively. As mentioned in Tanimoto et al. (2019), we infer that the XCLUMPY model leads to a flatter intrinsic spectrum because it contains a larger flux of the unabsorbed reflection component. Also, the differences in the adopted torus geometry inevitably affect the estimate of ${N}_{{\rm{H}}}^{\mathrm{Equ}}$. We refer the reader to Tanimoto et al. (2019) for detailed comparison of spectral analysis results between the XCLUMPY model and other torus models.

Our result that the metal abundance is supersolar ($Z\,={1.52}_{-0.06}^{+0.05}$) is consistent with Molendi et al. (2003), who estimated the iron abundance to be 1.2–1.7 times solar from the Fe Kα edge. As mentioned in Section 1, Hikitani et al. (2018) derived Z ≈ 1.75 from the Compton shoulder of the Fe Kα line utilizing a torus model developed by Furui et al. (2016). Our result is slightly smaller than theirs, which was based on a more geometrically-thick torus model.

According to our best-fit parameters of XCLUMPY, the expected number of clumps along the line of sight is ∼3. The hydrogen number density of each clump (n_H) can be calculated with Equation (9) (see also Equation (5) in Tanimoto et al. 2019). In our case, n_H = 8.2 × 10⁸ cm⁻³, which is almost consistent with those estimated by Markowitz et al. (2014) for nearby Seyfert galaxies:

$$\begin{eqnarray}&&{n}_{{\rm{H}}}=\displaystyle \frac{3{N}_{{\rm{H}}}^{{\rm{E}}{\rm{q}}{\rm{u}}}}{40{R}_{{\rm{c}}{\rm{l}}{\rm{u}}{\rm{m}}{\rm{p}}}}.\end{eqnarray} \tag{ 9 }$$

We have performed a simultaneous spectral analysis of the Chandra/HETG first-, second-, and third-order spectra of the Circinus galaxy, where we take into account the spatial extent of the Fe Kα line-emitting region. We obtain $\mathrm{log}({r}_{\mathrm{in}}/{r}_{{\rm{g}}})\,={5.28}_{-0.23}^{+0.42}$, which corresponds to a Keplerian velocity of ${690}_{-270}^{+200}\,\mathrm{km}\ {{\rm{s}}}^{-1}$ at the inner edge of the torus, and to ${r}_{\mathrm{in}}={1.6}_{-0.9}^{+1.6}\times {10}^{-2}$ pc for an SMBH mass of (1.7 ± 0.3) × 10⁶ M_⊙ (Section 5.2). Our inner radius is 2.5 times larger than that reported in Shu et al. (2011). This is most probably because they analyzed the first-order spectrum by ignoring the spatial extent and fitted the Fe Kα line with a single-Gaussian model; both led them to overestimate the true line width. By contrast, the torus inner radius obtained here is consistent with the location of the Si Kα line-emitting region estimated by Liu (2016b) (${0.03}_{-0.015}^{+0.06}$ pc), which was later interpreted by Liu et al. (2019) to mainly originate from the polar outflows. We note that our torus inner radius is smaller than the maser-disk radius (r = 0.11 ± 0.02 pc, Greenhill et al. 2003).

The innermost radius of the dusty region in a torus (dusty torus) can be estimated from the dust sublimation radius (R_sub), the limit where dust grains can exist against radiative heating from the central engine. Nenkova et al. (2008a, 2008b) derived the formula for the sublimation radius of a clumpy torus as

$$\begin{eqnarray}&&{R}_{\mathrm{sub}}=0.4{\left(\displaystyle \frac{{L}_{\mathrm{bol}}}{{10}^{45}\mathrm{erg}{{\rm{s}}}^{-1}}\right)}^{0.5}{\left(\displaystyle \frac{1500{\rm{K}}}{{T}_{\mathrm{sub}}}\right)}^{2.6}\ \mathrm{pc},\end{eqnarray} \tag{ 10 }$$

where L is the bolometric luminosity of the AGN and T_sub is the sublimation temperature. Adopting T_sub = 1500 K and the bolometric luminosity derived from the broadband spectral analysis (Section 4.2), we obtain that of the Circinus galaxy to be R_sub ∼ 0.14 pc. Kishimoto et al. (2007) found that the torus inner radius in an AGN derived from the near-infrared reverberation mapping was ∼3 times smaller than the sublimation radius calculated as above; the factor 3 difference can be explained by considering the anisotropy of emission from the accretion disk (Kawaguchi & Mori 2010). If we apply this relation, the inner radius of the dusty torus in the Circinus galaxy is estimated as ≈0.05 pc.

The torus inner radius we have derived from the Fe Kα line width is still significantly smaller than this value. Since the near-infrared reverberation observation only measures the location of dust, this result indicates that there is a significant amount of dust-free gas in the inner side of the dusty torus. Our result basically supports the arguments by Minezaki & Matsushita (2015) and Gandhi et al. (2015) that a significant fraction of the Fe Kα line originates from a region closer to the SMBH than the dusty torus. However, the torus inner radius we have derived is larger than these previous estimates, strongly suggesting that the region is well outside the broad-line region. We note that our result is currently limited by the uncertainty of the spatial extent in analyzing the grating spectra. Future nondispersive high-resolution spectroscopy, like that by the X-Ray Imaging and Spectroscopy Mission (XRISM), will push forward our understanding of the whole structure of an AGN including the torus and its inner region.