XCLUMPY: X-Ray Spectral Model from Clumpy Torus and Its Application to the Circinus Galaxy

It is widely accepted that in an active galactic nucleus (AGN) obscuring matter composed of gas and dust surrounds the supermassive black hole (SMBH; e.g., Antonucci 1993; Urry & Padovani 1995; Ramos Almeida & Ricci 2017). This structure, often referred to as the "torus," plays a key role in AGN feeding, serving as a mass reservoir linking the SMBH and host galaxy. It is also suggested that the torus may be produced by outflow from the accretion disk (Elitzur & Shlosman 2006), which is an important process of AGN feedback (Fabian 2012). Thus, elucidating the torus structure, and ultimately its physical origins, is essential to understand the mechanisms of the SMBH and galaxy coevolution (Kormendy & Ho 2013). Nevertheless, many of the basic properties of AGN tori still remain unclear.

X-ray observations are a powerful tool to investigate the nature of surrounding material around the SMBH. Unlike radio lines and far- to mid-infrared continuum emission, which are sensitive only to cool gas and dust, respectively, X-rays can trace all matter including gas and dust with various physical conditions. The X-ray spectrum of an AGN mainly consists of the direct power-law component from the center (emitted via Comptonization of softer photons by a hot corona) and its reflection components from the accretion disk and torus. This torus reflection component carries important information on the structure of the torus. For instance, the relative intensity to the direct component and shape of the reflected continuum, as well as those of the fluorescence Fe Kα line at 6.4 keV, strongly depend on the covering factor (solid angle) and total column density of the torus. Also, photoelectric absorption features of the reflection component constrain the overall torus geometry and inclination angle.

Various X-ray spectral models have been used to compare with the observation data. Many authors often employ the pexrav model (continuum only: Magdziarz & Zdziarski 1995), or the pexmon model (continuum plus fluorescence lines: Nandra et al. 2007), which analytically calculate the reflection component from cold gas in a semi-infinite (i.e., optically thick) plane. These analytic models are convenient to use but give only a rough approximation of the real data, because the geometry of a torus is more complex than a single plane and it is not trivial to assume a Compton-thick reflector.

To take account of more realistic torus geometry, numerical spectral models based on Monte Carlo ray-tracing simulations have been developed (MYTorus model: Murphy & Yaqoob 2009; Ikeda model: Ikeda et al. 2009; Torus model: Brightman & Nandra 2011a). Murphy & Yaqoob (2009) adopt a bagel-like (i.e., toroidal) shape whose opening angle is fixed. Ikeda et al. (2009) and Brightman & Nandra (2011a) assume essentially spherical geometry with two bipolar conical holes, where the opening angle of the torus can be varied as a free parameter (see Liu & Li 2015 and Baloković et al. 2018 for a note and an update of the original model by Brightman & Nandra 2011a, respectively). All these models assume a uniform density of the gas, and hence we refer to them as "smooth torus models." These models have also been widely used to fit the observed X-ray spectra of AGNs (Ikeda model: e.g., Awaki et al. 2009; Eguchi et al. 2011; Tazaki et al. 2011, 2013; Kawamuro et al. 2013, 2016a, 2016b; Tanimoto et al. 2016, 2018; Oda et al. 2017, 2018; Yamada et al. 2018; MYTorus model: e.g., Yaqoob 2012; Yaqoob et al. 2015, 2016; Koss et al. 2013, 2015, 2016, 2017; Ricci et al. 2014a, 2014b, 2015, 2016a, 2016b, 2017a, 2017b; Torus model: e.g., Brightman & Nandra 2011b, 2012; Brightman et al. 2013, 2014, 2015, 2016, 2017; Buchner et al. 2014, 2015; Gandhi et al. 2014, 2015, 2017).

Many observations indicate, however, that AGN tori must be composed of dusty clumps rather than of smooth gas (e.g., Krolik & Begelman 1988; Wada & Norman 2002; Hönig & Beckert 2007). Here we summarize four major pieces of observational evidence for clumpy tori: (1) geometrical thickness of tori, (2) 10 μm silicate emission feature in the infrared spectra of Seyfert 2 galaxies, (3) correlations between the infrared and X-ray luminosities, and (4) X-ray spectral feature of torus-reflection components:

• 1.  
  The velocity dispersion of matter must be as large as a typical rotation velocity of the torus (V ∼ 100 km s⁻¹) in order to sustain a geometrically thick torus as inferred from the absorbed AGN fraction (e.g., Ricci et al. 2015). In the case of smooth gas, it corresponds to the thermal velocity. However, the velocity of dusty gas cannot become so fast. This is because dust grains would reach a maximum sublimation temperature (T ∼ 1500 K: Laor & Draine 1993).
• 2.  
  Pier & Krolik (1992, 1993) constructed infrared spectral models from a smooth torus and predicted that the 10 μm silicate feature would appear only in absorption in Seyfert 2 galaxies. By contrast, Mason et al. (2009) and Nikutta et al. (2009) detected silicate emission line features in the infrared spectra of Seyfert 2 galaxies.
• 3.  
  An inner region of the torus has a higher temperature because dust is heated by radiation from the central accretion disk. In smooth tori, it is therefore expected that the ratio between the infrared and X-ray luminosities would be systematically higher in type 1 AGNs where inner parts of the torus are more visible. In reality, however, the correlations are very similar among type 1 and type 2 AGNs (Gandhi et al. 2009; Ichikawa et al. 2012, 2017, 2019; Asmus et al. 2015; Kawamuro et al. 2016a).
• 4.  
  The X-ray spectra of heavily absorbed AGNs often show unabsorbed torus-reflection components (e.g., Ueda et al. 2007). If we apply smooth torus models to such an X-ray spectrum, the inclination angle and torus half-opening angle become very close to each other (Awaki et al. 2009; Eguchi et al. 2011; Tazaki et al. 2011; Tanimoto et al. 2016, 2018). This corresponds to the geometry where the observer sees the AGN through the edge of the torus boundary and seems unrealistic in a statistical sense. Clumpy tori can naturally explain these features because it predicts that a significant fraction of the unabsorbed reflection component is from the far-side torus.

In the infrared band, Nenkova et al. (2008a, 2008b) constructed spectral models from clumpy tori, by assuming a power-law distribution in the radial direction and a normal distribution in the elevation direction for the configuration of clumps. This model, called CLUMPY, has been successfully applied to the infrared spectra of nearby AGNs (see Ramos Almeida & Ricci 2017 and references therein). Stalevski et al. (2012, 2016) also computed the infrared spectra from a clumpy torus of a two-phase medium with slightly different geometry from that in the CLUMPY model.

It was only recently that X-ray spectral models from clumpy torus were developed (CTorus model: Liu & Li 2014; Furui model: Furui et al. 2016). Liu & Li (2014) constructed such a model, using the Geant4 library (Agostinelli et al. 2003; Allison et al. 2006, 2016) for the first time. They adopted clump distribution confined in a partial sphere. Later, Furui et al. (2016) made an X-ray clumpy torus model with bagel-like geometry by using the Monte Carlo simulation for astrophysics and cosmology framework (MONACO: Odaka et al. 2011, 2016), which also utilizes the Geant4 library but is optimized for astrophysical applications. In this model, Compton down-scattering of fluorescence lines, which produces "Compton shoulder" in the line profile, is properly taken into account.

In this paper, we construct a new X-ray clumpy torus model designated as "XCLUMPY," by adopting the same geometry of clump distribution as that of the CLUMPY model in the infrared band (Nenkova et al. 2008a, 2008b). This enables us to directly compare the results inferred from the infrared and X-ray bands, which constrain the spatial distribution of dust and that of all matter including gas, respectively. The structure of this paper is as follows. Sections 2 and 3 describe the adopted torus geometry and the details of Monte Carlo simulations, respectively. In Section 4, we present major results of our model such as dependencies of the X-ray continuum and Fe Kα line profile on the torus parameters. We also compare our model with other torus models: MYTorus model (Murphy & Yaqoob 2009), Ikeda model (Ikeda et al. 2009), and CTorus model (Liu & Li 2014). In Section 5, we apply our model to the broadband X-ray spectra of the Circinus galaxy observed with XMM-Newton,  Suzaku, and NuSTAR. Throughout the paper we adopt the cosmological parameters (H₀ = 70 km s⁻¹ Mpc⁻¹, Ω_m = 0. 3, Ω_λ = 0.7). The errors on the spectral parameters correspond to the 90% confidence limits for a single parameter.

In our model, a torus is not continuously medium, but is composed of many clumps randomly distributed following a given number density function. For simplicity, each clump is a sphere with a radius of ${R}_{\mathrm{clump}}$, and has a uniform hydrogen number density n_H. As mentioned in Section 1, we adopt the same geometry as that in Nenkova et al. (2008a, 2008b), who assumed a power-law distribution of clumps in the radial direction between inner and outer radii, and a normal distribution in the elevation direction (Figure 1). Specifically, the number density function d(r, θ, ϕ) (in units of pc⁻³) is represented in the spherical coordinate system (where r is radius, θ is polar angle, and ϕ is azimuth) as:

$\begin{eqnarray}&&d(r,\theta ,\phi )=N{\left(\displaystyle \frac{r}{{r}_{\mathrm{in}}}\right)}^{-q}\exp \left(-\displaystyle \frac{{\left(\theta -\pi /2\right)}^{2}}{{\sigma }^{2}}\right).\end{eqnarray} \tag{ 1 }$

where N is the normalization, q is the index of the radial density profile, and σ is the torus angular width.

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The normalization N is related to the number of clumps along the equatorial plane ${N}_{\mathrm{clump}}^{\mathrm{Equ}}$ as

$\begin{eqnarray}\begin{array}{rcl}{N}_{\mathrm{clump}}^{\mathrm{Equ}} & = & {\displaystyle \int }_{{r}_{\mathrm{in}}}^{{r}_{\mathrm{out}}}d\,\left(r,\displaystyle \frac{\pi }{2},0\right)\,\pi {R}_{\mathrm{clump}}^{2}{dr}.\\ N & = & \displaystyle \frac{(1-q){N}_{\mathrm{clump}}^{\mathrm{Equ}}}{\pi {R}_{\mathrm{clump}}^{2}{r}_{\mathrm{in}}^{q}({r}_{\mathrm{out}}^{1-q}-{r}_{\mathrm{in}}^{1-q})}.\end{array}\end{eqnarray} \tag{ 2 }$

By substituting Equation (2) into Equation (1), we obtain the number of clumps along the line of sight at a given polar angle:

$\begin{eqnarray}&&{N}_{\mathrm{clump}}^{\mathrm{LOS}}(\theta )={N}_{\mathrm{clump}}^{\mathrm{Equ}}\exp \left(-\displaystyle \frac{{\left(\theta -\pi /2\right)}^{2}}{{\sigma }^{2}}\right).\end{eqnarray} \tag{ 3 }$

For instance, for ${N}_{\mathrm{clump}}^{\mathrm{Equ}}=10$ and σ = 60°, ${N}_{\mathrm{clump}}^{\mathrm{LOS}}(\pi /2)\approx 10,{N}_{\mathrm{clump}}^{\mathrm{LOS}}(\pi /3)\approx 7$, and ${N}_{\mathrm{clump}}^{\mathrm{LOS}}(\pi /6)\approx 3$.

The total number of clumps in the torus ${N}_{\mathrm{clump}}^{\mathrm{Tot}}$ is obtained by integrating the number density function,

$\begin{eqnarray}\begin{array}{rcl}{N}_{\mathrm{clump}}^{\mathrm{Tot}} & = & {\displaystyle \int }_{{r}_{\mathrm{in}}}^{{r}_{\mathrm{out}}}{\displaystyle \int }_{0}^{\pi }{\displaystyle \int }_{0}^{2\pi }d(r,\theta ,\phi ){r}^{2}\sin \,\theta {drd}\theta d\phi \\ & = & \displaystyle \frac{2{N}_{\mathrm{clump}}^{\mathrm{Equ}}(1-q)({r}_{\mathrm{out}}^{3-q}-{r}_{\mathrm{in}}^{3-q})}{{R}_{\mathrm{clump}}^{2}(3-q)({r}_{\mathrm{out}}^{1-q}-{r}_{\mathrm{in}}^{1-q})}\\ & & \times {\displaystyle \int }_{0}^{\pi }\exp \left(-\displaystyle \frac{{\left(\theta -\pi /2\right)}^{2}}{{\sigma }^{2}}\right)\sin \,\theta d\theta .\end{array}\end{eqnarray} \tag{ 4 }$

Typically, ${N}_{\mathrm{clump}}^{\mathrm{Tot}}\sim {10}^{6}$ for the adopted parameters (Table 1).

Table 1.  Summary of Parameters

Note	Parameter	Grid	Units
(01)	rin	0.05	pc
(02)	rout	1.00	pc
(03)	Rclump	0.002	pc
(04)	${N}_{\mathrm{clump}}^{\mathrm{Equ}}$	10.0	⋯
(05)	q	0.50	⋯
(06)	σ	10.0, 20.0, 30.0, 40.0, 50.0, 60.0, 70.0	degree
(07)	$\mathrm{log}\,{N}_{{\rm{H}}}^{\mathrm{Equ}}$/cm−2	22.00, 22.25, 22.50, 22.75, 23.00, 23.25, 23.50, 23.75
		24.00, 24.25, 24.50, 24.75, 25.00, 25.25, 25.50, 25.75, 26.00	⋯
(08)	i	18.2, 31.8, 41.4, 49.5, 56.6, 63.3, 69.5, 75.5, 81.4, 87.1	degree
(09)	Γ	1.50, 1.60, 1.70, 1.80, 1.90, 2.00, 2.10, 2.20, 2.30, 2.40, 2.50	⋯
(10)	$\mathrm{log}\,{E}_{\mathrm{cut}}$/keV	1.00, 1.50, 2.00, 2.50, 3.00

Note. Column (1): inner radius of the torus. Column (2): outer radius of the torus. Column (3): radius of the clump. Column (4): number of the clump along the equatorial plane. Column (5): index of the radial density profile. Column (6): torus angular width. Column (7): hydrogen column density along the equatorial plane. Column (8): inclination angle. Column (9): photon index. Column (10): cutoff energy.

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We also define the total hydrogen column density along the equatorial plane:

$\begin{eqnarray}&&{N}_{{\rm{H}}}^{\mathrm{Equ}}=\displaystyle \frac{4}{3}{R}_{\mathrm{clump}}{N}_{\mathrm{clump}}^{\mathrm{Equ}}{n}_{{\rm{H}}}.\end{eqnarray} \tag{ 5 }$

Here $\displaystyle \frac{4}{3}{R}_{\mathrm{clump}}(=\tfrac{4}{3}\pi {R}_{\mathrm{clump}}^{3}/(\pi {R}_{\mathrm{clump}}^{2}))$ corresponds to the average length crossing the line of sight in one clump (a sphere with a radius of R_clump) when the clumps are randomly located. The parameter ${N}_{{\rm{H}}}^{\mathrm{Equ}}$ can be directly compared with the total optical depth along the equatorial plane introduced in Nenkova et al. (2008a, 2008b).

To summarize, our model has eight independent parameters that define the torus properties: (1) inner radius of the torus (r_in), (2) outer radius of the torus (r_out), (3) radius of each clump (R_clump), (4) number of clumps along the equatorial plane (${N}_{\mathrm{clump}}^{\mathrm{Equ}}$), (5) index of the radial density profile (q), (6) torus angular width (σ), (7) hydrogen column density along the equatorial plane (${N}_{{\rm{H}}}^{\mathrm{Equ}}$), and (8) the inclination angle (i, the polar angle of the line of sight).

In our work, we fix (1) r_in, (2) r_out, (4) ${N}_{\mathrm{clump}}^{\mathrm{Equ}}$, and (5) q to the mean values obtained by Ichikawa et al. (2015), who applied the CLUMPY model to the infrared spectral energy distribution of nearby 21 AGNs. We note that the clump-size parameter (3) ${R}_{\mathrm{clump}}$ does not affect the calculation of the infrared spectra as long as it is sufficiently small (Nenkova et al. 2008a, 2008b). This is not the case for the X-ray spectra, however. We therefore assume a typical value (a logarithmic average) within the torus region based on a theoretical estimate by Kawaguchi & Mori (2010, 2011). The adopted value (0.002 pc) is compatible with the observations of transient X-ray absorption events by torus clumps in nearby AGNs (Markowitz et al. 2014). Thus, our model has three free parameters related to the torus: (6) σ, (7) ${N}_{{\rm{H}}}^{\mathrm{Equ}}$, and (8) i. Table 1 summarizes the values of the fixed parameters and the range of the free parameters. Although ${N}_{\mathrm{clump}}^{\mathrm{Equ}}$ and q are fixed in our table model, we examine the dependencies of the spectra on these parameters by running simulations for limited sets of parameters in Appendices A and B (see also Section 4.3).

3.1. Material Properties and Physical Processes

3.2. Table Model

4.1. Dependence of Reflected Continuum Spectrum on Torus Parameters

We investigate the dependence of the reflected X-ray spectrum on the torus parameters. Here we adopt the following values as default (fixed) parameters unless otherwise stated: $\mathrm{log}\,{N}_{{\rm{H}}}$/cm⁻² = 24.0, σ = 400, i = 600, Γ = 2.0, and E_cut = 100 keV. Figure 2 shows the dependence of the X-ray spectrum on the (a) hydrogen column density along the equatorial plane, (b) torus angular width, and (c) inclination angle.

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In Figure 2(a), we find that the continuum flux above ∼20 keV increases and the overall spectrum hardens with the hydrogen column density along the equatorial plane. This is because the intensity of the Compton-reflected continuum and the amount of self-absorption by the torus increase with the total mass of the torus, which is proportional to N_H when the other parameters are fixed. Figure 2(b) indicates that the X-ray flux below 7.1 keV (the K-edge of cold iron) and that above 7.1 keV decreases and increases with σ, respectively. The total mass and covering fraction of the reflector increase with σ for a fixed N_H, leading to stronger reflection and self-absorption by the torus. In Figure 2(c), we find that the flux below 20.0 keV decreases with the inclination angle. This is because the line-of-sight absorption of the reflection component increases with the viewing angle.

4.2. Dependence of Fe Kα Line Profile on Torus Parameters

We investigate the dependence of the Fe Kα line profile on the torus parameters. We adopt the same default parameters as in Section 4.1 ($\mathrm{log}\,{N}_{{\rm{H}}}$/cm⁻² = 24.0, σ = 400, i = 600, Γ = 2.0, and E_cut = 100 keV). Figure 3 shows the dependence of the Fe Kα on the (a) hydrogen column density along the equatorial plane, (b) torus angular width, and (c) inclination angle.

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We also investigate the dependence of the equivalent width of the total Fe Kα line, that of the Compton shoulder component, and the Compton shoulder fraction relative to the total line intensity. We define these quantities as follows:

$\begin{eqnarray}&&{\mathrm{EW}}_{{\rm{K}}\alpha }={\int }_{6.086\,\mathrm{keV}}^{6.404\,\mathrm{keV}}\displaystyle \frac{L(E)}{R(E)}{dE}\end{eqnarray} \tag{ 6 }$

$\begin{eqnarray}&&{\mathrm{EW}}_{\mathrm{CS}}={\int }_{6.086\,\mathrm{keV}}^{6.390\,\mathrm{keV}}\displaystyle \frac{L(E)}{R(E)}{dE}\end{eqnarray} \tag{ 7 }$

$\begin{eqnarray}&&{f}_{\mathrm{CS}}=\displaystyle \frac{{\int }_{6.086\,\mathrm{keV}}^{6.390\,\mathrm{keV}}L(E){dE}}{{\int }_{6.086\,\mathrm{keV}}^{6.404\,\mathrm{keV}}L(E){dE}},\end{eqnarray} \tag{ 8 }$

where R(E) and L(E) are the spectra of the reflection continuum and emission line, respectively. We set the upper boundary of the integrals to 6.404 keV for EW_Kα, which is just above the Fe Kα₁ (6.403 keV), and to 6.390 keV for EW_CS, just below Fe Kα₂ (6.390 keV). The lower boundary of the integrals are set to be 6.086 keV, corresponding to the lowest energy of the second-order Compton shoulder of Fe Kα₂.

In Figure 4, we plot the dependence of the equivalent widths and the Compton shoulder fraction on the (a)–(b) hydrogen column density, (c)–(d) torus angular width, and (e)–(f) inclination angle.

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As seen in Figures 4(a) and (c), the equivalent width of the Fe Kα line increases with N_H and σ, confirming the same trends found with smooth torus models (Ikeda et al. 2009; Murphy & Yaqoob 2009). Figures 4(b) and (d) show that the Compton shoulder fraction also increases with N_H and σ. This is because the probability that a fluorescent line is further Compton reflected by surrounding matter increases with the total mass of the torus. In Figures 4(e) and (f), we find that the equivalent width and the Compton shoulder fraction depend little on the inclination angle.

4.3. Comparison of Torus Models

We compare our model with other torus models: MYTorus model (Murphy & Yaqoob 2009), Ikeda model (Ikeda et al. 2009), and CTorus model (Liu & Li 2014). To consider similar geometry among the models as much as possible, we set the torus parameters as follows: for the MYTorus model ${N}_{{\rm{H}}}^{\mathrm{Equ}}\,=1.0\times {10}^{24}$ cm⁻² and θ_open = 600 (fixed in the model); for the Ikeda model ${N}_{{\rm{H}}}^{\mathrm{Equ}}=1.0\times {10}^{24}$ cm⁻², and θ_open = 600; for the CTorus model ${N}_{{\rm{H}}}^{\mathrm{Equ}}=1.5\times {10}^{24}$ cm⁻² and θ_open = 600 (fixed); and for the XCLUMPY model ${N}_{{\rm{H}}}^{\mathrm{Equ}}=1.0\,\times {10}^{24}$ cm⁻² and σ = 300. We set ${N}_{{\rm{H}}}^{\mathrm{Equ}}=1.5\times {10}^{24}$ cm⁻² in the CTorus model because Liu & Li (2014) define it as the value when all clumps are exactly aligned along the radial direction, whereas our definition refers to the case where the clumps are randomly distributed (see Equation (5)).

Figure 5 shows the comparison of the reflected X-ray continuum for (a) ${N}_{\mathrm{clump}}^{\mathrm{Equ}}=5.0$ (this parameter is relevant only for CTorus and XCLUMPY) and i = 200, (b) ${N}_{\mathrm{clump}}^{\mathrm{Equ}}=10.0$ and i = 200, (c) ${N}_{\mathrm{clump}}^{\mathrm{Equ}}=5.0$ and i = 870, and (d) ${N}_{\mathrm{clump}}^{\mathrm{Equ}}\,=10.0$ and i = 870. In Figures 5(c) and (d) (i.e., edge-on), we find that the fluxes above 20 keV are almost the same among all the models, whereas those below 20 keV in the clumpy torus models (CTorus and XCLUMPY) are larger than those in the smooth torus models (MYTorus and Ikeda torus). This is mainly because a significant fraction of photons reflected by the far-side torus can reach the observer without being absorbed by the near-side torus in clumpy geometry in the case of the edge-on view. This effect is more prominent in XCLUMPY than in CTorus. In CTorus, the clumps are confined within an elevation angle of 30° from the equatorial plane with a constant number density, whereas in XCLUMPY they are distributed to higher elevation angles with decreasing number densities. In XCLUMPY, photons can be reflected at higher elevation angles, which are subject to smaller line-of-sight absorption in the edge-on view, thus producing larger soft X-ray fluxes, than in CTorus. As we mentioned in Section 1, smooth torus models cannot explain a large amount of the unabsorbed reflection component often seen in the X-ray spectra of heavily obscured AGNs (Tanimoto et al. 2016, 2018). This feature can be naturally explained with the clumpy torus models.

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In Figures 5(a) and (b) (i.e., face-on), we find that the Ikeda model, which adopts a similar spherical torus geometry to those in CTorus and XCLUMPY, produces higher fluxes at energies below several keV than the clumpy torus models. The trend is opposite to the edge-on case; when viewed edge-on, in the Ikeda model the soft X-ray reflection component comes from the entire surface of the smooth torus without being absorbed, whereas in the clumpy torus models it comes from clumps at various depths (as measured from the observer) and hence is subject to absorption by other clumps while traveling inside the torus. We note that CTorus and XCLUMPY produce almost the same fluxes below 20 keV, unlike in the edge-on case. This is because the averaged column density along the line of sight responsible for the self-absorption is similar between the two models, even if the clump distribution in XCLUMPY is spread wider in elevation angles than in CTorus. In the torus geometry of MYTorus (bagel-like shape), the area of the irradiated surface is smaller and hence the soft X-ray flux of the reflection component becomes weaker than in the Ikeda model.

Figure 6 shows the comparison of the emission lines for (a) ${N}_{\mathrm{clump}}^{\mathrm{Equ}}=5.0$ and i = 200, (b) ${N}_{\mathrm{clump}}^{\mathrm{Equ}}=10.0$ and i = 200, (c) ${N}_{\mathrm{clump}}^{\mathrm{Equ}}=5.0$ and i = 870, and (d) ${N}_{\mathrm{clump}}^{\mathrm{Equ}}=10.0$ and i = 870. We note that there are limitations on the treatment of fluorescence lines in the previous models. MYTorus model includes only Fe Kα and Fe Kβ (with the Compton shoulder), and Ikeda model only Fe Kα (with the Compton shoulder). The CTorus model includes other lines than Fe Kα and Kβ (such as Ni Kα, Kβ), but the Compton shoulders are not taken into account. The XCLUMPY model includes all prominent fluorescence lines from many elements with the Compton shoulder. It should be also stressed that XCLUMPY accurately calculates the smeared profiles of the Compton shoulders because the MONACO framework considers atomic and molecular binding of electrons responsible for the scattering (Odaka et al. 2016).

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We apply the XCLUMPY model to broadband X-ray spectra of the Circinus galaxy. The Circinus galaxy (z = 0.0014) is one of the closest (4.2 Mpc: Freeman et al. 1977) obscured AGNs and is an ideal target for investigating torus structure. Ichikawa et al. (2015) applied the CLUMPY model to its infrared data and derived the torus parameters (Table 2). Table 3 summarizes the X-ray observations of the Circinus galaxy analyzed in this paper. Suzaku observed this object in 2006 July. Simultaneous observations with XMM-Newton and NuSTAR were performed in 2013 February.

Table 2.  Torus Structure from Infrared Observation

Rinner	Router	${N}_{\mathrm{clump}}^{\mathrm{Equ}}$	τv	σ	i	$\mathrm{log}\,{L}_{\mathrm{bol}}$/erg s−1
(1)	(2)	(3)	(4)	(5)	(6)	(7)
${0.071}_{-0.003}^{+0.003}$	${1.4}_{-0.2}^{+0.3}$	${7}_{-1}^{+1}$	${37}_{-2}^{+3}$	${65}_{-5}^{+2}$	${63}_{-2}^{+4}$	${43.5}_{-0.1}^{+1.1}$

Note. Column (1): inner radius of the torus in units of parsecs. Column (2): outer radius of the torus in units of parsecs. Column (3): number of the clump along the equatorial plane. Column (4): optical depth of each cloud. Column (5): torus angular width in units of degrees. Column (6): inclination angle in units of degrees. Column (7): logarithmic bolometric luminosity.

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5.1. Data Analysis

5.2. Spectral Analysis

Since our main interest is the reflection component from the torus, here we only analyze the spectra above 2 keV, in order to avoid complexity in modeling the soft X-ray emission (Matt et al. 1996). To best constrain the torus parameters, we perform simultaneous fits to the Suzaku/BIXIS (2–8 keV), Suzaku/FIXIS (2–10 keV), Suzaku/PIN (16-40 keV), Suzaku/GSO (50–100 keV), XMM-Newton/EPN (2–8 keV), XMM-Newton/MOS (2–10 keV), and NuSTAR/FPM (8–60 keV). Possible time variability between the two epochs (2006 and 2013) is ignored, which is found to not be required from the data. We apply the XCLUMPY model to reproduce the torus reflection component. The whole model is represented as follows in the XSPEC (Arnaud 1996) terminology:

$\begin{eqnarray}&&\begin{array}{l}{\mathsf{const}}{\mathsf{1}}\ast {\mathsf{phabs}}\\ \,\,* ({\mathsf{zphabs}}\ast {\mathsf{cabs}}\ast {\mathsf{zcutoffpl}}+{\mathsf{const}}{\mathsf{2}}* {\mathsf{zcutoffpl}}\\ \,\,+{\mathsf{atable}}\{{\mathsf{xclumpy}}\_{\mathsf{R}}.{\mathsf{fits}}\})\\ \,\,+{\mathsf{atable}}\{{\mathsf{xclumpy}}\_{\mathsf{L}}.{\mathsf{fits}}\}+{zgauss}+{zgauss}\\ \,\,+{\mathsf{phabs}}* {\mathsf{powerlw}}+{\mathsf{phabs}}* ({\mathsf{apec}}+{\mathsf{phabs}}* {\mathsf{mekals}})).\end{array}\end{eqnarray} \tag{ 9 }$

Below we explain the details of each component:

• 1.  
  Cross-normalization factor (const1). We multiply a constant to take into account the difference in the absolute flux calibration among the instruments. We set this value of Suzaku/FIXIS unity as a reference. The cross-normalizations of Suzaku/BIXIS (N_BIXIS), XMM-Newton/EPN (N_EPN), XMM-Newton/MOS (N_MOS), and NuSTAR/FPM (N_FPM) are left as a free parameter. The cross-normalization of Suzaku/PIN and Suzaku/GSO is set to 1.16, according to the calibration results obtained using the Crab Nebula.
• 2.  
  Galactic absorption (phabs). The hydrogen column density is fixed at 0.525 × 10²² cm⁻², a value estimated from the H_I map (Kalberla & Haud 2015).
• 3.  
  Transmitted component through the torus, which is subject to photoelectric absorption (zphabs) and Compton scattering (cabs). The line-of-sight column density is determined by the torus parameters (see Equation (3)). We model the intrinsic continuum by a power law with an exponential cutoff (zcutoffpl).
• 4.  
  Unabsorbed scattered component. The scattering fraction f_scat (const2) is multiplied to the same model as the intrinsic continuum by linking the photon index, cutoff energy, and normalization.
• 5.  
  Reflection continuum (xclumpy_R.fits) from the torus, based on the XCLUMPY model. The photon index, cutoff energy, and normalization are linked to those of the intrinsic continuum.
• 6.  
  Fluorescence lines (xclumpy_L.fits) from the torus, based on the XCLUMPY model. The photon index, cutoff energy, and normalization are linked to those of the intrinsic continuum. Since we find that the XCLUMPY model slightly underestimates the observed line fluxes, we add an additional two Gaussians for Fe Kα and Fe Kβ. The cause of the discrepancy is not clear: there might be diffuse Fe–K emission that did not originate from the torus (Marinucci et al. 2013), or the metal abundance is higher than the solar value (Hikitani et al. 2018).
• 7.  
  Contamination from CGX1 (X-ray binary). We adopt the same model and flux as in Arévalo et al. (2014), who examined the spectrum of CGX1 with Chandra.
• 8.  
  Contamination from CGX2 (supernova remnant). We also assume the same model and flux as in Arévalo et al. (2014).

5.3. Results and Discussion

Our model can well reproduce the broadband X-ray spectra observed with the three satellites. Table 4 summarizes the best-fit parameters. Figure 7 shows the (a) folded X-ray spectra and (b) best-fit models. We confirm that the torus of the Circinus galaxy is heavily Compton-thick; the column density in the line of sight and that along the equatorial plane are estimated to be ${4.86}_{-0.04}^{+0.07}\times {10}^{24}$ cm⁻² and ${9.08}_{-0.08}^{+0.14}\times {10}^{24}$ cm⁻², respectively. Accordingly, the X-ray spectrum is dominated by the reflection component rather than the transmitted one.

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Table 4.  Best-fit Parameters with the XCLUMPY Model

CBIXIS	CEPN	CMOS	CFPM	${N}_{{\rm{H}}}^{\mathrm{LOS}}$	${N}_{{\rm{H}}}^{\mathrm{Equ}}$	σ	i	Γ	χ2/dof
(01)	(02)	(03)	(04)	(05)	(06)	(07)	(08)	(09)
Ecut	NDir	fscat	EFeKα	NFeKα	EFeKβ	NFeKβ	$\mathrm{log}{L}_{2-10}$	$\mathrm{log}{L}_{10-50}$	reduced χ2
(10)	(11)	(12)	(13)	(14)	(15)	(16)	(17)	(18)
${1.08}_{-0.01}^{+0.01}$	${0.96}_{-0.01}^{+0.01}$	${1.02}_{-0.01}^{+0.01}$	${0.88}_{-0.01}^{+0.01}$	${4.86}_{-0.04}^{+0.07}$	${9.08}_{-0.08}^{+0.14}$	${14.7}_{-0.39}^{+0.44}$	${78.3}_{-0.15}^{+0.17}$	${1.80}_{-0.03}^{+0.01}$	3646/2989
${114}_{-8.91}^{+9.57}$	${0.41}_{-0.01}^{+0.01}$	${0.18}_{-0.01}^{+0.01}$	${6.43}_{-0.01}^{+0.01}$	${1.07}_{-0.01}^{+0.01}$	${7.12}_{-0.01}^{+0.01}$	${0.13}_{-0.01}^{+0.01}$	42.8	42.8	1.22

Note. Column (1): cross-calibration constant of the Suzaku/BIXIS relative to the Suzaku/FIXIS. Column (2): cross-calibration constant of the XMM-Newton/EPN relative to the Suzaku/FIXIS. Column (3): cross-calibration constant of the XMM-Newton/MOS relative to the Suzaku/FIXIS. Column (4): cross-calibration constant of the NuSTAR/FPM relative to the Suzaku/FIXIS. Column (5): hydrogen column density along the line of sight in units of 10²⁴ cm⁻². Column (6): hydrogen column density along the equatorial plane in units of 10²⁴ cm⁻². Column (7): torus angular width in units of degrees. Column (8): inclination angle in units of degrees. Column (9): photon index. Column (10): cutoff energy in units of kiloelectron volts. Column (11): normalization of the direct component in units of photons keV⁻¹ cm⁻² s⁻¹. Column (12): scattering fraction in units of percent. Column (13): energy of the additional Fe Kα emission line. Column (14): normalization of the additional Fe Kα emission line in units of 10⁻⁴ photons cm² s⁻¹. Column (15): energy of the additional Fe Kβ emission line. Column (16): normalization of the additional Fe Kβ emission line in units of 10⁻⁴ photons cm² s⁻¹. Column (17): logarithmic intrinsic luminosity in the 2–10 keV. Column (18): logarithmic intrinsic luminosity in the 10–50 keV.

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5.3.1. Comparison to Previous Research

Here we compare our results with the previous X-ray works using the same data (Yang et al. 2009; Arévalo et al. 2014). Yang et al. (2009) analyzed the Suzaku spectra with the pexrav model, and obtained a line-of-sight absorption of ${N}_{{\rm{H}}}^{\mathrm{LOS}}\,={4.70}_{-0.32}^{+0.50}\,\times {10}^{24}$ cm⁻² and a photon index of ${\rm{\Gamma }}={1.58}_{-0.10}^{+0.07}$. The simultaneous XMM-Newton and NuSTAR data in 2013 were analyzed by Arévalo et al. (2014). Applying the MYTorus model, they obtained ${N}_{{\rm{H}}}^{\mathrm{LOS}}={6.6}_{-0.9}^{+0.9}\times {10}^{24}$ cm⁻² and ${\rm{\Gamma }}={2.19}_{-0.02}^{+0.02}$. Our result of the line-of-sight column density (${N}_{{\rm{H}}}^{\mathrm{LOS}}={4.86}_{-0.04}^{+0.07}\,\times {10}^{24}$ cm⁻²) is consistent with both of them. The photon index (${\rm{\Gamma }}={1.77}_{-0.03}^{+0.06}$) is smaller than the Arévalo et al. (2014) result, however. We infer that this is because the XCLUMPY model contains a larger flux of the unabsorbed reflection component, leading to a flatter intrinsic slope, compared with the MYTorus model case.

5.3.2. Comparison of Torus Parameters by X-Ray and Infrared Spectra

It is interesting to compare the torus parameters obtained from the X-ray data (Table 4) with those from the infrared data (Table 2). The total V-band optical depth in the equatorial plane obtained with the CLUMPY model is ${\tau }_{{\rm{V}}}={173}_{-7}^{+26}$, which can be converted to ${N}_{{\rm{H}}}^{\mathrm{Equ}}={0.35}_{-0.05}^{+0.01}\times {10}^{24}$ cm⁻² by assuming the gas-to-dust ratio in the Galaxy (Draine 2003: N_H/A_V = 1.87 × 10²¹ cm⁻² mag⁻¹). This value is much (by a factor of ∼26) smaller than the X-ray result, ${N}_{{\rm{H}}}^{\mathrm{Equ}}={9.08}_{-0.08}^{+0.14}\,\times {10}^{24}$ cm⁻². The same conclusion holds when we compare the line-of-sight column density. This trend is consistent with the results of Burtscher et al. (2015, 2016), who estimated A_V from the near-to-mid infrared colors. The torus angular width obtained from the infrared data ($\sigma ={65}_{-5}^{+2}$ degree) is much larger than the X-ray results ($\sigma ={14.7}_{-0.39}^{+0.44}$ degree). These results may be explained by the presence of a dusty polar outflow observed in the infrared interfere-metric observations (Tristram et al. 2014; Stalevski et al. 2017), which apparently makes the distribution of dust wider than that of gas. Since the extended outflow is subject to smaller extinction than that toward the very center of the nucleus, it works to reduce the observed (averaged) A_V value.

• 1.  
  We have constructed the XCLUMPY model, a spectral model of X-ray reflection from the clumpy torus in an AGN, where the same torus geometry as in the infrared CLUMPY model is adopted. This enables us to directly compare the X-ray and infrared results, which trace the distribution of all matter and dust, respectively.
• 2.  
  We found that the equivalent width of Fe Kα line and the Compton shoulder fraction both increase with the hydrogen column density along the equatorial plane and torus angular width.
• 3.  
  Compared with smooth torus models, our model predicts a higher fraction of unabsorbed reflection components as observed in many obscured AGNs.
• 4.  
  Our model well reproduces the broadband X-ray spectra of the Circinus galaxy observed with XMM-Newton, Suzaku, and NuSTAR. We confirm that the torus is heavily Compton thick and the spectrum is dominated by the reflection component from the torus.
• 5.  
  In the Circinus galaxy, the column density obtained from the X-ray data is >20 times larger than that from the infrared data by assuming a Galactic gas-to-dust ratio. The torus angular width derived from X-rays is much smaller than that in the infrared band. This may be explained by the presence of a dusty polar outflow.

Part of this work was financially supported by the Grant-in-Aid for JSPS fellows for young researchers (A.T.) and for Scientific Research 17K05384 (Y.U.). 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 research has also made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.

Facilities: XMM-Newton (0701981001) - , Suzaku (701036010) - , NuSTAR (30002038004) - .

Software: HEAsoft 6.24 (HEASARC 2014), MONACO (Odaka et al. 2011, 2016), SAS 17.00 (Gabriel et al. 2004), XSPEC (Arnaud 1996).

We investigate the dependence of the spectrum on the number of clumps along the equatorial plane (${N}_{\mathrm{clump}}^{\mathrm{Equ}}$). Here we adopt the following default parameters: σ = 400, i = 600, Γ = 2.0, and E_cut = 100 keV. Figure 8 compares the broadband X-ray spectrum and Fe Kα line profile among different ${N}_{\mathrm{clump}}^{\mathrm{Equ}}$ values (5, 10, and 15) for $\mathrm{log}\,{N}_{{\rm{H}}}$/cm⁻² =  24.0 and 25.0. As noted, the spectrum depends little on ${N}_{\mathrm{clump}}^{\mathrm{Equ}}$ for $\mathrm{log}\,{N}_{{\rm{H}}}$/cm⁻² = 24.0. By contrast, for $\mathrm{log}\,{N}_{{\rm{H}}}$/cm⁻² = 25.0, the continuum flux below 20 keV and Fe Kα line flux become higher with ${N}_{\mathrm{clump}}^{\mathrm{Equ}}=5.0$ than with ${N}_{\mathrm{clump}}^{\mathrm{Equ}}=10.0$ or 15.0; the Fe Kα line flux with ${N}_{\mathrm{clump}}^{\mathrm{Equ}}=5.0$ is 25% higher than that with ${N}_{\mathrm{clump}}^{\mathrm{Equ}}=10.0$. The same trend is also reported in Liu & Li (2014). This is because the smaller number of clumps in the line of sight works to reduce the total probability of absorption for soft X-rays when each clump is already optically thick. Figure 9 plots the dependence of equivalent widths and Compton shoulder fraction on ${N}_{\mathrm{clump}}^{\mathrm{Equ}}$ for $\mathrm{log}\,{N}_{{\rm{H}}}$/cm⁻² = 24.0 and $\mathrm{log}\,{N}_{{\rm{H}}}$/cm⁻² = 25.0. We find that they show little dependence on ${N}_{\mathrm{clump}}^{\mathrm{Equ}}$ both for $\mathrm{log}\,{N}_{{\rm{H}}}$/cm⁻² = 24.0 and 25.0. This is because the changes of the continuum flux and Fe Kα line flux are almost canceled out by each other.

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We also investigate the dependence of the spectrum on the index of the radial density profile (q). We adopt the following default parameters: σ = 400, i = 600, Γ = 2.0, and E_cut = 100 keV). Figure 10 compares the broadband X-ray spectrum and Fe Kα line profile among different among different q values (0.0, 0.5, 1.0) for $\mathrm{log}\,{N}_{{\rm{H}}}$/cm⁻² =  24.0 and 25.0. Figure 11 plots the dependence of equivalent widths and Compton shoulder fraction on q for $\mathrm{log}\,{N}_{{\rm{H}}}$/cm⁻² = 24.0 and 25.0. We find that they show little dependence on q within a range of 0.0–1.0.

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