Circumnuclear Multiphase Gas in the Circinus Galaxy. V. The Origin of the X-Ray Polarization in the Circinus Galaxy

The Imaging X-ray Polarimetry Explorer (IXPE) detected X-ray polarization in the nearest Seyfert 2 galaxy, the Circinus galaxy, for the first time. To reproduce the IXPE results, we computed the degree of polarization based on two types of radiative hydrodynamic simulations: a parsec-scale three-dimensional model and a sub-parsec-scale axisymmetric model with a higher spatial resolution. In a series of papers, we confirmed that these models naturally explain the multiwavelength observations of the Circinus galaxy from radio to X-rays. We used a Monte Carlo Simulation for Astrophysics and Cosmology code to compute the linear polarization of continuum emission. We found that the degree of polarization based on the parsec-scale radiation-driven fountain model was smaller than that observed with the IXPE. The degree of polarization based on the sub-parsec-scale model depends on the hydrogen number density of the disk (d), and the degree of polarization obtained from our simulation is consistent with that observed with the IXPE in the case of logd/cm−3≥13 . We investigate where the photons are Compton scattered and imply that the origin of the X-ray polarization in the Circinus galaxy is the outflow inside 0.01 pc. In this case, the degree of polarization may change over a timescale of approximately 10 yr.


INTRODUCTION
A unified model of active galactic nuclei (AGNs) suggests that a structure composed of gas and dust, called a torus, surrounds accreting supermassive black holes (SMBHs) (Antonucci 1993;Urry & Padovani 1995;Netzer 2015;Ramos Almeida & Ricci 2017).This torus plays an essential role in the co-evolution between SMBHs and their host galaxies (e.g., Kormendy & Ho 2013).This is because the torus is believed to exist between the SMBH and the host galaxy, providing a mass from the host galaxy to the SMBH.However, the mechanism of torus formation and the structure of the sub-parsec-scale gas remain unclear.
X-ray observations are among the most powerful tools for probing the structures of torus-scale gases.In particular, the polarization of X-rays caused by Compton scattering can provide clues to the geometry of the torus, such as the hydrogen column density along the equatorial direction (log N Equ H /cm −2 ) and the opening angle of the torus (θ open ).In fact, several studies have investigated the dependence of the degree of polarization on torus properties (Goosmann & Matt 2011;Marin et al. 2016Marin et al. , 2018;;Ratheesh et al. 2021).For instance, Ratheesh et al. (2021) assumed a partially spherically symmetric torus and studied the dependence of the degree of polarization on log N Equ H /cm −2 and θ open .Ratheesh et al. (2021) found that the degree of polarization increased with log N Equ H /cm −2 (Ratheesh et al. 2021, Figure 10).Recently, the Imaging X-ray Polarimetry Explorer (IXPE; Weisskopf et al. 2022) measured the degree of polarization of the Circinus galaxy for the first time, one of the nearest (4.2 ± 0.8 Mpc: Freeman et al. 1977) Compton-thick AGNs whose hydrogen column density along the line of sight is greater than 10 24 cm −2 (Arévalo et al. 2014;Tanimoto et al. 2019;Uematsu et al. 2021).Ursini et al. (2023) has analyzed the observational data and indicated that the degree of polarization is 28 ± 7% for the neutral reflector.To explain the degree of polarization of the Circinus galaxy, Ursini et al. (2023) calculated it based on the simple torus model with the same geometric structure as that reported by Ratheesh et al. (2021).As a result, they were able to reproduce the degree of polarization of the Circinus galaxy with log N Equ H /cm −2 = 25 and θ open ≃ 50 • .However, in the case of the simple model, any geometric structure can be assumed to reproduce the observational data.Since the real structures of the central region of AGNs are still unknown, it is essential for us to study the origin of X-ray polarization based on radiative hydrodynamical simulations.
In the fifth paper in this series, we computed the degree of polarization based on radiative hydrodynamic simulations (Paper I: Wada et al. 2018a, Paper II: Izumi et al. 2018, Paper III: Wada et al. 2018b, and Paper IV: Uzuo et al. 2021).Here, we used two models: a parsec-scale three-dimensional model (Wada 2012(Wada , 2015) ) and a sub-parsec-scale axisymmetric model (Kudoh et al. 2023).Wada (2012) considered the radiative feedback from the central source such as the radiation pressure on the dusty gas and the X-ray heating and showed that a geometrically and optically thick torus-like structure could be naturally formed based on the three-dimensional radiative hydrodynamic simulation.In fact, their model successfully reproduced the molecular and atomic lines in the radio spectrum (Wada et al. 2018a;Izumi et al. 2018;Uzuo et al. 2021), the infrared spectral energy density (Wada et al. 2016), the properties of the narrow line regions (Wada et al. 2018b), and the X-ray spectrum observed with the Chandra/High Energy Transmission Grating (Ogawa et al. 2022) of the Circinus galaxy.However, Buchner et al. (2021) computed the X-ray spectra of neutral materials based on a parsec-scale radiation-driven fountain model, and suggested that their model could not explain the Compton hump in the Circinus galaxy.To reproduce the Compton hump, they reported that a Compton-thick material on the sub-parsec scale is required.If such a material exists on the sub-parsec scale, it affects the degree of polarization.Therefore, we computed the degree of polarization based on the sub-parsec-scale radiation-driven fountain model (Kudoh et al. 2023).The sub-parsec-scale radiation-driven fountain model has identified time variability in the Balmer lines over a scale of 1-10 years (Wada et al. 2023).The X-ray spectra also exhibit time variability in some AGNs (Ricci & Trakhtenbrot 2022).Hence, it would be interesting to investigate whether the degree of polarization displays similar variability and if the radiation-driven fountain contributes to it.
The remainder of this paper is organized as follows: In Section 2, we presented the Monte Carlo simulations and the radiationdriven fountain model.In Section 3, we described the results of our simulations.In Section 4, we discussed the origin of the X-ray polarization in the Circinus galaxy and the time variability of the degree of polarization.Finally, in Section 5, we presented our conclusions.

Stokes Parameters and Monte Carlo Simulations
To describe the polarization state, we defined the Stokes parameters.The Stokes parameters I, Q, U , and V are defined using the Poincare sphere as follows: V = IP sin 2χ. (3) Here, P is the degree of polarization, 2χ is the elevation angle of the Poincare sphere, and 2ψ is the azimuth angle of the Poincare sphere.As the IXPE can only detect linear polarization, we assumed that χ is equal to 0. In this case, the Stokes parameters I, Q, and U are defined as follows: From equations (4) and ( 5), the degree of polarization P can be expressed as, To compute the Stokes parameters, we used the Monte Carlo Simulation for Astrophysics and Cosmology (MONACO; Odaka et al. 2011Odaka et al. , 2016) ) code version 1.7.s1.This code uses the Geant4 code (Agostinelli et al. 2003;Allison et al. 2006Allison et al. , 2016) ) to track photons in complex geometric structures.Although the Geant4 code implements physical processes, MONACO uses physical processes optimized for astrophysics.Currently, MONACO has three sets of physical processes: (1) X-ray reflection from neutral matter (Odaka et al. 2011;Furui et al. 2016;Tanimoto et al. 2019Tanimoto et al. , 2022;;Uematsu et al. 2021), (2) Comptonization in a hot flow (Odaka et al. 2013(Odaka et al. , 2014)), and (3) photon interactions in a photoionized plasma (Watanabe et al. 2006;Hagino et al. 2015Hagino et al. , 2016;;Tomaru et al. 2018Tomaru et al. , 2020;;Mizumoto et al. 2021).
For simplicity, we used the X-ray reflection from neutral matter in this study.In other words, we assumed that the thermal motion of the gas and ionized matter was ignored.Three physical processes were considered: photoelectric absorption, fluorescence line emission, and Compton scattering caused by free electrons.We assumed that the primary photons were unpolarized.Furthermore, we considered the solar abundances from Anders & Grevesse (1989).First, we computed the degree of polarization based on the parsec-scale radiation-driven fountain model (Wada et al. 2016) (Section 3.1).Wada et al. (2016) computed the three-dimensional radiative dynamical simulation ranging from −16 pc to +16 pc in the 256 3 Cartesian coordinate system.The model consistently reproduced the observed spectral energy density of the Circinus galaxy when the inclination angle was greater than 75 • .They assumed that the black hole mass was 2.0 × 10 6 M ⊙ based on water maser observations (Greenhill et al. 2003), which is also consistent with the molecular gas kinematics revealed by ALMA (Izumi et al. 2023), the Eddington ratio was 20% (Arévalo et al. 2014), and the X-ray luminosity from 2 keV to 10 keV was 2.8 × 10 42 erg s −1 (Arévalo et al. 2014) of the Circinus galaxy.We used the same input data analyzed by Ogawa et al. (2022), which reformed the −16 pc to +16 pc range from a 256 3 Cartesian coordinate grid to a 64 3 spherical coordinate grid.Figure 1(a) shows the distribution of the hydrogen number density based on the parsec-scale radiation-driven fountain model and Figure 2(a) shows the hydrogen column density along the line of sight as a function of the inclination angle.Figure 2(a) shows that the parsec-scale radiation-driven fountain model is Compton-thin for almost all the inclination angles.We generated 10 8 photons in the 1-10 keV range with a photon index of 1.8 of the Circinus galaxy (Tanimoto et al. 2019).

Radiation-Hydrodynamic Models
The second hydrodynamic model is the sub-parsec-scale radiation-driven fountain model (Kudoh et al. 2023) (Section 3.2).Kudoh et al. ( 2023) computed the radiation-driven fountain model considering the more inner regions based on the two-dimensional radiative hydrodynamic simulations using the coordinated astronomical numerical software plus (CANS+: Matsumoto et al. 2019).To apply this model to the Circinus galaxy, we assumed the same black hole mass, Eddington ratio, and X-ray luminosity as in Wada et al. (2016).This model has the initial hydrogen number density of disk log d/cm −3 as a free parameter.In this study, we studied four cases of log d/cm −3 : log d/cm −3 = 12, 13, 14, and 15.This is because, if log d/cm −3 is less than 11, we cannot reproduce the observational results of the IXPE.On the other hand, an excessively large log d/cm −3 is unrealistic because it should be dynamically unstable.We performed two-dimensional axisymmetric radiative hydrodynamic simulations shows the hydrogen column density along the line of sight as the function of the inclination angle.We found that the sub-parsec-scale radiation-driven fountain model had a Compton-thick material when i was greater than ≃ 50 • .To study the dependence of the degree of polarization on log d/cm −3 and time, we generated 10 8 photons in the range of 1-10 keV, with a photon index of 1.8 for each of the four patterns of log d/cm −3 and four patterns of snapshots.Since we do not know how the Circinus galaxy is tilted with respect to the celestial north pole, we assumed coordinates where the z-axis direction of the radiative hydrodynamics simulation is negative in Stokes parameter Q.

Parsec-Scale Radiation-Driven Fountain Model
Figure 3 plots the dependence of (a) the Stokes parameter I, (b) the Stokes parameter Q, (c) the Stokes parameter U , and (d) the degree of polarization on the inclination angle (i).Although the IXPE is observable at energies ranging from 2 keV to 8 keV, we integrated these values over the range of 2-6 keV.This is because we avoid the influence of neutral iron X-ray fluorescence at approximately 6.4 keV.In fact, Ursini et al. (2023) removed the polarization contribution from the neutral iron fluorescent line by fixing polconst to zero for the neutral iron fluorescent line.Figure 3(a) shows that the Stokes parameter I is nearly constant below i ≃ 50 • , whereas it decreases as the inclination angle increase above i ≃ 50 • .This is because the Compton-thin material exists along the line of sight above i ≃ 50 • (Figure 2(a)).Figure 3(b) shows that the Stokes parameter Q is negative.The reason is that, in the parsec-scale radiation-driven fountain model, the material around the nucleus is Compton-thin, and Compton-scattered photons can pass through it.By contrast, if the material around the nucleus is Compton-thick, the Stokes parameter Q will be positive because the photons are Compton-scattered on the surface of the material around the nucleus.
Figure 3(d) compares the degrees of polarization obtained from our simulation with those of the Circinus galaxy observed with the IXPE (Ursini et al. 2023).Ursini et al. (2023) showed that the degree of polarization for the neutral reflector is 28 ± 7%.It is also known that the inclination angle of the Circinus galaxy is almost edge-on (i ≥ 70 • ) (Greenhill et al. 2003;Tristram et al. 2014;Izumi et al. 2018;Isbell et al. 2022;Ogawa et al. 2022).We found that the degree of polarization obtained from our simulation was smaller than that obtained from observations.This is because the hydrogen column density in this model is small and the polarization effect due to Compton scattering is small.This result is consistent with those of a previous study (Buchner et al. 2021).Buchner et al. (2021) computed the X-ray spectra of neutral materials based on the parsec-scale radiation-driven fountain model, and suggested that a Compton-thick material on the sub-parsec-scale is required.

Sub-Parsec-Scale Radiation-Driven Fountain Model
We then computed the Stokes parameters based on the sub-parsec-scale radiation-driven fountain model (Kudoh et al. 2023).Figure 4  Figure 4(d) compares the degrees of polarization obtained from our simulation with those of the Circinus galaxy.In the case of i ≥ 70 • and log d/cm −3 ≥ 13, we found that the degree of polarization obtained from our simulation was consistent with that inferred from the IXPE observation.We also compare the polarization angle obtained from our simulation with that observed with the IXPE.The polarization angle obtained from the IXPE observation is ψ = 18 ± 5 • (Ursini et al. 2023).This value is close to the direction of the inner H 2 O maser disk (29 • ; Greenhill et al. 2003) and is consistent with being perpendicular to the radio jet (295 • ; Elmouttie et al. 1998a) and to the axis of the Hα ionization cone (Elmouttie et al. 1998b).As explained in Section 2.2, we cannot compare the absolute values of the polarization angles from our calculations with those from the IXPE observations, but the value of the polarization angle from our calculations is almost 0 • , which is consistent with the disk direction.

Origin of X-Ray Polarization
To determine the origin of the X-ray polarization in the Circinus galaxy, we investigated where the photons were Comptonscattered.Figure 5 plots (a) the distribution of the hydrogen number density (log n H /cm −3 ) inside 0.064 pc, (b) the distribution of the number of Compton-scattered photons in the case of the edge-on view inside 0.064 pc, (c) the distribution of log n H /cm −3 inside 0.01 pc, and (d) the distribution of the number of Compton-scattered photons inside 0.01 pc.Although we assumed the hydrogen number density of the disk of log d/cm −3 = 15, we confirmed that the trend was the same for different values.Figure 5(b) suggests that almost all photons are Compton scattered inside 0.01 pc.In particular, the photons are mainly Compton scattered approximately r ≃ 0.005 pc whose hydrogen number density is approximately 10 7 cm −3 (Figure 5(c)-(d)).This implies that the origin of X-ray polarization in the Circinus galaxy is a sub-parsec-scale radiation-driven outflow.

Time Variability of Degree of Polarization
We examined the time variability in the degree of polarization.This is because the structures of the dense gas in the central region that contribute to the polarization depend on time.Figure 6 plots (a) the distribution of the hydrogen number density (log n H /cm −3 ) based on the sub-parsec-scale radiation-driven fountain model inside 0.064 pc, (b) the distribution of log n H /cm −3 after eight years, (c) the distribution of log n H /cm −3 after 16 years, and (d) the distribution of log n H /cm −3 after 24 years.Here we assume the hydrogen number density of the disk to be log d/cm −3 = 14. Figure 7 also plots the distribution of log n H /cm −3 inside 0.01 pc. Figure 7 suggests that the distribution of log n H /cm −3 inside 0.01 pc, which is thought to be the origin of X-ray polarization, changes on a timescale of approximately 10 years.This can affect the degree of polarization.to understand the origin of X-ray polarization.We also studied the time variability in the polarization angle and found that the polarization angles agreed within an error.Our simulations are based on two-dimensional axisymmetric radiative hydrodynamic simulation results, which may overestimate the time variability in the degree of polarization.

CONCLUSION
We computed the degree of polarization based on two types of radiative hydrodynamic simulations: the parsec-scale radiationdriven fountain model (Wada et al. 2016), and the sub-parsec-scale radiation-driven fountain model (Kudoh et al. 2023) using MONACO code (Odaka et al. 2011(Odaka et al. , 2016) ) version 1.7.s1.The following conclusions were drawn.3. We investigated where the photons are Compton scattered and implied that the origin of the X-ray polarization in the Circinus galaxy is the outflow inside 0.01 pc.
4. We evaluated the time variability in the degree of polarization.We found that the degree of polarization changed over approximately 10 years.If the time variability of the degree of polarization is detected in the Circinus galaxy in the future, it reinforces that the origin of the X-ray polarization is the gas inside 0.01 pc.We thank the anonymous referee for the helpful comments.Atsushi Tanimoto and the present research are partly supported by the Kagoshima University postdoctoral research program (KU-DREAM).This work is also supported by the Grant-in-Aid for JSPS Fellows (R.U.) and the Grants-in-Aid for Scientific Research 22H00128 (H.O.).Numerical computations were performed on Cray XC50 at the Center for Computational Astrophysics, National Astronomical Observatory of Japan.Software: CANS+ (Matsumoto et al. 2019), MONACO (Odaka et al. 2011(Odaka et al. , 2016)).

Figure 1 .Figure 2 .
Figure 1.(a)  The distribution of the hydrogen number density (log nH/cm −3 ) based on the parsec-scale radiation-driven fountain model(Wada et al. 2016).(b) The distribution of log nH/cm −3 based on the sub-parsec-scale radiation-driven fountain model(Kudoh et al. 2023).Here we assumed that the logarithmic initial disk density was log d/cm −3 = 13.

Figure 3 .
Figure 3. (a) The dependence of the Stokes parameter I on the inclination angle (i).(b) The dependence of the Stokes parameter Q on i. (c) The dependence of the Stokes parameter U on i.(d) Comparison of the degree of polarization obtained from our simulation with that of the Circinus galaxy observed with the IXPE (red region).The blue region represents a range of inclination angles of the Circinus galaxy suggested by observations (see Section 3.1).Here errors correspond to a 1σ credible interval.

Figure 4 .
Figure 4. Same as Figure 2, but for the sub-parsec-scale radiation-driven fountain model.
plots the dependence of (a) the Stokes parameter I, (b) the Stokes parameter Q, (c) the Stokes parameter U , and (d) the degrees of polarization on the hydrogen number density of the disk (d) and the inclination angle (i).Here we integrated the values from 2 keV to 6 keV. Figure 4(a) shows that the Stokes parameter I decrease with d and i. Figure 4(b) shows that the Stokes parameter Q is negative in the case of i ≥ 70 • and log d/cm −3 = 12, whereas the Stokes parameter Q is positive in the case of i ≥ 70 • and log d/cm −3 ≥ 13.As explained in Section 3.1, this is because the sub-parsec-scale radiation-driven fountain model has a Compton-thick material in the case of i ≥ 70 • (Figure 2(b)).Figure 4(c) shows that the Stokes parameter U is almost constant in the case of i ≥ 70 • and log d/cm −3 ≥ 13.

Figure 8 Figure 5 .
Figure 5. (a) The distribution of the hydrogen number density (log nH/cm −3 ) inside 0.064 pc.(b) The distribution of the number of Comptonscattered photons in the case of the edge-on view inside 0.064 pc.(c) The distribution of log nH/cm −3 inside 0.01 pc.(d) The distribution of the number of Compton-scattered photons inside 0.01 pc.Here we assume the hydrogen number density of the disk of log d/cm −3 = 15.

Figure 6 .Figure 7 .
Figure 6.(a) The distribution of the hydrogen number density (log nH/cm −3 ) based on the sub-parsec-scale radiation-driven fountain model inside 0.064 pc.(b) The distribution of log nH/cm −3 after eight years.(c) The distribution of log nH/cm −3 after 16 years.(d) The distribution of log nH/cm −3 after 24 years.Here we assume the hydrogen number density of the disk of log d/cm −3 = 14.

Figure 8 .
Figure 8.(a) The dependence of the Stokes parameter I on the time.(b) The dependence of the Stokes parameter Q on the time.(c) The dependence of the Stokes parameter U on the time.(d) Comparison of the degree of polarization obtained from our simulation with that of the Circinus galaxy observed with the IXPE (red region).The blue region represents a range of observational suggested inclination angles of the Circinus galaxy (see Section 3.1).Here errors correspond to a 1σ credible interval.