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The authors thank Alexandra Veledina for consulting the modelling of the Cygnus X-3 source, and the Strasbourg Astronomical Observatory for providing the necessary computational capacities. JP and MD also acknowledge the support from the Czech Science Foundation project GACR 21-06825X and the institutional support from the Astronomical Institute RVO:67985815.
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We present the expected X-ray polarization signal resulting from distant reprocessing material around black holes. Using a central isotropic power-law emission at the center of the simulated model, we add distant equatorial and axially symmetric media that are covering the central accreting sources. We include partial ionization and partial transparency effects, and the impact of various polarization and steepness of the primary radiation spectrum. The results are obtained with the Monte Carlo code STOKES that considers both line and continuum processes and computes the effects of scattering and absorption inside static homogenous wedge-shaped and elliptical toroidal structures, varying in relative size, composition and distance to the source. We provide first order estimates for parsec-scale reprocessing in Compton-thin and Compton-thick active galactic nuclei, as well as winds around accreting stellar-mass compact objects. The resulting polarization can reach tens of % with either parallel or perpendicular orientation with respect to the axis of symmetry, depending on subtle details of the geometry, density and ionization structure. We also show how principal parameters can be constrained from X-ray spectroscopy or polarimetry in other wavelengths to lift the shown degeneracies in the X-ray band. We provide an application example of the broad modelling discussion by revisiting the recent IXPE 2–8 keV X-ray polarimetric observation of the accreting stellar-mass black hole in Cygnus X-3 from the perspective of partial transparency and ionization of the obscuring outflows.
Since the establishment of the unification scenario of active galactic nuclei (AGN) (Antonucci 1993; Urry & Padovani 1995), the physical and – in particular – geometrical description of AGNs has reached much greater detail. The central supermassive black hole is believed to be surrounded by an accretion disc at sub-parsec scales with a dusty obscuring material reaching a few parsecs further out in the equatorial plane. Polarimetry not only allowed the discovery of the global AGN morphology back in the 60’s and 80’s (Dibai & Shakhovskoi 1966; Walker 1966; Angel et al. 1976; Antonucci 1982; Antonucci & Miller 1985), but also serves as a powerful microscope into these extragalactic objects. That is because polarization – as a geometrical property of light – traces the unresolved structures in the origin of emission. The successful launch and operation of the Imaging X-ray Polarimetry Explorer (IXPE) (Weisskopf et al. 2022) has recently brought fresh air into the often overlooked field of X-ray polarimetry and consequently enabled the opening of a new observational window for measuring polarization in the 2–8 keV band for virtually all X-ray sources, including AGNs. During the first year and a half of IXPE observations, a few brightest type-1 AGNs (viewed pole on, directly into the nucleus of the axially symmetric accreting structure) were observed: MCG 05-23- 16 (< 3.2% of polarization fraction in 2–8 keV at a 99% confidence level, Marinucci et al. 2022; Tagliacozzo et al. 2023), NGC 4151 (4.9 ± 1.1 % in 2–8 keV at a 68% confidence level, Gianolli et al. 2023), and IC 4329A (3.3 ± 1.9 % in 2–8 keV at a 90% confidence level, Ingram et al. 2023). In addition, the brightest prototypical type-2 AGN (viewed edge on through the parsec-scale obscuring equatorial material), the Circinus Galaxy, was observed (20.0 ± 3.8 % in 2–6 keV at a 68% confidence level, Ursini et al. 2023). Because more fascinating observational results in X-ray polarimetry are yet to come in this decade through the IXPE mission, or its successors [e.g. the XL-Calibur experiment in 15–80 keV (Abarr et al. 2021) or the eXTP mission in 2-12 keV (Zhang et al. 2016, 2019)], it is timely to put effort simultaneously in the theory and numerical modelling, in order to interpret these results in a meaningful manner. In this paper, we present an updated and revised summary of the Xray spectro-polarimetric models of the equatorial parsec-scale AGN components (i.e. the dusty tori) using the STOKES code (Goosmann & Gaskell 2007; Marin et al. 2012b, 2015; Marin 2018). STOKES is a Monte Carlo (MC) radiative transfer code that was originally developed to trace polarization signatures of absorption and scattering in the optical and UV bands, but more recently has been adapted to the X-rays. It includes all important line and continuum processes in the X-ray band and thus forms an ideal tool to study the interaction of
We compared the X-ray polarization properties in the 1–100 keV band of homogenous static equatorial obscuring media around accreting compact objects. We performed simulations of partially ionized and partially transparent 3D toroidal structures with the STOKES code (Goosmann & Gaskell 2007; Marin et al. 2012b, 2015; Marin 2018), which is an MC simulation suitable for studying the effects of scattering and absorption. Placing the source of low (up to a few %) polarized source of isotropic power-law emission in the center of the axially symmetric equatorial obscurer, we defined distinct geometries for the reprocessing studies: the wedge-shaped torus and elliptical tori with various eccentricities. When avoiding the observed polarization state of spectral lines by selecting the 3.5–6 keV and 30–60 keV bands, we found large dependence of the polarization fraction on inclination, half-opening angle, density of the scatterer and ionization level. We found relatively minor impact (up to a few %) of primary polarization state and moderate impact of the primary power-law index Γ (low tens of % in very specific geometries). Overall, the diversity in resulting polarization is striking. The polarization fraction can vary from completely unpolarized results up to high tens of %, with large degeneracies with respect to the geometries examined and the density and ionization effects. The resulting polarization angle can be either perpendicular or parallel with respect to the main axis of symmetry, as we do not take into account any general-relativistic effects. The former scenario is favoured for low half-opening angles, high column densities, high ionization levels and low inclinations. The opposite configurations will more likely result in a parallelly oriented polarization angle, while the intermediate cases depend on subtle details of relative size, shape and composition of the obscurer. The X-ray polarization fraction typically reaches a maximum for moderate inclinations per given half-opening angle, effectively providing 2 solutions as a diagnostic tool for energy-integrated observations. The modelling results are roughly consistent with other codes in the literature (Ghisellini et al. 1994; Ratheesh et al. 2021; Ursini et al. 2023; Veledina et al. 2023) and STOKES code computations performed for more specific configurations (Goosmann & Matt 2011). We obtained similar geometry effects of the equatorial obscurers on polarization studied in the optical and UV wavelengths (Kartje 1995; Goosmann & Gaskell 2007), confirming the fundamental geometrical explanations provided therein. In addition, we provided a different perspective and usage example of the MC simulations by studying in detail the equatorial obscuration in the context of recent IXPE observation of the XRB Cygnus X-3 (Veledina et al. 2023). Focusing on the IXPE operational band 2–8 keV, we showed maps of predicted polarization state with respect to inclination, half-opening angle, different toroidal geometries, equatorial column densities and ionization levels for singlescattered photons and all photons (including direct radiation). For constant density, ionization level and geometrical parameters, the actual chemical composition seems to have low effect, if one does not have ambitions to study the polarization signatures in spectral lines in detail. In the continuum 3.5–6 keV band we obtained a match between the moderate and high density full MC simulations with the single-scattering option and the analytical single-scattering results presented in Veledina et al. (2023). The parameters of the primary radiation are possible to explore through type-1 viewing angles, although the impact of equatorial reprocessing is present, resulting in change of polarization up to ∼ 1% from the initial state. For type-2 viewing angles the primary state of emission is washed out up to ∼ 10◦ of error in inclination and Θ, which is negligible compared to the effects of changing density and ionization. Although spectroscopy and polarimetry in other wavelengths can significantly help to lift the model degeneracies, X-ray polarimetry can do so already, if energy-dependent polarization is obtained with sufficient photon statistics in the 2–8 keV band, which is particularly sensitive to partial transparency effects and spectral lines. This was also illustrated on the recent IXPE observation of the obscured accreting stellar-mass black hole in Cygnus X-3 in comparison with the MC models within the limits of unavoidable numerical noise for reasonable computational times.
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