# A hard look at the X-ray spectral variability of NGC 7582

Mehdy Lefkir, Elias Kammoun, Didier Barret, Peter Boorman, Gabriele Matzeu, Jon M. Miller, Emanuele Nardini, Abderahmen Zoghbi

► To cite this version:

Mehdy Lefkir, Elias Kammoun, Didier Barret, Peter Boorman, Gabriele Matzeu, et al. A hard look at the X-ray spectral variability of NGC 7582. Monthly Notices of the Royal Astronomical Society, 2023, 522, pp.1169-1182. 10.1093/mnras/stad995. insu-04473181

HAL Id: insu-04473181

https://insu.hal.science/insu-04473181

Submitted on 23 Feb 2024

**HAL** is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

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<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# A hard look at the X-ray spectral variability of NGC 7582

Mehdy Lefkir, Elias Kammoun, Didier Barret, Peter Boorman, Gabriele Matzeu, Jon M. Miller, Emanuele Nardini, Abderahmen Zoghbi

► To cite this version:

Mehdy Lefkir, Elias Kammoun, Didier Barret, Peter Boorman, Gabriele Matzeu, et al. A hard look at the X-ray spectral variability of NGC 7582. Monthly Notices of the Royal Astronomical Society, 2023, 522, pp.1169-1182. 10.1093/mnras/stad995. insu-04473181

HAL Id: insu-04473181

https://insu.hal.science/insu-04473181v1

Submitted on 23 Feb 2024

**HAL** is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire **HAL**, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# A hard look at the X-ray spectral variability of NGC 7582

Mehdy Lefkir<sup>1,2*</sup> Elias Kammoun<sup>1,2,3</sup> Didier Barret<sup>1,2</sup> Peter Boorman<sup>1,4,5,6</sup> Gabriele Matzeu<sup>1,7,8</sup>

Jon M. Miller<sup>1,9</sup> Emanuele Nardini<sup>1,3</sup> and Abderahmen Zoghbi<sup>10,11,12</sup>

Accepted 2023 March 29. Received 2023 March 11; in original form 2022 December 8

## ABSTRACT

NGC 7582 ($z = 0.005264$; $D = 22.5$ Mpc) is a highly variable, changing-look AGN. In this work, we explore the X-ray properties of this source using *XMM-Newton* and *NuSTAR* archival observations in the 3–40 keV range, from 2001 to 2016. NGC 7582 exhibits a long-term variability between observations but also a short-term variability in two observations that has not been studied before. To study the variability, we perform a time-resolved spectral analysis using a phenomenological model and a physically motivated model (*uxclumpy*). The spectral fitting is achieved using a nested sampling Monte Carlo method. *uxclumpy* enables testing various geometries of the absorber that may fit AGN spectra. We find that the best model is composed of a fully covering clumpy absorber. From this geometry, we estimate the velocity, size, and distance of the clumps. The column density of the absorber in the line of sight varies from Compton-thin to Compton-thick between observations. Variability over the time-scale of a few tens of kiloseconds is also observed within two observations. The obscuring clouds are consistent with being located at a distance not larger than 0.6 pc, moving with a transverse velocity exceeding ~700 km s⁻<fnref n="1" />. We could put only a lower limit on the size of the obscuring cloud being larger than $10^{13}$ cm. Given the sparsity of the observations, and the limited exposure time per observation available, we cannot determine the exact structure of the obscuring clouds. The results are broadly consistent with comet-like obscuring clouds or spherical clouds with a non-uniform density profile.

**Key words:** galaxies: active – galaxies: Seyfert – X-rays: galaxies – accretion, accretion discs.

## 1 INTRODUCTION

Active Galactic Nuclei (AGN) are energetic sources exhibiting a high bolometric luminosity, located at galactic centres. They are powered by the accretion of matter onto a supermassive black hole with $M_{BH} \gtrsim 10^6$ M☉ via an inspiraling disc, known as the accretion disc. This disc is thought to be typically optically thick and geometrically thin (Shakura & Sunyaev 1973), emitting thermal radiation in the optical and ultraviolet range. In addition, a strong X-ray emission is observed in AGN and attributed to the up-scattering of disc photons by electrons in a hot plasma called the corona (Haardt & Maraschi 1993).

Using optical/UV spectra, active galaxies can be classified as: Type-1 that show narrow (Full Width at Half Maximum, FWHM, less

than $1000$ km s⁻<fnref n="1" />) and broad emission lines ($FWHM > 1000$ km s⁻<fnref n="1" />) and Type-2 that show narrow emission lines only. Optical lines are Doppler-broadened closer to the black hole in the eponymous region, Broad Line Region (BLR), in opposition to the Narrow Line Region (NLR) which is thought to be located farther from the black hole, where narrow lines are produced. The BLR is typically located at a distance less than one parsec (see Kaspi et al. 2005), whereas the NLR can extend from dozens to hundreds of parsecs (Mor & Netzer 2012).

The unified model of AGN (Antonucci & Miller 1985; Antonucci 1993; Urry & Padovani 1995) explained the variety in AGN by the difference in viewing angle at which we observe the source. In this model, Type-1 sources are observed face-on providing a direct look at the central engine. Instead, Type-2 sources are observed with a higher inclination where obscuration of the central engine and BLR clouds by the parsec-scale dusty torus becomes more important. X-ray observations can be used to estimate the equivalent hydrogen column

<footnote n="1"><sup>1</sup>Department of Physics and Astronomy, University of Leicester, Leicester LE1 7RH, UK</footnote>

<footnote n="2"><sup>2</sup>IRAP, Université de Toulouse, CNRS, UPS, CNES, 9 Avenue du Colonel Roche, BP 44346, F-31028 Toulouse Cedex 4, France</footnote>

<footnote n="3"><sup>3</sup>INAF – Osservatorio Astrofisico di Arcetri, Largo Enrico Fermi 5, I-50125 Firenze, Italy</footnote>

<footnote n="4"><sup>4</sup>Cahill Center for Astrophysics, California Institute of Technology, 1216 East California Boulevard, Pasadena, CA 91125, USA</footnote>

<footnote n="5"><sup>5</sup>Astronomical Institute of the Czech Academy of Sciences, Boční II 1401/IA, 14100 Praha 4, Czech Republic</footnote>

<footnote n="6"><sup>6</sup>School of Physics & Astronomy, University of Southampton, Highfield, Southampton SO17 1BJ, UK</footnote>

<footnote n="7"><sup>7</sup>Department of Physics and Astronomy (DIFA), University of Bologna, Via Gobetti 93/2, I-40129 Bologna, Italy</footnote>

<footnote n="8"><sup>8</sup>INAF – Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Gobetti 93/3, I-40129 Bologna, Italy</footnote>

<footnote n="9"><sup>9</sup>Department of Astronomy, University of Michigan, 1085 South University Avenue, Ann Arbor, MI 48109, USA</footnote>

<footnote n="10"><sup>10</sup>Department of Astronomy, University of Maryland, College Park, MD 20742, USA</footnote>

<footnote n="11"><sup>11</sup>HEASARC, Code 6601, NASA/GSFC, Greenbelt, MD 20771, USA</footnote>

<footnote n="12"><sup>12</sup>CRESST II, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA</footnote>

<footnote>*E-mail: ml556@leicester.ac.uk</footnote>
# A hard look at the X-ray spectral variability of NGC 7582

Mehdy Lefkir<sup>1,2*</sup> Elias Kammoun<sup>1,2,3</sup> Didier Barret<sup>1,2</sup> Peter Boorman<sup>1,4,5,6</sup> Gabriele Matzeu<sup>1,7,8</sup>

Jon M. Miller<sup>1,9</sup> Emanuele Nardini<sup>1,3</sup> and Abderahmen Zoghbi<sup>10,11,12</sup>

<sup>1</sup>Department of Physics and Astronomy, University of Leicester, Leicester LE1 7RH, UK

<sup>2</sup>IRAP, Université de Toulouse, CNRS, UPS, CNES, 9 Avenue du Colonel Roche, BP 44346, F-31028 Toulouse Cedex 4, France

<sup>3</sup>INAF – Osservatorio Astrofisico di Arcetri, Largo Enrico Fermi 5, I-50125 Firenze, Italy

<sup>4</sup>Cahill Center for Astrophysics, California Institute of Technology, 1216 East California Boulevard, Pasadena, CA 91125, USA

<sup>5</sup>Astronomical Institute of the Czech Academy of Sciences, Boční II 1401/IA, 14100 Praha 4, Czech Republic

<sup>6</sup>School of Physics & Astronomy, University of Southampton, Highfield, Southampton SO17 1BJ, UK

<sup>7</sup>Department of Physics and Astronomy (DIFA), University of Bologna, Via Gobetti 93/2, I-40129 Bologna, Italy

<sup>8</sup>INAF – Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Gobetti 93/3, I-40129 Bologna, Italy

<sup>9</sup>Department of Astronomy, University of Michigan, 1085 South University Avenue, Ann Arbor, MI 48109, USA

<sup>10</sup>Department of Astronomy, University of Maryland, College Park, MD 20742, USA

<sup>11</sup>HEASARC, Code 6601, NASA/GSFC, Greenbelt, MD 20771, USA

<sup>12</sup>CRESST II, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA

Accepted 2023 March 29. Received 2023 March 11; in original form 2022 December 8

## ABSTRACT

NGC 7582 ($z = 0.005264$; $D = 22.5$ Mpc) is a highly variable, changing-look AGN. In this work, we explore the X-ray properties of this source using *XMM-Newton* and *NuSTAR* archival observations in the 3–40 keV range, from 2001 to 2016. NGC 7582 exhibits a long-term variability between observations but also a short-term variability in two observations that has not been studied before. To study the variability, we perform a time-resolved spectral analysis using a phenomenological model and a physically motivated model (*uxclumpy*). The spectral fitting is achieved using a nested sampling Monte Carlo method. *uxclumpy* enables testing various geometries of the absorber that may fit AGN spectra. We find that the best model is composed of a fully covering clumpy absorber. From this geometry, we estimate the velocity, size, and distance of the clumps. The column density of the absorber in the line of sight varies from Compton-thin to Compton-thick between observations. Variability over the time-scale of a few tens of kiloseconds is also observed within two observations. The obscuring clouds are consistent with being located at a distance not larger than 0.6 pc, moving with a transverse velocity exceeding ~700 km s⁻¹. We could put only a lower limit on the size of the obscuring cloud being larger than $10^{13}$ cm. Given the sparsity of the observations, and the limited exposure time per observation available, we cannot determine the exact structure of the obscuring clouds. The results are broadly consistent with comet-like obscuring clouds or spherical clouds with a non-uniform density profile.

**Key words:** galaxies: active – galaxies: Seyfert – X-rays: galaxies – accretion, accretion discs.

## 1 INTRODUCTION

Active Galactic Nuclei (AGN) are energetic sources exhibiting a high bolometric luminosity, located at galactic centres. They are powered by the accretion of matter onto a supermassive black hole with $M_{BH} \gtrsim 10^6$ M☉ via an inspiraling disc, known as the accretion disc. This disc is thought to be typically optically thick and geometrically thin (Shakura & Sunyaev 1973), emitting thermal radiation in the optical and ultraviolet range. In addition, a strong X-ray emission is observed in AGN and attributed to the up-scattering of disc photons by electrons in a hot plasma called the corona (Haardt & Maraschi 1993).

Using optical/UV spectra, active galaxies can be classified as: Type-1 that show narrow (Full Width at Half Maximum, FWHM, less

than $1000$ km s⁻¹) and broad emission lines ($FWHM > 1000$ km s⁻¹) and Type-2 that show narrow emission lines only. Optical lines are Doppler-broadened closer to the black hole in the eponymous region, Broad Line Region (BLR), in opposition to the Narrow Line Region (NLR) which is thought to be located farther from the black hole, where narrow lines are produced. The BLR is typically located at a distance less than one parsec (see Kaspi et al. 2005), whereas the NLR can extend from dozens to hundreds of parsecs (Mor & Netzer 2012).

The unified model of AGN (Antonucci & Miller 1985; Antonucci 1993; Urry & Padovani 1995) explained the variety in AGN by the difference in viewing angle at which we observe the source. In this model, Type-1 sources are observed face-on providing a direct look at the central engine. Instead, Type-2 sources are observed with a higher inclination where obscuration of the central engine and BLR clouds by the parsec-scale dusty torus becomes more important. X-ray observations can be used to estimate the equivalent hydrogen column

<footnote>*E-mail: ml556@leicester.ac.uk</footnote>
density ($N_H$) of the obscurer which can be classified as Compton-thin or Compton-thick if $N_H$ is smaller or larger than ~ $1.5 \times 10^{24}$ cm$^{-2}$, respectively. However, many sources, can change from Type-1 to Type-2 and vice versa between observations, associated with the appearance/vanishing of broad optical lines (see e.g. LaMassa et al. 2015). Ricci & Trakhtenbrot (2022) referred to these objects as Changing accretion-state (CS) AGN, whereas AGN changing from Compton-thick to Compton-thin and vice versa in X-ray observations are referred to as Changing-obscuration (CO) AGN. The proposed interpretations for CO-AGN transitions are the passage of obscuring material in the BLR across our line of sight or absorption by ionized material. In the case of CS-AGN, the obscuration of the source is ruled out in favour of disc instabilities or stellar tidal disruption events (see e.g. Ricci et al. 2021).

In this work, we study NGC 7582, a nearby ($z = 0.005264$, $D = 22.5$ Mpc) type 2 Seyfert galaxy with a changing-look behaviour. Wold et al. (2006) estimated the black hole mass to be $M_{BH} = 5.5_{-2.3}^{+3.2} \times 10^7$ M$_\odot$ by modelling the gas dynamics in the mid-infrared. This source has been observed in X-rays in several occasions since the late 70s. Ward et al. (1978) associated the X-ray source 2A 2315-428, detected with the *Ariel* 5 survey, with the galaxy NGC 7582. These observations revealed the presence of a flux variability by a factor of 4 over 60 d. Mushotzky (1982) analysed three HEAO-1 observations. The source revealed short time-scale variability with a flare where the count-rate doubled over a time-scale of 1.5 d. Using a *Ginga* observation, Warwick et al. (1993) established the presence of a large intrinsic column density of absorbing material in the nuclear region. Later on, Aretxaga et al. (1999) reported on a broadening of the H\alpha line, which involved a transition from Type-2 to Type-1, which labelled NGC 7582 as a changing-look AGN. XMM-Newton observed the source for the first time in 2001, catching the source in a low-flux state. Dewangan & Griffiths (2005) and Awaki et al. (2006) analysed this observation, and confirmed the detection of a clear iron line at ~6.4 keV. Bianchi et al. (2007) mapped the nuclear region using *Chandra* and the *Hubble Space Telescope*. The authors report the presence of a dust lane in the optical, and concluded that soft X-ray emission (below 3 keV) corresponds to the region where the dust lane is thinner. Piconcelli et al. (2007) analysed XMM-Newton data from observations of 2001 and 2005. They proposed a model for the absorption that consists of a thin neutral absorber and an inner thick neutral absorber composed of clouds where X-ray photons are reflected via Compton scattering. Bianchi et al. (2009) analysed four *Suzaku* and one XMM-Newton observation, taking place in 2007, which were compared to the previous XMM-Newton observations of 2001 and 2005. The authors observed an increase in the column density of the inner thick absorber during the *Suzaku* campaign. They invoked a third, Compton-thin, absorber in their model, that is associated with the dust lanes outside of the torus observed with *Chandra* and *HST*. The authors ascribed the observed variability to absorbing material drifting in the BLR. Later on, Rivers et al. (2015) studied two NuSTAR observations and one Swift observation, taken in 2012. They modelled the absorption with a thick patchy torus and a thin full-covering absorber. They found the most plausible scenario explaining the variability to be the obscuration of the nucleus. More recently, Braito et al. (2017) analysed two *Chandra* HETG observations performed in 2014, and a *Suzaku* one performed in 2007. They found a constant reflection component associated with the inner edge of the clumpy torus. A highly ionized absorber was also detected in the *Chandra* spectra.

In this work, we present a comprehensive analysis of all the archival XMM-Newton and NuSTAR observations of NGC 7582

<table><caption>**Table 1.** Observations used in this work and their associated exposure time after removing the bad time intervals. For XMM-Newton the exposures are given for the EPIC instruments pn, MOS1 and MOS2, and for NuSTAR the net exposures are given for FPMA and FPMB.</caption><thead><tr><th>Observation ID</th><th>OBSERVATORY</th><th>Date</th><th>Exposure (ks)</th></tr></thead><tbody><tr><td>0112310201</td><td>XMM-Newton</td><td>2001 May 25</td><td>17.5/22.4/22.4</td></tr><tr><td>0204610101</td><td>XMM-Newton</td><td>2005 Apr 29</td><td>61.8/75.4/76.3</td></tr><tr><td>0405380701</td><td>XMM-Newton</td><td>2007 Apr 30</td><td>1.9/8.6/8.6</td></tr><tr><td>60061318002</td><td>NuSTAR</td><td>2012 Aug 31</td><td>16.5/16.4</td></tr><tr><td>60061318004</td><td>NuSTAR</td><td>2012 Sept 14</td><td>14.6/14.6</td></tr><tr><td>0782720301</td><td>XMM-Newton</td><td>2016 Apr 28</td><td>42/98.5/98.5</td></tr><tr><td>60201003002</td><td>NuSTAR</td><td>2016 Apr 28</td><td>48.5/48.3</td></tr></tbody></table>

with the aim of explaining the short- and long-term behaviour of the source. The paper is organized as follows. In Section 2, we describe the observations analysed in this work and the corresponding data reduction. In Section 3, we present the tools and models used for the X-ray spectral analysis. Our results are presented in Section 4 and discussed in Section 5. Conclusions are drawn in Section 6.

## 2 OBSERVATIONS AND DATA REDUCTION

NGC 7582 was observed five times by XMM-Newton between 2001 and 2018 and three times by NuSTAR between 2012 and 2016, including a simultaneous observation between XMM-Newton and NuSTAR in 2016. We use all of the archival XMM-Newton and NuSTAR observations, except the XMM-Newton observation of 2018. The source was off-axis by more than 10 arcmin, falling on a bad pixel column. The data from this observation could not be used as they suffered from calibration issues in energy and normalization. We present in Table 1 the observations used in this work and the associated net exposure times.

### 2.1 XMM-Newton

XMM-Newton data from the EPIC instruments pn (Strüder et al. 2001) and MOS (Turner et al. 2001) were reduced using the Science Analysis System (SAS 20.0; Gabriel et al. 2004). We used the recent empirical calibration<fnref n="1" /> to improve the spectral agreement between XMM-Newton and NuSTAR above 3 keV. We filtered periods of high background flaring activity in the event lists with the recommended rate threshold of 0.4 Count s⁻<fnref n="1" /> for the EPIC-pn and 0.35 Count s⁻<fnref n="1" /> for the EPIC-MOS detectors. The source was extracted from a circular region of 30" and the background was extracted from a circular source-free region of the same chip with a radius of 60". Source and background light-curves were extracted in the soft energy band 0.5-3 keV and in the hard energy band 3-10 keV using the task `evselect`. A binning of 1 ks was chosen for all observations. XMM-Newton source and background spectra are extracted with the task `evselect`. The Ancillary Response File (ARF) is generated with `arfgen` and the Redistribution Matrix File (RMF) is produced with `rmfgen`. The spectral files are grouped with `specgroup` to have a minimum signal-to-noise ratio of five and ensuring that the width of the bins is not narrower than one-third of the energy resolution.

<footnote n="1">¹https://xmmtweb.esac.esa.int/docs/documents/CAL-SRN-0388-1-4.pdf</footnote>
density ($N_H$) of the obscurer which can be classified as Compton-thin or Compton-thick if $N_H$ is smaller or larger than ~ $1.5 \times 10^{24}$ cm$^{-2}$, respectively. However, many sources, can change from Type-1 to Type-2 and vice versa between observations, associated with the appearance/vanishing of broad optical lines (see e.g. LaMassa et al. 2015). Ricci & Trakhtenbrot (2022) referred to these objects as Changing accretion-state (CS) AGN, whereas AGN changing from Compton-thick to Compton-thin and vice versa in X-ray observations are referred to as Changing-obscuration (CO) AGN. The proposed interpretations for CO-AGN transitions are the passage of obscuring material in the BLR across our line of sight or absorption by ionized material. In the case of CS-AGN, the obscuration of the source is ruled out in favour of disc instabilities or stellar tidal disruption events (see e.g. Ricci et al. 2021).

In this work, we study NGC 7582, a nearby ($z = 0.005264$, $D = 22.5$ Mpc) type 2 Seyfert galaxy with a changing-look behaviour. Wold et al. (2006) estimated the black hole mass to be $M_{BH} = 5.5_{-2.3}^{+3.2} \times 10^7$ M$_\odot$ by modelling the gas dynamics in the mid-infrared. This source has been observed in X-rays in several occasions since the late 70s. Ward et al. (1978) associated the X-ray source 2A 2315-428, detected with the *Ariel* 5 survey, with the galaxy NGC 7582. These observations revealed the presence of a flux variability by a factor of 4 over 60 d. Mushotzky (1982) analysed three HEAO-1 observations. The source revealed short time-scale variability with a flare where the count-rate doubled over a time-scale of 1.5 d. Using a *Ginga* observation, Warwick et al. (1993) established the presence of a large intrinsic column density of absorbing material in the nuclear region. Later on, Aretxaga et al. (1999) reported on a broadening of the H\alpha line, which involved a transition from Type-2 to Type-1, which labelled NGC 7582 as a changing-look AGN. XMM-Newton observed the source for the first time in 2001, catching the source in a low-flux state. Dewangan & Griffiths (2005) and Awaki et al. (2006) analysed this observation, and confirmed the detection of a clear iron line at ~6.4 keV. Bianchi et al. (2007) mapped the nuclear region using *Chandra* and the *Hubble Space Telescope*. The authors report the presence of a dust lane in the optical, and concluded that soft X-ray emission (below 3 keV) corresponds to the region where the dust lane is thinner. Piconcelli et al. (2007) analysed XMM-Newton data from observations of 2001 and 2005. They proposed a model for the absorption that consists of a thin neutral absorber and an inner thick neutral absorber composed of clouds where X-ray photons are reflected via Compton scattering. Bianchi et al. (2009) analysed four *Suzaku* and one XMM-Newton observation, taking place in 2007, which were compared to the previous XMM-Newton observations of 2001 and 2005. The authors observed an increase in the column density of the inner thick absorber during the *Suzaku* campaign. They invoked a third, Compton-thin, absorber in their model, that is associated with the dust lanes outside of the torus observed with *Chandra* and *HST*. The authors ascribed the observed variability to absorbing material drifting in the BLR. Later on, Rivers et al. (2015) studied two NuSTAR observations and one Swift observation, taken in 2012. They modelled the absorption with a thick patchy torus and a thin full-covering absorber. They found the most plausible scenario explaining the variability to be the obscuration of the nucleus. More recently, Braito et al. (2017) analysed two *Chandra* HETG observations performed in 2014, and a *Suzaku* one performed in 2007. They found a constant reflection component associated with the inner edge of the clumpy torus. A highly ionized absorber was also detected in the *Chandra* spectra.

In this work, we present a comprehensive analysis of all the archival XMM-Newton and NuSTAR observations of NGC 7582

<table><caption>**Table 1.** Observations used in this work and their associated exposure time after removing the bad time intervals. For XMM-Newton the exposures are given for the EPIC instruments pn, MOS1 and MOS2, and for NuSTAR the net exposures are given for FPMA and FPMB.</caption><thead><tr><th>Observation ID</th><th>OBSERVATORY</th><th>Date</th><th>Exposure (ks)</th></tr></thead><tbody><tr><td>0112310201</td><td>XMM-Newton</td><td>2001 May 25</td><td>17.5/22.4/22.4</td></tr><tr><td>0204610101</td><td>XMM-Newton</td><td>2005 Apr 29</td><td>61.8/75.4/76.3</td></tr><tr><td>0405380701</td><td>XMM-Newton</td><td>2007 Apr 30</td><td>1.9/8.6/8.6</td></tr><tr><td>60061318002</td><td>NuSTAR</td><td>2012 Aug 31</td><td>16.5/16.4</td></tr><tr><td>60061318004</td><td>NuSTAR</td><td>2012 Sept 14</td><td>14.6/14.6</td></tr><tr><td>0782720301</td><td>XMM-Newton</td><td>2016 Apr 28</td><td>42/98.5/98.5</td></tr><tr><td>60201003002</td><td>NuSTAR</td><td>2016 Apr 28</td><td>48.5/48.3</td></tr></tbody></table>

with the aim of explaining the short- and long-term behaviour of the source. The paper is organized as follows. In Section 2, we describe the observations analysed in this work and the corresponding data reduction. In Section 3, we present the tools and models used for the X-ray spectral analysis. Our results are presented in Section 4 and discussed in Section 5. Conclusions are drawn in Section 6.

## 2 OBSERVATIONS AND DATA REDUCTION

NGC 7582 was observed five times by XMM-Newton between 2001 and 2018 and three times by NuSTAR between 2012 and 2016, including a simultaneous observation between XMM-Newton and NuSTAR in 2016. We use all of the archival XMM-Newton and NuSTAR observations, except the XMM-Newton observation of 2018. The source was off-axis by more than 10 arcmin, falling on a bad pixel column. The data from this observation could not be used as they suffered from calibration issues in energy and normalization. We present in Table 1 the observations used in this work and the associated net exposure times.

### 2.1 XMM-Newton

XMM-Newton data from the EPIC instruments pn (Strüder et al. 2001) and MOS (Turner et al. 2001) were reduced using the Science Analysis System (SAS 20.0; Gabriel et al. 2004). We used the recent empirical calibration<fnref n="1" /> to improve the spectral agreement between XMM-Newton and NuSTAR above 3 keV. We filtered periods of high background flaring activity in the event lists with the recommended rate threshold of 0.4 Count s⁻<fnref n="1" /> for the EPIC-pn and 0.35 Count s⁻<fnref n="1" /> for the EPIC-MOS detectors. The source was extracted from a circular region of 30" and the background was extracted from a circular source-free region of the same chip with a radius of 60". Source and background light-curves were extracted in the soft energy band 0.5-3 keV and in the hard energy band 3-10 keV using the task `evselect`. A binning of 1 ks was chosen for all observations. XMM-Newton source and background spectra are extracted with the task `evselect`. The Ancillary Response File (ARF) is generated with `arfgen` and the Redistribution Matrix File (RMF) is produced with `rmfgen`. The spectral files are grouped with `specgroup` to have a minimum signal-to-noise ratio of five and ensuring that the width of the bins is not narrower than one-third of the energy resolution.

<footnote n="1">¹https://xmmtweb.esac.esa.int/docs/documents/CAL-SRN-0388-1-4.pdf</footnote>
<figure><img src="image_2.png" /><figcaption>**Figure 1.** Light curves of the XMM–Newton and NuSTAR observations in the 0.5–3 keV (top panel) energy band and 3–10 keV (bottom panel) energy band for the EPIC-pn (dark blue circles), EPIC-MOS1 (green squares), EPIC-MOS2 (light blue diamonds), FPMA (yellow hexagons), and FPMB (magenta pentagons). The count-rates are normalized to the count-rates of the observation of 2016. The dashed vertical lines show the chosen slices for the extraction of spectra, the slices are indicated by circled numbers (1), (2), (3),...</figcaption></figure>

<table><caption>**Table 2.** Mean count-rate (Counts s⁻¹) of XMM–Newton and NuSTAR observations in the 0.5–3 and 3–10 keV band.</caption><thead><tr><th rowspan="3">Epoch</th><th rowspan="3">pn</th><th colspan="4">Mean count-rate (Counts s<sup>-1</sup>)</th></tr><tr><th colspan="2">0.5 – 3 keV</th><th colspan="2">3 – 10 keV</th></tr><tr><th>MOS1</th><th>MOS2</th><th>FPMA</th><th>FPMB</th></tr></thead><tbody><tr><td rowspan="2">2001–05</td><td>0.276</td><td>0.0792</td><td>0.0887</td><td>—</td><td>—</td></tr><tr><td>0.282</td><td>0.0779</td><td>0.0828</td><td>—</td><td>—</td></tr><tr><td rowspan="2">2005–04</td><td>0.274</td><td>0.0779</td><td>0.0828</td><td>—</td><td>—</td></tr><tr><td>0.159</td><td>0.0428</td><td>0.0461</td><td>—</td><td>—</td></tr><tr><td rowspan="2">2007–04</td><td>0.319</td><td>0.0946</td><td>0.931</td><td>—</td><td>—</td></tr><tr><td>0.462</td><td>0.134</td><td>0.140</td><td>—</td><td>—</td></tr><tr><td>2012–08</td><td>—</td><td>—</td><td>—</td><td>0.193</td><td>0.194</td></tr><tr><td>2012–09</td><td>—</td><td>—</td><td>—</td><td>0.127</td><td>0.132</td></tr><tr><td rowspan="2">2016–04</td><td>0.285</td><td>0.0784</td><td>0.0787</td><td>0.377</td><td>0.386</td></tr><tr><td>0.521</td><td>0.154</td><td>0.169</td><td>—</td><td>—</td></tr></tbody></table>

## 2.2 NuSTAR

NuSTAR (Harrison et al. 2013) data were reduced using the NUS-TARDAS 2.1.1 package part of HEASOFT 6.29 and the calibration files of CALDB 20210210. The task nupipeline was used to produce calibrated data as well as filtered event lists. Source and background regions were selected as circular regions with a radius of 80" on both instruments FPMA and FPMB. Source and background light curves were extracted for the 3–10 keV and 10–40 keV energy bands using the task nuproducts. We use NuSTAR data only up to 40 keV as they are background dominated above this energy. To keep consistency with the XMM–Newton observations a temporal binning of 1 ks was chosen. Source and background spectra, ARF and RMF, are extracted using the task nuproducts and grouped to at least 30 counts per energy bin.

<figure><img src="image_3.png" /><figcaption>**Figure 2.** Light curves of NuSTAR observations in the 10–40 keV band for the detectors FPMA (yellow hexagons) and FPMB (magenta pentagons).</figcaption></figure>

## 2.3 Short-term and long-term variability

The light curves of the XMM–Newton and NuSTAR observations are shown in Fig. 1, normalized to the mean count-rates of the observation of 2016. The mean count-rates of the observations are given in Table 2. The light curves in the 0.5–3 keV range do not show any intra-/inter-observation variations. However, the variability is larger in the 3–10 keV range. The light curve of the observation of 2001 appears to be decreasing towards the end of the observation. No variability is observed in the observation of 2005, which has the lowest count-rate among the analysed observations. For the observation of 2007, as the light curve does not have sufficient data points, we cannot derive any conclusions on its variability. The two observations of 2012 do not present any strong short-term variability. The simultaneous observation of 2016 presents a strong variability with a flare appearing ~15 ks after the start of the observation. Fig. 2 shows the light curves of the NuSTAR observations in the 10–40 keV band. No strong variability is observed in 2012. The 10–40 keV light curve in 2016 shows similar variability to the one observed in the 3–10 keV range.
<figure><img src="image_2.png" /><figcaption>**Figure 1.** Light curves of the *XMM-Newton* and *NuSTAR* observations in the 0.5–3 keV (top panel) energy band and 3–10 keV (bottom panel) energy band for the EPIC-pn (dark blue circles), EPIC-MOS1 (green squares), EPIC-MOS2 (light blue diamonds), FPMA (yellow hexagons), and FPMB (magenta pentagons). The count-rates are normalized to the count-rates of the observation of 2016. The dashed vertical lines show the chosen slices for the extraction of spectra, the slices are indicated by circled numbers (1), (2), (3),...</figcaption></figure>

<table><caption>**Table 2.** Mean count-rate (Counts s⁻¹) of *XMM-Newton* and *NuSTAR* observations in the 0.5–3 and 3–10 keV band.</caption><thead><tr><th rowspan="3">Epoch</th><th rowspan="3">pn</th><th colspan="4">Mean count-rate (Counts s<sup>-1</sup>)</th></tr><tr><th colspan="2">0.5 – 3 keV</th><th colspan="2">3 – 10 keV</th></tr><tr><th>MOS1</th><th>MOS2</th><th>FPMA</th><th>FPMB</th></tr></thead><tbody><tr><td rowspan="2">2001–05</td><td>0.276</td><td>0.0792</td><td>0.0887</td><td>—</td><td>—</td></tr><tr><td>0.282</td><td>0.0779</td><td>0.0828</td><td>—</td><td>—</td></tr><tr><td rowspan="2">2005–04</td><td>0.274</td><td>0.0779</td><td>0.0828</td><td>—</td><td>—</td></tr><tr><td>0.159</td><td>0.0428</td><td>0.0461</td><td>—</td><td>—</td></tr><tr><td rowspan="2">2007–04</td><td>0.319</td><td>0.0946</td><td>0.931</td><td>—</td><td>—</td></tr><tr><td>0.462</td><td>0.134</td><td>0.140</td><td>—</td><td>—</td></tr><tr><td>2012–08</td><td>—</td><td>—</td><td>—</td><td>0.193</td><td>0.194</td></tr><tr><td>2012–09</td><td>—</td><td>—</td><td>—</td><td>0.127</td><td>0.132</td></tr><tr><td rowspan="2">2016–04</td><td>0.285</td><td>0.0784</td><td>0.0787</td><td>0.377</td><td>0.386</td></tr><tr><td>0.521</td><td>0.154</td><td>0.169</td><td>—</td><td>—</td></tr></tbody></table>

## 2.2 NuSTAR

NuSTAR (Harrison et al. 2013) data were reduced using the NUS-TARDAS 2.1.1 package part of HEASOFT 6.29 and the calibration files of CALDB 20210210. The task nupipeline was used to produce calibrated data as well as filtered event lists. Source and background regions were selected as circular regions with a radius of 80" on both instruments FPMA and FPMB. Source and background light curves were extracted for the 3–10 keV and 10–40 keV energy bands using the task nuproducts. We use NuSTAR data only up to 40 keV as they are background dominated above this energy. To keep consistency with the *XMM-Newton* observations a temporal binning of 1 ks was chosen. Source and background spectra, ARF and RMF, are extracted using the task nuproducts and grouped to at least 30 counts per energy bin.

<figure><img src="image_3.png" /><figcaption>**Figure 2.** Light curves of NuSTAR observations in the 10–40 keV band for the detectors FPMA (yellow hexagons) and FPMB (magenta pentagons).</figcaption></figure>

## 2.3 Short-term and long-term variability

The light curves of the *XMM-Newton* and *NuSTAR* observations are shown in Fig. 1, normalized to the mean count-rates of the observation of 2016. The mean count-rates of the observations are given in Table 2. The light curves in the 0.5–3 keV range do not show any intra-/inter-observation variations. However, the variability is larger in the 3–10 keV range. The light curve of the observation of 2001 appears to be decreasing towards the end of the observation. No variability is observed in the observation of 2005, which has the lowest count-rate among the analysed observations. For the observation of 2007, as the light curve does not have sufficient data points, we cannot derive any conclusions on its variability. The two observations of 2012 do not present any strong short-term variability. The simultaneous observation of 2016 presents a strong variability with a flare appearing ~15 ks after the start of the observation. Fig. 2 shows the light curves of the NuSTAR observations in the 10–40 keV band. No strong variability is observed in 2012. The 10–40 keV light curve in 2016 shows similar variability to the one observed in the 3–10 keV range.
<table><caption>**Table 3.** Normalized excess variance $\sigma_{NXS}$ and fractional variability amplitude $F_{var}$ of XMM–Newton and NuSTAR observations for the EPIC-pn in the 0.5–3 and 3–10 keV band and for FPMA/FPMB in the 3–10 and 10–40 keV.</caption><thead><tr><th rowspan="3">Epoch</th><th colspan="2">pn</th><th colspan="2">FPMA</th><th colspan="2">FPMB</th></tr><tr><th colspan="2">0.5 – 3 keV</th><th colspan="2">3 – 10 keV</th><th colspan="2">3 – 10 keV</th></tr><tr><th>σ<sub>NXS</sub>(10<sup>-3</sup>)</th><th>F<sub>var</sub>(%)</th><th>σ<sub>NXS</sub>(10<sup>-2</sup>)</th><th>F<sub>var</sub>(%)</th><th>σ<sub>NXS</sub>(10<sup>-2</sup>)</th><th>F<sub>var</sub>(%)</th></tr></thead><tbody><tr><td>2001–05</td><td>-1.1 ± 1.6<br>7.9 ± 3.3</td><td>–<br>8.7 ± 1.8</td><td></td><td></td><td></td><td></td></tr><tr><td>2005–07</td><td>-3.2 ± 1.5<br>4.9 ± 3.4</td><td>–<br>7.0 ± 2.4</td><td></td><td></td><td></td><td></td></tr><tr><td>2007–04</td><td>-17 ± 18<br>5.0 ± 18</td><td>–<br>7.1 ± 13</td><td></td><td></td><td></td><td></td></tr><tr><td>2012–08</td><td></td><td></td><td>3.4 ± 1.6<br>1.5 ± 1.0</td><td>18 ± 4.4<br>12 ± 4.2</td><td>1.2 ± 1.1<br>-0.21 ± 0.7</td><td>11 ± 5.0<br>–</td></tr><tr><td>2012–09</td><td></td><td></td><td>7.2 ± 2.8<br>-0.75 ± 0.64</td><td>27 ± 5.3<br>-5.1 ± 1.6</td><td>0.09 ± 1<br>22.5 ± 3.5</td><td>2.9 ± 17<br>–</td></tr><tr><td>2016–04</td><td>-1.6 ± 2<br>68 ± 6</td><td>26 ± 1<br>–</td><td>5.8 ± 0.6<br>2.3 ± 0.4</td><td>24 ± 1.3<br>15 ± 1.3</td><td>4.1 ± 0.5<br>2.3 ± 0.4</td><td>20 ± 1.3<br>15 ± 1.4</td></tr></tbody></table>

In Table 3, we compute the normalized excess variance $\sigma_{NXS}$ and the fractional variability amplitude $F_{var}$ following Vaughan et al. (2003). In the 0.5–3 keV band, the mean square error of the measurement is larger than the sample variance, therefore no variability is detected. In the 3–10 keV band, the observation of 2016 presents a fractional variability amplitude always greater than 20 per cent. The observations of 2012 also present significant values of $F_{var}$ hinting at a possible variability on a time-scale longer than these short observations.

To study the short-term spectral variability of this source, we decide to slice the observation of 2001 in two slices of 10 ks denoted by circled numbers ① and ②. The simultaneous observations of 2016 are sliced in seven slices of 15 ks indexed from ① to ⑦. The start of the EPIC-pn exposure serves as the origin of time for the intervals. The intervals are delimited by dashed vertical lines in the light curves of Fig. 1.

## 3 SPECTRAL ANALYSIS

In this work, the spectral analysis is performed with the X-ray Spectral Fitting Package (XSPEC; Arnaud 1996) and its PYTHON wrapper PyXspec. We adopt the cross-sections of Verner et al. (1996) and the chemical abundances reported in Wilms, Allen & McCray (2000).

Cash statistic (C-stat; Cash 1979) is used to account for the Poisson distribution of photons. The fitting is performed using the Bayesian X-ray Analysis package (BXA;<fnref n="2" /> Buchner et al. 2014) bridging XSPEC with nested sampling Monte Carlo algorithm implemented in UltraNest (Buchner 2016, 2019, 2021). We use nested sampling for its unsupervised global parameter exploration and its naturally self-convergence criterion. We use wide log-uniform priors for normalization and column density parameters and wide uniform priors for the other parameters. Using samples of the posterior distribution of the parameters, the median of the parameters is estimated. Uncertainties at 68 per cent confidence levels are computed using the 16th and 84th quantiles of the posterior distributions.

Cross-calibration factors between instruments are included in all models. These factors are estimated by fitting the phenomenological model. We assess the goodness of fit through simulations with

fakeit in XSPEC using the best-fitting values obtained from the fit. We simulate 1000 spectra for each instrument and rebin the spectra with a constant number of channels, 50 and 30, for XMM–Newton and NuSTAR, respectively. The realizations are then plotted against the observed data. Due to the lack of variability below 3 keV, we decided to perform the spectral analysis only above 3 keV. We found a cross-calibration mismatch between XMM–Newton and NuSTAR below ~4 keV, for that reason we fit NuSTAR data only above that energy.

### 3.1 Phenomenological model

First, we fitted a phenomenological model to the spectra, which can be written in XSPEC parlance as follows,

$$ \text{Model} = \text{constant} \times \text{TBabs} \\ \times (\text{cutoffpl} \times \text{TBpf} + \text{xillver}). \quad (1) $$

The first component constant is the cross-calibration factor between the different instruments. The second component TBabs (Wilms et al. 2000) models the absorption of X-ray photons in the line of sight by the gas and dust of our Galaxy with an equivalent hydrogen column density $N_H = 1.26 \times 10^{20} \text{ cm}^{-2}$ (HI4PI Collaboration et al. 2016). The primary X-ray emission from the hot corona is modelled using a power law with an exponential cutoff (cutoffpl). We tried to let the high-energy cutoff free to vary but no constraints were obtained so it was frozen to 500 keV for all the fits. We accounted for the absorption of the primary emission with TBpf (Wilms et al. 2000) where the partial covering fraction $f_{cov}$ was left free to vary. As their values converged to unity we fixed $f_{cov} = 1$, modelling a fully covering absorber, for the remainder of the analysis. The primary emission in Type-2 sources is thought to be reprocessed by distant neutral material leading to a reflection spectrum that we modelled using XILLVER (García & Kallman 2010; García et al. 2013, 2014). XILLVER is a tabulated model, computed by solving the radiative transfer equation in a plane-parallel geometry for a slab of gas illuminated by an X-ray source. We assume the reflector as distant and neutral, so the ionization parameter log $\xi$ is frozen to 0. As NGC 7582 is a type 2 Seyfert galaxy we freeze the inclination of the line of sight with respect to the normal of the disc to $\theta = 80^{\circ}$. The photon index and the high-energy cutoff of XILLVER are tied to the ones of the illuminating power law.

<footnote n="2">²https://johannesbuchner.github.io/BXA/index.html</footnote>
<table><caption>**Table 3.** Normalized excess variance $\sigma_{NXS}$ and fractional variability amplitude $F_{var}$ of XMM–Newton and NuSTAR observations for the EPIC-pn in the 0.5–3 and 3–10 keV band and for FPMA/FPMB in the 3–10 and 10–40 keV.</caption><thead><tr><th rowspan="3">Epoch</th><th colspan="2">pn</th><th colspan="2">FPMA</th><th colspan="2">FPMB</th></tr><tr><th colspan="2">0.5 – 3 keV</th><th colspan="2">3 – 10 keV</th><th colspan="2">3 – 10 keV</th></tr><tr><th>σ<sub>NXS</sub>(10<sup>-3</sup>)</th><th>F<sub>var</sub>(%)</th><th>σ<sub>NXS</sub>(10<sup>-2</sup>)</th><th>F<sub>var</sub>(%)</th><th>σ<sub>NXS</sub>(10<sup>-2</sup>)</th><th>F<sub>var</sub>(%)</th></tr></thead><tbody><tr><td>2001–05</td><td>-1.1 ± 1.6<br>7.9 ± 3.3</td><td>–<br>8.7 ± 1.8</td><td></td><td></td><td></td><td></td></tr><tr><td>2005–07</td><td>-3.2 ± 1.5<br>4.9 ± 3.4</td><td>–<br>7.0 ± 2.4</td><td></td><td></td><td></td><td></td></tr><tr><td>2007–04</td><td>-17 ± 18<br>5.0 ± 18</td><td>–<br>7.1 ± 13</td><td></td><td></td><td></td><td></td></tr><tr><td>2012–08</td><td></td><td></td><td>3.4 ± 1.6<br>1.5 ± 1.0</td><td>18 ± 4.4<br>12 ± 4.2</td><td>1.2 ± 1.1<br>-0.21 ± 0.7</td><td>11 ± 5.0<br>–</td></tr><tr><td>2012–09</td><td></td><td></td><td>7.2 ± 2.8<br>-0.75 ± 0.64</td><td>27 ± 5.3<br>-5.1 ± 1.6</td><td>0.09 ± 1<br>22.5 ± 3.5</td><td>2.9 ± 17<br>–</td></tr><tr><td>2016–04</td><td>-1.6 ± 2<br>68 ± 6</td><td>26 ± 1<br>–</td><td>5.8 ± 0.6<br>2.3 ± 0.4</td><td>24 ± 1.3<br>15 ± 1.3</td><td>4.1 ± 0.5<br>2.3 ± 0.4</td><td>20 ± 1.3<br>15 ± 1.4</td></tr></tbody></table>

In Table 3, we compute the normalized excess variance $\sigma_{NXS}$ and the fractional variability amplitude $F_{var}$ following Vaughan et al. (2003). In the 0.5–3 keV band, the mean square error of the measurement is larger than the sample variance, therefore no variability is detected. In the 3–10 keV band, the observation of 2016 presents a fractional variability amplitude always greater than 20 per cent. The observations of 2012 also present significant values of $F_{var}$ hinting at a possible variability on a time-scale longer than these short observations.

To study the short-term spectral variability of this source, we decide to slice the observation of 2001 in two slices of 10 ks denoted by circled numbers ① and ②. The simultaneous observations of 2016 are sliced in seven slices of 15 ks indexed from ① to ⑦. The start of the EPIC-pn exposure serves as the origin of time for the intervals. The intervals are delimited by dashed vertical lines in the light curves of Fig. 1.

## 3 SPECTRAL ANALYSIS

In this work, the spectral analysis is performed with the X-ray Spectral Fitting Package (XSPEC; Arnaud 1996) and its PYTHON wrapper PyXspec. We adopt the cross-sections of Verner et al. (1996) and the chemical abundances reported in Wilms, Allen & McCray (2000).

Cash statistic (C-stat; Cash 1979) is used to account for the Poisson distribution of photons. The fitting is performed using the Bayesian X-ray Analysis package (BXA;<fnref n="2" /> Buchner et al. 2014) bridging XSPEC with nested sampling Monte Carlo algorithm implemented in UltraNest (Buchner 2016, 2019, 2021). We use nested sampling for its unsupervised global parameter exploration and its naturally self-convergence criterion. We use wide log-uniform priors for normalization and column density parameters and wide uniform priors for the other parameters. Using samples of the posterior distribution of the parameters, the median of the parameters is estimated. Uncertainties at 68 per cent confidence levels are computed using the 16th and 84th quantiles of the posterior distributions.

Cross-calibration factors between instruments are included in all models. These factors are estimated by fitting the phenomenological model. We assess the goodness of fit through simulations with

fakeit in XSPEC using the best-fitting values obtained from the fit. We simulate 1000 spectra for each instrument and rebin the spectra with a constant number of channels, 50 and 30, for XMM–Newton and NuSTAR, respectively. The realizations are then plotted against the observed data. Due to the lack of variability below 3 keV, we decided to perform the spectral analysis only above 3 keV. We found a cross-calibration mismatch between XMM–Newton and NuSTAR below ~4 keV, for that reason we fit NuSTAR data only above that energy.

### 3.1 Phenomenological model

First, we fitted a phenomenological model to the spectra, which can be written in XSPEC parlance as follows,

$$ \text{Model} = \text{constant} \times \text{TBabs} \\ \times (\text{cutoffpl} \times \text{TBpf} + \text{xillver}). \quad (1) $$

The first component constant is the cross-calibration factor between the different instruments. The second component TBabs (Wilms et al. 2000) models the absorption of X-ray photons in the line of sight by the gas and dust of our Galaxy with an equivalent hydrogen column density $N_H = 1.26 \times 10^{20} \text{ cm}^{-2}$ (HI4PI Collaboration et al. 2016). The primary X-ray emission from the hot corona is modelled using a power law with an exponential cutoff (cutoffpl). We tried to let the high-energy cutoff free to vary but no constraints were obtained so it was frozen to 500 keV for all the fits. We accounted for the absorption of the primary emission with TBpf (Wilms et al. 2000) where the partial covering fraction $f_{cov}$ was left free to vary. As their values converged to unity we fixed $f_{cov} = 1$, modelling a fully covering absorber, for the remainder of the analysis. The primary emission in Type-2 sources is thought to be reprocessed by distant neutral material leading to a reflection spectrum that we modelled using XILLVER (García & Kallman 2010; García et al. 2013, 2014). XILLVER is a tabulated model, computed by solving the radiative transfer equation in a plane-parallel geometry for a slab of gas illuminated by an X-ray source. We assume the reflector as distant and neutral, so the ionization parameter log $\xi$ is frozen to 0. As NGC 7582 is a type 2 Seyfert galaxy we freeze the inclination of the line of sight with respect to the normal of the disc to $\theta = 80^{\circ}$. The photon index and the high-energy cutoff of XILLVER are tied to the ones of the illuminating power law.

<footnote n="2">²https://johannesbuchner.github.io/BXA/index.html</footnote>
<table><caption>**Table 4.** Best fit values of the phenomenological model across all epochs. The uncertainties are given with a 68 per cent confidence.</caption><thead><tr><th>Epoch</th><th>N<sub>H</sub><sup>a</sup></th><th>Γ<sup>b</sup></th><th>Norm<sup>c</sup></th><th>cutoff<sub>pl</sub><br>F<sub>3-10</sub><sup>d</sup></th><th>F<sub>10-40</sub><sup>d</sup></th><th>Norm<sup>c</sup></th><th>XILLVER<br>F<sub>3-10</sub><sup>d</sup></th><th>F<sub>10-40</sub><sup>d</sup></th><th>cstat/dof<sup>e</sup></th></tr></thead><tbody><tr><td>2001-05 ①</td><td>86.66<sup>+9.6</sup><sub>-10.0</sub></td><td>2.13 ± 0.1</td><td>6.90<sup>+2.9</sup><sub>-2.3</sub></td><td>10.53<sup>+1.8</sup><sub>-2.0</sub></td><td>9.94<sup>+0.8</sup><sub>-0.9</sub></td><td>3.56<sup>+0.4</sup><sub>-0.3</sub></td><td>1.95 ± 0.1</td><td>7.28<sup>+1.3</sup><sub>-1.6</sub></td><td>113.84/121</td></tr><tr><td>2001-05 ②</td><td>141.81<sup>+15.7</sup><sub>-14.4</sub></td><td>2.28 ± 0.1</td><td>14.16<sup>+7.2</sup><sub>-4.7</sub></td><td>16.90<sup>+3.5</sup><sub>-4.5</sub></td><td>13.19<sup>+2.0</sup><sub>-2.4</sub></td><td>4.13<sup>+0.8</sup><sub>-0.5</sub></td><td>1.91 ± 0.1</td><td>5.96<sup>+1.3</sup><sub>-1.2</sub></td><td>96.40/96</td></tr><tr><td>2005-04</td><td>216.57<sup>+16.4</sup><sub>-16.1</sub></td><td>1.97 ± 0.04</td><td>6.29<sup>+1.5</sup><sub>-1.2</sub></td><td>12.73<sup>+2.1</sup><sub>-2.5</sub></td><td>14.80<sup>+2.3</sup><sub>-2.8</sub></td><td>2.67<sup>+0.09</sup><sub>-0.08</sub></td><td>1.61 ± 0.04</td><td>7.39 ± 0.6</td><td>251.29/218</td></tr><tr><td>2007-04</td><td>64.52<sup>+17.8</sup><sub>-18.2</sub></td><td>1.88<sup>+0.5</sup><sub>-0.6</sub></td><td>6.27<sup>+15.2</sup><sub>-4.4</sub></td><td>14.94<sup>+3.5</sup><sub>-6.4</sub></td><td>19.32<sup>+5.6</sup><sub>-12</sub></td><td>3.85<sup>+3.7</sup><sub>-1.2</sub></td><td>1.52 ± 0.4</td><td>8.27<sup>+4.5</sup><sub>-7.2</sub></td><td>29.98/29</td></tr><tr><td>2012-08</td><td>32.36<sup>+4.6</sup><sub>-4.4</sub></td><td>1.38<sup>+0.04</sup><sub>-0.05</sub></td><td>1.22<sup>+0.2</sup><sub>-0.1</sub></td><td>6.91 ± 0.6</td><td>17.37 ± 1.72</td><td>7.45<sup>+0.7</sup><sub>-0.6</sub></td><td>1.93 ± 0.2</td><td>20.20 ± 1.8</td><td>272.41/227</td></tr><tr><td>2012-09</td><td>62.82<sup>+11.2</sup><sub>-9.1</sub></td><td>1.33 ± 0.06</td><td>0.92<sup>+0.2</sup><sub>-0.1</sub></td><td>5.61<sup>+0.6</sup><sub>-0.7</sub></td><td>14.89<sup>+1.6</sup><sub>-1.7</sub></td><td>7.23<sup>+0.8</sup><sub>-0.7</sub></td><td>1.68 ± 0.2</td><td>18.72<sup>+1.8</sup><sub>-1.7</sub></td><td>236.79/187</td></tr><tr><td>2016-04 ①</td><td>55.11<sup>+3.0</sup><sub>-2.6</sub></td><td>1.57<sup>+0.05</sup><sub>-0.04</sub></td><td>2.99<sup>+0.4</sup><sub>-0.3</sub></td><td>12.05<sup>+0.5</sup><sub>-0.6</sub></td><td>23.50<sup>+1.0</sup><sub>-1.1</sub></td><td>4.01 ± 0.3</td><td>1.61 ± 0.12</td><td>12.71 ± 0.9</td><td>385.72/332</td></tr><tr><td>2016-04 ②</td><td>50.61<sup>+1.6</sup><sub>-1.5</sub></td><td>1.62<sup>+0.03</sup><sub>-0.04</sub></td><td>6.22 ± 0.5</td><td>22.85 ± 0.7</td><td>41.81<sup>+1.6</sup><sub>-1.7</sub></td><td>3.45 ± 0.3</td><td>1.51 ± 0.2</td><td>11.20<sup>+1.1</sup><sub>-1.0</sub></td><td>419.22/395</td></tr><tr><td>2016-04 ③</td><td>43.57<sup>+2.0</sup><sub>-1.8</sub></td><td>1.50 ± 0.04</td><td>2.83<sup>+0.3</sup><sub>-0.2</sub></td><td>12.78 ± 0.5</td><td>27.24 ± 1.4</td><td>4.61<sup>+0.5</sup><sub>-0.4</sub></td><td>1.61 ± 0.1</td><td>13.94 ± 1.2</td><td>382.47/356</td></tr><tr><td>2016-04 ④</td><td>45.84 ± 1.6</td><td>1.51<sup>+0.04</sup><sub>-0.03</sub></td><td>3.77 ± 0.3</td><td>16.67 ± 0.6</td><td>34.87<sup>+1.6</sup><sub>-1.7</sub></td><td>3.02 ± 0.4</td><td>1.09 ± 0.15</td><td>9.23 ± 1.1</td><td>436.85/374</td></tr><tr><td>2016-04 ⑤</td><td>44.40<sup>+1.5</sup><sub>-1.6</sub></td><td>1.55 ± 0.03</td><td>3.81 ± 0.3</td><td>15.83<sup>+0.5</sup><sub>-0.6</sub></td><td>31.75<sup>+1.3</sup><sub>-1.3</sub></td><td>3.64 ± 0.3</td><td>1.41 ± 0.2</td><td>11.42 ± 1.0</td><td>470.41/417</td></tr><tr><td>2016-04 ⑥</td><td>42.89 ± 1.5</td><td>1.65 ± 0.03</td><td>6.38 ± 0.5</td><td>22.41 ± 0.9</td><td>39.60<sup>+1.9</sup><sub>-2.0</sub></td><td>3.68 ± 0.4</td><td>1.68 ± 0.2</td><td>11.98 ± 1.4</td><td>435.84/386</td></tr><tr><td>2016-04 ⑦</td><td>35.88 ± 2.2</td><td>1.57<sup>+0.05</sup><sub>-0.04</sub></td><td>5.10<sup>+0.6</sup><sub>-0.5</sub></td><td>20.30<sup>+1.2</sup><sub>-1.3</sub></td><td>39.48 ± 3.0</td><td>4.84 ± 0.7</td><td>1.95 ± 0.30</td><td>15.40 ± 2.4</td><td>232.30/227</td></tr></tbody></table>

Notes. $^a$Equivalent hydrogen column density modelled with TBpcf in $10^{22}$ cm$^{-2}$.

$^b$Photon index of the power law.

$^c$Normalization in $10^{-3}$ ($10^{-5}$) photon keV$^{-1}$ s$^{-1}$ cm$^{-2}$ for cutoffpl (XILLVER).

$^d$Flux of the component in unit of $10^{-12}$ erg s$^{-1}$ cm$^{-2}$ either in the 3–10 keV band or in the 10–40 keV band.

$^e$Total C-statistic/number of degrees of freedom.

We added a scattered primary emission component in the form of a constant times a power law to account for the scattered emission observed for instance in Turner et al. (1997). The constant was allowed to vary between 0 and 1 to model the scattered fraction, the parameters of the power law are tied to the ones of the primary power law. When fitting the phenomenological model with this component for the first slice of the observations of 2001 and 2016 and the observation of 2005 we find values of the scattered fraction less than 2 per cent. These results are consistent with the relation between the column density and the scattered fraction observed in Gupta et al. (2021). In fact, this component is supposed to be more important at soft X-rays, below ~2–3 keV, which are not analysed in this work. Thus, we do not include this component in the model as it does not improve the quality of the fit substantially.

## 3.2 Physically motivated model

We also use the physical Unified X-ray Clumpy model (uxclumpy; Buchner et al. 2019). This model takes into account Compton scattering, photo-electric absorption and line fluorescence effects due to the absorber. Buchner et al. (2019) produced this clumpy model assuming that the total number of clouds is constant but the observed distribution depends on the geometry of the absorber and the line of sight. The distribution of the angular size of the clumps is computed to reproduce eclipse events in AGN.

Two geometrical parameters are used: TORsigma, that is, the vertical extent of the cloud population, the smaller this value the more concentrated the clouds in the disc plane; and CTKcover, that is, the covering factor of the inner ring of clouds, the higher this value the larger the inner clouds. The inclination angle of the line of sight with respect to the normal to the disc is frozen to 80° as in the phenomenological model.

In XSPEC, the model can be written as follows,

$$ \text{Model} = \text{constant} \times \text{TBabs} \times (\text{atable}[\text{uxclumpy-cutoff}] + \text{constant} \times \text{atable}[\text{uxclumpy-cutoff-omni}]). \quad (2) $$

As mentioned earlier, the first constant component is the cross-calibration factor estimated with the phenomenological model and TBabs models the absorption of X-rays by gas and dust of our Galaxy. The table uxclumpy-cutoff models the spectrum with the reflected and transmitted components as well as fluorescent lines. The table uxclumpy-cutoff-omni models the incident spectrum of the X-ray corona with the power law. This component models unabsorbed emission of the corona, hence it is supposed to model a warm re-emission. The parameters of the uxclumpy-cutoff-omni component are tied to the ones of uxclumpy-cutoff, as they must represent the same geometry. A factor ranging between $10^{-5}$ and 0.1 is added for the warm emission model uxclumpy-cutoff-omni, this limits the contribution of the warm emission component up to 10 per cent of the transmitted and reflected component.

# 4 RESULTS

## 4.1 Phenomenological model

We fit the phenomenological model presented in Section 3.1, finding good fits in all epochs. The best-fit parameters are presented in Table 4, and the fitted spectra are shown in Fig. 3 and the samples of the posterior distributions on the parameters are plotted in Fig. A1. The evolution of the fitted physical parameters is plotted in blue circles in Fig. 4. The values of the cross-calibration factors are presented in Table A1. The cross-calibration factors obtained can be up to 35 per cent between EPIC and FPM instruments and up to 13 per cent between EPIC cameras. As stated in the calibration

<footnote>$^3$https://github.com/JohannesBuchner/xars/blob/master/doc/uxclumpy.rst</footnote>
<table><caption>**Table 4.** Best fit values of the phenomenological model across all epochs. The uncertainties are given with a 68 per cent confidence.</caption><thead><tr><th rowspan="2">Epoch</th><th rowspan="2">N<sub>H</sub><sup>a</sup></th><th rowspan="2">Γ<sup>b</sup></th><th colspan="3">cutoffpl</th><th colspan="3">XILLVER</th><th rowspan="2">cstat/dof<sup>e</sup></th></tr><tr><th>Norm<sup>c</sup></th><th>F<sub>3-10</sub><sup>d</sup></th><th>F<sub>10-40</sub><sup>d</sup></th><th>Norm<sup>c</sup></th><th>F<sub>3-10</sub><sup>d</sup></th><th>F<sub>10-40</sub><sup>d</sup></th></tr></thead><tbody><tr><td>2001-05 ①</td><td>86.66<sup>+9.6</sup><sub>-10.0</sub></td><td>2.13 ± 0.1</td><td>6.90<sup>+2.9</sup><sub>-2.3</sub></td><td>10.53<sup>+1.8</sup><sub>-2.0</sub></td><td>9.94<sup>+0.8</sup><sub>-0.9</sub></td><td>3.56<sup>+0.4</sup><sub>-0.3</sub></td><td>1.95 ± 0.1</td><td>7.28<sup>+1.3</sup><sub>-1.6</sub></td><td>113.84/121</td></tr><tr><td>2001-05 ②</td><td>141.81<sup>+15.7</sup><sub>-14.4</sub></td><td>2.28 ± 0.1</td><td>14.16<sup>+7.2</sup><sub>-4.7</sub></td><td>16.90<sup>+3.5</sup><sub>-4.5</sub></td><td>13.19<sup>+2.0</sup><sub>-2.4</sub></td><td>4.13<sup>+0.8</sup><sub>-0.5</sub></td><td>1.91 ± 0.1</td><td>5.96<sup>+1.3</sup><sub>-1.2</sub></td><td>96.40/96</td></tr><tr><td>2005-04</td><td>216.57<sup>+16.4</sup><sub>-16.1</sub></td><td>1.97 ± 0.04</td><td>6.29<sup>+1.5</sup><sub>-1.2</sub></td><td>12.73<sup>+2.1</sup><sub>-2.5</sub></td><td>14.80<sup>+2.3</sup><sub>-2.8</sub></td><td>2.67<sup>+0.09</sup><sub>-0.08</sub></td><td>1.61 ± 0.04</td><td>7.39 ± 0.6</td><td>251.29/218</td></tr><tr><td>2007-04</td><td>64.52<sup>+17.8</sup><sub>-18.2</sub></td><td>1.88<sup>+0.5</sup><sub>-0.6</sub></td><td>6.27<sup>+15.2</sup><sub>-4.4</sub></td><td>14.94<sup>+3.5</sup><sub>-6.4</sub></td><td>19.32<sup>+5.6</sup><sub>-12</sub></td><td>3.85<sup>+3.7</sup><sub>-1.2</sub></td><td>1.52 ± 0.4</td><td>8.27<sup>+4.5</sup><sub>-7.2</sub></td><td>29.98/29</td></tr><tr><td>2012-08</td><td>32.36<sup>+4.6</sup><sub>-4.4</sub></td><td>1.38<sup>+0.04</sup><sub>-0.05</sub></td><td>1.22<sup>+0.2</sup><sub>-0.1</sub></td><td>6.91 ± 0.6</td><td>17.37 ± 1.72</td><td>7.45<sup>+0.7</sup><sub>-0.6</sub></td><td>1.93 ± 0.2</td><td>20.20 ± 1.8</td><td>272.41/227</td></tr><tr><td>2012-09</td><td>62.82<sup>+11.2</sup><sub>-9.1</sub></td><td>1.33 ± 0.06</td><td>0.92<sup>+0.2</sup><sub>-0.1</sub></td><td>5.61<sup>+0.6</sup><sub>-0.7</sub></td><td>14.89<sup>+1.6</sup><sub>-1.7</sub></td><td>7.23<sup>+0.8</sup><sub>-0.7</sub></td><td>1.68 ± 0.2</td><td>18.72<sup>+1.8</sup><sub>-1.7</sub></td><td>236.79/187</td></tr><tr><td>2016-04 ①</td><td>55.11<sup>+3.0</sup><sub>-2.6</sub></td><td>1.57<sup>+0.05</sup><sub>-0.04</sub></td><td>2.99<sup>+0.4</sup><sub>-0.3</sub></td><td>12.05<sup>+0.5</sup><sub>-0.6</sub></td><td>23.50<sup>+1.0</sup><sub>-1.1</sub></td><td>4.01 ± 0.3</td><td>1.61 ± 0.12</td><td>12.71 ± 0.9</td><td>385.72/332</td></tr><tr><td>2016-04 ②</td><td>50.61<sup>+1.6</sup><sub>-1.5</sub></td><td>1.62<sup>+0.03</sup><sub>-0.04</sub></td><td>6.22 ± 0.5</td><td>22.85 ± 0.7</td><td>41.81<sup>+1.6</sup><sub>-1.7</sub></td><td>3.45 ± 0.3</td><td>1.51 ± 0.2</td><td>11.20<sup>+1.1</sup><sub>-1.0</sub></td><td>419.22/395</td></tr><tr><td>2016-04 ③</td><td>43.57<sup>+2.0</sup><sub>-1.8</sub></td><td>1.50 ± 0.04</td><td>2.83<sup>+0.3</sup><sub>-0.2</sub></td><td>12.78 ± 0.5</td><td>27.24 ± 1.4</td><td>4.61<sup>+0.5</sup><sub>-0.4</sub></td><td>1.61 ± 0.1</td><td>13.94 ± 1.2</td><td>382.47/356</td></tr><tr><td>2016-04 ④</td><td>45.84 ± 1.6</td><td>1.51<sup>+0.04</sup><sub>-0.03</sub></td><td>3.77 ± 0.3</td><td>16.67 ± 0.6</td><td>34.87<sup>+1.6</sup><sub>-1.7</sub></td><td>3.02 ± 0.4</td><td>1.09 ± 0.15</td><td>9.23 ± 1.1</td><td>436.85/374</td></tr><tr><td>2016-04 ⑤</td><td>44.40<sup>+1.5</sup><sub>-1.6</sub></td><td>1.55 ± 0.03</td><td>3.81 ± 0.3</td><td>15.83<sup>+0.5</sup><sub>-0.6</sub></td><td>31.75<sup>+1.3</sup><sub>-1.3</sub></td><td>3.64 ± 0.3</td><td>1.41 ± 0.2</td><td>11.42 ± 1.0</td><td>470.41/417</td></tr><tr><td>2016-04 ⑥</td><td>42.89 ± 1.5</td><td>1.65 ± 0.03</td><td>6.38 ± 0.5</td><td>22.41 ± 0.9</td><td>39.60<sup>+1.9</sup><sub>-2.0</sub></td><td>3.68 ± 0.4</td><td>1.68 ± 0.2</td><td>11.98 ± 1.4</td><td>435.84/386</td></tr><tr><td>2016-04 ⑦</td><td>35.88 ± 2.2</td><td>1.57<sup>+0.05</sup><sub>-0.04</sub></td><td>5.10<sup>+0.6</sup><sub>-0.5</sub></td><td>20.30<sup>+1.2</sup><sub>-1.3</sub></td><td>39.48 ± 3.0</td><td>4.84 ± 0.7</td><td>1.95 ± 0.30</td><td>15.40 ± 2.4</td><td>232.30/227</td></tr></tbody></table>

Notes. $^a$Equivalent hydrogen column density modelled with TBpcf in $10^{22}$ cm$^{-2}$.

$^b$Photon index of the power law.

$^c$Normalization in $10^{-3}$ ($10^{-5}$) photon keV$^{-1}$ s$^{-1}$ cm$^{-2}$ for cutoffpl (XILLVER).

$^d$Flux of the component in unit of $10^{-12}$ erg s$^{-1}$ cm$^{-2}$ either in the 3–10 keV band or in the 10–40 keV band.

$^e$Total C-statistic/number of degrees of freedom.

We added a scattered primary emission component in the form of a constant times a power law to account for the scattered emission observed for instance in Turner et al. (1997). The constant was allowed to vary between 0 and 1 to model the scattered fraction, the parameters of the power law are tied to the ones of the primary power law. When fitting the phenomenological model with this component for the first slice of the observations of 2001 and 2016 and the observation of 2005 we find values of the scattered fraction less than 2 per cent. These results are consistent with the relation between the column density and the scattered fraction observed in Gupta et al. (2021). In fact, this component is supposed to be more important at soft X-rays, below ~2–3 keV, which are not analysed in this work. Thus, we do not include this component in the model as it does not improve the quality of the fit substantially.

## 3.2 Physically motivated model

We also use the physical Unified X-ray Clumpy model (uxclumpy; Buchner et al. 2019). This model takes into account Compton scattering, photo-electric absorption and line fluorescence effects due to the absorber. Buchner et al. (2019) produced this clumpy model assuming that the total number of clouds is constant but the observed distribution depends on the geometry of the absorber and the line of sight. The distribution of the angular size of the clumps is computed to reproduce eclipse events in AGN.

Two geometrical parameters are used: TORsigma, that is, the vertical extent of the cloud population, the smaller this value the more concentrated the clouds in the disc plane; and CTKcover, that is, the covering factor of the inner ring of clouds, the higher this value the larger the inner clouds. The inclination angle of the line of sight with respect to the normal to the disc is frozen to 80° as in the phenomenological model.

In XSPEC, the model can be written as follows,

$$ \text{Model} = \text{constant} \times \text{TBabs} \times (\text{atable}[\text{uxclumpy-cutoff}] + \text{constant} \times \text{atable}[\text{uxclumpy-cutoff-omni}]). \quad (2) $$

As mentioned earlier, the first constant component is the cross-calibration factor estimated with the phenomenological model and TBabs models the absorption of X-rays by gas and dust of our Galaxy. The table uxclumpy-cutoff models the spectrum with the reflected and transmitted components as well as fluorescent lines. The table uxclumpy-cutoff-omni models the incident spectrum of the X-ray corona with the power law. This component models unabsorbed emission of the corona, hence it is supposed to model a warm re-emission. The parameters of the uxclumpy-cutoff-omni component are tied to the ones of uxclumpy-cutoff, as they must represent the same geometry. A factor ranging between $10^{-5}$ and 0.1 is added for the warm emission model uxclumpy-cutoff-omni, this limits the contribution of the warm emission component up to 10 per cent of the transmitted and reflected component.

# 4 RESULTS

## 4.1 Phenomenological model

We fit the phenomenological model presented in Section 3.1, finding good fits in all epochs. The best-fit parameters are presented in Table 4, and the fitted spectra are shown in Fig. 3 and the samples of the posterior distributions on the parameters are plotted in Fig. A1. The evolution of the fitted physical parameters is plotted in blue circles in Fig. 4. The values of the cross-calibration factors are presented in Table A1. The cross-calibration factors obtained can be up to 35 per cent between EPIC and FPM instruments and up to 13 per cent between EPIC cameras. As stated in the calibration

<footnote>$^3$https://github.com/JohannesBuchner/xars/blob/master/doc/uxclumpy.rst</footnote>
<figure><img src="image_4.png" /><figcaption>**Figure 3.** Phenomenological model fitted on all epochs with the spectra (upper panels) and residuals (lower panels). The instruments are plotted as follows: EPIC-pn in dark blue, EPIC-MOS1 in green, EPIC-MOS2 in light blue, FPMA in yellow, and FPMB in magenta. The additive individual components of the model are depicted in coloured dashed lines. The circled numbers ①, ②,..., ⑦ indicate the slices corresponding to the given observation.</figcaption></figure>

technical note<fnref n="4" /> these factors are expected to be high when using the most recent calibration files.

The photon index value is usually higher when using *XMM–Newton* data because the data only extend between 3 and 10 keV. The column density of the absorber varies between the two slices of the 2001 observation. It increased from 0.87 ± 0.1 to 1.4 ± 0.2 × 10²<fnref n="4" /> cm⁻². A hint of softening in Γ can also be seen during this observation. However, the two values are consistent within 1σ, increasing from 2.1 ± 0.1 to 2.3 ± 0.1. The observation of 2005 revealed the highest column density $N_H = 2.16 ± 0.16 × 10^{24}$ cm⁻² and the lowest flux of the reflection component. The two observations of 2012 present the hardest photon index (Γ = 1.38 ± 0.05 and Γ = 1.33 ± 0.06), and the lowest column density 0.32 ± 0.04 × 10²<fnref n="4" /> cm⁻². In 2016, the column density decreased continuously from 0.55 ± 0.03 to 0.36 ± 0.02 × 10²<fnref n="4" /> cm⁻² from the start to the end of the observation. In the meantime, the photon index varied as well as the normalization. Given the low quality of the observation of 2007, only poor constraints on the parameters could be found.

## 4.2 Physical model

Assuming the geometry of the absorber does not change over time, we expect to find a unique geometry fitting to the data for all epochs. We fitted the physical model on all epochs by freezing the geometrical parameters *TORsigma* and *CTKcover*. We performed the fits for 11 out of 20 available geometries because we do not use the geometries which do not include clumps (where *TORsigma* = 0) or which include large clouds in the thick ring of clouds, that is, where *CTKCover* = 0.6.

UltraNest provides an estimate of the marginal likelihood also called evidence *Z* and samples of the posterior probability distributions. Assuming two models *M*₁ and *M*₂ with respective evidences *Z*₁ and *Z*₂, the Bayes factor *K* is the ratio of the two marginal likelihoods, that is, *K* = *Z*₁/*Z*₂. Jeffreys (1939) gives an empirical interpretation of the values of the Bayes factor, which can be used for model selection. For instance, if *K* < 1, then model *M*₁ is rejected, if 10 < *K* < 10³/², model *M*₁ is supported with strong evidence over model *M*₂.

Table A2 shows the natural logarithm of the evidence for the 11 geometries fitted. We sum the logarithm of the evidence over all epochs and use it as a criterion to select the three geometries with the highest ln *Z*. This rules out the geometries dominated by the inner ring of clouds (with *TORsigma* = 7) and the partial covering geometry

<footnote n="4">⁴https://xmmweb.esac.esa.int/docs/documents/CAL-TN-0230-1-3.pdf</footnote>
<figure><img src="image_4.png" /><figcaption>**Figure 3.** Phenomenological model fitted on all epochs with the spectra (upper panels) and residuals (lower panels). The instruments are plotted as follows: EPIC-pn in dark blue, EPIC-MOS1 in green, EPIC-MOS2 in light blue, FPMA in yellow, and FPMB in magenta. The additive individual components of the model are depicted in coloured dashed lines. The circled numbers ①, ②,..., ⑦ indicate the slices corresponding to the given observation.</figcaption></figure>

technical note<fnref n="4" /> these factors are expected to be high when using the most recent calibration files.

The photon index value is usually higher when using *XMM–Newton* data because the data only extend between 3 and 10 keV. The column density of the absorber varies between the two slices of the 2001 observation. It increased from 0.87 ± 0.1 to 1.4 ± 0.2 × 10²<fnref n="4" /> cm⁻². A hint of softening in Γ can also be seen during this observation. However, the two values are consistent within 1σ, increasing from 2.1 ± 0.1 to 2.3 ± 0.1. The observation of 2005 revealed the highest column density $N_H = 2.16 ± 0.16 × 10^{24}$ cm⁻² and the lowest flux of the reflection component. The two observations of 2012 present the hardest photon index (Γ = 1.38 ± 0.05 and Γ = 1.33 ± 0.06), and the lowest column density 0.32 ± 0.04 × 10²<fnref n="4" /> cm⁻². In 2016, the column density decreased continuously from 0.55 ± 0.03 to 0.36 ± 0.02 × 10²<fnref n="4" /> cm⁻² from the start to the end of the observation. In the meantime, the photon index varied as well as the normalization. Given the low quality of the observation of 2007, only poor constraints on the parameters could be found.

## 4.2 Physical model

Assuming the geometry of the absorber does not change over time, we expect to find a unique geometry fitting to the data for all epochs. We fitted the physical model on all epochs by freezing the geometrical parameters *TORsigma* and *CTKcover*. We performed the fits for 11 out of 20 available geometries because we do not use the geometries which do not include clumps (where *TORsigma* = 0) or which include large clouds in the thick ring of clouds, that is, where *CTKCover* = 0.6.

UltraNest provides an estimate of the marginal likelihood also called evidence *Z* and samples of the posterior probability distributions. Assuming two models $M_1$ and $M_2$ with respective evidences $Z_1$ and $Z_2$, the Bayes factor *K* is the ratio of the two marginal likelihoods, that is, $K = Z_1/Z_2$. Jeffreys (1939) gives an empirical interpretation of the values of the Bayes factor, which can be used for model selection. For instance, if $K < 1$, then model $M_1$ is rejected, if $10 < K < 10^{3/2}$, model $M_1$ is supported with strong evidence over model $M_2$.

Table A2 shows the natural logarithm of the evidence for the 11 geometries fitted. We sum the logarithm of the evidence over all epochs and use it as a criterion to select the three geometries with the highest ln *Z*. This rules out the geometries dominated by the inner ring of clouds (with *TORsigma* = 7) and the partial covering geometry

<footnote n="4">⁴https://xmmweb.esac.esa.int/docs/documents/CAL-TN-0230-1-3.pdf</footnote>
<figure><img src="image_5.png" /><figcaption>**Figure 4.** Best fit values of the best physical model (see Section 4.2) (red diamonds) and phenomenological model (blue circles) in all epochs, given within 68 per cent-confidence levels. Panels from top to bottom: equivalent hydrogen column density, photon index, normalization of *uxclumpy*, normalization of *cutoffpl*, and normalization of *xillver*.</figcaption></figure>

associating clumps and larger thick clouds (TORSigma = 28). All the accepted geometries consist of a fully covering clumpy absorber (TORSigma = 84).

We compute the Bayes factor for the selected geometries in Table 6 with respect to the best geometry. The Bayes factor is then defined as: $\ln K = \ln Z_{(84,0)} - \ln Z$. Using the Jeffrey scale (Jeffreys 1939), we notice that $K > 10^2$, hence the fully covering clumpy geometry (TORSigma = 84 and CTKCover = 0) is statistically favoured over all geometries and the phenomenological model.

Fig. 4 shows the best-fit parameters obtained using this geometry in red diamonds and in blue circles the best-fit parameters of the phenomenological model. In Fig. 5, we show this model fitted to all epochs and give the values of the parameters in all epochs in Table 5. The samples of the posterior distributions on the parameters for this geometry are plotted in Fig. A2.

The values of $\Gamma$ in all epochs are found to be larger than the ones obtained using the phenomenological model, however they are all consistent within $2\sigma$. Values of $N_H$ of the physical model are smaller than values of the phenomenological model but they follow the same variations. This is most likely due to the different assumptions of each of the models. The normalization of *uxclumpy* follows also the same trend as the one of the *cutoffpl*.

# 5 DISCUSSION

## 5.1 The origin of the variability

In Fig. 6, we plot the fluxes in the 3–40 keV energy band for the primary X-ray emission and the reflection component of the phenomenological model. The 10–40 keV fluxes in the *XMM–Newton* observations are obtained by extrapolating the best-fit model to larger energy bands. The fluxes are obtained with *flux* command of *XSPEC*, on each individual component, that is, *cutoffpl* and

*xillver*, for all samples of the posterior distribution. The median and the 16th and 84th quantiles of the flux distributions are then computed to estimate the 68 per cent confidence levels. We use the phenomenological model as a proxy for distinguishing the contribution of the reflection from one of the power law. The separation between these two components cannot be done using our current modelling with *uxclumpy*. The flux of both components varies over long time-scales. However, at short time-scale, the reflection component appears to be less variable than the power law (this can be seen in the observation of 2016). This suggests that the response of the reflecting component to the incident primary X-ray emission is not instantaneous. As the observation is 100 ks long, the reflecting/absorbing material must be located at a distance of $d > t_{obs} \times c \sim 400 R_g$ away from the X-ray source. This would put the absorber farther from the black hole, in the BLR.

Figs 6 and 7 demonstrate that the variability on both short- and long-time-scales is due to an interplay between intrinsic and absorption-induced variations. NGC 7582 exhibited at least three episodes of nearly Compton-thick state (with $N_H > 10^{24} \text{ cm}^{-2}$) between 2005 and 2014, which could explain the Changing-look classification of this source. It is worth noting that in 2007, $N_H$ may have increased continuously from $4.4_{-0.2}^{+0.3} \times 10^{23} \text{ cm}^{-2}$ to $(12 \pm 2) \times 10^{23} \text{ cm}^{-2}$ over the course of six months. However, due to the lack of intense monitoring and long observations during this period it is hard to tell whether indeed this rise was continuous or if it also varied on short time-scales, similar to the behaviour of the source in 2016. The same reasoning can be applied in 2012, where we observe a decrease of $N_H$ between observations separated by 15 d but with no way to probe the short-term variability.

In 2001 and 2016, the source exhibited a strong absorption variability. To study this short-term absorption variability, we fitted the evolution of $N_H$ with a linear function in these observations using UltraNest. It is worth noting that this model is employed to evaluate the rate at which $N_H$ varies without having any physical motivation. The results are presented in Table 7. As shown in Fig. 8, we observe a sharp increase in $N_H$ in 2001 compared to a slower decrease in 2016. On the contrary, the absorption was constant over 100 ks during the 2005 observation and over ~25 ks during the observations of 2012. The absence of short-term variability during the 2005 observations suggests that the X-ray emission is absorbed by the same dense absorber during the whole observation.

The behaviour of the absorber in the different observations can be summarized as follows: a sharp increase in $N_H$ (while being Compton thin) in 2001, a constant high $N_H$ ($> 10^{24} \text{ cm}^{-2}$) absorption over 100 ks in 2005, an increase of $N_H$ between 15 d in 2012 and a slow decrease in $N_H$ over 100 ks in 2016. These independent episodes could correspond to occultations by various clumps, in agreement with the favoured physical model of a clumpy medium. If the different clumps have similar structures, then these events could agree with a scenario in which the absorbing BLR clouds have a ‘cometary’ structure, with a dense head and a gradually less dense tail. This structure has been proposed to explain the observed eclipsing events in NGC 1365 (Maiolino et al. 2010) and Mrk 766 (Risaliti et al. 2011). If this were true, then the observation of 2001 would correspond to the start of an eclipsing event, the observation of 2005 would correspond to the obscuration by the dense head of the comet, and the observation of 2016 would correspond to the end of an eclipse where the tail of the comet is obscuring the line of sight. However, this scenario cannot be confirmed or ruled out as none of the observations could represent a full eclipse.

An alternative explanation for the short-term variability is a spherical clump with a density profile peaking in the core and slowly
<figure><img src="image_5.png" /><figcaption>**Figure 4.** Best fit values of the best physical model (see Section 4.2) (red diamonds) and phenomenological model (blue circles) in all epochs, given within 68 per cent-confidence levels. Panels from top to bottom: equivalent hydrogen column density, photon index, normalization of *uxclumpy*, normalization of *cutoffpl*, and normalization of *xillver*.</figcaption></figure>

associating clumps and larger thick clouds (TORSigma = 28). All the accepted geometries consist of a fully covering clumpy absorber (TORSigma = 84).

We compute the Bayes factor for the selected geometries in Table 6 with respect to the best geometry. The Bayes factor is then defined as: $\ln K = \ln Z_{(84,0)} - \ln Z$. Using the Jeffrey scale (Jeffreys 1939), we notice that $K > 10^2$, hence the fully covering clumpy geometry (TORSigma = 84 and CTKCover = 0) is statistically favoured over all geometries and the phenomenological model.

Fig. 4 shows the best-fit parameters obtained using this geometry in red diamonds and in blue circles the best-fit parameters of the phenomenological model. In Fig. 5, we show this model fitted to all epochs and give the values of the parameters in all epochs in Table 5. The samples of the posterior distributions on the parameters for this geometry are plotted in Fig. A2.

The values of $\Gamma$ in all epochs are found to be larger than the ones obtained using the phenomenological model, however they are all consistent within $2\sigma$. Values of $N_H$ of the physical model are smaller than values of the phenomenological model but they follow the same variations. This is most likely due to the different assumptions of each of the models. The normalization of *uxclumpy* follows also the same trend as the one of the *cutoffpl*.

# 5 DISCUSSION

## 5.1 The origin of the variability

In Fig. 6, we plot the fluxes in the 3–40 keV energy band for the primary X-ray emission and the reflection component of the phenomenological model. The 10–40 keV fluxes in the *XMM–Newton* observations are obtained by extrapolating the best-fit model to larger energy bands. The fluxes are obtained with *flux* command of *XSPEC*, on each individual component, that is, *cutoffpl* and

*xillver*, for all samples of the posterior distribution. The median and the 16th and 84th quantiles of the flux distributions are then computed to estimate the 68 per cent confidence levels. We use the phenomenological model as a proxy for distinguishing the contribution of the reflection from one of the power law. The separation between these two components cannot be done using our current modelling with *uxclumpy*. The flux of both components varies over long time-scales. However, at short time-scale, the reflection component appears to be less variable than the power law (this can be seen in the observation of 2016). This suggests that the response of the reflecting component to the incident primary X-ray emission is not instantaneous. As the observation is 100 ks long, the reflecting/absorbing material must be located at a distance of $d > t_{obs} \times c \sim 400 R_g$ away from the X-ray source. This would put the absorber farther from the black hole, in the BLR.

Figs 6 and 7 demonstrate that the variability on both short- and long-time-scales is due to an interplay between intrinsic and absorption-induced variations. NGC 7582 exhibited at least three episodes of nearly Compton-thick state (with $N_H > 10^{24} \text{ cm}^{-2}$) between 2005 and 2014, which could explain the Changing-look classification of this source. It is worth noting that in 2007, $N_H$ may have increased continuously from $4.4_{-0.2}^{+0.3} \times 10^{23} \text{ cm}^{-2}$ to $(12 \pm 2) \times 10^{23} \text{ cm}^{-2}$ over the course of six months. However, due to the lack of intense monitoring and long observations during this period it is hard to tell whether indeed this rise was continuous or if it also varied on short time-scales, similar to the behaviour of the source in 2016. The same reasoning can be applied in 2012, where we observe a decrease of $N_H$ between observations separated by 15 d but with no way to probe the short-term variability.

In 2001 and 2016, the source exhibited a strong absorption variability. To study this short-term absorption variability, we fitted the evolution of $N_H$ with a linear function in these observations using UltraNest. It is worth noting that this model is employed to evaluate the rate at which $N_H$ varies without having any physical motivation. The results are presented in Table 7. As shown in Fig. 8, we observe a sharp increase in $N_H$ in 2001 compared to a slower decrease in 2016. On the contrary, the absorption was constant over 100 ks during the 2005 observation and over ~25 ks during the observations of 2012. The absence of short-term variability during the 2005 observations suggests that the X-ray emission is absorbed by the same dense absorber during the whole observation.

The behaviour of the absorber in the different observations can be summarized as follows: a sharp increase in $N_H$ (while being Compton thin) in 2001, a constant high $N_H$ ($> 10^{24} \text{ cm}^{-2}$) absorption over 100 ks in 2005, an increase of $N_H$ between 15 d in 2012 and a slow decrease in $N_H$ over 100 ks in 2016. These independent episodes could correspond to occultations by various clumps, in agreement with the favoured physical model of a clumpy medium. If the different clumps have similar structures, then these events could agree with a scenario in which the absorbing BLR clouds have a ‘cometary’ structure, with a dense head and a gradually less dense tail. This structure has been proposed to explain the observed eclipsing events in NGC 1365 (Maiolino et al. 2010) and Mrk 766 (Risaliti et al. 2011). If this were true, then the observation of 2001 would correspond to the start of an eclipsing event, the observation of 2005 would correspond to the obscuration by the dense head of the comet, and the observation of 2016 would correspond to the end of an eclipse where the tail of the comet is obscuring the line of sight. However, this scenario cannot be confirmed or ruled out as none of the observations could represent a full eclipse.

An alternative explanation for the short-term variability is a spherical clump with a density profile peaking in the core and slowly
<figure><img src="image_6.png" /><figcaption>**Figure 5.** Best-fit geometry of the fully covering clumpy geometry of the physical model fitted on all epochs with the spectra (upper panels) and residuals (lower panels). The instruments are plotted as follows: EPIC-pn in dark blue, EPIC-MOS1 in green, EPIC-MOS2 in light blue, FPMA in yellow, and FPMB in magenta. The circled numbers (①, ②,..., ⑦) indicate the slices corresponding to a given observation.</figcaption></figure>

decreasing towards the surface of the clump. The scenario of an eclipse is still valid for a spherical cloud. Thus, longer observations and a closer monitoring may be required to better understand the structure of the absorber in this source.

## 5.2 Determining the properties of the BLR clouds

Assuming that the obscuring clouds are located in the BLR, following a Keplerian orbit, we derive below some of the properties of these clouds.

Velocity: Aretxaga et al. (1999) observed NGC 7582 in a type 1 Seyfert galaxy state with broad optical lines on the 1998 July 11. The estimated FWHM of the Hα and Hβ lines is FWHM=12 400 km s⁻¹; over the time-scale of a few months the FWHM decreased to reach 6660 km s⁻¹ at the end of October 1998 (Aretxaga et al. 1999). Ricci et al. (2018) reported a FWHM of 2382 ± 44 km s⁻¹, in an observation of 2004. With a 2014 *Chandra* observation, Braito et al. (2017) estimated the FWHM of the Fe Kα line to be FWHM=1500<sup>+900</sup><sub>-800</sub> km s⁻¹, thus *v* = 637 km s⁻¹. Because no measurement of the FWHM of Hα was made close to our observations, it is impossible to predict the state of the source in the optical at the time of our archival observations. We tried to estimate the FWHM of the Fe Kα in our *XMM–Newton* observations but the uncertainties were too

high to draw any conclusions. We use the most recent measurement by Braito et al. (2017) to provide a lower limit on the velocity of the clouds: *v* ≥ 637 km s⁻¹.

Size of the clouds: as we do not observe complete eclipsing events, we can only set lower limits on the size of the clouds. The typical duration of an eclipse is at least twice the exposure time $t_{exp} = 100$ ks. Assuming a spherical cloud of diameter $D_c$ moving at a velocity $v_c$, the duration of an eclipse is $t_{ec} = D_c/v_c$. The diameter of the cloud is then $D_c \ge 2v_c \times t_{exp}$. Using the value of velocity obtained above, $D_c \gtrsim 1.5 R_g (1.2 \times 10^{13} \text{ cm})$.

Location of the BLR: assuming a Keplerian circular orbit for the clumps in the BLR. The radius of the orbit in the BLR is given by $R = \frac{GM}{v^2} = c^2/v^2 R_g$, this gives an upper limit on the location of the clouds in the BLR, $R_{BLR}/R_g \lesssim 22000$, $R_{BLR} \sim 0.6$ pc.

## 5.3 Comparison with previous works

NGC 7582 has been observed by many X-ray observatories. In Fig. 7, we plot the values of the column density, the photon index, and the observed flux obtained from previous studies (in circles) and the ones obtained in this work (in diamonds). The previous works mostly used phenomenological models, thus we show the parameters obtained with our best-fit phenomenological model, for consistency.
<figure><img src="image_6.png" /><figcaption>**Figure 5.** Best-fit geometry of the fully covering clumpy geometry of the physical model fitted on all epochs with the spectra (upper panels) and residuals (lower panels). The instruments are plotted as follows: EPIC-pn in dark blue, EPIC-MOS1 in green, EPIC-MOS2 in light blue, FPMA in yellow, and FPMB in magenta. The circled numbers (①, ②,..., ⑦) indicate the slices corresponding to a given observation.</figcaption></figure>

decreasing towards the surface of the clump. The scenario of an eclipse is still valid for a spherical cloud. Thus, longer observations and a closer monitoring may be required to better understand the structure of the absorber in this source.

## 5.2 Determining the properties of the BLR clouds

Assuming that the obscuring clouds are located in the BLR, following a Keplerian orbit, we derive below some of the properties of these clouds.

Velocity: Aretxaga et al. (1999) observed NGC 7582 in a type 1 Seyfert galaxy state with broad optical lines on the 1998 July 11. The estimated FWHM of the Hα and Hβ lines is FWHM=12 400 km s⁻¹; over the time-scale of a few months the FWHM decreased to reach 6660 km s⁻¹ at the end of October 1998 (Aretxaga et al. 1999). Ricci et al. (2018) reported a FWHM of 2382 ± 44 km s⁻¹, in an observation of 2004. With a 2014 *Chandra* observation, Braito et al. (2017) estimated the FWHM of the Fe Kα line to be FWHM=1500±800 km s⁻¹, thus *v* = 637 km s⁻¹. Because no measurement of the FWHM of Hα was made close to our observations, it is impossible to predict the state of the source in the optical at the time of our archival observations. We tried to estimate the FWHM of the Fe Kα in our *XMM–Newton* observations but the uncertainties were too

high to draw any conclusions. We use the most recent measurement by Braito et al. (2017) to provide a lower limit on the velocity of the clouds: *v* ≥ 637 km s⁻¹.

Size of the clouds: as we do not observe complete eclipsing events, we can only set lower limits on the size of the clouds. The typical duration of an eclipse is at least twice the exposure time $t_{exp} = 100$ ks. Assuming a spherical cloud of diameter $D_c$ moving at a velocity $v_c$, the duration of an eclipse is $t_{ec} = D_c/v_c$. The diameter of the cloud is then $D_c \ge 2v_c \times t_{exp}$. Using the value of velocity obtained above, $D_c \gtrsim 1.5 R_g (1.2 \times 10^{13} \text{ cm})$.

Location of the BLR: assuming a Keplerian circular orbit for the clumps in the BLR. The radius of the orbit in the BLR is given by $R = \frac{GM}{v^2} = c^2/v^2 R_g$, this gives an upper limit on the location of the clouds in the BLR, $R_{BLR}/R_g \lesssim 22000$, $R_{BLR} \sim 0.6$ pc.

## 5.3 Comparison with previous works

NGC 7582 has been observed by many X-ray observatories. In Fig. 7, we plot the values of the column density, the photon index, and the observed flux obtained from previous studies (in circles) and the ones obtained in this work (in diamonds). The previous works mostly used phenomenological models, thus we show the parameters obtained with our best-fit phenomenological model, for consistency.
<table><caption>**Table 5.** Best fit values of the fully covering clumpy geometry of the physical model. The uncertainties are given with a 68 per cent confidence.</caption><thead><tr><th>Epoch</th><th>N<sub>H</sub><sup>a</sup></th><th>Γ<sup>b</sup></th><th>uxclumpy<br>Norm<sup>c</sup></th><th>Factor<br>× 10<sup>-2</sup></th><th>cstat/dof<sup>d</sup></th></tr></thead><tbody><tr><td>2001-05 ①</td><td>64.10 ± 3.7</td><td>2.39 ± 0.1</td><td>32.97<sup>+9.0</sup><sub>-5.9</sub></td><td>8.79<sup>+0.9</sup><sub>-1.4</sub></td><td>123.05/123</td></tr><tr><td>2001-05 ②</td><td>82.60<sup>+6.0</sup><sub>-5.3</sub></td><td>2.25 ± 0.1</td><td>29.16<sup>+8.0</sup><sub>-4.9</sub></td><td>8.99<sup>+0.8</sup><sub>-1.3</sub></td><td>94.92/98</td></tr><tr><td>2005-04</td><td>126.51<sup>+4.5</sup><sub>-4.6</sub></td><td>2.07 ± 0.1</td><td>19.79<sup>+7.5</sup><sub>-4.5</sub></td><td>6.86<sup>+1.4</sup><sub>-1.3</sub></td><td>252.08/220</td></tr><tr><td>2007-04</td><td>37.76<sup>+10.9</sup><sub>-10.3</sub></td><td>1.88<sup>+0.5</sup><sub>-0.6</sub></td><td>10.82<sup>+22.1</sup><sub>-8.0</sub></td><td>6.44<sup>+2.4</sup><sub>-2.9</sub></td><td>30.11/31</td></tr><tr><td>2012-08</td><td>20.43<sup>+2.6</sup><sub>-2.5</sub></td><td>1.33<sup>+0.04</sup><sub>-0.05</sub></td><td>2.16<sup>+0.4</sup><sub>-0.3</sub></td><td>6.93<sup>+2.3</sup><sub>-3.6</sub></td><td>291.17/228</td></tr><tr><td>2012-09</td><td>34.63<sup>+8.7</sup><sub>-3.4</sub></td><td>1.30<sup>+0.1</sup><sub>-0.07</sub></td><td>1.87<sup>+0.9</sup><sub>-0.3</sub></td><td>7.99<sup>+1.6</sup><sub>-3.5</sub></td><td>250.03/188</td></tr><tr><td>2016-04 ①</td><td>36.54<sup>+1.4</sup><sub>-1.5</sub></td><td>1.70 ± 0.04</td><td>7.11 ± 0.8</td><td>9.45<sup>+0.4</sup><sub>-0.8</sub></td><td>379.67/336</td></tr><tr><td>2016-04 ②</td><td>30.26<sup>+1.6</sup><sub>-1.4</sub></td><td>1.72<sup>+0.03</sup><sub>-0.04</sub></td><td>11.55<sup>+1.2</sup><sub>-1.1</sub></td><td>2.73 ± 1.3</td><td>429.12/399</td></tr><tr><td>2016-04 ③</td><td>27.80<sup>+1.9</sup><sub>-1.5</sub></td><td>1.59<sup>+0.05</sup><sub>-0.03</sub></td><td>5.69<sup>+0.8</sup><sub>-0.6</sub></td><td>8.33<sup>+1.2</sup><sub>-2.4</sub></td><td>384.70/360</td></tr><tr><td>2016-04 ④</td><td>27.79<sup>+0.9</sup><sub>-0.8</sub></td><td>1.62<sup>+0.03</sup><sub>-0.03</sub></td><td>7.17<sup>+0.6</sup><sub>-0.5</sub></td><td>2.04<sup>+1.9</sup><sub>-1.4</sub></td><td>440.63/378</td></tr><tr><td>2016-04 ⑤</td><td>26.74<sup>+0.9</sup><sub>-0.8</sub></td><td>1.65 ± 0.03</td><td>7.26<sup>+0.6</sup><sub>-0.5</sub></td><td>2.05<sup>+2.2</sup><sub>-1.5</sub></td><td>463.93/421</td></tr><tr><td>2016-04 ⑥</td><td>26.22<sup>+1.0</sup><sub>-0.9</sub></td><td>1.75<sup>+0.02</sup><sub>-0.03</sub></td><td>12.28 ± 0.9</td><td>1.97<sup>+2.5</sup><sub>-1.4</sub></td><td>433.36/389</td></tr><tr><td>2016-04 ⑦</td><td>22.07<sup>+1.5</sup><sub>-1.4</sub></td><td>1.66 ± 0.05</td><td>9.29<sup>+1.3</sup><sub>-1.0</sub></td><td>4.13<sup>+3.6</sup><sub>-2.9</sub></td><td>231.85/229</td></tr></tbody></table>

Notes. $^a$Equivalent hydrogen column density modelled with uxclumpy in $10^{22}$ cm$^{-2}$.

$^b$Photon index of the power law.

$^c$Normalization in $10^{-3}$ photon keV$^{-1}$ s$^{-1}$ cm$^{-2}$.

$^d$Total C-statistic/number of degrees of freedom.

<figure><img src="image_7.png" /><figcaption>**Figure 6.** Unabsorbed flux of the power law and reflection components of the phenomenological model in the 3–40 keV band. The fluxes are in units of $10^{-12}$ erg cm$^{-2}$ s$^{-1}$. The solid lines in each of the panels represent the weighted mean in the given panel and the shaded areas represent the 1σ, 2σ, and 3σ levels (shades of green in the full panel and red to yellow in the zoomed panel).</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Figure 7.** Historical values of the photon index $\Gamma$, the column density $N_H$, and the observed flux in the 2–10 keV band for NGC 7582. The values from the literature (available in Table A3) are in coloured circles, whereas the values obtained with the phenomenological model in this work are in coloured diamonds.</figcaption></figure>

The long-term variability is visible since early observations. As seen in this figure, BeppoSAX observed NGC 7582 in an unobscured state, as opposed to the very absorbed state of 2005 seen by XMM–Newton. We provide a non-exhaustive list of values from the literature in Table A3, where we did not include results from the five observations with the Einstein observatory as it was not possible to get access to all the fitted parameters. Below, we present a comparison between the values reported in the literature to the ones obtained in this work.

Observation 2001: for this observation, the values of the photon index obtained in this work are consistent with the values obtained by Dewangan & Griffiths (2005) and Piconcelli et al. (2007). The value of $N_H$ obtained in the two works are in the same order of magnitude as the value found in slice ①. It is worth noting that Piconcelli et al.

<table><caption>**Table 6.** Values of the natural logarithm of the evidence Z and of the Bayes factor K for the best three geometries and the phenomenological model. The geometries are visualizations of the absorber as seen by the X-ray source. Extracted from the uxclumpy webpage, courtesy of Johannes Buchner.</caption><thead><tr><th>Model</th><th>Evidence ln Z</th><th>Bayes factor ln K</th></tr></thead><tbody><tr><td>(84,0)</td><td>-2106</td><td>-</td></tr><tr><td>(84,0.2)</td><td>-2111</td><td>5</td></tr><tr><td>(84,0.3)</td><td>-2129</td><td>23</td></tr><tr><td>xillver</td><td>-2187</td><td>81</td></tr></tbody></table>
<table><caption>**Table 5.** Best fit values of the fully covering clumpy geometry of the physical model. The uncertainties are given with a 68 per cent confidence.</caption><thead><tr><th>Epoch</th><th>N<sub>H</sub><sup>a</sup></th><th>Γ<sup>b</sup></th><th>uxclumpy Norm<sup>c</sup></th><th>Factor × 10<sup>-2</sup></th><th>cstat/dof<sup>d</sup></th></tr></thead><tbody><tr><td>2001-05 ①</td><td>64.10 ± 3.7</td><td>2.39 ± 0.1</td><td>32.97<sup>+9.0</sup><sub>-5.9</sub></td><td>8.79<sup>+0.9</sup><sub>-1.4</sub></td><td>123.05/123</td></tr><tr><td>2001-05 ②</td><td>82.60<sup>+6.0</sup><sub>-5.3</sub></td><td>2.25 ± 0.1</td><td>29.16<sup>+8.0</sup><sub>-4.9</sub></td><td>8.99<sup>+0.8</sup><sub>-1.3</sub></td><td>94.92/98</td></tr><tr><td>2005-04</td><td>126.51<sup>+4.5</sup><sub>-4.6</sub></td><td>2.07 ± 0.1</td><td>19.79<sup>+7.5</sup><sub>-4.5</sub></td><td>6.86<sup>+1.4</sup><sub>-1.3</sub></td><td>252.08/220</td></tr><tr><td>2007-04</td><td>37.76<sup>+10.9</sup><sub>-10.3</sub></td><td>1.88<sup>+0.5</sup><sub>-0.6</sub></td><td>10.82<sup>+22.1</sup><sub>-8.0</sub></td><td>6.44<sup>+2.4</sup><sub>-2.9</sub></td><td>30.11/31</td></tr><tr><td>2012-08</td><td>20.43<sup>+2.6</sup><sub>-2.5</sub></td><td>1.33<sup>+0.04</sup><sub>-0.05</sub></td><td>2.16<sup>+0.4</sup><sub>-0.3</sub></td><td>6.93<sup>+2.3</sup><sub>-3.6</sub></td><td>291.17/228</td></tr><tr><td>2012-09</td><td>34.63<sup>+8.7</sup><sub>-3.4</sub></td><td>1.30<sup>+0.1</sup><sub>-0.07</sub></td><td>1.87<sup>+0.9</sup><sub>-0.3</sub></td><td>7.99<sup>+1.6</sup><sub>-3.5</sub></td><td>250.03/188</td></tr><tr><td>2016-04 ①</td><td>36.54<sup>+1.4</sup><sub>-1.5</sub></td><td>1.70 ± 0.04</td><td>7.11 ± 0.8</td><td>9.45<sup>+0.4</sup><sub>-0.8</sub></td><td>379.67/336</td></tr><tr><td>2016-04 ②</td><td>30.26<sup>+1.6</sup><sub>-1.4</sub></td><td>1.72<sup>+0.03</sup><sub>-0.04</sub></td><td>11.55<sup>+1.2</sup><sub>-1.1</sub></td><td>2.73 ± 1.3</td><td>429.12/399</td></tr><tr><td>2016-04 ③</td><td>27.80<sup>+1.9</sup><sub>-1.5</sub></td><td>1.59<sup>+0.05</sup><sub>-0.03</sub></td><td>5.69<sup>+0.8</sup><sub>-0.6</sub></td><td>8.33<sup>+1.2</sup><sub>-2.4</sub></td><td>384.70/360</td></tr><tr><td>2016-04 ④</td><td>27.79<sup>+0.9</sup><sub>-0.8</sub></td><td>1.62<sup>+0.03</sup><sub>-0.03</sub></td><td>7.17<sup>+0.6</sup><sub>-0.5</sub></td><td>2.04<sup>+1.9</sup><sub>-1.4</sub></td><td>440.63/378</td></tr><tr><td>2016-04 ⑤</td><td>26.74<sup>+0.9</sup><sub>-0.8</sub></td><td>1.65 ± 0.03</td><td>7.26<sup>+0.6</sup><sub>-0.5</sub></td><td>2.05<sup>+2.2</sup><sub>-1.5</sub></td><td>463.93/421</td></tr><tr><td>2016-04 ⑥</td><td>26.22<sup>+1.0</sup><sub>-0.9</sub></td><td>1.75<sup>+0.02</sup><sub>-0.03</sub></td><td>12.28 ± 0.9</td><td>1.97<sup>+2.5</sup><sub>-1.4</sub></td><td>433.36/389</td></tr><tr><td>2016-04 ⑦</td><td>22.07<sup>+1.5</sup><sub>-1.4</sub></td><td>1.66 ± 0.05</td><td>9.29<sup>+1.3</sup><sub>-1.0</sub></td><td>4.13<sup>+3.6</sup><sub>-2.9</sub></td><td>231.85/229</td></tr></tbody></table>

Notes. $^a$Equivalent hydrogen column density modelled with uxclumpy in $10^{22}$ cm$^{-2}$.

$^b$Photon index of the power law.

$^c$Normalization in $10^{-3}$ photon keV$^{-1}$ s$^{-1}$ cm$^{-2}$.

$^d$Total C-statistic/number of degrees of freedom.

<figure><img src="image_7.png" /><figcaption>**Figure 6.** Unabsorbed flux of the power law and reflection components of the phenomenological model in the 3–40 keV band. The fluxes are in units of $10^{-12}$ erg cm$^{-2}$ s$^{-1}$. The solid lines in each of the panels represent the weighted mean in the given panel and the shaded areas represent the 1σ, 2σ, and 3σ levels (shades of green in the full panel and red to yellow in the zoomed panel).</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Figure 7.** Historical values of the photon index $\Gamma$, the column density $N_H$, and the observed flux in the 2–10 keV band for NGC 7582. The values from the literature (available in Table A3) are in coloured circles, whereas the values obtained with the phenomenological model in this work are in coloured diamonds.</figcaption></figure>

The long-term variability is visible since early observations. As seen in this figure, BeppoSAX observed NGC 7582 in an unobscured state, as opposed to the very absorbed state of 2005 seen by XMM–Newton. We provide a non-exhaustive list of values from the literature in Table A3, where we did not include results from the five observations with the Einstein observatory as it was not possible to get access to all the fitted parameters. Below, we present a comparison between the values reported in the literature to the ones obtained in this work.

Observation 2001: for this observation, the values of the photon index obtained in this work are consistent with the values obtained by Dewangan & Griffiths (2005) and Piconcelli et al. (2007). The value of $N_H$ obtained in the two works are in the same order of magnitude as the value found in slice ①. It is worth noting that Piconcelli et al.

<table><caption>**Table 6.** Values of the natural logarithm of the evidence Z and of the Bayes factor K for the best three geometries and the phenomenological model. The geometries are visualizations of the absorber as seen by the X-ray source. Extracted from the uxclumpy webpage, courtesy of Johannes Buchner.</caption><thead><tr><th>Model</th><th>Evidence ln Z</th><th>Bayes factor ln K</th></tr></thead><tbody><tr><td>(84,0)</td><td>-2106</td><td>-</td></tr><tr><td>(84,0.2)</td><td>-2111</td><td>5</td></tr><tr><td>(84,0.3)</td><td>-2129</td><td>23</td></tr><tr><td>xillver</td><td>-2187</td><td>81</td></tr></tbody></table>
<table><caption>**Table 7.** Best fit values of the parameters of the linear function fitted onto the evolution of the column density. Errors are given with a 68 per cent confidence level.</caption><thead><tr><th>Observation date</th><th>Slope<br>(10<sup>22</sup> cm<sup>-2</sup> ks<sup>-1</sup>)</th><th>Offset<br>(10<sup>22</sup> cm<sup>-2</sup>)</th></tr></thead><tbody><tr><td>2001 May 25</td><td>1.80<sup>+0.96</sup><sub>-0.96</sub></td><td>54.99<sup>+9.00</sup><sub>-8.91</sub></td></tr><tr><td>2016 Apr 28</td><td>-0.12<sup>+0.02</sup><sub>-0.02</sub></td><td>34.58<sup>+1.50</sup><sub>-1.51</sub></td></tr></tbody></table>

(2007) used a two-absorber model. Thus, we compare only with the highest column density, as the fitting range we adopt ($E \ge 3$ keV) is not sensitive to the low column density absorber.

Observation 2005: in this observation, the column density and photon index obtained by Piconcelli et al. (2007) are also consistent with the ones obtained in this work. Laha et al. (2020) fitted a double-absorber model on this observation and the total column density as well as the photon index are consistent with our work.

Observation 2007: Bianchi et al. (2009) fitted simultaneously the Suzaku observations with the XMM-Newton observation of 2007. Given the poor quality of our data, the values are poorly constrained and de facto consistent with values from the literature (e.g. Laha et al. 2020).

Observation 2012: For the NuSTAR observations of 2012, the values of $N_H$ are consistent with the findings of Rivers et al. (2015). However, the values of $\Gamma$ are smaller than the ones found previously (1.33 against 1.78). It is worth mentioning that they fitted simultaneously the first observation with a Swift observation and tied several parameters between the two observations of 2012.

Observation 2016: Tanimoto et al. (2022) applied a physical clumpy model (XCLUMPY; Tanimoto et al. 2019) to the time-averaged spectrum of the observation of 2016. Baloković et al. (2018) applied a torus model to the NuSTAR observation only. The values of $\Gamma$ and $N_H$ we obtain on average are consistent with the ones obtained by both Tanimoto et al. (2022) and Baloković et al. (2018). These works found a covering factor of 80–90 per cent, which

<figure><img src="image_9.png" /><figcaption>**Figure 8.** Evolution of the column density of the clumpy absorber (triangles) as a function of time in the observations of 2001, 2005, 2012, and 2016 (bottom panel). The solid line is a linear fit and the shaded area represents the $2\sigma$ level. The Compton-thick column density is delimited by a purple dotted line. The light curves of XMM-Newton EPIC instruments and the NuSTAR FPM instruments in the 3–10 keV band are plotted in the upper-panel, see Fig. 1 for more details.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Figure 9.** Simulations of spectra with microcalimeter detectors assuming the best-fit *uxclumpy* model. On the left, simulations of the first two slices of 2016, using *Athena/X-IFU* with an exposure time of 5 ks. The simulated spectrum of the first slice is in light blue and the second slice is in dark blue. On the right, simulations of the observation of 2005, using *Athena/X-IFU* (in cyan) *XRISM/Resolve* (in green) with an exposure time of 90 ks. The spectra are shown in the 6–8 keV range. The inset shows a zoom in the 6.1–6.5 keV range, where the Fe Kα and the Compton shoulder are resolved.</figcaption></figure>
<table><caption>**Table 7.** Best fit values of the parameters of the linear function fitted onto the evolution of the column density. Errors are given with a 68 per cent confidence level.</caption><thead><tr><th>Observation date</th><th>Slope<br>(10<sup>22</sup> cm<sup>-2</sup> ks<sup>-1</sup>)</th><th>Offset<br>(10<sup>22</sup> cm<sup>-2</sup>)</th></tr></thead><tbody><tr><td>2001 May 25</td><td>1.80<sup>+0.96</sup><sub>-0.96</sub></td><td>54.99<sup>+9.00</sup><sub>-8.91</sub></td></tr><tr><td>2016 Apr 28</td><td>-0.12<sup>+0.02</sup><sub>-0.02</sub></td><td>34.58<sup>+1.50</sup><sub>-1.51</sub></td></tr></tbody></table>

(2007) used a two-absorber model. Thus, we compare only with the highest column density, as the fitting range we adopt ($E \ge 3$ keV) is not sensitive to the low column density absorber.

Observation 2005: in this observation, the column density and photon index obtained by Piconcelli et al. (2007) are also consistent with the ones obtained in this work. Laha et al. (2020) fitted a double-absorber model on this observation and the total column density as well as the photon index are consistent with our work.

Observation 2007: Bianchi et al. (2009) fitted simultaneously the Suzaku observations with the XMM-Newton observation of 2007. Given the poor quality of our data, the values are poorly constrained and de facto consistent with values from the literature (e.g. Laha et al. 2020).

Observation 2012: For the NuSTAR observations of 2012, the values of $N_H$ are consistent with the findings of Rivers et al. (2015). However, the values of $\Gamma$ are smaller than the ones found previously (1.33 against 1.78). It is worth mentioning that they fitted simultaneously the first observation with a Swift observation and tied several parameters between the two observations of 2012.

Observation 2016: Tanimoto et al. (2022) applied a physical clumpy model (XCLUMPY; Tanimoto et al. 2019) to the time-averaged spectrum of the observation of 2016. Baloković et al. (2018) applied a torus model to the NuSTAR observation only. The values of $\Gamma$ and $N_H$ we obtain on average are consistent with the ones obtained by both Tanimoto et al. (2022) and Baloković et al. (2018). These works found a covering factor of 80–90 per cent, which

<figure><img src="image_9.png" /><figcaption>**Figure 8.** Evolution of the column density of the clumpy absorber (triangles) as a function of time in the observations of 2001, 2005, 2012, and 2016 (bottom panel). The solid line is a linear fit and the shaded area represents the $2\sigma$ level. The Compton-thick column density is delimited by a purple dotted line. The light curves of XMM-Newton EPIC instruments and the NuSTAR FPM instruments in the 3–10 keV band are plotted in the upper-panel, see Fig. 1 for more details.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Figure 9.** Simulations of spectra with microcalimeter detectors assuming the best-fit *uxclumpy* model. On the left, simulations of the first two slices of 2016, using *Athena/X-IFU* with an exposure time of 5 ks. The simulated spectrum of the first slice is in light blue and the second slice is in dark blue. On the right, simulations of the observation of 2005, using *Athena/X-IFU* (in cyan) *XRISM/Resolve* (in green) with an exposure time of 90 ks. The spectra are shown in the 6–8 keV range. The inset shows a zoom in the 6.1–6.5 keV range, where the Fe Kα and the Compton shoulder are resolved.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>**Figure 10.** Simulated HEX-P/HET spectra of the first two slices of 2016 with an exposure time of 5 ks assuming the best-fit *uxclumpy* model.</figcaption></figure>

is roughly consistent with our full covering geometry. It is worth noting that these papers did not study the short-term variability seen in this observation.

## 5.4 Prospects with future X-ray missions

Future X-ray missions will bring the opportunity to improve the current work and better constrain the physical parameters. We simulate data for several instruments assuming the best-fit fully covering model with *uxclumpy* and we rebin all spectra with at least 25 counts per bin. In Fig. 9(a), we show two simulated *Athena/X-IFU* (Barret et al. 2023) spectra for the observation of 2016 with an exposure time of 5 ks each. Thanks to the large effective area and the high resolution of *Athena/X-IFU*,<fnref n="5" /> it will be possible to probe the spectral variability on shorter time-scales with better constraints. In Fig. 9(b), we show simulated spectra for the observation of 2005 with an exposure time of 90 ks with *Athena/X-IFU* and *XRISM/Resolve*<fnref n="6" /> (Tashiro et al. 2020). The inset of Figs 9(a) and (b) show a view in the 6.1 – 6.5 keV range. The Fe Kα doublet at 6.404 and 6.391 keV cannot be resolved, nevertheless the Compton shoulder can be observed with the 90-ks simulations. *Athena* and *XRISM* will enable high-resolution spectroscopy of the low-luminosity state of the AGN as observed in the observation of 2005. Finally, with the High-Energy Telescope (HET) of the concept mission HEX-P<fnref n="7" /> (Madsen et al. 2018), observations above 10 keV could constrain both the photon index and the high-energy cutoff. In Fig. 10, we show two simulated HET spectra for the observation of 2016 with an exposure time of 5 ks each. Thus, each of these three instruments will enable a better understanding of both the accretion in AGN but also the geometry of the absorbing material surrounding the X-ray source.

## 6 CONCLUSIONS

To model the spectra we have used two different models, a physically motivated model accounting for the geometry of the absorber and a phenomenological model. The main results can be summarized as follows:

(i) The absorption is best described by a fully covering clumpy absorber. This geometry is statistically favoured using Bayes factors.

(ii) Long-term and short-term variability are due to intrinsic changes in the X-ray luminosity of the source, and changes in the absorption in the line of sight. The latter can explain the changing-look classification of this source, more specifically changing-obscuration, as the source switches between Compton-thick and Compton-thin due to changes in the obscuring column along the line of sight, respectively.

(iii) The absorber is located at a distance not larger than 0.6 pc.

(iv) Assuming a single cloud in the line of sight, we estimate the size of the cloud to be larger than $10^{13}$ cm, for a velocity of ~700 km s⁻¹.

(v) Given the variety of behaviour of the absorption at different time-scales, and the fact that the observations are not long enough to constrain a full eclipsing event, we cannot make strong arguments on the shape of the clouds. However, our results strongly suggest the presence of a variety of cloud densities, or even a gradient in the density within a single cloud (as seen in 2016), favouring comet-shaped clouds or at least a non-uniform cloud.

## ACKNOWLEDGEMENTS

We thank the anonymous referee for their comments and suggestions. ML acknowledges useful discussions with Johannes Buchner on the *UXCLUMPY* model. DB/ESK/ML acknowledge financial support from the Centre National d'Etudes Spatiales (CNES). ML acknowledges financial support through the UK Science and Technology Facilities Council (STFC). AZ is supported by NASA under award number 80GSFC21M0002.

This research has made use of data and/or software provided by the 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 made use of Astropy, a community-developed core PYTHON package for Astronomy (Astropy Collaboration et al. 2013, 2018), NUMPY (Harris et al. 2020), and MATPLOTLIB, a PYTHON library for publication quality graphics (Hunter 2007). This work has made use of GetDist (Lewis 2019), a PYTHON library for analysing Monte Carlo samples. This research made use of XSPEC (Arnaud 1996). We have made use of data from the NuSTAR mission, a project led by the California Institute of Technology, managed by the Jet Propulsion Laboratory, and funded by the National Aeronautics and Space Administration. NuSTAR data was reduced with the NuSTAR Data Analysis Software (NuSTARDAS) jointly developed by the ASI Science Data Center (ASDC, Italy) and the California Institute of Technology (USA). We have also made use of data based on observations obtained with XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA.

## DATA AVAILABILITY

The data used in this paper are publicly available to access and download from the High Energy Astrophysics Science Archive Research Center (HEASARC) for NuSTAR and from the XMM-Newton Science Archive. Final data products from this study can be provided on reasonable request to the corresponding author.

## REFERENCES

Antonucci R., 1993, ARA&A, 31, 473

Antonucci R. R. J., Miller J. S., 1985, ApJ, 297, L621

Aretxaga I., Joguet B., Kunth D., Melnick J., Terlevich R. J., 1999, ApJ, 519, L123

<footnote n="5">⁵http://x-ifu.irap.omp.eu/</footnote>

<footnote n="6">⁶https://heasarc.gsfc.nasa.gov/docs/xrism/</footnote>

<footnote n="7">⁷https://hexp.org</footnote>
<figure><img src="image_11.png" /><figcaption>**Figure 10.** Simulated HEX-P/HET spectra of the first two slices of 2016 with an exposure time of 5 ks assuming the best-fit *uxclumpy* model.</figcaption></figure>

is roughly consistent with our full covering geometry. It is worth noting that these papers did not study the short-term variability seen in this observation.

## 5.4 Prospects with future X-ray missions

Future X-ray missions will bring the opportunity to improve the current work and better constrain the physical parameters. We simulate data for several instruments assuming the best-fit fully covering model with *uxclumpy* and we rebin all spectra with at least 25 counts per bin. In Fig. 9(a), we show two simulated *Athena/X-IFU* (Barret et al. 2023) spectra for the observation of 2016 with an exposure time of 5 ks each. Thanks to the large effective area and the high resolution of *Athena/X-IFU*,<fnref n="5" /> it will be possible to probe the spectral variability on shorter time-scales with better constraints. In Fig. 9(b), we show simulated spectra for the observation of 2005 with an exposure time of 90 ks with *Athena/X-IFU* and *XRISM/Resolve*<fnref n="6" /> (Tashiro et al. 2020). The inset of Figs 9(a) and (b) show a view in the 6.1–6.5 keV range. The Fe Kα doublet at 6.404 and 6.391 keV cannot be resolved, nevertheless the Compton shoulder can be observed with the 90-ks simulations. *Athena* and *XRISM* will enable high-resolution spectroscopy of the low-luminosity state of the AGN as observed in the observation of 2005. Finally, with the High-Energy Telescope (HET) of the concept mission HEX-P<fnref n="7" /> (Madsen et al. 2018), observations above 10 keV could constrain both the photon index and the high-energy cutoff. In Fig. 10, we show two simulated HET spectra for the observation of 2016 with an exposure time of 5 ks each. Thus, each of these three instruments will enable a better understanding of both the accretion in AGN but also the geometry of the absorbing material surrounding the X-ray source.

## 6 CONCLUSIONS

To model the spectra we have used two different models, a physically motivated model accounting for the geometry of the absorber and a phenomenological model. The main results can be summarized as follows:

(i) The absorption is best described by a fully covering clumpy absorber. This geometry is statistically favoured using Bayes factors.

(ii) Long-term and short-term variability are due to intrinsic changes in the X-ray luminosity of the source, and changes in the absorption in the line of sight. The latter can explain the changing-look classification of this source, more specifically changing-obscuration, as the source switches between Compton-thick and Compton-thin due to changes in the obscuring column along the line of sight, respectively.

(iii) The absorber is located at a distance not larger than 0.6 pc.

(iv) Assuming a single cloud in the line of sight, we estimate the size of the cloud to be larger than 10¹³ cm, for a velocity of ~700 km s⁻¹.

(v) Given the variety of behaviour of the absorption at different time-scales, and the fact that the observations are not long enough to constrain a full eclipsing event, we cannot make strong arguments on the shape of the clouds. However, our results strongly suggest the presence of a variety of cloud densities, or even a gradient in the density within a single cloud (as seen in 2016), favouring comet-shaped clouds or at least a non-uniform cloud.

## ACKNOWLEDGEMENTS

We thank the anonymous referee for their comments and suggestions. ML acknowledges useful discussions with Johannes Buchner on the *UXCLUMPY* model. DB/ESK/ML acknowledge financial support from the Centre National d'Etudes Spatiales (CNES). ML acknowledges financial support through the UK Science and Technology Facilities Council (STFC). AZ is supported by NASA under award number 80GSFC21M0002.

This research has made use of data and/or software provided by the 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 made use of Astropy, a community-developed core PYTHON package for Astronomy (Astropy Collaboration et al. 2013, 2018), NUMPY (Harris et al. 2020), and MATPLOTLIB, a PYTHON library for publication quality graphics (Hunter 2007). This work has made use of GetDist (Lewis 2019), a PYTHON library for analysing Monte Carlo samples. This research made use of XSPEC (Arnaud 1996). We have made use of data from the NuSTAR mission, a project led by the California Institute of Technology, managed by the Jet Propulsion Laboratory, and funded by the National Aeronautics and Space Administration. NuSTAR data was reduced with the NuSTAR Data Analysis Software (NuSTARDAS) jointly developed by the ASI Science Data Center (ASDC, Italy) and the California Institute of Technology (USA). We have also made use of data based on observations obtained with XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA.

## DATA AVAILABILITY

The data used in this paper are publicly available to access and download from the High Energy Astrophysics Science Archive Research Center (HEASARC) for NuSTAR and from the XMM-Newton Science Archive. Final data products from this study can be provided on reasonable request to the corresponding author.

## REFERENCES

Antonucci R., 1993, ARA&A, 31, 473

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Aretxaga I., Joguet B., Kunth D., Melnick J., Terlevich R. J., 1999, ApJ, 519, L123

<footnote n="5">⁵http://x-ifu.irap.omp.eu/</footnote>

<footnote n="6">⁶https://heasarc.gsfc.nasa.gov/docs/xrism/</footnote>

<footnote n="7">⁷https://hexp.org</footnote>
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## APPENDIX A: TABLES AND FIGURES

<table><caption>**Table A1.** Calibration factors across all epochs for all instruments. The uncertainties are given with a 68 per cent confidence.</caption><thead><tr><th rowspan="2">Epoch</th><th rowspan="2">EPN</th><th colspan="4">Instruments</th></tr><tr><th>EMOS1</th><th>EMOS2</th><th>FPMA</th><th>FPMB</th></tr></thead><tbody><tr><td>2001-05 ①</td><td>1</td><td>1.08<sup>+0.04</sup><sub>-0.05</sub></td><td>1.08<sup>+0.05</sup><sub>-0.04</sub></td><td>—</td><td>—</td></tr><tr><td>2001-05 ②</td><td>1</td><td>1.08<sup>+0.05</sup><sub>-0.05</sub></td><td>1.02<sup>+0.05</sup><sub>-0.05</sub></td><td>—</td><td>—</td></tr><tr><td>2005-04</td><td>1</td><td>1.04<sup>+0.02</sup><sub>-0.02</sub></td><td>1.08<sup>+0.02</sup><sub>-0.02</sub></td><td>—</td><td>—</td></tr><tr><td>2007-04</td><td>1</td><td>1.19<sup>+0.09</sup><sub>-0.09</sub></td><td>1.25<sup>+0.06</sup><sub>-0.08</sub></td><td>—</td><td>—</td></tr><tr><td>2012-08</td><td>—</td><td>—</td><td>—</td><td>1</td><td>0.98<sup>+0.02</sup><sub>-0.02</sub></td></tr><tr><td>2012-09</td><td>—</td><td>—</td><td>—</td><td>1</td><td>1.00<sup>+0.03</sup><sub>-0.03</sub></td></tr><tr><td>2016-04 ①</td><td>1</td><td>1.04<sup>+0.03</sup><sub>-0.03</sub></td><td>1.10<sup>+0.03</sup><sub>-0.03</sub></td><td>1.31<sup>+0.03</sup><sub>-0.03</sub></td><td>1.28<sup>+0.03</sup><sub>-0.04</sub></td></tr><tr><td>2016-04 ②</td><td>1</td><td>1.09<sup>+0.03</sup><sub>-0.03</sub></td><td>1.06<sup>+0.03</sup><sub>-0.02</sub></td><td>1.26<sup>+0.03</sup><sub>-0.03</sub></td><td>1.20<sup>+0.03</sup><sub>-0.03</sub></td></tr><tr><td>2016-04 ③</td><td>1</td><td>1.02<sup>+0.03</sup><sub>-0.03</sub></td><td>1.09<sup>+0.04</sup><sub>-0.03</sub></td><td>1.27<sup>+0.04</sup><sub>-0.04</sub></td><td>1.27<sup>+0.04</sup><sub>-0.04</sub></td></tr><tr><td>2016-04 ④</td><td>1</td><td>1.04<sup>+0.03</sup><sub>-0.03</sub></td><td>1.11<sup>+0.03</sup><sub>-0.03</sub></td><td>1.26<sup>+0.04</sup><sub>-0.04</sub></td><td>1.28<sup>+0.04</sup><sub>-0.04</sub></td></tr><tr><td>2016-04 ⑤</td><td>1</td><td>1.08<sup>+0.03</sup><sub>-0.03</sub></td><td>1.13<sup>+0.03</sup><sub>-0.03</sub></td><td>1.29<sup>+0.03</sup><sub>-0.03</sub></td><td>1.34<sup>+0.01</sup><sub>-0.02</sub></td></tr><tr><td>2016-04 ⑥</td><td>—</td><td>1</td><td>1.06<sup>+0.03</sup><sub>-0.03</sub></td><td>1.24<sup>+0.04</sup><sub>-0.03</sub></td><td>1.25<sup>+0.04</sup><sub>-0.04</sub></td></tr><tr><td>2016-04 ⑦</td><td>—</td><td>1</td><td>—</td><td>1.25<sup>+0.05</sup><sub>-0.05</sub></td><td>1.25<sup>+0.05</sup><sub>-0.04</sub></td></tr></tbody></table>
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Haardt F., Maraschi L., 1993, ApJ, 413, L507

Harris C. R., et al., 2020, Nature, 585, 357

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Piconcelli E., Bianchi S., Guainazzi M., Fiore F., Chiaberge M., 2007, A&A, 466, 855

Ricci C., Trakhtenbrot B., 2022, preprint (arXiv:2211.05132)

Ricci T. V., Steiner J. E., May D., Garcia-Rissmann A., Menezes R. B., 2018, MNRAS, 473, 5334

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Risaliti G., Nardini E., Salvati M., Elvis M., Fabbiano G., Maiolino R., Pietrini P., Torricelli-Ciamponi G., 2011, MNRAS, 410, 1027

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Xue S.-J., Otani C., Mihara T., Cappi M., Matsuoka M., 1998, PASJ, 50, 519

## APPENDIX A: TABLES AND FIGURES

<table><caption>**Table A1.** Calibration factors across all epochs for all instruments. The uncertainties are given with a 68 per cent confidence.</caption><thead><tr><th rowspan="2">Epoch</th><th rowspan="2">EPN</th><th colspan="4">Instruments</th></tr><tr><th>EMOS1</th><th>EMOS2</th><th>FPMA</th><th>FPMB</th></tr></thead><tbody><tr><td>2001-05 ①</td><td>1</td><td>1.08<sup>+0.04</sup><sub>-0.05</sub></td><td>1.08<sup>+0.05</sup><sub>-0.04</sub></td><td>—</td><td>—</td></tr><tr><td>2001-05 ②</td><td>1</td><td>1.08<sup>+0.05</sup><sub>-0.05</sub></td><td>1.02<sup>+0.05</sup><sub>-0.05</sub></td><td>—</td><td>—</td></tr><tr><td>2005-04</td><td>1</td><td>1.04<sup>+0.02</sup><sub>-0.02</sub></td><td>1.08<sup>+0.02</sup><sub>-0.02</sub></td><td>—</td><td>—</td></tr><tr><td>2007-04</td><td>1</td><td>1.19<sup>+0.09</sup><sub>-0.09</sub></td><td>1.25<sup>+0.06</sup><sub>-0.08</sub></td><td>—</td><td>—</td></tr><tr><td>2012-08</td><td>—</td><td>—</td><td>—</td><td>1</td><td>0.98<sup>+0.02</sup><sub>-0.02</sub></td></tr><tr><td>2012-09</td><td>—</td><td>—</td><td>—</td><td>1</td><td>1.00<sup>+0.03</sup><sub>-0.03</sub></td></tr><tr><td>2016-04 ①</td><td>1</td><td>1.04<sup>+0.03</sup><sub>-0.03</sub></td><td>1.10<sup>+0.03</sup><sub>-0.03</sub></td><td>1.31<sup>+0.03</sup><sub>-0.03</sub></td><td>1.28<sup>+0.03</sup><sub>-0.04</sub></td></tr><tr><td>2016-04 ②</td><td>1</td><td>1.09<sup>+0.03</sup><sub>-0.03</sub></td><td>1.06<sup>+0.03</sup><sub>-0.02</sub></td><td>1.26<sup>+0.03</sup><sub>-0.03</sub></td><td>1.20<sup>+0.03</sup><sub>-0.03</sub></td></tr><tr><td>2016-04 ③</td><td>1</td><td>1.02<sup>+0.03</sup><sub>-0.03</sub></td><td>1.09<sup>+0.04</sup><sub>-0.03</sub></td><td>1.27<sup>+0.04</sup><sub>-0.04</sub></td><td>1.27<sup>+0.04</sup><sub>-0.04</sub></td></tr><tr><td>2016-04 ④</td><td>1</td><td>1.04<sup>+0.03</sup><sub>-0.03</sub></td><td>1.11<sup>+0.03</sup><sub>-0.03</sub></td><td>1.26<sup>+0.04</sup><sub>-0.04</sub></td><td>1.28<sup>+0.04</sup><sub>-0.04</sub></td></tr><tr><td>2016-04 ⑤</td><td>1</td><td>1.08<sup>+0.03</sup><sub>-0.03</sub></td><td>1.13<sup>+0.03</sup><sub>-0.03</sub></td><td>1.29<sup>+0.03</sup><sub>-0.03</sub></td><td>1.34<sup>+0.01</sup><sub>-0.02</sub></td></tr><tr><td>2016-04 ⑥</td><td>—</td><td>1</td><td>1.06<sup>+0.03</sup><sub>-0.03</sub></td><td>1.24<sup>+0.04</sup><sub>-0.03</sub></td><td>1.25<sup>+0.04</sup><sub>-0.04</sub></td></tr><tr><td>2016-04 ⑦</td><td>—</td><td>1</td><td>—</td><td>1.25<sup>+0.05</sup><sub>-0.05</sub></td><td>1.25<sup>+0.05</sup><sub>-0.04</sub></td></tr></tbody></table>
<figure><img src="image_12.png" /><figcaption>**Figure A1.** Contours of the samples of the posterior distributions of the parameters of the phenomenological model. For all epochs (left) and all slices of the observation of 2016 (right).</figcaption></figure>

<table><caption>**Table A2.** Values of lnZ for 11 geometries of the physical model and the phenomenological model over all epochs. The gradient of colour shows for each row maximal values (dark blue) to minimal (yellow). The last row gives the total lnZ for all epochs. The geometries are visualizations of the absorber as seen by the X-ray source. Extracted from the uxclumpy webpage, courtesy of Johannes Buchner.</caption><thead><tr><th rowspan="2">Epoch</th><th rowspan="2">xillver</th><th colspan="11">Geometries uxclumpy (TORsigma, CTKcover)</th></tr><tr><th>(7.0)</th><th>(7.0.3)</th><th>(7.0.5)</th><th>(28.0)</th><th>(28.0.2)</th><th>(28.0.3)</th><th>(28.0.5)</th><th>(84.0)</th><th>(84.0.2)</th><th>(84.0.3)</th><th>(84.0.5)</th></tr></thead><tbody><tr><td>2001 ①</td><td>-77</td><td>-97</td><td>-113</td><td>-108</td><td>-83</td><td>-88</td><td>-93</td><td>-106</td><td>-76</td><td>-80</td><td>-85</td><td>-99</td></tr><tr><td>2001 ②</td><td>-68</td><td>-74</td><td>-80</td><td>-79</td><td>-62</td><td>-65</td><td>-68</td><td>-78</td><td>-62</td><td>-64</td><td>-67</td><td>-73</td></tr><tr><td>2005</td><td>-149</td><td>-177</td><td>-196</td><td>-204</td><td>-159</td><td>-171</td><td>-176</td><td>-201</td><td>-142</td><td>-145</td><td>-149</td><td>-161</td></tr><tr><td>2007</td><td>-30</td><td>-27</td><td>-27</td><td>-27</td><td>-26</td><td>-26</td><td>-26</td><td>-27</td><td>-26</td><td>-26</td><td>-27</td><td>-27</td></tr><tr><td>2012-a</td><td>-156</td><td>-172</td><td>-174</td><td>-180</td><td>-167</td><td>-167</td><td>-170</td><td>-175</td><td>-161</td><td>-159</td><td>-160</td><td>-163</td></tr><tr><td>2012-b</td><td>-137</td><td>-143</td><td>-142</td><td>-140</td><td>-132</td><td>-134</td><td>-136</td><td>-148</td><td>-140</td><td>-139</td><td>-139</td><td>-143</td></tr><tr><td>2016 ①</td><td>-220</td><td>-230</td><td>-243</td><td>-235</td><td>-210</td><td>-212</td><td>-216</td><td>-227</td><td>-208</td><td>-212</td><td>-219</td><td>-235</td></tr><tr><td>2016 ②</td><td>-238</td><td>-233</td><td>-238</td><td>-234</td><td>-226</td><td>-224</td><td>-225</td><td>-228</td><td>-231</td><td>-230</td><td>-228</td><td>-225</td></tr><tr><td>2016 ③</td><td>-219</td><td>-237</td><td>-243</td><td>-237</td><td>-215</td><td>-216</td><td>-220</td><td>-229</td><td>-209</td><td>-209</td><td>-211</td><td>-218</td></tr><tr><td>2016 ④</td><td>-246</td><td>-243</td><td>-244</td><td>-243</td><td>-236</td><td>-235</td><td>-236</td><td>-239</td><td>-237</td><td>-237</td><td>-236</td><td>-235</td></tr><tr><td>2016 ⑤</td><td>-265</td><td>-271</td><td>-274</td><td>-270</td><td>-254</td><td>-253</td><td>-255</td><td>-262</td><td>-248</td><td>-247</td><td>-247</td><td>-249</td></tr><tr><td>2016 ⑥</td><td>-244</td><td>-245</td><td>-247</td><td>-245</td><td>-235</td><td>-235</td><td>-237</td><td>-242</td><td>-234</td><td>-234</td><td>-234</td><td>-235</td></tr><tr><td>2016 ⑦</td><td>-138</td><td>-139</td><td>-138</td><td>-136</td><td>-132</td><td>-131</td><td>-131</td><td>-133</td><td>-131</td><td>-129</td><td>-129</td><td>-129</td></tr><tr><td>Sum</td><td>-2187</td><td>-2289</td><td>-2360</td><td>-2337</td><td>-2137</td><td>-2157</td><td>-2188</td><td>-2293</td><td>-2106</td><td>-2111</td><td>-2129</td><td>-2192</td></tr></tbody></table>
<figure><img src="image_12.png" /><figcaption>**Figure A1.** Contours of the samples of the posterior distributions of the parameters of the phenomenological model. For all epochs (left) and all slices of the observation of 2016 (right).</figcaption></figure>

<table><caption>**Table A2.** Values of lnZ for 11 geometries of the physical model and the phenomenological model over all epochs. The gradient of colour shows for each row maximal values (dark blue) to minimal (yellow). The last row gives the total lnZ for all epochs. The geometries are visualizations of the absorber as seen by the X-ray source. Extracted from the uxclumpy webpage, courtesy of Johannes Buchner.</caption><thead><tr><th rowspan="2">Epoch</th><th rowspan="2">xillver</th><th colspan="11">Geometries uxclumpy (TORsigma, CTKcover)</th></tr><tr><th>(7.0)</th><th>(7.0.3)</th><th>(7.0.5)</th><th>(28.0)</th><th>(28.0.2)</th><th>(28.0.3)</th><th>(28.0.5)</th><th>(84.0)</th><th>(84.0.2)</th><th>(84.0.3)</th><th>(84.0.5)</th></tr></thead><tbody><tr><td>2001 ①</td><td>-77</td><td>-97</td><td>-113</td><td>-108</td><td>-83</td><td>-88</td><td>-93</td><td>-106</td><td>-76</td><td>-80</td><td>-85</td><td>-99</td></tr><tr><td>2001 ②</td><td>-68</td><td>-74</td><td>-80</td><td>-79</td><td>-62</td><td>-65</td><td>-68</td><td>-78</td><td>-62</td><td>-64</td><td>-67</td><td>-73</td></tr><tr><td>2005</td><td>-149</td><td>-177</td><td>-196</td><td>-204</td><td>-159</td><td>-171</td><td>-176</td><td>-201</td><td>-142</td><td>-145</td><td>-149</td><td>-161</td></tr><tr><td>2007</td><td>-30</td><td>-27</td><td>-27</td><td>-27</td><td>-26</td><td>-26</td><td>-26</td><td>-27</td><td>-26</td><td>-26</td><td>-27</td><td>-27</td></tr><tr><td>2012-a</td><td>-156</td><td>-172</td><td>-174</td><td>-180</td><td>-167</td><td>-167</td><td>-170</td><td>-175</td><td>-161</td><td>-159</td><td>-160</td><td>-163</td></tr><tr><td>2012-b</td><td>-137</td><td>-143</td><td>-142</td><td>-140</td><td>-132</td><td>-134</td><td>-136</td><td>-148</td><td>-140</td><td>-139</td><td>-139</td><td>-143</td></tr><tr><td>2016 ①</td><td>-220</td><td>-230</td><td>-243</td><td>-235</td><td>-210</td><td>-212</td><td>-216</td><td>-227</td><td>-208</td><td>-212</td><td>-219</td><td>-235</td></tr><tr><td>2016 ②</td><td>-238</td><td>-233</td><td>-238</td><td>-234</td><td>-226</td><td>-224</td><td>-225</td><td>-228</td><td>-231</td><td>-230</td><td>-228</td><td>-225</td></tr><tr><td>2016 ③</td><td>-219</td><td>-237</td><td>-243</td><td>-237</td><td>-215</td><td>-216</td><td>-220</td><td>-229</td><td>-209</td><td>-209</td><td>-211</td><td>-218</td></tr><tr><td>2016 ④</td><td>-246</td><td>-243</td><td>-244</td><td>-243</td><td>-236</td><td>-235</td><td>-236</td><td>-239</td><td>-237</td><td>-237</td><td>-236</td><td>-235</td></tr><tr><td>2016 ⑤</td><td>-265</td><td>-271</td><td>-274</td><td>-270</td><td>-254</td><td>-253</td><td>-255</td><td>-262</td><td>-248</td><td>-247</td><td>-247</td><td>-249</td></tr><tr><td>2016 ⑥</td><td>-244</td><td>-245</td><td>-247</td><td>-245</td><td>-235</td><td>-235</td><td>-237</td><td>-242</td><td>-234</td><td>-234</td><td>-234</td><td>-235</td></tr><tr><td>2016 ⑦</td><td>-138</td><td>-139</td><td>-138</td><td>-136</td><td>-132</td><td>-131</td><td>-131</td><td>-133</td><td>-131</td><td>-129</td><td>-129</td><td>-129</td></tr><tr><td>Sum</td><td>-2187</td><td>-2289</td><td>-2360</td><td>-2337</td><td>-2137</td><td>-2157</td><td>-2188</td><td>-2293</td><td>-2106</td><td>-2111</td><td>-2129</td><td>-2192</td></tr></tbody></table>
<figure><img src="image_13.png" /><figcaption>**Figure A2.** Contours of the samples of the posterior distributions of the parameters of the physical model’s best geometry. For all epochs (left) and all slices of the observation of 2016 (right).</figcaption></figure>

<table><caption>**Table A3.** Historical values of the photon index Γ, the column density $N_H$, and observed flux in the 2–10 keV band.† refers to parameters frozen or tied during the fits.</caption><thead><tr><th>Date</th><th>Observatory</th><th>Γ</th><th>N<sub>H</sub><br>10<sup>22</sup>cm<sup>-2</sup></th><th>Flux (2 – 10) keV<br>10<sup>-12</sup> erg cm<sup>-2</sup> s<sup>-1</sup></th><th>References</th></tr></thead><tbody><tr><td>1984 June 09</td><td>EXOSAT</td><td>1.70</td><td>16.70<sup>+5.80</sup><sub>-4.90</sub></td><td>17</td><td>Turner & Pounds (1989)</td></tr><tr><td>1988 Oct 25</td><td>Ginga</td><td>1.70</td><td>48.40<sup>+25.40</sup><sub>-15.20</sub></td><td>6</td><td>Warwick et al. (1993)</td></tr><tr><td>1994 Nov 14</td><td>ASCA</td><td>1.38<sup>+0.12</sup><sub>-0.11</sub></td><td>8.60<sup>+0.80</sup><sub>-0.80</sub></td><td>15.10<sup>+3.60</sup><sub>-4.20</sub></td><td>Turner et al. (1997)</td></tr><tr><td>1996 Nov 21</td><td>ASCA</td><td>1.52<sup>+0.09</sup><sub>-0.07</sub></td><td>12.40<sup>+0.60</sup><sub>-0.80</sub></td><td>15.50<sup>+2.40</sup><sub>-2.20</sub></td><td>Xue et al. (1998)</td></tr><tr><td>1998 Nov 09</td><td>BeppoSAX</td><td>1.95<sup>+0.09</sup><sub>-0.18</sub></td><td>14.40<sup>+0.90</sup><sub>-1</sub></td><td>19.70<sup>+3</sup><sub>-3</sub></td><td>Turner et al. (2000)</td></tr><tr><td>2000 Oct 14</td><td>Chandra</td><td>1.84<sup>-0.12</sup><sub>-0.12</sub></td><td>17.95<sup>+2.11</sup><sub>-2.11</sub></td><td>13.8</td><td>Laha et al. (2020)</td></tr><tr><td>2000 Oct 15</td><td>Chandra</td><td>1.45<sup>†</sup></td><td>19.9<sup>+3.85</sup><sub>-3.85</sub></td><td>14.1</td><td>Laha et al. (2020)</td></tr><tr><td>2001 May 25</td><td>XMM–Newton</td><td>1.90<sup>+0.05</sup><sub>-0.02</sub></td><td>54.90<sup>+6.60</sup><sub>-2.10</sub></td><td>4</td><td>Piconcelli et al. (2007)</td></tr><tr><td>2003 June 01</td><td>RXTE</td><td>2.10<sup>+0.10</sup><sub>-0.10</sub></td><td>-</td><td>6.50<sup>+0.60</sup><sub>-0.60</sub></td><td>Rivers et al. (2015)</td></tr><tr><td>2003 Oct 01</td><td>RXTE</td><td>2.10<sup>†</sup></td><td>15<sup>+2</sup><sub>-2</sub></td><td>13.20<sup>+0.20</sup><sub>-0.60</sub></td><td>Rivers et al. (2015)</td></tr><tr><td>2004 Feb 01</td><td>RXTE</td><td>2.10<sup>†</sup></td><td>-</td><td>6.50<sup>+0.20</sup><sub>-0.20</sub></td><td>Rivers et al. (2015)</td></tr><tr><td>2004 Aug 01</td><td>RXTE</td><td>2.10<sup>†</sup></td><td>16<sup>+5</sup><sub>-5</sub></td><td>8.80<sup>+0.20</sup><sub>-0.20</sub></td><td>Rivers et al. (2015)</td></tr><tr><td>2005 Apr 29</td><td>XMM–Newton</td><td>1.93<sup>+0.01</sup><sub>-0.01</sub></td><td>129.30<sup>+5.50</sup><sub>-6.70</sub></td><td>2.30</td><td>Piconcelli et al. (2007)</td></tr><tr><td>2007 Apr 30</td><td>XMM–Newton</td><td>1.92<sup>+0.24</sup><sub>-0.16</sub></td><td>33<sup>+4</sup><sub>-5</sub></td><td>7.60<sup>+0.40</sup><sub>-0.40</sub></td><td>Bianchi et al. (2009)</td></tr><tr><td>2007 May 01</td><td>Suzaku</td><td>1.92<sup>†</sup></td><td>44<sup>+3</sup><sub>-2</sub></td><td>5.30<sup>+0.30</sup><sub>-0.30</sub></td><td>Bianchi et al. (2009)</td></tr><tr><td>2007 May 28</td><td>Suzaku</td><td>1.92<sup>†</sup></td><td>68<sup>+6</sup><sub>-7</sub></td><td>4.10<sup>+0.30</sup><sub>-0.30</sub></td><td>Bianchi et al. (2009)</td></tr><tr><td>2007 Nov 09</td><td>Suzaku</td><td>1.92<sup>†</sup></td><td>110<sup>+14</sup><sub>-11</sub></td><td>3.20<sup>+0.20</sup><sub>-0.20</sub></td><td>Bianchi et al. (2009)</td></tr><tr><td>2007 Nov 16</td><td>Suzaku</td><td>1.92<sup>†</sup></td><td>120<sup>+20</sup><sub>-20</sub></td><td>2.60<sup>+0.50</sup><sub>-0.50</sub></td><td>Bianchi et al. (2009)</td></tr><tr><td>2012 Aug 31</td><td>NuSTAR</td><td>1.78<sup>+0.07</sup><sub>-0.07</sub></td><td>24<sup>+3</sup><sub>-7</sub></td><td>4.8<sup>+0.1</sup><sub>-0.1</sub></td><td>Rivers et al. (2015)</td></tr><tr><td>2012 Sept 15</td><td>NuSTAR</td><td>1.78<sup>+0.07</sup><sub>-0.07</sub></td><td>56<sup>+10</sup><sub>-20</sub></td><td>3.2<sup>+0.1</sup><sub>-0.1</sub></td><td>Rivers et al. (2015)</td></tr><tr><td>2014 Nov 16</td><td>Chandra</td><td>1.74<sup>+0.18</sup><sub>-0.18</sub></td><td>120<sup>+20</sup><sub>-20</sub></td><td>3.3</td><td>Braito et al. (2017)</td></tr><tr><td>2016 Apr 28</td><td>XMM–Newton</td><td>1.44<sup>+0.04</sup><sub>-0.02</sub></td><td>32<sup>+1</sup><sub>-2</sub></td><td>7.9</td><td>Tanimoto et al. (2022)</td></tr><tr><td>2016 Apr 28</td><td>NuSTAR</td><td>1.44<sup>†</sup></td><td>32<sup>†</sup></td><td>7.9<sup>†</sup></td><td>Tanimoto et al. (2022)</td></tr></tbody></table>

This paper has been typeset from a TEX/LATEX file prepared by the author.
<figure><img src="image_13.png" /><figcaption>**Figure A2.** Contours of the samples of the posterior distributions of the parameters of the physical model's best geometry. For all epochs (left) and all slices of the observation of 2016 (right).</figcaption></figure>

<table><caption>**Table A3.** Historical values of the photon index Γ, the column density $N_H$, and observed flux in the 2–10 keV band.† refers to parameters frozen or tied during the fits.</caption><thead><tr><th>Date</th><th>Observatory</th><th>Γ</th><th>N<sub>H</sub><br>10<sup>22</sup>cm<sup>-2</sup></th><th>Flux (2 – 10) keV<br>10<sup>-12</sup> erg cm<sup>-2</sup> s<sup>-1</sup></th><th>References</th></tr></thead><tbody><tr><td>1984 June 09</td><td>EXOSAT</td><td>1.70</td><td>16.70<sup>+5.80</sup><sub>-4.90</sub></td><td>17</td><td>Turner & Pounds (1989)</td></tr><tr><td>1988 Oct 25</td><td>Ginga</td><td>1.70</td><td>48.40<sup>+25.40</sup><sub>-15.20</sub></td><td>6</td><td>Warwick et al. (1993)</td></tr><tr><td>1994 Nov 14</td><td>ASCA</td><td>1.38<sup>+0.12</sup><sub>-0.11</sub></td><td>8.60<sup>+0.80</sup><sub>-0.80</sub></td><td>15.10<sup>+3.60</sup><sub>-4.20</sub></td><td>Turner et al. (1997)</td></tr><tr><td>1996 Nov 21</td><td>ASCA</td><td>1.52<sup>+0.09</sup><sub>-0.07</sub></td><td>12.40<sup>+0.60</sup><sub>-0.80</sub></td><td>15.50<sup>+2.40</sup><sub>-2.20</sub></td><td>Xue et al. (1998)</td></tr><tr><td>1998 Nov 09</td><td>BeppoSAX</td><td>1.95<sup>+0.09</sup><sub>-0.18</sub></td><td>14.40<sup>+0.90</sup><sub>-1</sub></td><td>19.70<sup>+3</sup><sub>-3</sub></td><td>Turner et al. (2000)</td></tr><tr><td>2000 Oct 14</td><td>Chandra</td><td>1.84<sup>-0.12</sup><sub>-0.12</sub></td><td>17.95<sup>+2.11</sup><sub>-2.11</sub></td><td>13.8</td><td>Laha et al. (2020)</td></tr><tr><td>2000 Oct 15</td><td>Chandra</td><td>1.45<sup>†</sup></td><td>19.9<sup>+3.85</sup><sub>-3.85</sub></td><td>14.1</td><td>Laha et al. (2020)</td></tr><tr><td>2001 May 25</td><td>XMM–Newton</td><td>1.90<sup>+0.05</sup><sub>-0.02</sub></td><td>54.90<sup>+6.60</sup><sub>-2.10</sub></td><td>4</td><td>Piconcelli et al. (2007)</td></tr><tr><td>2003 June 01</td><td>RXTE</td><td>2.10<sup>+0.10</sup><sub>-0.10</sub></td><td>-</td><td>6.50<sup>+0.60</sup><sub>-0.60</sub></td><td>Rivers et al. (2015)</td></tr><tr><td>2003 Oct 01</td><td>RXTE</td><td>2.10<sup>†</sup></td><td>15<sup>+2</sup><sub>-2</sub></td><td>13.20<sup>+0.20</sup><sub>-0.60</sub></td><td>Rivers et al. (2015)</td></tr><tr><td>2004 Feb 01</td><td>RXTE</td><td>2.10<sup>†</sup></td><td>-</td><td>6.50<sup>+0.20</sup><sub>-0.20</sub></td><td>Rivers et al. (2015)</td></tr><tr><td>2004 Aug 01</td><td>RXTE</td><td>2.10<sup>†</sup></td><td>16<sup>+5</sup><sub>-5</sub></td><td>8.80<sup>+0.20</sup><sub>-0.20</sub></td><td>Rivers et al. (2015)</td></tr><tr><td>2005 Apr 29</td><td>XMM–Newton</td><td>1.93<sup>+0.01</sup><sub>-0.01</sub></td><td>129.30<sup>+5.50</sup><sub>-6.70</sub></td><td>2.30</td><td>Piconcelli et al. (2007)</td></tr><tr><td>2007 Apr 30</td><td>XMM–Newton</td><td>1.92<sup>+0.24</sup><sub>-0.16</sub></td><td>33<sup>+4</sup><sub>-5</sub></td><td>7.60<sup>+0.40</sup><sub>-0.40</sub></td><td>Bianchi et al. (2009)</td></tr><tr><td>2007 May 01</td><td>Suzaku</td><td>1.92<sup>†</sup></td><td>44<sup>+3</sup><sub>-2</sub></td><td>5.30<sup>+0.30</sup><sub>-0.30</sub></td><td>Bianchi et al. (2009)</td></tr><tr><td>2007 May 28</td><td>Suzaku</td><td>1.92<sup>†</sup></td><td>68<sup>+6</sup><sub>-7</sub></td><td>4.10<sup>+0.30</sup><sub>-0.30</sub></td><td>Bianchi et al. (2009)</td></tr><tr><td>2007 Nov 09</td><td>Suzaku</td><td>1.92<sup>†</sup></td><td>110<sup>+14</sup><sub>-11</sub></td><td>3.20<sup>+0.20</sup><sub>-0.20</sub></td><td>Bianchi et al. (2009)</td></tr><tr><td>2007 Nov 16</td><td>Suzaku</td><td>1.92<sup>†</sup></td><td>120<sup>+20</sup><sub>-20</sub></td><td>2.60<sup>+0.50</sup><sub>-0.50</sub></td><td>Bianchi et al. (2009)</td></tr><tr><td>2012 Aug 31</td><td>NuSTAR</td><td>1.78<sup>+0.07</sup><sub>-0.07</sub></td><td>24<sup>+3</sup><sub>-7</sub></td><td>4.8<sup>+0.1</sup><sub>-0.1</sub></td><td>Rivers et al. (2015)</td></tr><tr><td>2012 Sept 15</td><td>NuSTAR</td><td>1.78<sup>+0.07</sup><sub>-0.07</sub></td><td>56<sup>+10</sup><sub>-20</sub></td><td>3.2<sup>+0.1</sup><sub>-0.1</sub></td><td>Rivers et al. (2015)</td></tr><tr><td>2014 Nov 16</td><td>Chandra</td><td>1.74<sup>+0.18</sup><sub>-0.18</sub></td><td>120<sup>+20</sup><sub>-20</sub></td><td>3.3</td><td>Braito et al. (2017)</td></tr><tr><td>2016 Apr 28</td><td>XMM–Newton</td><td>1.44<sup>+0.04</sup><sub>-0.02</sub></td><td>32<sup>+1</sup><sub>-2</sub></td><td>7.9</td><td>Tanimoto et al. (2022)</td></tr><tr><td>2016 Apr 28</td><td>NuSTAR</td><td>1.44<sup>†</sup></td><td>32<sup>†</sup></td><td>7.9<sup>†</sup></td><td>Tanimoto et al. (2022)</td></tr></tbody></table>

This paper has been typeset from a TEX/LATEX file prepared by the author.