arXiv subjects

G. Branduardi-Raymont

Publications and source records attributed to G. Branduardi-Raymont.

At least 37 records · Page 2Linked to original sources

arXiv2017

Multi-wavelength campaign on NGC7469 II. Column densities and variability in the X-ray spectrum

We investigate the ionic column density variability of the ionized outflows associated with NGC$\sim$7469, to estimate their location and power. This could allow a better understanding of galactic feedback of AGNs to their host galaxies. Analysis of seven XMM-Newton grating observations from 2015 is reported. We use an individual-ion spectral fitting approach, and compare different epochs to accurately determine variability on time-scales of years, months, and days. We find no significant column density variability in a 10 year period implying that the outflow is far from the ionizing source. The implied lower bound on the ionization equilibrium time, 10 years, constrains the lower limit on the distance to be at least 12 pc, and up to 31 pc, much less but consistent with the 1 kpc wide starburst ring. The ionization distribution of column density is reconstructed from measured column densities, nicely matching results of two 2004 observations, with one large high ionization parameter ($ξ$) component at $2<\log ξ<3.5$, and one at $0.5<\log ξ<1$ in cgs units. The strong dependence of the expression for kinetic power, $\propto1/ξ$, hampers tight constraints on the feedback mechanism of outflows with a large range in ionization parameter, which is often observed and indicates a non-conical outflow. The kinetic power of the outflow is estimated here to be within 0.4 and 60 \% of the Eddington luminosity, depending on the ion used to estimate $ξ$.

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arXiv2017

Chasing obscuration in type-I AGN: discovery of an eclipsing clumpy wind at the outer broad-line region of NGC 3783

In 2016 we carried out a Swift monitoring program to track the X-ray hardness variability of eight type-I AGN over a year. The purpose of this monitoring was to find intense obscuration events in AGN, and thereby study them by triggering joint XMM-Newton, NuSTAR, and HST observations. We successfully accomplished this for NGC 3783 in December 2016. We found heavy X-ray absorption produced by an obscuring outflow in this AGN. As a result of this obscuration, interesting absorption features appear in the UV and X-ray spectra, which are not present in the previous epochs. Namely, the obscuration produces broad and blue-shifted UV absorption lines of Ly$α$, C IV, and N V, together with a new high-ionisation component producing Fe XXV and Fe XXVI absorption lines. In soft X-rays, only narrow emission lines stand out above the diminished continuum as they are not absorbed by the obscurer. Our analysis shows that the obscurer partially covers the central source with a column density of few $10^{23}$ cm$^{-2}$, outflowing with a velocity of few thousand km s$^{-1}$. The obscuration in NGC 3783 is variable and lasts for about a month. Unlike the commonly-seen warm-absorber winds at pc-scale distances from the black hole, the eclipsing wind in NGC 3783 is located at about 10 light days. Our results suggest the obscuration is produced by an inhomogeneous and clumpy medium, consistent with clouds in the base of a radiatively-driven disk wind at the outer broad-line region of the AGN.

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arXiv2016

The Filter Wheel and Filters development for the X-IFU instrument on-board Athena

Athena is the large mission selected by ESA in 2013 to investigate the science theme "Hot and Energetic Universe" and presently scheduled for launch in 2028. One of the two instruments located at the focus of the 12 m-long Athena telescope is the X-ray Integral Field Unit (X-IFU). This is an array of TES micro-calorimeters that will be operated at temperatures of 50 mK in order to perform high resolution spectroscopy with an energy resolution down to 2.5 eV at energies < 7 keV. In order to cope with the large dynamical range of X-ray fluxes spanned by the celestial objects Athena will be observing, the X-IFU will be equipped with a filter wheel. This will allow the user to fine tune the instrument set-up based on the nature of the target, thus optimizing the scientific outcomes of the observation. A few positions of the filter wheel will also be used to host a calibration source and to allow the measurement of the instrument intrinsic background.

astro-ph.IM↗

arXiv2016

X-ray narrow emission lines from the nuclear region of NGC 1365

NGC 1365 is a Seyfert 2 galaxy with a starburst ring in its nuclear region. In this work we look at the XMM Reflection Grating Spectrometer (RGS) data from four 2012-13, three 2007 and two 2004 observations of NGC 1365. We characterise the narrow-line emitting gas visible by XMM RGS and make comparisons between the 2012-13 spectra and those from 2004-07, already published. This source is usually absorbed within the soft X-ray band, with a typical neutral column density of >1.5 x 10$^{23}$ cm$^{-2}$, and only 1 observation of the 9 we investigate shows low enough absorption for the continuum to emerge in the soft X-rays. We stack all observations from 2004-07, and separately three of the four observations from 2012-13, analysing the less absorbed observation separately. We first model the spectra using gaussian profiles representing the narrow line emission. We fit physically motivated models to the 2012-13 stacked spectra, with collisionally ionised components representing the starburst emission and photoionised line emission models representing the AGN line emission. The collisional and photoionised emission line models are fitted together on top of a physical continuum and absorption model. The X-ray narrow emission line spectrum of NGC 1365 is well represented by a combination of two collisionally ionised and three photoionised phases of emitting gas, all with higher than solar nitrogen abundances. This physical model was fitted to the 2012-13 stacked spectrum, and yet also fits well to the 2004-07 stacked spectrum, without changing any characteristics of the emitting gas phases. Our 2004-07 results are consistent with previous emission line work using these data, with 5 additional emission lines detected in both this and the 2012-13 stacked spectra. We also estimate the distance of the X-ray line-emitting photoionised gas from the central source to be <300 pc.

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arXiv2016

Multiwavelength campaign on Mrk 509 XV. A global modeling of the broad emission lines in the Optical, UV and X-ray bands

We model the broad emission lines present in the optical, UV and X-ray spectra of Mrk 509, a bright type 1 Seyfert galaxy. The broad lines were simultaneously observed during a large multiwavelength campaign, using the XMM-Newton-OM for the optical lines, HST-COS for the UV lines and XMM-Newton-RGS and Epic for the X-ray lines respectively. We also used FUSE archival data for the broad lines observed in the far-ultra-violet. The goal is to find a physical connection among the lines measured at different wavelengths and determine the size and the distance from the central source of the emitting gas components. We used the "Locally optimally emission Cloud" (LOC) model which interprets the emissivity of the broad line region (BLR) as regulated by powerlaw distributions of both gas density and distances from the central source. We find that one LOC component cannot model all the lines simultaneously. In particular, we find that the X-ray and UV lines likely may originate in the more internal part of the AGN, at radii in the range ~5x10^{14}-3x10^{17} cm, while the optical lines and part of the UV lines may likely be originating further out, at radii ~3x10^{17}-3x^{18} cm. These two gas components are parametrized by a radial distribution of the luminosities with a slope gamma of ~1.15 and ~1.10, respectively, both of them covering at least 60% of the source. This simple parameterization points to a structured broad line region, with the higher ionized emission coming from closer in, while the emission of the low-ionization lines is more concentrated in the outskirts of the broad line region.

astro-ph.GA↗

arXiv2016

Anatomy of the AGN in NGC 5548 VIII. XMM-Newton's EPIC detailed view of an unexpected variable multilayer absorber

In 2013 we conducted a large multi-wavelength campaign on the archetypical Seyfert 1 galaxy NGC 5548. Unexpectedly, this usually unobscured source appeared strongly absorbed in the soft X-rays during the entire campaign, and signatures of new and strong outflows were present in the almost simultaneous UV HST/COS data. Here we carry out a comprehensive spectral analysis of all available XMM-Newton observations of NGC 5548 (for a total of ~763 ks) in combination with 3 simultaneous NuSTAR obs. We obtain a best-fit composed by i) a weakly varying flat (Gamma~1.5-1.7) power-law component; ii) a constant, cold reflection (FeK + continuum) component; iii) a soft excess, possibly due to thermal Comptonization; and iv) a constant, ionized scattered emission-line dominated component. Our main findings are that, during the 2013 campaign, the first 3 of these components appear to be partially covered by a heavy and variable obscurer located along the l.o.s. that is consistent with a multilayer of cold and mildly ionized gas. We characterize in detail the short timescale (~ks-to-days) spectral variability of this new obscurer, and find it is mostly due to a combination of Nh and Cf variations, on top of intrinsic power-law variations. In addition, our best-fit spectrum is left with several (but marginal) absorption features at rest-frame energies ~6.7-6.9 keV and ~8 keV, as well as a weak broad emission line feature redwards of the 6.4 keV emission line. These could indicate a more complex underlying model, e.g. a P-Cygni-type profile if allowing for a large velocity and wide-angle outflow. These findings are consistent with a picture where the obscurer represents the manifestation along the l.o.s. of a multilayer of gas that is likely outflowing at high speed, and simultaneously producing heavy obscuration and scattering in the X-rays and broad absorption features in the UV.

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arXiv2016

Anatomy of the AGN in NGC 5548: VII. Swift study of obscuration and broadband continuum variability

We present our investigation into the long-term variability of the X-ray obscuration and optical-UV-X-ray continuum in the Seyfert 1 galaxy NGC 5548. In 2013 and 2014, the Swift observatory monitored NGC 5548 on average every day or two, with archival observations reaching back to 2005, totalling about 670 ks of observing time. Both broadband spectral modelling and temporal rms variability analysis are applied to the Swift data. We disentangle the variability caused by absorption, due to an obscuring weakly-ionised outflow near the disk, from variability of the intrinsic continuum components (the soft X-ray excess and the power-law) originating from the disk and its associated coronae. The spectral model that we apply to this extensive Swift data is the global model that we derived for NGC 5548 from analysis of the stacked spectra from our multi-satellite campaign of summer 2013 (including XMM-Newton, NuSTAR and HST). The results of our Swift study show that changes in the covering fraction of the obscurer is the primary and dominant cause of variability in the soft X-ray band on timescales of 10 days to ~ 5 months. The obscuring covering fraction of the X-ray source is found to range between 0.7 and nearly 1.0. The contribution of the soft excess component to the X-ray variability is often much less than that of the obscurer, but it becomes comparable when the optical-UV continuum flares up. We find that the soft excess is consistent with being the high-energy tail of the optical-UV continuum and can be explained by warm Comptonisation: up-scattering of the disk seed photons in a warm, optically thick corona as part of the inner disk. To this date, the Swift monitoring of NGC 5548 shows that the obscurer has been continuously present in our line of sight for at least 4 years (since at least February 2012).

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arXiv2016

Anatomy of the AGN in NGC 5548. VI. Long-term variability of the warm absorber

(Abridged) The archetypal Seyfert 1 galaxy NGC 5548 was observed in 2013-2014 in the context of an extensive multiwavelength campaign, which revealed the source to be in an extraordinary state of persistent heavy obscuration. We re-analyzed the archival grating spectra obtained by XMM-Newton and Chandra between 1999 and 2007 in order to characterize the classic warm absorber (WA) using consistent models and up-to-date photoionization codes and atomic physics databases and to construct a baseline model that can be used as a template for the WA in the 2013 observations. The WA in NGC 5548 is composed of 6 distinct ionization phases outflowing in 4 kinematic regimes in the form of a stratified wind with several layers intersected by our line of sight. If the changes in the WA are solely due to ionization or recombination processes in response to variations in the ionizing flux among the different observations, we are able to estimate lower limits on the density of the WA, finding that the farthest components are less dense and have a lower ionization. These limits are used to put stringent upper limits on the distance of the WA components from the central ionizing source, with the lowest ionization phases <50, <20, and <5 pc, respectively, while the intermediately ionized components lie at <3.6 and <2.2 pc from the center, respectively. The highest ionization component is located at ~0.6 pc or closer to the AGN central engine. The mass outflow rate summed over all WA components is ~0.3 Msun/yr, about six times the nominal accretion rate of the source. The total kinetic luminosity injected into the ISM is a small fraction (~0.03%) of the bolometric luminosity of the source. After adding the contribution of the UV absorbers, this value augments to ~0.2% of the bolometric luminosity, well below the minimum amount of energy required by current feedback models to regulate galaxy evolution.

astro-ph.HE↗

arXiv2015

Anatomy of the AGN in NGC 5548: V. A clear view of the X-ray narrow emission lines

Context. Our consortium performed an extensive multi-wavelength campaign of the nearby Seyfert 1 galaxy NGC 5548 in 2013-14. The source appeared unusually heavily absorbed in the soft X-rays, and signatures of outflowing absorption were also present in the UV. He-like triplets of neon, oxygen and nitrogen, and radiative recombination continuum (RRC) features were found to dominate the soft X-ray spectrum due to the low continuum flux. Aims. Here we focus on characterising these narrow emission features using data obtained from the XMM-Newton RGS (770 ks stacked spectrum). Methods. We use SPEX for our initial analysis of these features. Self-consistent photoionisation models from Cloudy are then compared with the data to characterise the physical conditions of the emitting region. Results. Outflow velocity discrepancies within the O VII triplet lines can be explained if the X-ray narrow-line region (NLR) in NGC 5548 is absorbed by at least one of the six warm absorber components found by previous analyses. The RRCs allow us to directly calculate a temperature of the emitting gas of a few eV ($\sim10^{4}$ K), favouring photoionised conditions. We fit the data with a Cloudy model of log $ξ= 1.45 \pm 0.05$ erg cm s$^{-1}$, log $N_H = 22.9 \pm 0.4$ cm$^{-2}$ and log v$_{turb} = 2.25 \pm 0.5$ km s$^{-1}$ for the emitting gas; this is the first time the X-ray NLR gas in this source has been modelled so comprehensively. This allows us to estimate the distance from the central source to the illuminated face of the emitting clouds as $13.9 \pm 0.6$ pc, consistent with previous work.

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arXiv2015

Anatomy of the AGN in NGC 5548 IV. The short-term variability of the outflows

During an extensive multiwavelength campaign that we performed in 2013-14 the prototypical Seyfert 1 galaxy NGC 5548 has been found in an unusual condition of heavy and persistent obscuration. The newly discovered "obscurer" absorbs most of the soft X-ray continuum along our line of sight and lowers the ionizing luminosity received by the classical warm absorber. Here we present the analysis of the high resolution X-ray spectra collected with XMM-Newton and Chandra throughout the campaign, which are suitable to investigate the variability of both the obscurer and the classical warm absorber. The time separation between these X-ray observations range from 2 days to 8 months. On these timescales the obscurer is variable both in column density and in covering fraction. This is consistent with the picture of a patchy wind. The most significant variation occurred in September 2013 when the source brightened for two weeks. A higher and steeper intrinsic continuum and a lower obscurer covering fraction are both required to explain the spectral shape during the flare. We suggest that a geometrical change of the soft X-ray source behind the obscurer cause the observed drop in the covering fraction. Due to the higher soft X-ray continuum level the September 2013 Chandra spectrum is the only X ray spectrum of the campaign where individual features of the warm absorber could be detected. The spectrum shows absorption from Fe-UTA, \ion{O}{iv}, and \ion{O}{v}, consistent to belong to the lower-ionization counterpart of the historical NGC 5548 warm absorber. Hence, we confirm that the warm absorber has responded to the drop in the ionizing luminosity caused by the obscurer.

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arXiv2015

Anatomy of the AGN in NGC 5548: I. A global model for the broadband spectral energy distribution

An extensive multi-satellite campaign on NGC 5548 has revealed this archetypal Seyfert-1 galaxy to be in an exceptional state of persistent heavy absorption. Our observations taken in 2013-2014 with XMM-Newton, Swift, NuSTAR, INTEGRAL, Chandra, HST and two ground-based observatories have together enabled us to establish that this unexpected phenomenon is caused by an outflowing stream of weakly ionised gas (called the obscurer), extending from the vicinity of the accretion disk to the broad-line region. In this work we present the details of our campaign and the data obtained by all the observatories. We determine the spectral energy distribution of NGC 5548 from near-infrared to hard X-rays by establishing the contribution of various emission and absorption processes taking place along our line of sight towards the central engine. We thus uncover the intrinsic emission and produce a broadband continuum model for both obscured (average summer 2013 data) and unobscured ($<$ 2011) epochs of NGC 5548. Our results suggest that the intrinsic NIR/optical/UV continuum is a single Comptonised component with its higher energy tail creating the 'soft X-ray excess'. This component is compatible with emission from a warm, optically-thick corona as part of the inner accretion disk. We then investigate the effects of the continuum on the ionisation balance and thermal stability of photoionised gas for unobscured and obscured epochs.

astro-ph.HE↗

arXiv2014

Anatomy of the AGN in NGC 5548: II. The Spatial, Temporal and Physical Nature of the Outflow from HST/COS Observations

(Abridged) Our deep multiwavelength campaign on NGC 5548 revealed an unusually strong X-ray obscuration. The resulting dramatic decrease in incident ionizing flux allowed us to construct a comprehensive physical, spatial and temporal picture for the long-studied AGN wind in this object. Here we analyze the UV spectra of the outflow acquired during the campaign as well as from four previous epochs. We find that a simple model based on a fixed total column-density absorber, reacting to changes in ionizing illumination, matches the very different ionization states seen in five spectroscopic epochs spanning 16 years. Absorption troughs from C III* appeared for the first time during our campaign. From these troughs, we infer that the main outflow component is situated at 3.5+-1 pc from the central source. Three other components are situated between 5-70 pc and two are further than 100 pc. The wealth of observational constraints and the disparate relationship of the observed X-ray and UV flux between different epochs make our physical model a leading contender for interpreting trough variability data of quasar outflows.

astro-ph.GA↗

arXiv2014

Multiwavelength campaign on Mrk 509 XIV. Chandra HETGS spectra

We present in this paper the results of a 270 ks Chandra HETGS observation in the context of a large multiwavelength campaign on the Seyfert galaxy Mrk 509. The HETGS spectrum allows us to study the high ionisation warm absorber and the Fe-K complex in Mrk 509. We search for variability in the spectral properties of the source with respect to previous observations in this campaign, as well as for evidence of ultra-fast outflow signatures. The Chandra HETGS X-ray spectrum of Mrk 509 was analysed using the SPEX fitting package. We confirm the basic structure of the warm absorber found in the 600 ks XMM-Newton RGS observation observed three years earlier, consisting of five distinct ionisation components in a multikinematic regime. We find little or no variability in the physical properties of the different warm absorber phases with respect to previous observations in this campaign, except for component D2 which has a higher column density at the expense of component C2 at the same outflow velocity (-240 km/s). Contrary to prior reports we find no -700 km/s outflow component. The O VIII absorption line profiles show an average covering factor of 0.81 +/- 0.08 for outflow velocities faster than -100 km/s, similar to those measured in the UV. This supports the idea of a patchy wind. The relative metal abundances in the outflow are close to proto-solar. The narrow component of the Fe Kalpha emission line shows no changes with respect to previous observations which confirms its origin in distant matter. The narrow line has a red wing that can be interpreted to be a weak relativistic emission line. We find no significant evidence of ultra-fast outflows in our new spectrum down to the sensitivity limit of our data.

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arXiv2014

A fast and long-lived outflow from the supermassive black hole in NGC 5548

Supermassive black holes in the nuclei of active galaxies expel large amounts of matter through powerful winds of ionized gas. The archetypal active galaxy NGC 5548 has been studied for decades, and high-resolution X-ray and UV observations have previously shown a persistent ionized outflow. An observing campaign in 2013 with six space observatories shows the nucleus to be obscured by a long-lasting, clumpy stream of ionized gas never seen before. It blocks 90% of the soft X-ray emission and causes simultaneous deep, broad UV absorption troughs. The outflow velocities of this gas are up to five times faster than those in the persistent outflow, and at a distance of only a few light days from the nucleus, it may likely originate from the accretion disk.

astro-ph.HE↗

arXiv2014

Multiwavelength campaign on Mrk 509. XIII. Testing ionized-reflection models on Mrk 509

Active Galactic Nuclei (AGN) are the most luminous persistent objects in the universe. An excess of X-ray emission below about 2 keV, called soft-excess, is very common in Type 1 AGN spectra. The origin of this feature remains debated. Originally modeled with a blackbody, there are now several possibilities to model the soft-excess, including warm Comptonization and blurred ionized reflection. In this paper, we test ionized-reflection models on Mrk 509, a bright Seyfert 1 galaxy for which we have a unique data set, in order to determine whether it can be responsible for the strong soft-excess. We use ten simultaneous XMM-Newton and INTEGRAL observations performed every four days. We present here the results of the spectral analysis, the evolution of the parameters and the variability properties of the X-ray emission. The application of blurred ionized-reflection models leads to a very strong reflection and an extreme geometry, but fails to reproduce the broad-band spectrum of Mrk 509. Two different scenarios for blurred ionized reflection are discussed: stable geometry and lamp-post configuration. In both cases we find that the model parameters do not follow the expected relations, indicating that the model is fine-tuned to fit the data without physical justification. A large, slow variation of the soft-excess without counterpart in the hard X-rays could be explained by a change in ionization of the reflector. However, such a change does not naturally follow from the assumed geometrical configuration. Warm Comptonization remains the most probable origin of the soft-excess in this object. Nevertheless, it is possible that both ionized reflection and warm Comptonization mechanisms can explain the soft-excess in all objects, one dominating the other one, depending on the physical conditions of the disk and the corona.

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arXiv2013

Athena+: The first Deep Universe X-ray Observatory

The Advanced Telescope for High-energy Astrophysics (Athena+) is being proposed to ESA as the L2 mission (for a launch in 2028) and is specifically designed to answer two of the most pressing questions for astrophysics in the forthcoming decade: How did ordinary matter assemble into the large scale structures we see today? and how do black holes grow and shape the Universe? For addressing these two issues, Athena+ will provide transformational capabilities in terms of angular resolution, effective area, spectral resolution, grasp, that will make it the most powerful X-ray observatory ever flown. Such an observatory, when opened to the astronomical community, will be used for virtually all classes of astrophysical objects, from high-z gamma-ray bursts to the closest planets in our solar neighborhood. In this paper, we briefly review the core science objectives of Athena+, present the science requirements and the foreseen implementation of the mission, and illustrate its transformational capabilities compared to existing facilities.

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arXiv2013

The Hot and Energetic Universe: Solar system and exoplanets

The high resolution non-dispersive spectroscopy and unprecedented sensitivity of Athena+ will revolutionize solar system observing: the origin of the ions producing Jupiter's X-ray aurorae via charge exchange will be conclusively established, as well as their dynamics, giving clues to their acceleration mechanisms. X-ray aurorae on Saturn will be searched for to a depth unattainable by current Earth-bound observatories. The X-ray Integral Field Unit of Athena+ will map Mars' expanding exosphere, which has a line-rich solar wind charge exchange spectrum, under differing solar wind conditions and through the seasons; relating Mars' X-ray emission to its atmospheric loss will have significant impact also on the study of exoplanet atmospheres. Spectral mapping of cometary comae, which are spectacular X-ray sources with extremely line-rich spectra, will probe solar wind composition and speed at varying distances from the Sun. Athena+ will provide unique contributions also to exoplanetary astrophysics. Athena+ will pioneer the study of ingress/eclipse/egress effects during planetary orbits of hot-Jupiters, and will confirm/improve the evidence of Star-Planet Interactions (SPI) in a wider sample of planetary systems. Finally Athena+ will drastically improve the knowledge of the X-ray incident radiation on exoplanets, a key element for understanding the effects of atmospheric mass loss and of the chemical and physical evolution of planet atmospheres, particularly relevant in the case of young systems.

astro-ph.HE↗

arXiv2012

Multiwavelength campaign on Mrk 509 XII. Broad band spectral analysis

(Abridged) The simultaneous UV to X-rays/gamma rays data obtained during the multi-wavelength XMM/INTEGRAL campaign on the Seyfert 1 Mrk 509 are used in this paper and tested against physically motivated broad band models. Each observation has been fitted with a realistic thermal comptonisation model for the continuum emission. Prompted by the correlation between the UV and soft X-ray flux, we use a thermal comptonisation component for the soft X-ray excess. The UV to X-rays/gamma-rays emission of Mrk 509 can be well fitted by these components. The presence of a relatively hard high-energy spectrum points to the existence of a hot (kT~100 keV), optically-thin (tau~0.5) corona producing the primary continuum. On the contrary, the soft X-ray component requires a warm (kT~1 keV), optically-thick (tau~15) plasma. Estimates of the amplification ratio for this warm plasma support a configuration close to the "theoretical" configuration of a slab corona above a passive disk. An interesting consequence is the weak luminosity-dependence of its emission, a possible explanation of the roughly constant spectral shape of the soft X-ray excess seen in AGNs. The temperature (~ 3 eV) and flux of the soft-photon field entering and cooling the warm plasma suggests that it covers the accretion disk down to a transition radius $R_{tr}$ of 10-20 $R_g$. This plasma could be the warm upper layer of the accretion disk. On the contrary the hot corona has a more photon-starved geometry. The high temperature ($\sim$ 100 eV) of the soft-photon field entering and cooling it favors a localization of the hot corona in the inner flow. This soft-photon field could be part of the comptonised emission produced by the warm plasma. In this framework, the change in the geometry (i.e. $R_{tr}$) could explain most of the observed flux and spectral variability.

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