Free Access
Issue
A&A
Volume 619, November 2018
Article Number A149
Number of page(s) 7
Section Extragalactic astronomy
DOI https://doi.org/10.1051/0004-6361/201833623
Published online 19 November 2018

© ESO 2018

1. Introduction

Accretion disk winds are believed to play a fundamental role in the feedback from active galactic nuclei (AGN) to their host galaxy. Both theoretical and observational evidence shows that they are potentially able to transfer a significant fraction of the AGN’s power (Di Matteo et al. 2005), up to ∼3 − 5% LAGN (King & Pounds 2015; Tombesi et al. 2015; Feruglio et al. 2015; Bischetti et al. 2017; Fiore et al. 2017). This amount of energy could overcome the binding energy of the host galaxy, and is often invoked to explain the observed relation between the supermassive black hole (SMBH) mass and the bulge velocity dispersion (the “Mσ” relation, see e.g., Kormendy & Ho 2013). According to the most accepted scenario (see, e.g., King & Pounds 2015), the gas is accelerated at accretion disk scales, propagates towards the host galaxy, and impacts the interstellar matter (ISM), producing a shock front (Zubovas & King 2012; Faucher-Giguère & Quataert 2012). If the kinetic energy is conserved during this process, the shocked gas may drive a massive, galaxy-scale outflow, with mass transfer rates up to ∼103 M yr−1 and velocities = 1000 km s−1.

In this two-phase scenario, the covering fraction of the disk wind, Cf, together with its velocity, density, and launching radius, are fundamental quantities to understand the amount of momentum and energy deposited into the ISM. The accurate measurement of these quantities is crucial to reliably constrain the role of the disk winds in the co-evolution of AGN and their host galaxies.

In this paper, we present the application of our novel model of AGN wind emission (WINE) to the broadband XMM-Newton and NuSTAR spectrum of PDS 456. This nearby (z = 0.184) luminous quasar exhibits the prototype of an ultra fast outflow (UFO) traced by a P-Cygni feature, due to highly-ionized Fe, with a ionization parameter , where Lion is the luminosity in the 1–1000 Rydberg interval (1 Rd = 13.6 eV), n is the gas number density, and R is the distance from the ionizing source. The outflow velocity is ∼0.25 c and the launching radius is < 200 r g 1 (Reeves et al. 2003; Nardini et al. 2015; hereafter N15). N15 inferred a Cf of the UFO of 0.8 (=3.2π) and a kinetic power of ∼20% of the bolometric luminosity of the quasar. These estimates are based on a spectral fitting using XSTAR tables (Kallman & Bautista 2001) to model both UFO emission and absorption features, in which the outflowing gas is approximated as a spherical shell with constant radial velocity.

The present paper is organized as follows. In Sect. 2 we describe the wind model. In Sect. 3 we present the X-ray data analysis and the results of the spectral fitting obtained by applying our model. Section 4 is devoted to the discussion of our findings, with particular emphasis on Cf and the velocity of the outflow, the derived mass and energy transfer rates, and their implications for AGN feedback.

2. The WINd Emission (WINE) model

In the WINE model the wind is approximated as a conical region, with the vertex centered on the SMBH, the same symmetry axis as the accretion disk, and the gas velocity directed radially outward. This conical shape is consistent with the most popular accretion disk wind simulations (e.g., Proga & Kallman 2004; Fukumura et al. 2010; Oshuga et al. 2009). As the UFOs originate from the innermost region of the accretion disk, we consider that the rear cone is not observable (see Fig. 1).

thumbnail Fig. 1.

Sketch of the WINE model. Further details can be found in Sect. 2.

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The free parameters of the model are the opening angle of the cone (i.e., θout in Fig. 1), the inclination angle i of the line of sight (LOS) with respect to the symmetry axis, the maximum velocity of the wind (vmax), and the deceleration factor of the wind radial velocity (s). The radial velocity of the wind is defined as

(1)

where and rcone is the height of the cone. Equation (1) represents a first-order expansion of the velocity with respect to r and provides a basic description of the wind kinematic2. Given the observed UFO absorption feature, we require that i < θout, that is, that the LOS has to lie inside the wind. We also consider a more refined version of the model, allowing for an internal cavity with variable angular aperture θin.

The conical geometry of the wind is approximated by a large number l (i.e., 100) of conical shells, equally spaced between r = 0 and r = rcone. These shells have angular opening θout with respect to the symmetry axis. For each shell, we assign angular coordinates to a number n of points (n = 104 by default) through a Monte Carlo method. The radial velocity is a function of radius, according to the linear relation of Eq. (1), in which s ranges from 0 to 1 and represents the deceleration factor of the wind as a function of r′, which is the distance from the vertex normalized to the height of the cone (rcone). The latter is not a parameter of the WINE model, as in Eq. (1) the radial velocity only depends on the dimensionless radius r′≡r/rcone spanning the range [0, 1]. Accordingly, the radial velocity of the wind at the vertex is vmax, while the velocity at r = rcone is defined as vmin.

We assume the same intrinsic brightness Bint for each point all over the cone (see Eq. (3) and following discussion). Then, using special relativity, we calculate for each point of the shell the projected value of Bint and v(r) along the LOS: Bproj and v(r)proj, respectively. Values of Bproj are then grouped into bins of 3600 km s−1. In this way we obtain the spectrum of a single shell. The combination of each shell spectrum at all radii (i.e., from r = 0 to r = rcone) provides the global spectrum emitted by the wind.

The total observed emissivity of the wind is therefore and parametrized in xspec through the normalization of the WINE model component (see Sect. 3). Notwithstanding the fact that Bint can be estimated from Btot, it is not possible to derive from it a reliable value for the Fe ions’ emissivity, given the current stage of the WINE model, which would allow us to infer the column density of the wind. This would require an accurate treatment of the ionic abundances and emissivities, as well as the photoionization equilibrium and radiative transfer within the medium. This will be accounted for in a future version of the WINE model by incorporating XSTAR tables into the present modelization of the wind (see Sect. 4).

Our model assumes a radial density profile of the wind ρrα. In the case of the UFO in PDS 456, we choose α = −2, an isothermal density profile. This ensures that the ionization parameter as a function of the radius of the wind, ξ(r), is constant at all radii, in accordance with the observations of PDS 456 showing that the wind ionization is dominated by Fe XXVI (Reeves et al. 2003, 2009; N15). In fact, the number density of the wind can be written as

(2)

where n0 is the density of the wind at a fiducial radius r0. Using Eq. (2), ξ(r) can be expressed as

(3)

where there is no dependence on r. A constant ξ, as shown in Eq. (3), indicates that the relative abundance of the ions, including Fe XXVI, is roughly constant within the medium and therefore justifies our assumption of constant Bint.

In the following we provide a detailed description of the free parameters of the WINE model:

  • vmax: the maximum velocity of the wind (in units of c) corresponding to the starting velocity at the vertex of the cone. We assume [0.1 c, 0.6 c] as the possible range of vmax and we span this interval with a resolution of 0.01 c.

  • The opening angle θout can range from 0 to 90 deg (see Fig. 1). This interval is sampled by nine equally-space steps of 10 deg.

  • i: the upper limit of this parameter is set by the requirement of having an LOS inside the cone aperture, that is, iθout. The possible range for i, [0, θout], is sampled with 11 equally spaced steps.

  • The deceleration factor of the wind s (Eq. (1)) ranges from 0 to 1 and it is sampled through steps of 0.1.

  • Furthermore, an inner cavity in the cone can be accounted for by an additional parameter θin, which represents the angular amplitude with respect to the symmetry axis. Parameter θin can span the open interval (0, i).

From this set of free parameters, it is possible to derive (i)v(r), as defined by Eq. (1), and (ii)Cf, the covering factor of the wind defined as the fraction of sky covered by the cone, as seen from the vertex:

(4)

In the case of a cone with an inner cavity, Eq. (4) becomes

(5)

3. Spectral analysis

We merge the simultaneous XMM-Newton and NuSTAR spectra from Epoch 3 (September 15, 2013) and Epoch 4 (September 20, 2013) in N15 (see Table 1) in order to increase the signal-to-noise ratio. We consider these two datasets since they are virtually indistinguishable in terms of flux and spectral shape.

Table 1.

Journal of the observations.

Data reduction and spectral extraction are performed using the data analysis software SAS 16.0.0 and NUSTARDAS v1.7.1 (calibration database version 20170222) for XMM-Newton and NuSTAR, respectively. Table 1 lists the journal of the observations. We adopt the same filtering scheme and spectral extraction regions as in N15.

We co-add the spectra of Epochs 3 and 4, both for XMM-Newton and for NuSTAR, using the ftools task addascaspec, and finally group them to a minimum of 100 and 50 counts per energy bin, respectively.

We base our fitting procedure on that of N15, with a lower energy bound of 3 keV. This allows us to avoid two complex spectral features: the soft excess at energies below ∼1 keV and the warm absorber at ≲2 keV. The upper bounds are 10 and 30 keV for the XMM-Newton and NuSTAR spectra, respectively. The spectra are always jointly fitted, with an intercalibration constant left free to vary.

3.1. Phenomenological fit

Similarly to N15, we first perform a preliminary fit to describe the continuum emission using a power law modified by a neutral partial covering absorber, responsible for the spectral curvature below 4 keV. We ignore the energy interval around the Fe K shell features, from 5 and 14 keV. Using directly the xspec notation, the fitting model can be expressed by the analytical expression

(6)

where constant is a constant multiplicative factor, set ≡ 1 for XMM-Newton data and left free to vary for the two NuSTAR modules. This is necessary to account for intercalibration differences between the three instruments. Galactic absorption is represented through phabs, which is set to (see N15). The neutral partial covering absorber is described by zpcfabs. Finally, the spectral index Γ and normalization K of the power-law continuum are left free to vary.

We obtain a spectral index Γ = 2.40 ± 0.06 for the continuum component. For the absorber, we find a column density of NH = 2.4 ± 0.3 × 1023 cm−2 and covering fraction of Cf = 0.42 ± 0.05, suggesting a more distant feature from the AGN with respect to the UFO. These findings are in agreement with the low values for NH and ξ and the low variability found in N15 for this component. The resulting χ2 is 309 for 362 degrees of freedom (d.o.f.). Table 2 shows the best-fit parameters. Figure 2 shows the residuals in terms of data-to-model ratios over the 3–30 keV band.

Table 2.

Best-fit values for the continuum fitting (see relation 6).

thumbnail Fig. 2.

Ratio between data and the best-fit continuum model to the 3–5 keV + 15–30 keV spectrum, once the 5–14 keV region is included (see Sect. 3.1 for details). Black, green, and red crosses indicate XMM-Newton/pn, NuSTAR FPMA, and FPMB data.

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Then, in order to have a first description of the absorption and emission features related to the Fe K shell, we consider the whole energy band adding a Gaussian emission line with energy corresponding to Fe XXVI Lyα (E = 6.97 keV rest frame) and free width and redshift. We model the absorption including two Gaussian lines for Fe XXVI Lyα and Lyβ (E = 8.25 keV rest frame) and a photoelectric edge at E = 9.28 keV rest frame, to take into account the K shell edge from Fe XXVI.

The inclusion of these spectral components is based on the phenomenological analysis reported in N15, in order to fully characterize the observed Fe K spectral features. The resulting model is

(7)

In addition to the components in expression (6), zgauss_em_Lyα indicates the Gaussian emission associated to Fe XXVI Lyα and zgauss_abs_Lyα, zgauss_abs_Lyβ represents the Gaussian absorption for Lyα and Lyβ lines, respectively. The term zedge corresponds to the photoelectric edge due to the Fe K shell.

A simple fit leaving all the parameters free returns an almost identical redshift for both the absorption lines, z = −0.100 ± 0.009, −0.107 ± 0.005, for Lyα and Lyβ respectively, corresponding to a blueshifted velocity of ≃0.26, 0.27 c, while the redshift of the K shell edge, z = −0.071 ± 0.1, implies a velocity of ≃0.24 c. Since we expect that the same medium is responsible for all the absorption features, we impose the same redshift for the lines and the edge. Moreover, we link the Gaussian line widths in order to have the same velocity dispersion. Table 3 lists the best-fit values for these emission and absorption components, obtained by keeping the continuum and the partial covering absorption parameters fixed to the values shown in Table 2. The best-fit results in a χ2 = 649 for 705 d.o.f., confirming the validity of our hypothesis.

Table 3.

Best-fit values for the phenomenological fit (see relation 7).

Interestingly, the redshift of the emitting component is significantly shifted with respect of that of the host galaxy: z = 0.117 versus z = 0.184. This corresponds to a difference in terms of blue-shifted velocity along the LOS of ≃0.06 c (∼18 000 km s−1), lending support to the idea that we are observing the approaching component of the biconical outflow as in Fig. 1.

3.2. Fit with the WINE model

As a further step, we replace the Gaussian emission line of the phenomenological fit with two WINE model components, corresponding to Lyα and Lyβ emission. The continuum and neutral partial covering absorber are still parametrized as in Sect. 3.1.

The fitting model is described by the expression

(8)

where WINE_Lyα and WINE_Lyβ represent the two WINE model emission components. The two Gaussian absorption lines, zgauss_Lyα and zgauss_Lyβ, account for Lyα and Lyβ absorption, respectively, and smedge (Ebisawa et al. 1994) is a smeared photoelectric edge, to account for the velocity gradient of the wind (see Eq. (1)). WINE_Lyα and WINE_Lyβ have identical parameters, except for rest-frame energy and normalization. Specifically, the ratio between the normalizations corresponds to the ratio of the oscillator strength of Fe XXVI Lyα and Lyβ (Molendi et al. 2003; Tombesi et al. 2011).

Since we expect that both the emission and absorption features are due to the same medium, we tie the redshift and broadening of zgauss_Lyα, zgauss_Lyβ, and smedge to the emission parameters in the WINE model. Specifically, since our LOS intercepts the UFO, the velocity component of the gas along the LOS (i.e., the gas responsible for the absorption) coincides with the radial velocity v(r). So, the average redshift zavg of zgauss_Lyα, zgauss_Lyβ and smedge corresponds to the average outflow velocity, vavgv (rcone/2), according to the equation

(9)

where zPDS = 0.184. Moreover, we assume that the standard deviation σ of zgauss_Lyα and zgauss_Lyβ is dominated by the velocity shear of the wind. Hence, we set σ, in terms of velocity, equal to the difference vmaxvavg, while in terms of energy it can be expressed as

(10)

where E is the rest frame line energy. The same formula, using the photoionization energy threshold, can be used to express the smearing characteristic width in the smedge component.

Figure 3 shows the result of the fit assuming a full cone (without inner cavity). The associated χ2 (d.o.f.) is 652 (715). The best-fit values are listed in Table 4. The radial velocity v(r) ranges from ≃0.28 c to ≃0.17 c. Regarding the outflow geometry, we obtain θout ∼ 70 deg, i ∼ 60 deg, and a covering fraction (calculated as the fraction of visible hemisphere covered by the wind) of Cf ∼ 0.7.

thumbnail Fig. 3.

Top panel: data (symbols as in Fig. 2) and best-fit model (solid line) including two WINE model components (dotted lines). Bottom panel: ratios between data and best fit model. See Sect. 3.2 for more details.

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Table 4.

Best-fit values for the absorption and emission components using the WINE model (see relation 8).

We also evaluate the inclusion of the cavity and find that it is not statistically required by the data, with a poorly constrained value of θin, with an upper limit of 21 deg (90% c.l.).

3.3. Reliability of the WINE model

We perform extensive simulations in order to check the reliability of the WINE model. In particular here we present two cases. We first use as input our best-fit values (see Sect. 3.2 and Table 4) and simulate XMM-Newton and NuSTAR FPMA and FPMB spectra with the same summed (Epoch 3 + Epoch 4) net exposure times reported in Table 1. We adopt the same spectral grouping as described in Sect. 3. For each simulation, we first perform a fit in the range 3–10(3–30) keV for XMM-Newton(NuSTAR), ignoring the interval between 5 and 14 keV, to find the best-fit continuum and cold absorber parameters. Then, we freeze these parameters and we fit the WINE model (together with the two Gaussian absorption lines and the photoelectric edge), considering also the energy interval 5–14 keV.

Table 5, first column, reports the differences Δ between the input values and the results, according to the formula

(11)

Table 5.

Results of the simulations to check the reliability of the WINE model.

where Vi is the input value, V̄ is the mean of the distribution of the best-fit values from 100 simulated spectra, and σout is the standard deviation of the distribution. The agreement between the mean values and the input parameters is remarkably good. We then perform an additional set of simulations, using different arbitrary input values, to check the capability of the WINE model to discriminate between different scenarios. Columns 2 and 3 of Table 5 report the input values and the resulting Δ, respectively.

4. Discussion

Using the novel wind emission (WINE) model, we constrained the velocity (mean value ∼0.23c), opening angle (71 deg), and covering fraction (0.7) of the UFO in the quasar PDS 456. The results of our analysis are in agreement with the estimates on the bulk wind velocity and Cf in N15. For the first quantity they estimated ∼0.25 c, which is inside our radial excursion (0.17 − 0.28 c).

The covering fraction in N15 is evaluated in different ways. The normalization of the XSTAR wind emission tables yields an average value between all the observations of Cf = 0.8 ± 0.1, while the fraction of the absorbed continuum luminosity re-emitted by the wind gives Cf > 0.5.

We find a wind opening angle of deg, implying . This value is consistent with N15 and with UFO detection rates in the larger AGN population (see, e.g., Tombesi et al. 2010, 2014; Gofford et al. 2013).

Covering fraction is a key property in the calculation of the mass outflow rate, as expressed in Crenshaw & Kraemer (2012),

(12)

with r the launching radius, μ the mean atomic mass per proton (≈1.2, Gofford et al. 2015), mp the proton mass, and v the outflow velocity. From out and v, it is possible to estimate the momentum rate, out = out v, and the energy transfer rate, . These quantities are fundamental in the determination of the AGN feedback towards the host galaxy, and hence of their coupled evolution.

For the outflow velocity, we use v = (0.23 ± 0.06) c, that is, the average velocity of the UFO vavg as the mean value, and vmax and vmin (i.e., v(rcone)) as upper and lower limit, respectively. Moreover, we consider our covering fraction Cf = 0.7, while the following quantities are taken from N15: NH = 6 × 1023 cm−2, r = 100 rg (=1.5 × 1016 cm), Lbol ∼ 1047 erg s−1, and the black hole mass MBH = 109 M. We find out ~ 16 ± 4 Msun yr−1 ~ 0.23 ± 0.06 Edd, for a radiative efficiency η = 0.3, as expected for luminous quasars such as PDS 456 (see, e.g., Davis & Laor 2011; Trakhtenbrot 2014). We derive a momentum rate out = 7 ± 3 × 1036 dyne, ∼2.1 ± 1.1 times the radiation momentum rate rad = Lbol/c, and an energy rate Ėout = 3 ± 2 × 1046 erg s−1, that is, ∼30 ± 20% LAGN.

The average values for out and Ėout are a factor of ∼1.5 and ∼1.3 times greater than that found in N15, respectively. This is mainly due to the different covering fractions (0.7 versus 0.5) and because they assume μ ≡ 1 (i.e., the gas is composed only by hydrogen).

To investigate the possibility that the quality of the observations did not allow us to constrain the presence of an inner cavity, we run a set of 100 simulations of observation with the X-ray Integral Field Unit (X-IFU) instrument of the Advanced Telescope for High-Energy Astrophysics (ATHENA; Nandra et al. 2013). We adopt the best fit model (see Eq. (8) and Table 4), including an internal cavity with angular amplitude θin = 21 deg, the 90% upper limit reported in Sect. 3.2. We find that 500 ks are necessary to constrain the presence of the cavity, with a confidence level of 90%. With this exposure time we can measure the parameters with an accuracy higher than 6%, except for θin and Cf, for which the relative uncertainties are 18% and 11%, respectively. Further details are in Appendix A.

The results of this work show the robustness of the WINE model and its utility to constrain the properties of the outflow. This could be useful especially for those cases in which it is not clear whether the emission and/or absorption features are mainly due to disk reflection or nuclear winds (see, e.g., Hagino et al. 2016 for 1H 0707-495 and de La Calle Pérez et al. 2010; Patrick et al. 2012 for type I AGNs). More generally, this model represents a physically and geometrically based approach to explore outflow kinematics and can shed new light also on known UFOs from quasar sources (see, e.g., Hagino et al. 2017; Parker et al. 2017; Tombesi et al. 2017). With some minor changes, this model can be applied also to larger scale outflows, such as broad line regions (Vietri et al. 2018) up to galactic-scale outflows (Feruglio et al. 2015).

In the forthcoming version of the WINE model we will use the XSTAR code to calculate the ionic abundances and emissivities. This will allow us to accurately take into account all the relevant transitions as a function of the density and the ionization parameter of the wind. We will also be able to constrain the launching radius and the spatial extent of the wind. Accordingly, the next version of the model will self-consistently represent both the emission and absorption features.


1

The gravitational radius rg is defined as rg = GM/c2, with G the gravitational constant and M the black hole mass.

2

We are aware that the velocity profile of the wind may differ from the one we are assuming here. Specifically, the wind may be accelerated by radiation pressure or MHD driving, showing a non-linear dependence both on the radius r and on the azimuthal angle with respect to the accretion disk. We will check these dependences in a forthcoming work.

3

We use response files and background spectra available at http://x-ifu.irap.omp.eu/resources-for-users-and-x-ifu-consortium-members/. We simulate the case of a mirror module radius of 1469 mm and adopt a background spectrum for an extraction area of 5 arcsec radius.

Acknowledgments

We thank the referee for useful comments and suggestions that helped improve the quality and the presentation of the paper. EP and LZ acknowledge financial support from the Italian Space Agency (ASI) under the contract ASI-INAF I/037/12/0 (NARO): “The unprecedented NuSTAR look at AGN through broadband X-ray spectroscopy”. FT acknowledges support by the Programma per Giovani Ricercatori – anno 2014 “Rita Levi Montalcini”. We thank Dr. K. Fukumura for helpful discussions.

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Appendix A: ATHENA simulations

In order to assess the capability of the next-generation X-ray observatory ATHENA (Nandra et al. 2013) to constrain the presence of an internal cavity, we run a series of simulations with the X-IFU instrument3, using variable exposure times. We adopt the best-fit model found in Sect. 3.2, including also a cavity with θin = 21 deg, the 90% upper limit estimated in Sect. 3.2. We simulate a set of 100 spectra. For each one, we group the spectrum to a minimum of 100 counts per bin; then, we perform two different spectral fittings of the data, in the energy range 3–12 keV. In the first one, we assume a full cone geometry and in the second one we include the inner cavity. Finally, we perform the F-test to check if the difference in the statistics of the two fits is enough to justify the introduction of the cavity. We verify that an exposure time of 500 ks ensures that 90% of the simulated spectra allows us to discriminate the presence of the cavity with an F-test probability < 1%.

Table A.1 reports the mean and the standard deviation of the distribution of the best-fit values using an exposure of 500 ks. Figure A.1 reports one of the simulated 500 ks spectra along with the best-fit inner cavity model.

Table A.1.

Best fit values of the ATHENA simulations.

thumbnail Fig. A.1.

Particular of one of the ATHENA X-IFU 500 ks simulated spectrum, along with the best-fit model including an inner cavity (solid red line). The two Lyα and Lyβ WINE model components are reported as dotted lines.

Open with DEXTER

All Tables

Table 1.

Journal of the observations.

Table 2.

Best-fit values for the continuum fitting (see relation 6).

Table 3.

Best-fit values for the phenomenological fit (see relation 7).

Table 4.

Best-fit values for the absorption and emission components using the WINE model (see relation 8).

Table 5.

Results of the simulations to check the reliability of the WINE model.

Table A.1.

Best fit values of the ATHENA simulations.

All Figures

thumbnail Fig. 1.

Sketch of the WINE model. Further details can be found in Sect. 2.

Open with DEXTER
In the text
thumbnail Fig. 2.

Ratio between data and the best-fit continuum model to the 3–5 keV + 15–30 keV spectrum, once the 5–14 keV region is included (see Sect. 3.1 for details). Black, green, and red crosses indicate XMM-Newton/pn, NuSTAR FPMA, and FPMB data.

Open with DEXTER
In the text
thumbnail Fig. 3.

Top panel: data (symbols as in Fig. 2) and best-fit model (solid line) including two WINE model components (dotted lines). Bottom panel: ratios between data and best fit model. See Sect. 3.2 for more details.

Open with DEXTER
In the text
thumbnail Fig. A.1.

Particular of one of the ATHENA X-IFU 500 ks simulated spectrum, along with the best-fit model including an inner cavity (solid red line). The two Lyα and Lyβ WINE model components are reported as dotted lines.

Open with DEXTER
In the text

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