A DETAILED ANALYSIS OF THE HIGH-RESOLUTION X-RAY SPECTRA OF NGC 3516: VARIABILITY OF THE IONIZED ABSORBERS

NGC 3516 is a Seyfert 1.5 galaxy (Véron-Cetty & Véron 2006) at z = 0.00886 (Keel 1996) that presents an extreme X-ray flux variability (Edelson et al. 2000; Netzer et al. 2002; Turner et al. 2008; Markowitz et al. 2008). NGC 3516 is also extremely variable in optical and UV emission (see as examples Voit et al. 1987; Walter et al. 1990; Crenshaw et al. 1998; Goad et al. 1999; Edelson & Nandra 1999; Maoz et al. 2002; Kraemer et al. 2002).

The source has been observed in X-rays from 1979 (Maccacaro et al. 1987) to 2009 (Turner et al. 2011) with all the X-ray observatories (Kolman et al. 1993; Nandra & Pounds 1994; Morse et al. 1995; Kriss et al. 1996; Edelson & Nandra 1999; Costantini et al. 2000; Guainazzi et al. 2001; George et al. 2002; Turner et al. 2008, 2011). NGC 3516 presents a complex spectrum: in the soft X-ray range (0.3–2 keV), the spectrum shows the so-called soft excess, several absorption features attributed to the presence of warm absorbers and few emission lines (Costantini et al. 2000; Guainazzi et al. 2001; George et al. 2002; Turner et al. 2005, 2008; Mehdipour et al. 2010). In the hard band (2–200 keV), it presents the fluorescence iron emission line Kα and two absorption lines by Fe xxv and Fe xxvi. To fit the hard band X-ray continuum of this source, Turner et al. (2005) fitted a power law, finding a photon index Γ ∼ 2 in the 10–200 keV regime. Also, Markowitz et al. (2008) fitted an absorbed power law with Γ = 2 over the 0.3–76 keV range. Recently, Mehdipour et al. (2010) reported a significant change in the slope of the power law among the 2006 XMM-Newton observations: Γ varied from 1.70 ± 0.2 to 1.85 ± 0.2, in addition to significant changes in the 0.2 to 10 keV range flux.

To model the soft excess emission Markowitz et al. (2008) added a second power law, with the same photon index as the primary power law but not obscured by any absorber. Mehdipour et al. (2010) added a modified blackbody component which describes the spectrum of a blackbody reprocessed by coherent Compton scattering. The best-fit temperature varied from 186 ± 3 eV to 211 ± 4 eV. We note that the soft excess physical interpretation is still an issue (see Ricci et al. 2010).

The complex absorption in NGC 3516 soft X-ray band was detected by two strong absorption features at 0.74 and 0.87 keV with the ROSAT (Mathur et al. 1997) and ASCA X-ray telescopes (Kriss et al. 1996). These features were originally interpreted as absorbing K edges due to O vii and O viii bound–free transitions. More recently, a few high ionization absorption components producing both absorption lines and edges have been detected in high-resolution spectra. Turner et al. (2005) reported three ionization states: (1) a "cool" absorber with a column density N_H  ∼ 6 × 10²¹ cm⁻² and an outflow velocity v_out = −200 km s⁻¹ (all the outflow velocities in this work were fixed to a given value), associated with the "UV absorber" found by Kraemer et al. (2002); (2) a "high ionization" absorber with N_H  ∼ 10²² cm⁻² and a fixed v_out = −1100 km s⁻¹; and (3) a "heavy" absorber with N_H  ∼ 10²³ cm⁻² and v_out = −1100 km s⁻¹ that covers only 50% of the continuum source. Later on, Turner et al. (2008) discovered a fourth absorbing component with an even higher ionization state through the positive detection of H-like and He-like features of Fe xxv and xxvi. This component, only detectable in the hard X-ray band, has N_H  ∼ 10²³ cm⁻² and v_out ∼ −1000 km s⁻¹. Turner et al. (2008) interpreted the flux variations in the X-ray band as the result of variations in the covering fraction of the "heavy absorber."

Using low-resolution Suzaku data, Markowitz et al. (2006) found two absorbing components: a "primary absorber" with properties consistent with the "heavy" absorber reported by Turner et al. (2008; although with a covering fraction of 96–100%) and a mildly ionized medium, consistent with the "UV absorber." Mehdipour et al. (2010) analyzed the XMM-Newton data of the source. They detected the same three absorbing components as Turner et al. (2008), but they reported that partial covering is not required by the data for the heavy absorber. If these authors impose a partial absorber in their models, they further find that variations in the covering fraction are not consistent with the data (in contrast to the results by Turner et al. 2008).

Finally, Holczer & Behar (2012) found a kinematic structure in the absorber, consisting of four different outflow components intrinsic to NGC 3516: (1) v_out = −350 ± 100 km s⁻¹, (2) v_out = −1500 ± 150 km s⁻¹, (3) v_out = −2600 ± 200 km s⁻¹, and (4) v_out = −4000 ± 400 km s⁻¹. Holczer & Behar (2012) analyzed the Chandra high-resolution spectra obtained in 2001 and 2006. They detect variability in this structure, noting that the high velocity components are only present in the 2006 observations. They further report that the covering factor plays a minor role in the absorption lines.

In the UV band, Kraemer et al. (2002) have reported eight different kinematic absorbing components. Using data obtained by the GHRS (Goddard High Resolution Spectrograph) on board the Hubble Space Telescope (HST), these authors detected four of these components through Lyα, CIV, and NV absorption lines with radial velocities of −376, −183, and −36 km s⁻¹ (where the last system is comprised by a blend of two different kinematic components). Later on, the other four kinematic components were detected with the Space Telescope Imaging Spectrograph (STIS) on board the HST. These components present radial velocities of −692, −837, −994, and −1372 km s⁻¹. These authors suggest that the emergence of the new components is the result of variations of ionized gas in response to changes in the ionizing continuum.

As it has been reported NGC 3516 presents strong flux variations in time, from the optical–UV to the X-rays (see for example Koratkar et al. 1996 and Kraemer et al. 2002). The source presents extreme X-ray flux variations by a factor of five on timescales of hours (Turner et al. 2008), and by a factor of 50 in timescales of years (Netzer et al. 2002). These variations are often associated with spectral changes (e.g., Netzer et al. 2002; Turner et al. 2008 and references therein) not only in the energy flux, but also with evidence of spectral feature variability (Mathur et al. 1997; Netzer et al. 2002; Turner et al. 2008; Holczer & Behar 2012). To understand the nature of the variability, some scenarios invoking obscuration have been proposed. Costantini et al. (2000) suggested neutral clouds that hide the central source (using Beppo SAX telescope spectra), and Markowitz et al. (2008; with Suzaku spectra) proposed a model in which flux variations could be explained by the presence of discrete blobs or filaments located within few light years of the black hole, traversing the line of sight during the observation time. Turner et al. (2008) suggested a simple explanation were that only parameter varying among observations (and producing both the flux and spectral variations) is the covering factor of the heavy absorber phase.

Other interpretations suggest that rather, the variations might be intrinsic to the source. Mehdipour et al. (2010) arrived at this conclusion using 2006 XMM-Newton spectra.

However, in a most recent X-ray NGC 3516 analysis, using 2009 Suzaku X-ray observations, Turner et al. (2011) claim an absence of reverberation signals. This led them to conclude that intrinsic continuum variability is not possible. They suggested that the variability can be a consequence of Compton-thick clumps of gas in the line of slight.

In this paper, we present the analysis of all 2006 X-ray observations available in the XMM-Newton Science Archive (XSA) and Chandra Data Archive (CDA) of NGC 3516. We study both high- and low-resolution spectra to cover the range between 0.3 keV to 10 keV. We first present the analysis over individual spectra to characterize the spectral components and then study the time variability of the absorber among observations. In our analysis, we find variations in two of the ionized absorbers in response to continuum variations.

Section 2 describes the X-ray observations and the data reduction. In Section 3, we present 2006 X-ray data analysis and the best model for XMM-Newton data; we also describe the Chandra analysis. Section 4 contains our results, including the time variability behavior and a physical scenario proposed to explain the X-ray proprieties and the flux variability of NGC 3516. We discuss our results in Section 5. Finally, in Section 6, we present the conclusions.

We studied all the NGC 3516 XMM-Newton X-ray spectra from the RGS (Reflection Grating Spectrometer) and the EPIC-PN (European Photon Imaging Camera). The observations were performed between 2006 October 6 and 12.

The RGS data were processed with the standard pipeline of Science Analysis System (SAS) v8.0.1 (Gabriel et al. 2004). We produced source and background spectra, as well as response matrices for the RGS data with the rgsproc task. The RGS spectra were grouped into two channels per bin. We considered the wavelength range from 8 to 38 Å [0.33–1.55 keV], which covers most of the soft X-ray band.

EPIC-PN spectra were also generated using SAS. First, intervals of flaring particle background were selected in order to clean the event list using the method presented in Piconcelli et al. (2004). The spectra were extracted from a circle with center on the observed position of NGC 3516 and radius ∼40'' in all observations. The background spectra were obtained from a circular region with similar radius in the same chip of the source. No sign of pile-up was detected in any of the observations as reported before by Turner et al. (2008) and Mehdipour et al. (2010). The source and background spectra were generated with the evselect task. Then, the redistribution matrix and the ancillary files were created with the rmfgen and the arfgen tasks, respectively. The spectra were grouped to a minimum of 20 counts per bin in order to be able to use χ² statistics. We selected the interval from 0.3 keV to 10 keV that includes the soft and hard X-ray bands. In Table 1, the net count rate and the exposure time for each ObsID and detector of the XMM-Newton observations of NGC 3516 are shown.

The Chandra X-ray observations were performed from 2006 October 9 to October 14 using the High Energy Transmission Grating (HETGS) with the ACIS-S (Advanced CCD Imaging Spectrometer). The HETGS (Canizares et al. 2000) contains two grating assemblies, the Medium-Energy Grating (MEG) and High-Energy Grating (HEG). We extracted spectra from both gratings using the Chandra Interactive Analysis of Observations software (CIAO v.3.4, Fruscione et al. 2006; we followed the standard pipeline processes). Negative and positive first-order spectra and their response matrices were obtained and co-added. The spectra were grouped into two channels per bin. The count rates and the exposure time in the MEG and HEG spectra are given in Table 2.

The 2006 X-ray observations of NGC 3516 were performed with almost continuous time coverage (with XMM-Newton and/or Chandra) on a timescale of nine days (see Tables 1 and 2). We have numbered the observations in sequential order according to the date of observation, and further included an x suffix if performed by XMM-Newton or a c suffix if obtained with Chandra.

There is strong flux variability among different observations with the same observatory (compare count rates for observations with the same observatory/instrument in Tables 1 and 2) and within single observations. A detailed light curve of the nine observations can be observed in Figures 1 and 2 of Turner et al. (2008). In this paper, we study the temporal evolution of the absorbing components in response to these flux changes.

We performed the analysis of the XMM-Newton observations using simultaneously both the EPIC-PN and RGS data sets. All spectra were analyzed with the Sherpa (Freeman et al. 2001) package included in the CIAO software. Throughout the paper, we attenuate all models with an equivalent H column density N_H = 3.23 × 10²⁰ cm⁻² (Dickey & Lockman 1990) to account for the Galactic absorption in the line of sight toward NGC 3516.

3.2.1. Analysis in the X-Ray Hard Energy Band

First, we modeled the NGC 3516 EPIC-PN spectra in the 2.5–10 keV band. We fit the data using a redshifted power law model plus a Gaussian to account for the Fe-Kα emission line reported by Turner et al. (2008) and Mehdipour et al. (2010). This model presents strong negative residuals around 7 keV, confirming the two significant absorption lines reported by Turner et al. (2008) and Mehdipour et al. (2010), corresponding to Fe K transitions of Fe xxv and Fe xxvi. These features were modeled with Gaussians at this initial stage (although a self consistent photoionization model was applied to this absorption system later on). Table 3 lists the best-fit parameters for each observation. The model is statistically acceptable for all observations (Table 3).

Table 3. Hard Band Fit: 2.5–10 keV Energy Band

Obs	Power Law		Fe–Kα	Fe xxv	Fe xxvi	Statistics
	Γ	Norma	Pos(keV)	Pos(keV)	Pos(keV)	χred/dof
			σ (keV)	σ (keV)	σ (keV)	(2.5–10 keV)
			Normb	Normb	Normb
1x	1.64 ± 0.02	1.22 ± 0.02	$6.38^{+0.03}_{-0.02}$	6.73 ± 0.03	7.04 ± 0.02	0.79/1364
			$0.13^{+0.05}_{-0.03}$	0.04 ± 0.04	0.05 ± 0.04
			$5.89^{+0.64}_{-0.84}$	$-1.42^{+0.31}_{-0.30}$	−1.58 ± 0.03
2x	1.59 ± 0.02	0.99 ± 0.02	6.39 ± 0.02	6.703 ± 0.019	7.05 ± 0.02	1.08/1411
			0.12 ± 0.02	0.03 ± 0.04	0.05 ± 0.04
			$7.37^{+0.43}_{-0.45}$	−1.15 ± 0.23	−1.38 ± 0.23
5x	1.45 ± 0.02	0.65 ± 0.02	6.38 ± 0.02	6.75 ± 0.02	7.08 ± 0.02	1.17/1357
			0.13 ± 0.02	0.02 ± 0.04	0.03 ± 0.03
			$7.29^{+0.44}_{-0.45}$	−1.06 ± 0.21	−1.16 ± 0.22
8x	1.54 ± 0.02	0.95 ± 0.02	6.41 ± 0.02	6.78 ± 0.02	$7.11^{+0.03}_{-0.02}$	0.79/1483
			0.09 ± 0.02	0.04 ± 0.03	0.05 ± 0.03
			$5.89^{+0.48}_{-0.47}$	−1.84 ± 0.31	−1.86 ± 0.32

Notes. ^a In 10⁻² photons keV⁻¹ cm⁻² s⁻¹ at 1 keV. ^b In 10⁻⁵ photons cm⁻² s⁻¹ in the line.

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Table 4. Whole Band Fit: 0.3–10 keV

Obs		Power Law		Blackbody		Statistics
		Γ		kT (keV)		χred/dof
		Norma		Normb		(0.3, 10 keV)
1x		1.31 ± 0.02		0.08 ± 0.02		4.5/4534
		0.78 ± 0.02		5.92 ± 0.05
2x		1.30 ± 0.02		0.09 ± 0.02		5.2/4581
		0.66 ± 0.02		5.85 ± 0.04
5x		1.05 ± 0.02		0.09 ± 0.02		4.2/4527
		0.36 ± 0.02		2.99 ± 0.03
8x		1.21 ± 0.02		0.09 ± 0.02		5.2/4655
		0.61 ± 0.02		6.38 ± 0.04

Notes. ^a In 10⁻² photons keV⁻¹ cm⁻² s⁻¹ in al 1 keV. ^b In 10⁻⁴ $L_{39}/D_{10}^{2}$ units, L₃₉ is the source luminosity in units of 10³⁹ erg s⁻¹ and D₁₀ is the distance to the source in units of 10 kpc.

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3.2.2. X-Ray Broadband Analysis

3.2.3. Modeling the Ionized Absorber in NGC 3516

There have been several studies of the warm absorbers in NGC 3516 reporting a different number of ionization components. In order to establish the presence of each component, we decided to add one absorber component at a time in our models. This allows us to test statistically its presence and also to inspect visually its contribution to the overall opacity.

The PHASE code (Krongold et al. 2003) was used to fit the warm absorbers (WA). The model has four free parameters: (1) the ionization parameter U (U = Q/(4πR²n_Hc))⁶; (2) the equivalent hydrogen column density N_H; (3) the outflow velocity v_z; and (4) the internal micro-turbulence velocity v_turb. The spectral energy distribution (SED) of the source, also required in the models, was obtained from NED (NASA/IPAC Extragalactic Database) between the radio and the UV regimes and complemented with our fits to the X-ray band. The SED is shown in Figure 1.

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We note that the estimated errors in the outflow velocity of the absorber are too small, in general, smaller than the resolution of the detectors. For this reason, throughout the paper we consider a conservative error in this parameter as half the minimum spectral resolution of the RGS (700 km s⁻¹ in 15 Å): Δv_out = 350 km s⁻¹. We prefer this conservative value given that the fits to the data include several blended absorption lines from different charge states as well as the blend of several velocity components present in absorption.

Our first model (Model A) consists of a single ionization component and an F-test confirms its presence with >99.99% confidence level for all observations. This component models absorbing lines produced mainly by O vii, O viii, as well as part of the Fe M-shell unresolved transition array (UTA), among others. The outflow velocity is −532 ± 350 km s⁻¹.

Model B included a second WA absorbing phase. A statistically better fit than Model A is supported by an F-test (>99.99% of significance for all XMM-Newton observations). The second absorber fits absorption lines with a higher level of ionization, mainly Fe L-shell absorption from charge states xvii to xxii, also including absorption by Ne x. The outflow velocity is higher also, −1845 ± 350 km s⁻¹. We note that the two ionized absorption phases had different U and N_H values among observations. We will analyze these changes in Section 4.1.

Given that residuals were still present, we further included a third WA phase (Model C). At the beginning, all the parameters were free to vary. However, for each absorbing component, the best-fit value of the outflow velocity v_out among the observations was similar, with differences lower than the RGS resolution: 700 km s⁻¹ (in 15 Å). Thus, we left the outflow velocity of each absorber as a free parameter but constrained it to have the same best-fit value in all the observations (we link this parameter in the models for all observations, assuming no acceleration or deceleration in the flow during the total observing time). Given that the best-fit values of the turbulent velocity v_turb were also very similar among observations with differences lower than RGS resolution, we performed the same procedure with the turbulent velocity, linking this free parameter to a single value in all data sets. According to an F-test, the third absorber included in model C is statistically required by the data (probability >99.99%). This third absorber is modeling low ionization lines produced by charge states such as Ne v and Ne vi, and a fraction of the Fe M-shell UTA. This component had an outflow velocity best-fit value higher than the other two absorbers, v_out = −2425 ± 350 km s⁻¹.

Thus, this final model includes of three absorbing components. The first one consists of a medium level of ionization (hereafter phase MI), the second phase presents high ionization (hereafter phase HI), and the third one is produced by low ionized gas (hereafter phase LI). Tables 5 and 6 summarize the models applied in the four XMM-Newton spectra.

Table 5. Models to Fit NGC 3516 in XMM-Newton Observations

Model	Power Law		Blackbody		WA Parameters			Statistics
	Γ	Norma	KT	Normb	Phase LI	Phase MI	Phase HI	χred/dof
Obs 1x
A	1.69 ± 0.02	1.36 ± 0.02	0.10 ± 0.02	9.18 ± 0.06		√		1.44/4530
B	1.78 ± 0.02	1.58 ± 0.04	0.10 ± 0.02	$5.29^{+0.04}_{-0.09}$		√	√	0.95/4526
C	1.81 ± 0.02	1.67 ± 0.06	0.09 ± 0.02	6.47 ± 0.02	√	√	√	0.86/4504
Obs 2x
A	1.66 ± 0.02	1.11 ± 0.02	0.10 ± 0.02	$5.82^{+0.08}_{-0.05}$		√		1.73/4577
B	1.71 ± 0.02	1.23 ± 0.02	0.10 ± 0.02	5.78 ± 0.04		√	√	1.16/4573
C	1.74 ± 0.05	1.31 ± 0.09	0.09 ± 0.02	6.50 ± 0.40	√	√	√	1.04/4557
Obs 5x
A	1.47 ± 0.02	0.68 ± 0.02	0.10 ± 0.02	$5.82^{+0.08}_{-0.05}$		√		1.23/4523
B	1.54 ± 0.02	0.79 ± 0.02	0.10 ± 0.02	$3.06^{+0.03}_{-0.05}$		√	√	0.98/4519
C	1.61 ± 0.02	0.89 ± 0.02	0.09 ± 0.02	4.39 ± 0.04	√	√	√	0.88/4503
Obs 8x
A	1.63 ± 0.02	1.13 ± 0.02	0.10 ± 0.02	8.09 ± 0.05		√		1.74/4649
B	1.70 ± 0.02	1.28 ± 0.02	0.09 ± 0.02	$6.23^{+0.05}_{-0.03}$		√	√	1.12/4645
C	1.75 ± 0.05	1.4 ± 0.2	0.09 ± 0.02	7.9 ± 0.4	√	√	√	0.97/4629

Notes. ^a In 10⁻² photons keV⁻¹ cm⁻² s⁻¹ in at 1 keV. ^b In 10⁻⁴ $L_{39}/D_{10}^{2}$ units, L₃₉ is the source luminosity in units of 10³⁹ erg s⁻¹ and D₁₀ is the distance to the source in units of 10 kpc.

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Table 6. WA Parameters of NGC 3516

Model C		Phase LI			Phase MI			Phase HI
		logU	logNH		logU	logNH		logU	logNH
		velz (km s−1)	velturb (km s−1)		velz (km s−1)	velturb (km s−1)		velz (km s−1)	velturb (km s−1)
Obs 1x
A					$0.29^{+0.03}_{-0.02}$	21.82 ± 0.02
					−888 ± 350	286 ± 350
B					0.16 ± 0.02	21.65 ± 0.02		$1.65 ^{+0.12}_{-0.02}$	22.07 ± 0.02
					−995 ± 350	220 ± 350		−2302 ± 350	320 ± 350
C		$-0.93 ^{+0.03}_{-0.02}$	21.14 ± 0.02		0.38 ± 0.02	21.56 ± 0.02		1.69 ± 0.02	22.25 ± 0.02
		−2425 ± 350	88 ± 350		−532 ± 350	239 ± 350		−1845 ± 350	112 ± 350
Obs 2x
A					0.27 ± 0.02	21.82 ± 0.02
					−1018 ± 350	207 ± 350
B					0.18 ± 0.02	21.68 ± 0.02		1.95 ± 0.02	22.29 ± 0.08
					−1082 ± 350	195 ± 350		−1851 ± 350	77 ± 350
C		−0.78 ± 0.05	20.98 ± 0.08		0.27 ± 0.02	21.52 ± 0.09		1.68 ± 0.09	22.197 ± 0.164
		=> 1x	=> 1x		=> 1x	=> 1x		=> 1x	=>1x
Obs 5x
A					0.215 ± 0.024	21.94 ± 0.02
					−1388 ± 350	168 ± 350
B					0.12 ± 0.02	21.75 ± 0.02		1.68 ± 0.02	22.22 ± 0.03
					−1066 ± 350	199 ± 350		−885 ± 350	143 ± 350
C		−1.22 ± 0.02	21.25 ± 0.02		0.29 ± 0.02	21.62 ± 0.02		1.77 ± 0.02	22.33 ± 0.14
		=> 1x	=> 1x		=> 1x	=> 1x		=> 1x	=>1x
Obs 8x
A					0.33 ± 0.02	21.93 ± 0.02
					−1154 ± 350	202 ± 350
B					0.18 ± 0.03	21.69 ± 0.02		1.77 ± 0.02	22.07 ± 0.02
					−619 ± 350	234.9 ± 350		−2293 ± 350	417 ± 350
C		−0.78 ± 0.02	21.25 ± 0.09		0.38 ± 0.02	21.512 ± 0.032		1.96 ± 0.22	22.48 ± 0.22
		=> 1x	=> 1x		=> 1x	=> 1x		=> 1x	=>1x

Notes. In Model C, we referred the v_out and v_out to the values of observation 1x; however, the final values were fitted taking into account the four XMM-Newton observations.

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Although the data does not present strong residuals consistent with additional absorption features, we tested a possible fourth WA component in the soft X-ray RGS data. An F-test does not show a statistical improvement over Model C.

3.2.4. Emission Features in the Spectra

The presence of positive residuals in the spectra, associated with emission lines in the rest frame of the object, is evident in the data. Through a detailed visual inspection we identified nine emission features using ATOMDB version 1.3.1 from the Chandra X-ray Center (http://asc.harvard.edu/atomdb/WebGUIDE/), and modeled them with Gaussian components. The FWHM was fixed to 300 km s⁻¹, given that they are not resolved. We found two emission lines corresponding to Ne transitions (Ne vi and Ne ix), five corresponding to O vii, three of them belonging to the triplet between 21.6–22.1 Å, and two lines of highly ionized Iron (Fe xix and Fe xxi). Table 7 shows the nine emission lines detected in the soft X-ray band for each observation.

Table 7. Emission Lines in the Soft Band of XMM-Newton and Chandra

Transitiona	Ne ix	Fe xix	O vii	Fe xix	O vii	O vii	O vii	Fe xxi	Ne vi
	λ13.69*	λ13.91*	λ17.39*	λ17.86*	λ21.60*	λ21.81*	λ22.10*	λ28.53*	λ28.92*
	Wavelength Observed (Å)
Observation	Energy Fluxb
1x	13.79 ± 0.08	14.04 ± 0.04	17.73 ± 0.02	18.05 ± 0.12	21.64 ± 0.02	21.93 ± 0.02	22.29 ± 0.22	28.83 ± 0.03	29.19 ± 0.02
	1.4 ± 0.5	2.4 ± 0.6	1.9 ± 0.05	1.9 ± 0.05	9.8 ± 3.2	3.9 ± ...	0.9 ± 0.8	0.5 ± 0.2	2.6 ± 0.7
2x	13.79 ± 0.02	14.04 ± 0.02	17.67 ± 0.03	18.19 ± 0.03	21.59 ± 0.02	21.89 ± 0.08	22.29 ± 0.09	28.86 ± 0.02	29.18 ± 0.02
	2.4 ± 0.5	1.6 ± 0.5	0.9 ± 0.4	1.2 ± 0.5	0.9 ± 0.8	1.2 ± 0.9	2.9 ± 0.7	0.2 ± 0.5	2.9 ± 0.7
3c	13.81 ± 0.10	14.06 ± 0.02	17.67 ± ...c	18.16 ± 0.72	21.6 ± ...	21.91 ± ...	22.30 ± ...	O.R.d	O.R.
	1.5 ± 0.9	2.6 ± 1.3	1.5 ± 1.8	2.2 ± 2.1	0 ± ...	3.4 ± ...	3.4 ± ...
4c	13.82 ± 0.04	14.06 ± 0.06	17.74 ± 0.08	18.21 ± ...	21.59 ± ...	21.82 ±	22.31 ± ...	O.R.	O.R.
	0.8 ± 0.5	1.07 ± 0.7	0.7 ± 0.6	0.7 ± 0.9	1.5 ± ...	7.7 ± 7.2	6.2 ± 5.5
5x	13.79 ± 0.02	14.04 ± 0.02	17.65 ± 0.02	18.16 ± ...	21.64 ±	21.89 ± 0.2	22.29 ± 0.02	28.82 ± ...	29.19 ± 0.04
	0.9 ± 0.3	2.7 ± 1.2	1.2 ± 0.4	0.7 ± 0.5	8.2 ± 3.3	1.6 ± 0.4	1.9 ± 0.5	0.4 ± 0.6	1.2 ± 0.5
6c	13.82 ± 0.04	14.06 ± 0.02	17.64 ± ...	18.11 ± 0.10	21.62 ± 0.02	21.90 ± 0.04	22.31 ± ...	O.R.	O.R.
	0.9 ± 0.6	2.2 ± 0.8	0.4 ± 0.4	2.6 ± 1.5	709 ± 645	3.6 ± 2.2	4.5 ± 2.6
7c	13.81 ± ...	14.05 ± 0.02	17.71 ± 0.04	18.08 ± ...	N.D.e	21.92 ± 0.36	22.26 ±	O.R.	O.R.
	0.6 ± 0.7	1.4 ± 0.9	2.2 ± 1.4	1.02 ± 1.33	0 ± ...	2.2 ± 3.2	1.2 ± 6.2
8x	13.79 ± ...	14.04 ±	17.78 ± 0.02	18.07 ± 0.15	21.62 ± 0.12	21.88 ±	22.31 ± 0.02	N.D.	29.21 ± .08
	1.1 ± 1.9	0.8 ± 0.9	0.6 ± 0.5	6.2 ± 4.8	123 ± 115	2.4 ± 0.6	1.99 ± 0.75	0 ± ...	2.2 ± 1.7
9c	13.82 ± 0.2	14.07 ± 1.8	17.714 ± 0.12	18.02 ± 0.7	N.D.	N.D.	22.3 ± ...	O.R.	O.R.
	0.9 ± 1.3	3.6 ± 4.2	1.15 ± 1.3	1.6 ± 1.5	0 ± ...	0 ± ...	1.6 ± ...

Notes. ^a Ion name and transition rest-frame wavelength (Å)*. ^b In 10⁻⁴ photons cm⁻² s⁻¹ in the line. ^c ... means indeterminate. ^d O.R. means line out of detector range. ^e N.D. means line not detected.

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We stress that not all the emission lines were detected in a significant way in all the observations. However, the fluxes of all lines are consistent with each other among all the observations, with the only exception of the O vii–Kα transition at λ ∼ 21.6 Å. The differences in this transition are probably due to the strong blending of this line with the strong absorption feature produced by the WA. We point out that Mehdipour et al. (2010) only modeled one emission line in the soft X-ray energy band, namely, O vii (f). These authors only include this feature as it is the only one significant in all observations. Nevertheless, in their Figure 6, it is possible to observe residuals coincident with the emission lines identified here. For instance, at wavelengths around λ ∼ 13.8, ∼17.8, ∼18, ∼22.2, and ∼29.2 Å.

Summarizing, our final model consists of Model C (including the three absorbing component in the soft band) plus the fourth absorbing phase (VH) in the hard band, plus the nine emission lines described above. The figures with the final models (including a simultaneous fit to the Chandra and XMM-Newton data; see Section 3.3) are presented in Figures 2–6. Table 8 contains the observed energy flux values for all observations. The flux was integrated in two different energy ranges: in the soft energy band [8–25 Å: 0.49–1.55 keV] and in the hard energy band [1.55–10 keV]. The reported quantities correspond to the intrinsic flux of the source without attenuation by Galactic absorption (see Section 3.2) and the warm absorber components.

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Table 8. Energy Flux [F_hν] of NGC 3516: Soft X-Ray Band and Hard X-Ray Band

Obs		Soft Band		Hard Band
		Fhνa (8–25 Å: 0.49–1.55 keV)		Fhνa (1.55–10 keV)
1x		1.87 ± 0.05		2.59 ± 0.03
2x		1.69 ± 0.03		2.34 ± 0.02
3c		1.09 ± 0.04		2.04 ± 0.03
4c		0.707 ± 0.019		1.58 ± 0.03
5x		0.88 ± 0.03		1.97 ± 0.02
6c		1.54 ± 0.03		2.22 ± 0.05
7c		1.72 ± 0.03		$2.13^{+0.08}_{-0.06}$
8x		1.84 ± 0.04		2.46 ± 0.03
9c		0.50 ± 0.02		$0.35^{+0.03}_{-0.02}$

Note. ^aIn 10⁻¹¹ erg cm⁻² s⁻¹.

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Once we had a satisfactory fit with XMM-Newton, we proceeded to model the contemporary Chandra spectra. We fit the Chandra data, applying a model consisting of Model C (including the three ionized absorbers detected in the soft energy band) plus the nine emission lines included in the XMM-Newton fits. Both MEG [2–25 Å: 0.5–6.2 keV] and HEG data [1.6–15 Å: 0.8–7.7 keV] were fitted simultaneously.

All nine observations (including those from XMM-Newton and Chandra) were fitted simultaneously, leaving free to vary independently in each observation the photon index and normalization of the power law and the normalization of the blackbody. The temperature kT [keV] of the blackbody emission was free to vary, but constrained to have a single value in all data. The ionization parameter and the column density of the three absorbing components was also fitted independently among different observations. However, as before, the outflow and turbulent velocities of each phase were free to vary, but linked between the nine observations to give a single best-fit value.

The best-fit parameters of this final model are presented in Table 9. The fits over the high-resolution (RGS) spectra are shown in Figures 2, 3, 4, and 5 for observations 1x, 2x, 5x, and 8x, respectively. The MEG of Chandra data and best-fit models are shown in Figure 6. All statistical results are satisfactory with χ_red  ∼ 1 (Table 9). We note that the values for the ionization parameter and column density on each XMM-Newton observation are consistent within 35% (and within the errors) with those found over the fits excluding the Chandra data (Model C, Section 3.2).

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Table 9. Model C: All XMM-Newton and Chandra Observations

Observation	Power Law	Blackbody	Phase HI	Phase MI	Phase LI	Statistics
	Γ	kT (keV)	logU	logU	logU	χred/dof
	Norma	Normb	logNH	logNH	logNH
			vout (km s−1)	vout (km s−1)	vout (km s−1)
			−1847 ± 350	−605 ± 350	−2426 ± 350
1x	1.82 ± 0.02	0.09 ± 0.02	1.76 ± 0.02	0.42 ± 0.02	−1.07 ± 0.04	0.87/4504
	1.69 ± 0.02	$6.47^{+0.06}_{-0.09}$	22.33 ± 0.02	21.56 ± 0.02	21.13 ± 0.05
			−1847 ± 13	−605 ± 27	−2426 ± 5
2x	1.77 ± 0.02		1.77 ± 0.02	0.36 ± 0.02	−0.73 ± 0.02	1.01/4558
	1.33 ± 0.02	6.67 ± 0.05	$22.27^{+0.04}_{-0.02}$	21.46 ± 0.02	21.17 ± 0.03
3c	$1.509^{+0.033}_{-0.028}$		$2.14^{+0.08}_{-0.09}$	$0.28^{+0.17}_{-0.12}$	$-0.815^{+0.204}_{-0.207}$	0.62/980
	1.05 ± 0.02	4.14 ± 0.06	$22.37^{+0.09}_{-0.08}$	$21.408^{+0.119}_{-0.082}$	$21.53^{+0.07}_{-0.08}$
4c	$1.39^{+0.03}_{-0.02}$		2.05 ± 0.08	$0.16^{+0.17}_{-0.19}$	$-0.59^{+0.16}_{-0.17}$	0.68/980
	0.66 ± 0.02	2.84 ± 0.04	22.22 ± 0.09	$21.40^{+0.09}_{-0.07}$	21.55 ± 0.06
5x	1.62 ± 0.02		$1.82^{+0.05}_{-0.08}$	0.27 ± 0.03	−1.13 ± 0.02	0.87/4504
	$0.905^{+0.009}_{-0.011}$	4.25 ± 0.06	22.49 ± 0.12	21.59 ± 0.02	$21.29^{+0.04}_{-0.02}$
6c	1.58 ± 0.02		2.24 ± 0.03	$0.65^{+0.045}_{-0.24}$	−0.54 ± 0.17	1.08/980
	1.38 ± 0.03	5.65 ± 0.04	$22.44^{+0.04}_{-0.05}$	$21.67^{+0.03}_{-0.04}$	$21.45^{+0.03}_{-0.06}$
7c	1.69 ± 0.02		$2.06^{+0.07}_{-0.03}$	$0.53^{+0.04}_{-0.08}$	$-0.65^{+0.13}_{-0.17}$	0.95/980
	$1.58^{+0.05}_{-0.04}$	6.13 ± 0.05	22.40 ± 0.05	$21.61^{+0.04}_{-0.06}$	$21.403^{+0.039}_{-0.077}$
8x	1.75 ± 0.02		2.03 ± 0.02	0.45 ± 0.02	−0.81 ± 0.04	0.95/4630
	1.41 ± 0.02	5.33 ± 0.02	22.52 ± 0.02	21.47 ± 0.02	21.31 ± 0.02
9c	$1.27^{+0.03}_{-0.02}$		$2.45^{+0.05}_{-0.12}$	0.17 ± 0.15	$-0.83^{+0.22}_{-0.26}$	0.74/980
	$0.62^{+0.03}_{-0.02}$	2.94 ± 0.05	$22.44^{+0.08}_{-0.09}$	21.57 ± 0.06	$21.54^{+0.06}_{-0.07}$

Notes. ^a In 10⁻² photons keV⁻¹ cm⁻² s⁻¹ in at 1 keV. ^b In 10⁻⁴ $L_{39}/D_{10}^{2}$.

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We further included in our models the fourth absorbing component (present only in the hard energy band), leaving free to vary independently among the observations the ionization parameter and column density, but constraining the outflow and turbulent velocities to a single best-fit value in all observations. Our results are summarized in Tables 9 and 10.

Table 10. Phase VH Applied in the Hard Band Spectra [3–10 keV], EPIC-PN of XMM-Newton, and HEG [3–7.7 keV] of Chandra

Obs	VH.log U	VH.log NH	Statistics
			χred/dof
1x	3.87$^{+0.09}_{-0.08}$	23.22 ± 0.02	0.65/1067
2x	3.88$^{+0.08}_{-0.06}$	23.22 ± 0.02	0.81/1116
3c	3.99±...a	23.26$^{+0.07}_{-0.24}$	0.76/103
4c	3.91$^{+...}_{-0.32}$	23.22 ± 0.06	1.25/103
5x	3.88 ± 0.42	23.23 ± 0.02	0.78/1062
6c	4.14$^{+...}_{-0.06}$	23.27$^{+0.03}_{-0.59}$	1.33/103
7c	3.51$^{+...}_{-0.91}$	23.18$^{+0.02}_{-0.52}$	1.01/103
8x	3.75 ± 1.08	23.22 ± 0.02	0.7/1188
9c	3.49$^{+1.27}_{-0.37}$	23.28$^{+0.27}_{-0.37}$	0.82/103

Note. The outflow velocity is given by v_out = −2650 ± 350 km s⁻¹. ^a ... means indeterminate.

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Finally, given that the outflow velocities of components HI and LI are similar, we tried a model with these parameters linked to a single value for both components. The warm absorber best-fit parameters did not change significantly as with the Model C, Section 3.2. The velocity found for those two phases (phase HI and LI) is v_out = −1905 ± 350 km s⁻¹.

We included in our models a fourth WA component with a very high ionization level to fit the two absorption lines detected in the hard band (these lines were initially identified with transitions by Fe xxv and Fe xxvi and fitted with Gaussians over the EPIC-PN data). This fourth absorber was modeled only on the EPIC-PN data of XMM-Newton from 3 to 10 keV and the HEG spectra of Chandra in the 3–7.7 keV hard X-ray band. An F-test gives us a confidence level larger than 99.99% for the existence of this absorber (hereafter VH) in all XMM-Newton observations. We found log U ∼ 3.8 and log N_H ∼ 23.2 (see Table 10). Figure 7 shows the spectra and best fit over the EPIC-PN data.

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It is important to clarify that the hard X-rays were fitted separately from the soft X-ray band. However, to fix the power law in the soft energy band, we took into account the hard band in the fit, with the aim to have the best-fit value connected with the soft energy band. We also note that the soft absorbers have no effect on the hard energy band.

First, we fitted simultaneously three spectra of each XMM-Newton observation, RGS 1 & RGS 2 [8–38 Å: 0.33–1.55 keV] and EPIC-PN spectra in the energy range of 0.3–10 keV; the EPIC-PN spectra were included with the aim to obtain the best parameter of the power law. Then, we fitted the Fe–Kα emission line in 6.38 keV and two absorption lines of Fe xxv and xxvi in 6.7 and 6.96 keV, respectively. In this model (Model C), we included 10 emission lines in the soft energy band. Then model C was applied successfully in the five MEG [2–25 Å: 0.5–6.2 keV] and HEG spectra [1.6–15 Å: 0.8–7.7 keV], both Chandra high-resolution detectors. Finally, we cut the spectra of EPIC-PN from 3 to 10 keV and HEG spectra from 3 to 7.7 keV to obtain the fourth and highest ionized absorber, VH.

In this section, we perform a time-resolved analysis of the ionized absorber in NGC 3516. In particular, we identify the parameters that show significant variations among the observations and explore a possible correlation with the changes in flux.

4.1.1. Ionization Parameter U

Phase HI. The most significant change in ionization parameter is given at a 4σ level between observation 8x and the others. This parameter, along the nine observations, is plotted in Figure 9 (top plot). We also plot a scaled version of the flux values. This scaled version of the light curve represents the expected changes of U if the gas were instantly in photoionization equilibrium with the ionizing source (for gas in photoionization equilibrium, changes in flux must be followed by changes by the same factor in U). Clearly, this is not observed in Figure 9, indicating that there is no clear response of this component to the flux variations.

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Phase MI. This component presents strong significant changes between observations 1x and 5x at 7σ and between observations 5x to 8x at 8σ. Interestingly, these changes are correlated with the flux variations. Among observations 1x, 2x, 3c, and 4c, the ionization degree of the phase MI changes by nearly the same factor as the X-ray flux. This indicates that this component is responding to the continuum changes close to photoionization equilibrium.

Phase LI. The most important variations in U are found between observations 1x and 4c and between observations 2x and 5x, both at 4σ. For this phase, there is a reaction to the larger changes in flux in longer timescales, as observed in Figure 9 (bottom). From observations 2x and 4c the gas presents a delay in recombining as expected in photoionization equilibrium (PhE). Yet, at the time of observation 5x, the gas seems to have found equilibrium again. As the flux increases from observations 5x to 6c the gas re-ionizes to reach an ionization state consistent again with PhE. Overall, this component also seems to respond, albeit with larger delays and in a more complex way to the changes in the continuum.

Finally, we note that the highest ionization component VH (detected only in the hard X-ray band) does not present significant changes in the ionization parameter. This behavior is expected because the ionization potential of Fe xxv is 8.8 keV and that of Fe xxvi is 9.3 keV, and the hard X-rays always vary much less compared to the soft X-ray band. Therefore, it is possible that at these relevant energies, the continuum did not vary much. We conclude that the lack of variability cannot be used as a limit on density for this component.

4.1.2. Equivalent H Column Density

There are mild variations (by a factor of ≲2.5) in the H equivalent column density along the nine observations, for the three phases detected in the soft X-ray band. The variations are not anti-correlated with the energy flux, as it would be expected in a scenario where the WA consists of material crossing our line of sight, and this material was responsible for producing the flux variation observed in the light curve. Figure 10 shows the changes in this parameter of each ionized phase (phases HI, MI, and LI).

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In order to study how significant the changes are in column density, we performed a test, fitting all data sets with a single value of N_H. The best-fit value for this parameter is similar to the values obtained when modeling individual observations, as expected. However, it is noteworthy that the other parameters are fully consistent with those obtained in Model C. In particular, the values for the ionization parameter are the same, within errors, as those found if N_H is free to vary in each observation. This implies that the variations found in U are not produced or correlated by possible variations in the column density.

Given that the models predict variations in the ionization degree of two ionization phases (MI and LI), we have studied in detail the spectra of the source to identify clear signatures of such variations.

4.2.1. The Iron M-shell Unresolved Transition Array

This Fe M-shell UTA (Unresolved Transition Array) is extremely useful to look for opacity changes in the absorber phases (as shown by Krongold et al. 2005b). To look for these changes, we performed a comparison between spectra 1x and 5x in the 15–18 Å range. Both spectra were normalized using a simple power law to the local continuum. The residuals were overplotted to search for possible differences. The results are shown in Figure 11. An evident variation in the position of the Fe UTA can be observed between spectra 1x and 5x (upper panels in Figure 11).

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In the bottom panel of Figure 11, we present the expected opacity changes in this spectral region in response to a variation by a factor of ∼ two in the ionizing flux. This change is similar to the flux variation between observations 1x and 5x, so it closely matches a scenario where the gas is in photoionization equilibrium. It is clear the observed variations are consistent with those expected in photoionization equilibrium for components MI and LI, which produce the UTA.

Figure 12 compares the Fe M-shell UTA between different Chandra spectra. This plot shows a similar variability trend (although less significant) between observations 4c and 6c, again pointing to gas close to photoionization equilibrium. Furthermore, no spectral variations are found between observations 6c and 7c, where the flux remains constant.

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4.2.2. Testing Possible Changes in Covering Factor

The observed changes in column density (although not very drastic) could be produced by real changes in the total column density toward the source or by possible variations in the covering factor of partial covering absorbers. To further investigate this, and to explore if the changes in flux might be connected with changes in covering factor (as suggested by Turner et al. 2008), we have also looked at the two extreme XMM-Newton flux states (1x and 5x). We used two intense oxygen absorption lines, O viii-Kα and O vii-Kβ, to track these possible changes. As seen in Figure 8, these two lines track absorption by the three components found in the soft X-ray band. Given that these lines are saturated, their maximum depth should depend mainly on the fraction of the source covered by the absorber (i.e., the residual observed emission should give us directly the part of the source not covered). Therefore, changes in covering factor should produce variations in the depth of these lines. This is clearly shown in Figure 13 (upper left panel) where we present a model assuming a change in the covering factor from 40% to 70% (as reported in Turner et al. 2008). In Figure 13 (upper right and bottom panels), we present the normalized data for spectra 1x, 5x, 7c, and 9c. It is clear that the absorption lines do not change significantly between these states—the variations are within the error bars. Any possible variations do not follow the expected direction for a change in covering factor responsible for the flux changes. Rather, the data hint at a change where the absorption lines become deeper during the high states, as expected if the gas is responding to the changes in the continuum. The same comparison was performed among the Chandra data with similar results.

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The most striking result is obtained when comparing the Ne ix absorption feature between Chandra observations. As can be observed in Figure 14, there is a significant change in the depth of Ne ix transition, between observations 7c and 9c. This change can be easily understood as the response in the ionization state of the gas to the impinging flux. Furthermore, the change is exactly opposite to the one expected if the changes in flux were produced by changes in the covering factor.

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Therefore, the high-resolution spectra do not support a scenario where the covering factor of the absorber is changing. This result is consistent with those of Mehdipour et al. (2010), who reached the same conclusion using data models. Thus, both data and models suggest that the changes in flux are not due to changes in the covering factor of the ionized absorber as suggested by Turner et al. (2008). Rather, our analysis (using models and direct comparison of spectra) indicates that the changes in spectral features are consistent with opacity changes following flux variations.

The time-variability analysis of the ionized absorber can lead us to constrain the number density of the gas and thus break the degeneracy between this quantity and the distance to the continuum source. As shown by Nicastro et al. (1999), the photoionization equilibrium time of a cloud of gas in response to variations in the ionized continuum is inversely proportional to the density of the cloud, according to the following formula:

$$\begin{equation*} t_{{\rm eq}}^{x^{i},x^{i+1}} \sim \lbrace \frac{1}{\alpha _{{\rm rec}}(x^{i},T_{e})_{{\rm eq}}n_{e}} \rbrace \end{equation*}$$

$$\begin{equation*} \times \displaystyle \left \lbrace \displaystyle \frac{1}{[\alpha _{{\rm rec}}(x^{i-1},T_{e})/\alpha _{{\rm rec}}(x^{i},T_{e})]_{{\rm eq}}+ (n_{X^{i+1}}/n_{X^{i}})] }\right \rbrace, \end{equation*}$$$

where t_eq is the photoionization equilibrium time, T_e is the electron temperature, and α_rec(xⁱ) is the radiative recombination rate coefficient (obtained from Shull & van Steenberg 1982 for the ions xⁱ and x^{i + 1}). We have used the response times detected in Section 4.1 to constrain the photoionization equilibrium timescale of the gas, and thus, the density of the gas.

5.1.1. Phase MI Location

5.1.2. Phase LI Location

5.1.3. Phase HI Location

It has been suggested by several studies (e.g., Krongold et al. 2003, 2005a, 2005b; Cardaci et al. 2009) that the structure of ionized absorbers could be that of a multi-phase medium in pressure balance. A multi-phase medium requires absorbers with similar outflow velocities to avoid drag forces from destroying one of the components. Clearly, component MI cannot be part of the same flow as components LI and HI, as these components are located farther out from the central source and they have a much faster outflow velocity. However, components LI and HI have a similar outflow velocity and they may be located at a similar distance from the central source. Then, it is possible that these components indeed form a multi-phase medium.

In order to further study this possibility, the thermal equilibrium (S curve) obtained for the SED in this analysis is plotted in Figure 15. This curve presents the points where the gas temperature (log T) and pressure lie in thermal equilibrium. The gas pressure is inversely proportional to the quantity log(U/T), which can be directly derived in our analysis. Thus, two components can be part of a multi-phase flow if they have different temperatures but similar log(U/T) values. Assuming solar metallicities (Z_☉) the S curve for NGC 3516 (Figure 15) is not multi-valued. Thus, it is not possible that these two components exist in pressure equilibrium.

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However, the shape of the S-curve results is very sensitive to external heating and cooling sources. Additional cooling can be produced by material with metallicities higher than the solar one. In fact, in AGNs, supra-solar metallicities are expected (e.g., Mihalszki & Ferland 1983 and Fields et al. 2007). A higher amount of cooling material creates a more vertical S-curve and together a possible "multi-phase" system. With the goal to explore this possibility, we present a model with five times solar metallicity (5 Z_☉). Figure 16 shows that if the metallicity of the WA is higher than solar, then components LI and HI could coexist in pressure equilibrium given that the pressure of both absorbers are in the same order of magnitude. As seen in the plot for a metallicity of 5 Z_☉, the difference between the gas pressure of these components is not significant.

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Two possible scenarios have been suggested to explain the observed variability in the X-ray emission of NGC 3516. The first one suggests intrinsic variations of the central source (Mehdipour et al. 2010). In the second scenario, explored by Turner et al. (2008) and Markowitz et al. (2008), they proposed that the variations are due to obscuration of the central source produced by nearby blobs of material, either ionized or neutral. In particular, Turner et al. (2008) suggest that an absorbing component of ionized material (their "heavy absorber") presents a change in the covering factor, which is responsible for the observed flux variations. Such component would produce absorption by ions of O viii and O vii (Turner et al. 2008). However, we could not find evidence of covering factor variations in the O vii–Kβ and O viii–Kα lines (Figure 13).

To further explore this possibility, we fit the spectra using a partial covering absorber. We note that partial covering is not required by the data, as a fit including it does not improve over a fit with fully covering absorbers (in agreement with Mehdipour et al. 2010). Nevertheless, based on Model C, a partial covering was tested in all the possible combinations, including this factor, in one, two, and three ionizing components that imprint spectral features in the soft X-ray band.

The best solution found included partial covering in phase HI. However, the value of the covering factor is almost unity in all observations (see Table 12), and does not anti-correlate with the flux. An F-test indicates that varying the covering factor is not needed (confidence of 57% if we compare the model that does not include the covering factor and this model). Thus our results do not support a scenario in which the covering factor of the warm absorbers is responsible for the flux variations. If these variation are indeed produced by obscuring material, this material should be located closer in than the warm absorbing components, as components LI and MI are responding to the observed flux variations.