THE HARD X-RAY PERSPECTIVE ON THE SOFT X-RAY EXCESS

We perform all of our simulations using the xspec package (Arnaud 1996). The "fakeit" command in xspec provides the ability to generate a simulated spectrum for a given input model and instrumental response. We first create a grid of simulated spectra for the ionized reflection case, stepping through all available parameters over physically realistic ranges based on previous studies using this model. The model combination used for generating simulated spectra is pexrav + kdblur(reflionx). The key component is reflionx (Ross & Fabian 2005), which provides all of the essential features of the reflected continuum including the Compton reflection hump, broad iron line, and soft lines which are thought to be blurred to give rise to a soft excess. This model takes the following parameters: the iron abundance relative to solar iron abundance, A_Fe (we step this between 0.11 and 3.0, the range allowed by the model); the photon index of the illuminating coronal spectrum being reflected from the disk, Γ_refl (for an input photon counts spectrum $N(E) \propto E^{-\Gamma _{\rm refl}}$ we step this between 1.5 and 3.0, e.g., V13; Corral et al. 2011); the ionization parameter ξ (the ratio of the illuminating flux to the hydrogen number density, stepped between 1 and 1000, e.g., Reynolds & Fabian 2008) and the normalization N_reflionx. We blur this component with the kdblur model, which requires a radial emissivity index of the disk (we set this at 5.0 to allow for modest light-bending), the inner and outer radii of the disk (R_in and R_out, here frozen at 3.0R_g and 100.0R_g, respectively, again to allow for relativistic effects from a spinning black hole allowing an innermost stable orbit within 6R_g), and the inclination (which we leave at a default of 30° for all realizations, assuming relatively face-on, Seyfert-1–like geometry).

The final component of the model combination to be considered is pexrav, which in our representation here represents the direct or illuminating power-law coronal continuum, along with simple reflection from distant, neutral material (e.g., the inner surface of the surrounding dusty gas clouds or "torus"). The pexrav model requires the photon index Γ_direct, the cut-off energy (high energy fall-off) of the spectrum E_cut, the reflection fraction R_distant, the abundances of iron and other metals A_{Fe, distant} and A_{other, distant}, and the cosine of the inclination angle and the normalization (N_pexrav). We link the photon index of the direct component to the reflected component (Γ_direct = Γ_refl) and freeze the cut-off energy at the maximal value, 10⁶ keV, since current BAT-based studies suggest that the average cut-off energy for AGN consistently lies above a few hundred keV in the majority of AGNs (37 out of 49 AGNs fit with pexrav in V13 AGN and have E_cut values consistent with being outside the BAT band, or are poorly constrained); at any rate, we make the assumption that it lies outside the NuSTAR band, to consider the simplest case first in our simulations. We freeze the abundances at their default values (these represent the abundances of the distant reflector) and keep the inclination angle at its default value. Nandra et al. (2007) deconvolve distant and inner reflection in a sample of Seyfert AGN and, on average, find that the distant component of the reflector has a strength of R_distant = 0.455 with a standard deviation of σ_{R, dist} = 0.295. For each realization of the input spectrum, we randomly generate a Gaussian-distributed distant reflection value using these parameters, to introduce a realistic amount of spread due to the presence of some distant reflection.

Finally, the crucial parameter in this model set-up is the ratio of the normalizations of the direct and reflected components. Before addressing this, we first need to understand a complication presented by the published version of the reflionx model: changing the ionization parameter actually changes the flux of the source in addition to changing the spectrum, so the normalization is not a simple flux-multiplier. We modify the table model such that the normalization is divided out from the ionization parameter and variations in ξ only produce spectral shape changes (not overall flux changes). Having made this change, we can use the normalization of the reflionx model as a simple flux multiplier. We allow the ratio N_pexrav/N_reflionx to go between 1.0 (representing the reflection-dominated case) and 1000.0 (where the power law dominates and ionized reflection signatures should be barely discernible in the spectrum). We finally set the overall 1–200 keV flux of the input model to be 4 × 10⁻¹¹ erg s⁻¹ cm⁻², which is the measured flux for the well-known Seyfert NGC 4051 using XMM and BAT observations, and the flux of a typical NuSTAR target.

Using the above set-up, we now simulate spectra in both the XMM and NuSTAR bands. We employ more "pessimistic" assumptions for the simulated spectra and just simulate spectra for the PN instrument from XMM and the FPMA instrument from NuSTAR; if more detectors are used in data fits, then the accuracy of results obtained should only increase. For the simulated XMM spectrum, we use the response and ancillary files from an observation of NGC 4051 reduced in V13, and for the NuSTAR simulated spectrum, we use the latest available canned response files for the FPMA instrument. Since both the NuSTAR and XMM responses oversample the spectrum, we rebin the responses for quicker fits of the simulated spectra. This was done using the ftools tasks rbnrmf and marfrmf for rebinning the response by user-specified amounts in each group of channels and finally combining the effective area and response files. We again assume a relatively conservative exposure time of 10 ks in both XMM and NuSTAR, typical of the snapshots of BAT AGN currently being taken by NuSTAR; longer observations will provide better constraints on the soft and hard excess strengths. However, the key point of this study is to see whether physical models for the soft excess can be distinguished using broadband X-ray data of typical quality rather than using the longest observations available and using simple models rather than the more complex, physically motivated models. We present an example of the model spectrum and resultant simulated spectrum in Figure 2.

Zoom In Zoom Out Reset image size

Having simulated the spectra, we group them both using the grppha tool to have a minimum of 20 counts per bin and reload the binned spectra into xspec. We ignore any data outside of the range 0.4–10 keV in the simulated XMM data and any data above 80 keV and below 3 keV in the simulated NuSTAR data, as well as ignoring any "bad" channels. We then fit the spectra with what is henceforth referred to as the "observer's model": the simplest combination of a blackbody, a Gaussian, and a pexrav reflection model (bbody + gauss + pexrav) required to account for the components seen in the spectrum. We use initial conditions that mimic a typical soft excess, power law, iron line, and hard excess spectral shape. We set the normalizations of the blackbody, Gaussian line and pexrav components to be 10⁻⁴, 10⁻⁴, and 10⁻², respectively, and constrain the blackbody temperature to lie between 0.01 and 2 keV, the line energy to lie between 6.3 and 7 keV, and the linewidth to lie between 0 and 0.5 keV, as is commonly done when fitting real observations. This provides a sensible starting point for the fit to ensure that the simulated spectra have a good probability of being fit successfully.

While the soft excess is probably not intrinsically blackbody emission and the hump above 10 keV may not intrinsically be due to reflection, these model components serve to parameterize the spectral shape in a way most commonly done by observers. The purpose of the first component is to measure the strength of the soft excess when modeled as a blackbody and to calculate its strength using the simple parameterization L_BB/L_PL introduced in V13. The purpose of the Gaussian component is to model the iron line feature that is naturally introduced around 6.4 keV by the reflionx model, and the purpose of the pexrav component is to measure the overall strength of the resultant Compton hump, which, in general, will be the sum of both distant and inner reflection or an artifact of complex absorption. For data of typical quality, the abundances and inclination are not usually uniquely determinable so we do not thaw them here for fitting and freeze them at their defaults. We also freeze the cut-off energy at the maximal 10⁶ keV in our observer's model fit, since experience shows that this is rarely constrained to be below ∼200 keV in real AGN fits using BAT and XMM data (V13). We fit each simulated spectrum with this observer's model and record all of the best-fit parameters (especially the measured soft excess and reflection strengths) for each set of input (simulated) parameters (A_Fe, Γ_direct, ξ, and the ratio of direct-to-reflected components, N_pexrav/N_reflionx).

We step each parameter within the ranges indicated above, using seven steps for four primary variables (ξ, Γ, A_Fe, and N_pexrav/N_reflionx), amounting to 2401 total simulated spectra. After the fits to the simulated data are complete, we then plot the "measured" soft excess strength against the reflection to investigate the presence of any relation (Figure 3). We filter out poor fits to the simulated spectra using a dual measurement of the reduced χ², requiring χ²/dof < 6.0 in the soft band (<3.0 keV) and χ²/dof < 2.5 in the hard band (>10 keV), to ensure that our observer's model fits both the soft excess and the hard excess simultaneously; a single band-wide reduced χ² criterion was found to be insufficient to ensure this. These reduced-χ² thresholds were chosen by visual inspection of the spectral fits for different cut-off χ² values, fine-tuning the thresholds until only those spectra with visually good fits to the soft and hard excesses remained. We adopt different reduced-χ² thresholds in the two bands, as there are many more bins in the soft band than the hard band; it is therefore expected to be more difficult to get a good fit in the soft band using a simple two-parameter model. A total of 1962 of the 2401 fits (82%) were deemed "good" fits according to these criteria. The "bad" fits represent parameter combinations for which the simple "observer's model" could not adequately represent the soft and hard excesses. We omit error bars and do not calculate errors on individual simulated spectrum fits but note that the error on S_softex for typical XMM-quality data are very small, as shown in Figure 1. We know NuSTAR will constrain R much more robustly than XMM+BAT fits; therefore, errors on R will assuredly be smaller than in Figure 1 and errors on S_softex will be comparable.

Zoom In Zoom Out Reset image size

We see a large degree of spread in Figure 3, but the contours of the highest density of points show a modest but clear trend of increasing R with S_softex. Part of the region of high R (R ≳ 30) shows a high density of points. Performing a Kendall's τ correlation analysis on the good fits only yields a correlation coefficient of 0.33 with a null-hypothesis probability <1 × 10⁻¹⁰.

To illustrate the power of the R–S_softex diagnostic plot, we also perform this exercise for the ionized wind model, swind1. Although Schurch & Done (2008) find this model to require unphysically high terminal velocities of the outflow, a partially covering ionized absorber would resolve this problem, and therefore, the swind1 model can still be taken as representative of an important class of multiple-absorber, partially covering, ionized absorber models that can account for the soft excess. We therefore simulate spectra using this model, using the range of parameters identified in the Middleton et al. (2007) study on PG quasars, to see whether such a model can produce soft "excesses" and hard "excesses" that can be modeled as a "blackbody plus reflection" model combination.

We use the model combination swind1(pexrav) to simulate spectra, where the pexrav component represents the primary X-ray continuum along with some distant reflection. In Middleton et al. (2007), a more complex model for the primary X-ray power law and distant reflection is used but the salient features of such a model are reproduced here by pexrav for our purposes. We follow exactly the same rationale for randomly seeding the distant reflection with values appropriate for the distribution found in Nandra et al. (2007) and follow identical rationale to that given above in Section 3.1 for determining the primary continuum parameters; the primary continuum is common to both the ionized reflection and absorption cases. For the ionized absorption component, we step the column density of the wind between 3 and 50 × 10²² cm⁻²; the photon index of the primary continuum (pexrav) Γ is varied between 1.5 and 3; the logarithm of the ionization parameter ξ is varied between 2.1 < log (ξ) < 4.0; and the Gaussian velocity dispersion of the wind is varied between 0.1 and 0.5, all based on the parameters found from fitting data on real AGN in Middleton et al. (2007). We simulate spectra in a grid using seven steps between the maxima and minima for each parameter (see Figure 4 for an example of simulated spectra) and plot the resulting soft excess and reflection strengths in Figure 5. For this input model, 2073 out of 2401 potential parameter combinations yield successful "observer's Model" fits (86%); in the remainder of cases, a "blackbody plus reflection" model combination entirely failed to fit the simulated spectrum (i.e., xspec could not compute a fit at all to produce a fit statistic). Using the same dual reduced-χ² criteria as for ionized reflection, we find that 1595 of the successful fits were "good" fits (i.e., 77% of successful fits, or 66% of the total 2401 simulated spectra).

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

We see a large degree of spread in Figure 5, without any clear trend linking R with S_softex. Notably, a large number of simulated spectra show prominent soft excesses with negligible R. Performing a Kendall's τ correlation analysis on the good fits only yields a correlation coefficient of –0.003 with a null-hypothesis probability of 0.88, indicating that there is a high chance of the two properties being completely uncorrelated.

For both models tested in this paper, there are a cluster of points at R ≳ 100, which so far have not been observed in the real AGN population. For the ionized reflection case, further investigation reveals that all of the simulated spectra that produce R > 100 have N_pexrav/N_reflionx < 10, and all of the very extreme R values (i.e., R > 200) measured from "good" fits have N_pexrav/N_reflionx = 1, the lowest value of the ratio included in the simulations corresponding to the most reflection-dominated case (see Figure 7, top panel). This suggests that for reflection-dominated spectra, the spectral shapes produced can genuinely give rise to very high, "anomalous" R values (under the fitting assumptions adopted in this study), depending on the spread of other intrinsic parameters, i.e., A_Fe, ξ and Γ. We then focus only on the subset of objects with reflection-dominated spectra (1 < N_pexrav/N_reflionx < 10, Figure 7, lower panel). We split the results into different bins of A_Fe, ξ, and Γ, selecting three bins for each (using logarithmic spacing for ξ). We find that the ionization parameter ξ produces the greatest variation in measured R. The lowest ionization parameters, 1.0 < ξ < 10.0, give rise to almost all of the R > 100 points. In conclusion, the most reflection-dominated spectra (1.0 < N_pexrav/N_reflionx < 10.0) coupled with the most weakly ionized reflectors (1.0 < ξ < 10.0) can produce very strong hard excesses.

Zoom In Zoom Out Reset image size

This range of R values has not been seen in the real AGN population so far but only a handful of observations currently exist of reflection-dominated states of AGNs (e.g., Zoghbi et al. 2008; Fabian et al. 2012). Such prominent hard excesses may be found with new NuSTAR observations. Since the ionization parameter is proportional to the luminosity, the very low luminosity sources (with potential for the most prominent hard excesses) may also be selected out of most X-ray surveys.

For the ionized absorption model, the highest values of the measured R occur for log (ξ) < 2.75. From inspection of the spectra, we find that many of these low ionization absorbers have absorption troughs that look more like extended "edges." The hard portion of the spectrum can then be fit as a pure reflection component in some cases, leading to high values of R. In the remainder of low ionization absorber spectra, the slope of the intermediate (3–10 keV) region is too extreme to be fit by the pexrav component and the fit fails altogether (discussed further in Section 4.2).

We also consider the possibility that the low exposure time (10 ks) and resulting poor-quality data at high energies could lead to such anomalous R values. However, increasing the observation time to 20 ks (for both ionized reflection and absorption models, Figure 8) did not produce any significant change in the results and the broad trends seen.

Zoom In Zoom Out Reset image size

As mentioned in Section 3.2, 14% of the simulated ionized absorption spectra result cannot be fit with the observer's model. We investigate this class of objects in more detail. We find that the only weak discriminant of whether a spectrum fits successfully or not is the ionization parameter of the absorber, log (ξ). Failed fits only occur for spectra simulated with 2.1 < log (ξ) < 2.75. There are 1029 possible parameter combinations/simulated spectra in this range (i.e., three bins in log (ξ) and seven bins for each other parameter), out of which 328 model combinations fail completely. On inspection, these spectra exhibit ionized absorber troughs that look more like edges with a very steep rise in flux towards higher energies. When manually fit with the observer's model combination, we find that the fits consistently fail. The power law regime of the pexrav component attempts to fit to the rising part of the edge below 10 keV but the photon index required is too extreme (see Figure 9). This would be a readily identifiable subset of spectral shapes which cannot be fit with a simple blackbody and reflection model, and any soft "excess" seen would clearly be distinguishable from one produced by ionized reflection.

Zoom In Zoom Out Reset image size

Of the remaining 701 low log ξ spectra which are successfully fit by the observer's model, only 50% qualify as "good fits" according to the dual-χ² criteria. Inspection of these "good fits" reveals that the power-law component is able to fit the rising 1–6 keV portion of the spectrum successfully. It is therefore not straightforward to identify a very specific part of ionized absorber parameter space that eludes fitting with the observer's model but we can say that the failing of the fit is restricted to low ionization absorbers. The success rate of fitting such unusual spectral shapes may also be subtly dependent on the initial conditions employed in the observer's model, the exploration of which is beyond the scope of this paper.

We have presented results for the XMM–NuSTAR instrument combination since NuSTAR is newly launched and this instrument combination is already being used to obtain simultaneous broadband X-ray data on AGNs (e.g., Risaliti et al. 2013; Matt et al. 2014); therefore, it is the most relevant prediction for the current circumstances with real near-term prospects of verifying the work in this paper. ASTRO-H and ASTROSAT are also on the horizon, and to check whether our predictions hold for other instruments, we also perform simulations for the ionized reflection model using the current ASTRO-H predicted response matrices, assuming the same 10 ks exposure time. We caution that these responses may be more uncertain than the XMM–NuSTAR responses, as real responses are likely to differ significantly from the prelaunch predicted ones. The resulting R–S diagram does not show any significant difference to that obtained for XMM–NuSTAR (Figure 10), suggesting that the conclusions in this paper should hold for other similarly equipped future broadband X-ray observatories.

Zoom In Zoom Out Reset image size

The simulations here outline the trends expected in R–S_softex space for two different models using a large grid of 2401 parameter combinations. AGN samples are typically much smaller due to the competition for observation time, so we require a measure of how feasible it will be to detect these trends in real samples of AGNs. We perform further simulations to estimate the typical AGN sample size required before a correlation (or the absence of one) can be seen between R and S_softex.

We use a Monte-Carlo rejection method to simulate N values of R and S_softex (corresponding to a sample of N AGN) randomly determined throughout the available R–S_softex space, using the contours determined from Figures 3 and 5 as the probability distribution with which to distribute the points in R–S_softex space. We vary N and measure the resultant Kendall's τ correlation coefficient of the faked sample to determine when the strength of the correlation approaches that seen in the full simulations. We do this for both ionized reflection and ionized absorption. The variation of the correlation coefficient with N for each input model is shown in Figure 11.

Zoom In Zoom Out Reset image size

We see that at N ≳ 60, the uncertainty in the correlation coefficients produced by the two processes drops such that the two processes can be distinguished at a 2σ–3σ level. Therefore, even though the physical process may be ambiguous for an individual object based on its location in the R–S_softex plane, the trend exhibited by a well-selected, representative AGN sample in this plane can provide an indication of the physics most relevant for the majority of AGNs in the sample.

We outline some issues to be further explored in future work. First, the ratio N_pexrav/N_reflionx is currently used as an estimator of the degree of light bending in the reflection scenario. A more physical understanding of this parameter is needed to place appropriate upper and lower limits on it for the simulations. It is easy to conceive of a situation where the direct power law dominates; however, understanding the lower limit on the range of physically viable ratios (here assumed to be unity) is more complex and requires a more complete consideration of the energetics of the reflection dominated state than is undertaken here. This may impact the strongest observable strengths of the soft excess from the reflection scenario, as initially investigated by Chevallier et al. (2006), but the observation of AGN in fully reflection-dominated states does support the possibility that N_pexrav/N_reflionx can take very low values (even <1).

We have assumed uniform or log-uniform distributions for the input parameters in these simulations as the simplest possible scenario. However, it may be the case that the real underlying distributions are not uniform or that there are correlations between the input parameters. There are a handful of studies on this in the literature, presenting the photon index and luminosity distributions in AGNs (e.g., Corral et al. 2011; Vasudevan et al. 2013). Previous works (e.g., Reynolds & Fabian 2008; Ballantyne et al. 2011) have found a range of ionization parameters for ionized reflection consistent with that assumed here. There are suggestions of a weak correlation between photon index and luminosity (e.g., Saez et al. 2008), and hence potential for a correlation between Γ and ξ. However, there is no detailed work on the true underlying distributions of physical parameters of reflectors. It is possible that the observed trends highlighted in this work in the R–S plane could be changed and the density of points in different parts of the plot could be altered, if different underlying distributions are used. To allow for this to be investigated in the future, we make our simulation results public with the online data accompanying this paper. The interested researcher can then draw from the provided results in a nonuniform way using more updated distributions or correlations between parameters, if and when such details become more well constrained. However, one instinctively expects some degree of correlation between hard and soft excess strengths in the ionized reflection scenario, regardless of the precise underlying parameter distributions.

One of the latest models to be proposed for the soft excess is the optxagnf model (Done et al. 2012). Their model combines disk emission, Comptonization, and a power law in an energetically self-consistent way, where the inner part of the accretion flow below a coronal radius is Comptonized to produce the soft excess. Comptonization is the engine behind the soft excess in this model, and one does not expect it to exert any influence on the hard X-ray emission based on simple models (e.g., Page et al. 2004) providing a purely standalone component for the soft excess. Therefore, one does not expect any link between the soft excess and hard excess in this scenario. However, this may not be the case for optxagnf, where the disk and corona geometries are linked by energetic considerations, and we are currently undertaking a study of this model in detail, with a view to produce a similar R–S_softex diagnostic plot to compare it with the models in this paper. The optxagnf model is able to fully reproduce the optical-to-X-ray SED up to 10 keV, as shown by the comprehensive study of Jin et al. (2012), but its hard X-ray signatures have not been studied. Additionally, distant reflection needs to be added in a consistent fashion if we want to compare it with the models studied here, where pexrav was used to provide the direct continuum along with the distant reflection. How to do this is not clear, and since optxagnf has many more model parameters to consider than the models in this paper, we defer this study to a future paper (in preparation).