The Nature of the Compton-thick X-ray Reprocessor in NGC 4945

The Nature of the Compton-thick X-ray Reprocessor in NGC 4945

Tahir Yaqoob
Department of Physics and Astronomy, Johns Hopkins University, 3400 N. Charles St., Baltimore, MD 21218.
Accepted for publication in MNRAS 18 April, 2012
Abstract

We present an exhaustive methodology for fitting Compton-thick X-ray reprocessor models to obscured active galactic nuclei (AGNs) and for interpreting the results. We focus on the mytorus model but also include some analysis from other models. The models are applied specifically to Suzaku, BeppoSAX, and Swift BAT spectra of the Seyfert 2 galaxy NGC 4945 but the basic methodology is applicable to other AGNs, including Compton-thin sources. The models overcome a major restriction of disk-reflection models, namely the assumption of an infinite column density. Finite column-density models produce a rich variety of spectral shapes and characteristics that cannot be produced by disk-reflection models, even for Compton-thin AGN with column densities in the range . In the Compton-thick regime we show that even though NGC 4945 is one of the brightest AGNs above 10 keV, there are significant spectral degeneracies that correspond to very different physical scenarios. The models that fit the data span nearly a factor of 3 in column density ( to ) and two orders of magnitude in the intrinsic 2–195 keV luminosity. Models in which the continuum above 10 keV is dominated by the direct (unscattered) continuum give the highest intrinsic luminosities and column densities. Models in which the Compton-scattered continuum dominates the spectrum above 10 keV give the lowest intrinsic luminosities and column densities. Utilizing variability information from other studies of NGC 4945, namely the fact that the Fe K emission line does not vary whilst the continuum above 10 keV varies significantly, we can select the solutions in which the direct continuum dominates above 10 keV. The data require that the Compton-scattered continuum and Fe K line emission come predominantly from the illuminated surfaces of the X-ray reprocessor, implying a clumpy medium with a global covering factor that is small enough that the Compton-scattered continuum does not dominate the spectrum above 10 keV. The line of sight may be obscured by matter in the same distribution but a separate ring-like structure observed edge-on is not ruled out. The Fe K line-emitting region must be the same one recently reported to be spatially-resolved by Chandra, so it must be extended on a scale of  pc or so. As found in previous studies of NGC 4945, the implied intrinsic bolometric luminosity is close to, or greater than, the Eddington luminosity. However, a scenario that is also consistent with the data and the models is that NGC 4945 is a strongly beamed AGN embedded in a shell of Compton-thick (but clumpy) matter, with a covering factor that needs less fine-tuning than the case of an isotropic intrinsic X-ray continuum. The intensity of the intrinsic X-ray continuum would be strongly aligned along or close to the line of sight, so that the true intrinsic luminosity could easily be an order of magnitude less than that deduced for an isotropic X-ray source. Beaming also appears to be consistent with recent radio and Fermi results for NGC 4945. Such beamed Compton-thick AGNs would be preferentially selected in hard X-ray surveys over unbeamed Compton-thick AGNs.

keywords:
galaxies: active - galaxies: individual (NGC 4945, 3C 273) - radiation mechanism: general - scattering - X-rays: general
pagerange: The Nature of the Compton-thick X-ray Reprocessor in NGC 494510pubyear: 2012

1 Introduction

Obscured active galactic nuclei (AGNs) are of broad astrophysical interest because it is thought that a significant fraction of the power from accretion onto black holes is shrouded by a veil of circumnuclear matter (e.g., Fabian 1999), and such a population of obscured AGNs may play a significant role in contributing to the Cosmic X-ray Background (e.g., Gilli, Comastri, & Hasinger 2007, and references therein). Moreover, the connection between obscuration in AGNs and starburst activity is an area that still requires elucidation. Modeling the properties of the obscuring structure is also critical for understanding the unification of type 1 and type 2 AGN. Compton-thick obscured AGN, in which the circumnuclear matter has a Compton-scattering optical depth of or greater (at energies of  keV) have been particularly difficult to study in the X-ray band. This is not only because of the relative weakness of the sources compared to unobscured AGNs, but also because the reprocessing of the incident X-rays in the obscuring medium affects such a large range in energy that the intrinsic, direct continuum may not be observed anywhere in the observational bandpass of a given instrument or set of instruments. The reprocessed X-ray spectrum is characterized by significant continuum curvature that peaks between –50 keV, and often a strong fluorescent Fe K emission line. However, the detailed shape of the X-ray spectrum depends on many factors, including the geometry and orientation of the reprocessor, and the shape of the incident continuum itself.

NGC 4945 is a nearby () Seyfert 2 galaxy that has been known for some time to be obscured by Compton-thick matter (see Done, Madejski, and Smith 1996) and has been observed by every X-ray astronomy satellite since Ginga. The source is one of the brightest AGNs above  keV, yet is an order of magnitude weaker below 10 keV, a property that is characteristic of obscuration by material with a column density in the line of sight of the order of but less than . BeppoSAX was first able to obtain a broadband X-ray spectrum extending up to  keV with good sensitivity (Guainazzi et al. 2000; Dadina 2007). A recent RXTE study that included NGC 4945 observations spanning a period of about a decade shows a consistent 2–10 keV flux level over that period of time, which is also consistent with flux levels in this energy band before the RXTE observations (Rivers, Markowitz, and Rothschild 2011). However, above 10 keV, NGC 4945 is much brighter and highly variable, and it is one of the brightest AGNs in the 14–195 keV Swift BAT all-sky survey (e.g., see Winter et al. 2008, 2009; Tueller et al. 2009, 2010). NGC 4945 is also one of only two Seyfert 2 galaxies that is detected in the GeV band with Fermi, the other being NGC 1068 (Lenain et al. 2011).

In 2006, Suzaku provided the best broadband spectrum in the  keV band, in terms of the combination of high sensitivity above 10 keV and good spectral resolution in the critical  keV region that contains the Fe K, Fe K, Ni K emission lines, and the Fe K absorption edge, features which can potentially provide powerful constraints on models. Itoh et al. (2008) and Fukazawa et al. (2011) presented results of modeling the Suzaku data using ad hoc models consisting of line-of-sight extinction that does not correctly model the Compton-scattering cross section, an X-ray reflection model based on a point-source illuminating a semi-infinite slab, and discrete Gaussian components for the fluorescent emission lines that were allowed to have arbitrary fluxes. This type of model has been universally applied to the X-ray spectra of both type 1 and type 2 AGN for over 15 years. However, such a model of the Compton-thick obscuring matter is not physical and the X-ray reflection continuum model does not have a column density parameter because it is assumed to be infinite. Therefore, the matter out of the line of sight responsible for the reflection continuum (produced by Compton-scattering and absorption) cannot be related to the column density along the line of sight, and the physics relating the fluorescent line fluxes to the Compton-scattered continuum is forsaken. Moreover, the intrinsic continuum luminosity inferred from these ad hoc models is not straightforward to interpret, and as we shall show in the present paper, could be wrong by an order of magnitude or more. A further sacrifice that has to be made when using a disk-reflection model as a substitute for the true Compton-scattered continuum from a toroidal or spherical reprocessor is that one is forced to choose an arbitrary inclination angle for the disk. Yet, the shape of the reflection spectrum is sensitive to geometry and to the orientation of the reprocessor with respect to the observer. Different authors have adopted different values for the inclination angle, so different studies in the literature may not even be directly comparable.

More recently, Marinucci et al. (2012) have presented results from 5 new Suzaku monitoring observations of NGC 4945. They found that the total Fe K emission-line flux varies by less than 10% whilst the continuum above 10 keV varied by a factor of . Marinucci et al. (2012) also showed using Chandra data that a component of the Fe K line emission is spatially resolved on a scale of at least 30 pc. These findings are important for distinguishing between various degenerate models. However, it is beyond the scope of the present paper to reanalyze the new Suzaku observations. Rather, our purpose is to lay out the methodology in detail using the first long Suzaku observation of 2006, the BeppoSAX observation of 1999, and the Swift BAT all-sky survey data. By considering a variety of possible scenarios and the associated issues involved, the methodology will help to model and interpret data from other obscured AGNs, which in general will have a lower signal-to-noise ratio than the NGC 4945 data.

In summary, the currently popular scheme for spectral-fitting analysis of Compton-thick AGN does not extract all of the physical information contained in the data, and what is extracted may not have a straightforward physical meaning (if any). Murphy and Yaqoob (2009, hereafter MY09) described and made available for general use, a toroidal model (called mytorus) of the Compton-thick X-ray reprocessor in AGN that addresses some of these limitations. Applying such a model entails many complexities because there may be several different types of degeneracy in the data. In the present paper we give an exhaustive account of the application of the mytorus model to noncontemporaneous Suzaku, BeppoSAX, and Swift BAT spectra of NGC 4945. We use the BeppoSAX data in addition to the Suzaku data because of the broadband coverage and good sensitivity above 10 keV of BeppoSAX, even though the spectral resolution is not as good as Suzaku. The Swift BAT data provide information on long-term variability of the very high-energy continuum, as well as a long-term (58-month) average of the 14–195 keV spectrum that serves as a useful baseline. We also apply the toroidal and spherical models that were made available after mytorus by Brightman and Nandra (2011; hereafter BN11), although these models are more restrictive than the mytorus model because they do not allow for time delays between the different model components. Such a generalized detailed investigation is necessary to fully interpret the NGC 4945 data, and to establish a methodology for the application and interpretation of Compton-thick X-ray reprocessor models to other AGN. NGC 4945 is an excellent candidate for a prototype Compton-thick AGN because it is so bright, the column density is not too high so that the Compton-hump is well-sampled in sensitivity by Suzaku, and the spectrum in the –10 keV band is not contaminated by numerous emission lines from very hot gas has as it is in NGC 1068. This means that the data in the bandpass that includes the Fe K line and Fe K edge are relatively “clean” (although there is an emission line due to Fe xxv). When the modeling is applied to other AGN, such a detailed analysis will not be necessary in most cases, and our detailed description of the methodology for NGC 4945 is designed to save time by enabling the researcher to establish which procedures are not necessary for a given source and data set.

The paper is organized as follows. In §2 we describe the basic data, and reduction procedures where relevant, from Suzaku, BeppoSAX, and the Swift BAT. In §3 we summarize what is already known about the general form of the X-ray spectrum of NGC 4945. In §4 we describe the overall strategy of the analysis that we will present, including detailed procedures for setting up the various forms of the Compton-thick reprocessing models, and for spectral fitting. In the following three sections (§5 to §7), we give the results from fitting three classes of Compton-thick reprocessor models that correspond to very distinct physical scenarios. In §8 we bring together all the results from applying the different models and discuss the implied intrinsic luminosities and Eddington ratios of the different spectral fits, as well as the physical implications of each type of solution. In §9 we summarize our findings. In the appendix we present results of spectral fitting to some Suzaku 3C 273 data in order to establish some important calibration information pertinent to fitting the Suzaku NGC 4945 data.

2 Observations and Data Reduction

2.1 Suzaku Data

The joint Japan/US X-ray astronomy satellite, Suzaku (Mitsuda et al.  2007), was launched on 10 July, 2005. The present study focuses on an observation campaign on NGC 4945 that was carried out early in the life of Suzaku. The campaign consisted of three observations of NGC 4945 performed in 2005, August, and one in 2006, January 15. The first two observations (in 2005, August) had relatively short exposure times ( ks and 177 s), and given the historical amplitude and spectral variability of NGC 4945 (e.g. Fukazawa et al. 2011; Itoh et al. 2008, and references therein), in the present paper we only report results from the third observation, which had an exposure time of nearly  ks.

Suzaku carries four X-ray Imaging Spectrometers (XIS – Koyama et al.  2007) and a collimated Hard X-ray Detector (HXD – Takahashi et al.  2007). Each XIS consists of four CCD detectors at the focal plane of its own thin-foil X-ray telescope (XRT – Serlemitsos et al.  2007), and has a field-of-view (FOV) of . One of the XIS detectors (XIS1) is back-side illuminated (BI) and the other three (XIS0, XIS2, and XIS3) are front-side illuminated (FI). The bandpass of the FI detectors is  keV and  keV for the BI detector. The useful bandpass depends on the signal-to-noise ratio of the source since the effective area is significantly diminished at the extreme ends of the operational bandpasses. Although the BI CCD has higher effective area at low energies, the background level across the entire bandpass is higher compared to the FI CCDs. Although we used the standard response matrix generator for modeling the XIS data, we measured the widths of the Mn  lines from the on-board calibration sources (two per XIS) using the actual NGC 4945 observations in order to independently check the spectral resolution degradation corrections in the response generator. Details are given below.

The HXD consists of two non-imaging instruments (the PIN and GSO – see Takahashi et al.  2007) with a combined bandpass of  keV. Both of the HXD instruments are background-limited, more so the GSO, which has a smaller effective area than the PIN. For AGNs, the source count rate is typically much less than the background. In order to obtain reliable background-subtracted spectra, the background spectrum must be modeled as a function of energy and time. The background models for the HXD/PIN and HXD/GSO have an advertised systematic uncertainty of 1.3% 111http://heasarc.gsfc.nasa.gov/docs/suzaku/analysis/pinbgd.html and 2% 222http://heasarc.gsfc.nasa.gov/docs/suzaku/analysis/gsobgd.html respectively. However, the signal is background-dominated, and the source count rate may be a small fraction of the background count rate, so the net systematic error in the background-subtracted spectra could be significant. The problem is worse for the GSO than it is for the PIN. The observation of NGC 4945 was optimized for the HXD in terms of positioning the source at the aimpoint for the HXD (the so-called “HXD-nominal pointing”) which gives a somewhat lower count-rate in the XIS than the “XIS-nominal” pointing, but gives higher HXD effective area.

The calibration of the relative cross-normalizations of the three instruments involves many factors, and these are discussed in detail in the appendix, where we derive the instrument cross-normalization factors from a Suzaku observation of 3C 273 as a guide for the analysis of the NGC 4945 data. In the appendix we also give details of the data reduction and screening procedures that we used for both the 3C 273 and NGC 4945 data, as well as details of the background subtraction and spectral responses for all instruments. The principal data selection and screening criteria for the XIS were the selection of only ASCA grades 0, 2, 3, 4, and 6, the removal of flickering pixels with the FTOOL cleansis, and exclusion of data taken during satellite passages through the South Atlantic Anomaly (SAA), as well as for time intervals less than  s after passages through the SAA, using the T_SAA_HXD house-keeping parameter. Data were also rejected for Earth elevation angles (ELV) less than , Earth day-time elevation angles (DYE_ELV) less than , and values of the magnetic cut-off rigidity (COR) less than 6 . Residual uncertainties in the XIS energy scale are on the order of 0.2% or less (or  eV at 6.4 keV – see Koyama et al.  2007). We confirmed this from an analysis of the onboard calibration line data taken during the NGC 4945 observations (see below for details).

The cleaning and data selection resulted in net exposure times that are reported in Table 1. NGC 4945 is known to have many nonnuclear X-ray sources (e.g. Schurch, Warwick, & Roberts 2002), but most cannot be resolved by the XIS. However, most of the nonnuclear sources are very soft and relatively weak. We excluded the data below 0.7 keV not only to avoid contamination from the nonnuclear sources, but also because we found that the count rate from the background below 0.7 keV is comparable to the source, giving a background-subtracted spectrum that has unacceptably large systematic errors. We did exclude two nonnuclear sources that are resolved in the XIS, by using circular masking regions, and one of these sources was a new transient discovered in the Suzaku data that has been discussed in detail by Isobe et al. (2008).

We extracted XIS spectra of NGC 4945 by using a circular extraction region with a radius of 3.5’, excluding any masked area containing the contaminating sources. The size of the extraction region is a trade off. If it is too small, the XRT response function is less accurate and there are less source counts than a larger region would provide. A region that is too large on the other hand, has a higher background. The selected region size is a good compromise for the NGC 4945 data. Background XIS spectra were made from off-source areas of the detector, after removing a circular region with a radius of 4.5’ centered on the source, the calibration sources (using rectangular masks), and the two prominent nonnuclear sources. There may still be residual contamination from unresolved nonnuclear sources above 0.7 keV and we shall bear this in mind when interpreting the spectral-fitting results. The XIS spectra from all four detectors (1–4) were combined into a single spectrum for spectral fitting. The background subtraction method for the HXD/PIN and HXD/GSO followed standard procedures, summarized in the appendix. The spectral response matrices used for each instrument are also described in the appendix. The energy bandpass used for the spectrum from each instrument was determined by the reliability of the background subtraction. Excluding lower and upper energy ranges that gave negative counts in the background-subtracted spectra result in the final energy ranges shown in Table 1. In addition, the 1.83–1.93 keV region in the XIS spectrum was excluded due to a known line-like residual calibration feature (e.g. see Yaqoob et al. 2007). The energy ranges, count rates, and the relative importance of the background in the relevant energy ranges are shown in Table 1.


Detector
Exposure Energy Range Rate Percentage of
(ks) (keV) (ct/s) On-Source Rate
XIS 95.1 0.7–1.83, 1.93–9.82 85.8%
PIN 80.1 11.6–47.7 34.7%
GSO 80.1 80–165 2.0%

Background-subtracted count rate in the energy bands specified. The background-subtracted source count rate as a percentage of the total on-source count rate, in the utilized energy intervals.

Table 1: Exposure Times and Count Rates for the Suzaku Spectra

Although the X-ray spectrum of NGC 4945 varies in amplitude and shape during the Suzaku observation, we will utilize only the time-averaged spectrum over the entire observation in order to obtain the highest signal-to-noise ratio to model the nominal average spectrum. Spectral variability will be kept in mind when interpreting the results. Itoh et al. (2008) discussed in detail the nature of the variability in NGC 4945 during the Suzaku observation, finding that the source is variable on timescales as short as  ks.

Binning of the spectra based upon a minimum number of counts per energy bin (or a threshold signal-to-noise ratio per bin) was avoided because such a procedure distorts the spectrum, especially in regions that contain emission or absorption features. Results of spectral fitting to such spectra can be incorrect. Instead, the XIS and PIN spectra were examined, and uniform energy bin sizes were selected for energy ranges that resulted in all individual bins contained more than 20 counts. Thus, the statistic could be used for spectral fitting. For the GSO, the special energy bin boundaries that matched the boundaries used for the available background files were adopted, and these were binned by a factor of 2, as described in the appendix.

We measured the centroid energies of the Mn  lines from the calibration sources, using spectra from the individual XIS detectors, as well as a spectrum combined from all four XIS detectors and both calibration sources. The expected energies of the Mn  and Mn  lines are 5.89875 keV and 5.88765 keV respectively (Bearden 1967). Since the branching ratio is 2:1, the expected centroid energy is then 5.89505 keV. If the spectral response functions in the XIS response matrices were perfect we should find that the calibration lines are unresolved. Using a single Gaussian with the centroid energy, intrinsic width, and overall normalization allowed to be free parameters, we found that the offset of the centroid energy (relative to the theoretical value) and the spectral resolution was different for the different XIS detectors. Since the final NGC 4945 analysis was performed using data combined from all XIS detectors, we used the calibration spectra averaged over all XIS detectors and all calibration sources to obtain a measurement of the line centroid offset and instrumental broadening at 5.9 keV. We obtained an offset for the centroid of  eV (i.e. a best-fitting energy of  keV), and a Gaussian width of  eV. The statistical errors quoted are 90% confidence for 3 interesting parameters. We will use these measurements to help model the Fe K line emission in NGC 4945. Although the energy scale and spectral resolution depend somewhat on the spatial position of the source on the XIS detectors, the data do not warrant a more sophisticated treatment.

2.2 BeppoSAX Data

NGC 4945 was observed by BeppoSAX in 1999, July 1. The BeppoSAX mission carried on board three imaging medium energy concentrator spectrometer units (MECS, Boella et al. 1997), and a phoswich detector system (PDS, Frontera et al. 1997). The MECS operated in the energy band  keV, and the PDS operated in the energy band  keV. There was also a low energy concentrator spectrometer (LECS, Parmar et al. 1997) and a high energy gas scintillation proportional counter (HPGSPC, Manzo et al. 1997) on board, but we did not utilize these in the present study. The LECS had a spectral resolution that is too low for the present study, and the HPGSPC had insufficient signal-to-noise ratio for AGN in general.

Spectra and response matrices for the MECS and PDS data were downloaded from HEASARC. The data, including background spectra, are already cleaned and prepared for spectral fitting by the pipeline processing. For the PDS, the background spectrum that was made using the so-called “Variable Rise Time” method was used333http://heasarc.gsfc.nasa.gov/docs/sax/abc/saxabc/saxabc.html, appropriate for weak sources. At the time of the NGC 4945 observation, one of the MECS detectors was already nonoperational and the combined spectrum from MECS2 and MECS3 was utilized in the spectral fitting. The exposure times for the MECS and PDS spectra were 46.8 ks and 43.8 ks respectively. We found that the background subtraction for the MECS below 2 keV and above 9.5 keV was poor so we only utilized the energy range 2–9.5 keV. For the PDS it was found that background-subtraction systematics restricted the useful energy range of the spectrum to 16.5–100 keV. The net background-subtracted count rates in the utilized energy intervals were ct/s and ct/s respectively. The MECS and PDS spectra were binned uniformly, the bin widths being 185 eV and 2.25 keV respectively. For both spectra, each energy bin had at least 20 counts, validating the use of the statistic for spectral fitting.

The cross-normalization of the PDS and MECS spectra was set at 0.85:1 for PDS:MECS, consistent with measurements for 3C 273 in the “BeppoSAX Cookbook”444http://heasarc.gsfc.nasa.gov/docs/sax/abc/saxabc/saxabc.html, after correction for the “Variable Rise Time” method of background subtraction.

2.3 Swift BAT Data

The Burst Alert telescope (BAT, Barthelmy et al. 2005) aboard the Swift satellite (Geherls et al. 2004) has been conducting an all-sky hard X-ray survey in the 14–195 keV band since 2004, November (e.g. see Tueller et al. 2010; Burlon et al. 2011). NGC 4945 is one of the brightest AGN that is detected in the Swift BAT all-sky hard X-ray survey. The 58-month catalog lists the 14–195 keV flux of NGC 4945 as 555http://swift.gsfc.nasa.gov/docs/swift/results/bs58mon/. The 58-month BAT spectrum for NGC 4945 and the associated response matrix were downloaded from the archive 666http://swift.gsfc.nasa.gov/docs/swift/results/bs58mon/SWIFT_J1305.4-4928. The standard 8-channel spectrum from the BAT is time-averaged over a period of 58 months and was already prepared for spectral analysis. The net count rate of the spectrum is ct/s. Also available as a standard product is a 66-month, 14–195 keV lightcurve that has time bins that have a duration of 1 month (since November 2004), and flux units relative to the Crab flux. This lightcurve is shown in Fig. 1 and it can be seen that the 14–195 keV flux is highly variable on timescales of months to years, showing a dynamic range of about a factor of 8 between the highest and lowest flux states. The straight average of the flux (in the Crabweighted units shown in the lightcurve) is . The Suzaku spectrum corresponds to about in these units (obtained by renormalizing the Suzaku spectrum to the Swift BAT data). This puts the Suzaku observation near the top of the range in Fig. 1.

Figure 1: The NGC 4945 Swift BAT 66-month lightcurve in the 14–195 keV band. Each time bin corresponds to a one month time interval, the first bin corresponding to 2004, November. The flux is given in “Crab” units.

3 General Form of the X-ray Spectrum of NGC 4945

The general form of the broadband X-ray spectrum of NGC 4945 is now well established (e.g. Itoh et al. 2008 and references therein). The spectrum below  keV is heavily suppressed relative to that in the –30 keV band, due to heavy obscuration. Below  keV the spectrum is dominated by scattered emission of the intrinsic X-ray continuum in an extended optically-thin medium (e.g., Turner et al.  1997; Marinucci et al. 2012, and references therein). Below  keV there is evidence of an additional soft excess that is due to thermal emission from extended circumnuclear matter (at least some of this has been directly spatially resolved by Chandra, as described by Marinucci et al. 2012). Such a spectrum is typical of obscured AGN, although the amount of suppression below 10 keV (compared to the flux above 10 keV) varies from source to source. The intrinsic X-ray continuum in NGC 4945 has to be inferred indirectly (and therefore is model-dependent) because of the complexity and breadth of the various X-ray spectral features. In our analysis we will adopt two forms for the intrinsic continuum, the first being a simple power law (with a photon index of ), and a termination energy, . The second continuum form is that of a Comptonized Wien spectrum, characterized by the temperature and optical depth of the Comptonizing plasma ( and respectively). The exact form of the initial spectrum (in this case a Wien spectrum) is unimportant for values of the Compton- parameter that result in a Comptonized spectrum that is roughly a power law with a high-energy rollover (i.e. observationally relevant to NGC 4945). This model of the intrinsic continuum is described in Titarchuck (1994), in which it is explained that the Wien spectrum was adopted because it is lends itself to certain computational advantages. In XSPEC the model is known as comptt. The temperature of the Wien spectrum was fixed at  keV, below the lower end of the bandpass for any of the data sets that we used, and this choice does not affect the values and used to fit the data. Again, this is because for a Compton- parameter greater than unity, the Comptonized spectrum is not sensitive to the exact form of the initial spectrum.

A fraction of the direct continuum is scattered into the line of sight by optically-thin matter, extended on the same or larger size scale as the putative torus, and we refer to this fraction as . In the optically-thin limit, the Thomson depth, , of the scattering region is simply equal to for a fully covering spherical distribution of material. More realistically, , where is the solid angle as a fraction of subtended by the scattering zone at the X-ray source. Only that part of the scattering zone visible to the observer should be included in this solid angle. We assume that the optically-thin scattered continuum has an identical spectral shape to the intrinsic continuum, although the former is allowed to have its own uniform, Compton-thin absorption (column density ). Part, or all of this column density may be due to absorption in the host galaxy. In reality the above two assumptions are oversimplistic, but given the complexity of the overall baseline model, a more detailed treatment of the optically-thin scattered continuum is not warranted. We add to these continuum components an optically-thin thermal continuum emission component using the apec model with abundances fixed at the solar values, but with the normalization and temperature of the thermal component ( and respectively) allowed to float in fits. This optically-thin emission component is of course not absorbed by the large, Compton-thick column density (or at least, we observe only the portion that is unobscured by it). However, we do include a lower, uniform column density as a free parameter to allow for the possibility of absorption by material in addition to the primary X-ray reprocessing structure (we will refer to it as ). The column densities and are not tied together (even though they cover a similar physical region) as this allows for the most general situation. Preliminary spectral fitting showed that both and are less than (i.e., Compton-thin) and in fact similar in value to each other. Since these column densities are so small (Thomson depth ) it is not necessary to model Compton scattering or fluorescent line emission from these absorption components.

In §4 we describe in detail how the Compton-thick absorption, scattering and fluorescent Fe K and Fe K line emission in NGC 4945 are modeled. The Ni K line emission is weak in the NGC 4945 data and is not yet included in the mytorus model but it is included in some of the other Compton-thick reprocessor models that we used. In the former case, the Ni K is modeled as a separate unresolved Gaussian component (characterized by a centroid energy and line flux denoted by and respectively). The Suzaku data also show line emission centered around  keV, which we ascribe to Fe xxv, and this is also modeled by a separate Gaussian component. It very likely originates in the ionized extended zone and does not originate in the Compton-thick X-ray reprocessor which produces the Fe K line centered at 6.4 keV in neutral matter. The centroid energy, intrinsic Gaussian width, and flux of the line centered at  keV are donated by , , and respectively. We note that individual lines of the Fe xxv triplet cannot be resolved by Suzaku and the emission that is observed may even have some contribution from lower ionization states so the line width should not be interpreted as necessarily due entirely to velocity broadening.

All spectral fits to the BeppoSAX data will have fewer free model parameters than the models fitted to the Suzaku data because the BeppoSAX MECS spectrum only extends down to 2 keV. Our approach is to freeze the normalization and temperature of the soft X-ray, optically-thin, thermal continuum at values obtained from the Suzaku fits. The same is done for the column density associated with the optically-thin thermal emission (). In addition, since the spectral resolution of the MECS is greater than 600 eV at the energies of the Gaussian emission-line components (i.e., in the 6–8 keV range), the centroid energies of the lines were fixed at 6.700 keV and 7.472 keV, corresponding to the theoretical energies of the Fe xxv(r) and Ni K lines respectively. Moreover, the intrinsic width of the Fe xxv(r) line was fixed at a best-fitting value obtained from the Suzaku data, and the intrinsic widths of the Fe K and Ni K lines were fixed at FWHM because these lines in the Suzaku data were unresolved. Whereas the Suzaku fits have two relative normalization parameters (which we refer to as and ), the BeppoSAX data only have one (which we refer to as ). The value of was fixed at 1.12 (see appendix), was allowed to float unless stated otherwise, and was fixed at 0.85 (see §2.2).

Models for the Swift BAT data of course always have fewer model components than those for the Suzaku and BeppoSAX data because the soft X-ray emission component, the optically-thin scattered continuum, the associated column densities, and the fluorescent emission lines can omitted.

4 Analysis Strategy

There are a number of critical steps in the analysis scheme that we will pursue, and in this section we outline the key motivators and drivers at each stage of the complex analysis. These steps in the analysis will be described in more detail in later sections when necessary.

4.1 Constraints from Variability

The large-amplitude, short and long-timescale continuum variability above 10 keV, as demonstrated by the Swift BAT (Fig. 1) and other data (Itoh et al. 2008; Marinucci et al. 2012, and references therein), imposes a constraint on the size of the Compton-thick region responsible for producing the narrow Fe K emission and the associated Compton-scattered continuum. Since the flux of the Fe K line in NGC 4945 does not respond to the variable continuum above 10 keV, it is a robust inference that the continuum above 10 keV cannot be dominated by the Compton-scattered component of the continuum since that latter component has to originate in the same region as the Fe K line. Therefore, the continuum above 10 keV must be dominated by the direct (unscattered) continuum transmitted through the Compton-thick medium in the line of sight (we refer to this component in general as the zeroth-order continuum). However, since we will be describing a methodology that should be applicable to AGNs in general, we will also consider cases in which the high-energy continuum above 10 keV is dominated instead by the Compton-scattered continuum. For example, as we shall see, an AGN shrouded in a fully-covering Compton-thick spherical distribution of matter will have a high-energy continuum that is dominated by the Compton-scattered continuum (this is reversed if the source is Compton-thin). For most AGNs there may not be sufficient data (in quantity and/or quality) to determine the variability properties of the high-energy continuum and Fe K line, so both cases (zeroth-order continuum dominating and not dominating above 10 keV) would need to be considered if they may provide degenerate spectral solutions. However, we note that if an AGN is Compton-thin in the line of sight, with a column density in the range to , there will be much less ambiguity because the zeroth-order continuum will impose strong and characteristic features on the spectrum in terms of the detailed shape of the Fe K edge and the continuum below it. The EW of the Fe K line with respect to the total continuum then narrows down the parameter space even further. Even spectra of weak AGNs in this regime of intermediate Compton depth may yield less ambiguity in the model solutions than much brighter AGNs that are Compton thick. (Sources with column densities less than are of course far less complex, since they are dominated by the zeroth-order continuum at all energies.)

4.1.1 Separability of the Zeroth-Order Continuum and the Compton-scattered Continuum

In our analysis we will explore and derive results for several scenarios, including those that are ruled out by the variability properties of NGC 4945. The purpose here is to illustrate how the different scenarios can give degenerate spectral solutions even for the high signal-to-noise ratio of the NGC 4945 data. For weaker AGNs, and those that lack vital variability information, being aware of the spectral degeneracies and correctly interpreting them will be important. We point out that in order to adequately model NGC 4945, and any other source for which time variability of the Compton-thick scattered continuum needs to be considered, ideally we need a Compton-thick reprocessor model in which the zeroth-order continuum and the Compton-scattered continuum are separable (i.e. they must be allowed to have independent normalizations for the purpose of spectral fitting). In the Compton-thick spectral-fitting models of BN11 the two continuum components are not separable. The only model that is currently publicly available that has the required capabilities to handle the possibility of different timescales of variability of the Compton-scattered and zeroth-order continuum components is the mytorus model (see MY09). Nevertheless, we will still make use of the BN11 models.

4.2 Constraints from the Intrinsic Fe K Line Width

In principle, we can estimate the light-crossing time across any spatially unresolved X-ray reprocessor that might be present, using measurements of the Fe K intrinsic line width. If the FHWM velocity of the line is , using a virial estimate of the velocity dispersion of (following Netzer 1990), and a simple Keplerian assumption, gives a light-travel time from the X-ray source to the reprocessor of  ks, where is the measured FWHM in units of , and is the central black-hole mass in units of . The Chandra high-energy grating (HEG) measured an intrinsic width of the narrow Fe K line in NGC 4945 of  FWHM, with a two-parameter, 99% confidence range of to  FWHM (Shu, Yaqoob, & Wang 2011). The HEG has the best spectral resolution in the Fe K band currently available. Using (Greenhill et al. 1997), we see that for a nominal value of of , the light-crossing timescale is  ks, and for a value of (around the upper limit for ), the timescale is  ks. The fastest timescale for high-energy continuum variability in NGC 4945 reported so far is  ks for a flux doubling (Itoh et al. 2008). However, it is likely that the line broadening is due to the component of the Fe K line that is spatially extended, because grating spectrometers cannot distinguish between spatial and true spectral broadening. Nevertheless, we refer to the calculation of velocity broadening for the sake of application to AGNs other than NGC 4945, for which the line emission is spatially unresolved. We note in passing that the HEG centroid energy of the Fe K line in NGC 4945 is extremely well constrained ( keV), confirming its origin in neutral Fe or nearly neutral Fe.

We should also bear in mind that the case of NGC 4945 does not rule out the possibility of two physically distinct regions of Compton-thick matter. Although the Fe K line emission that is spatially resolved and extended, on a scale of 30 pc or greater, could account for the bulk of the total Fe K line emission (Marinucci et al. 2012), it is possible that there could be a smaller Compton-thick region that obscures the line of sight but has a sufficiently small covering factor that it does not make a significant contribution to the Fe K line.

4.3 Intrinsic Luminosities

It is important to understand that, in addition to finding solutions that fit the various X-ray spectra of NGC 4945 (and other AGNs), we must keep a check on the implied intrinsic continuum luminosities because they can differ by an order of magnitude or more for different degenerate scenarios. In fact, we shall see that it is possible for different spectrally degenerate models applied to two observations of a source to predict opposite senses of variability under some circumstances. In other words, one set of models may imply a decreasing intrinsic luminosity going from one observation to the next, whilst a different set of models may imply an increasing intrinsic luminosity going from one observation to the next. Here we simply point out a general characteristic of the various models, namely that the higher the contribution of the zeroth-order continuum relative to the Compton-scattered continuum, the greater the intrinsic luminosity is. This is because Compton scattering shifts more of the intrinsic continuum into the observer’s line of sight compared to the case when the observer receives only the zeroth-order continuum. In other words, if there is a Compton-scattered continuum component observed in the spectrum, it can only decrease the burden on the intrinsic continuum to produce the observed luminosity for a given column density. To put it another way, the intrinsic continuum must lie above the zeroth-order continuum by a very specific amount that depends only on the line-of-sight column density, regardless of geometry and regardless of the level of the Compton-scattered continuum. There are two particular corollaries of this. One is that if the observed spectrum can be well-fitted by only the zeroth-order continuum (e.g., if the reprocessor has a negligible global covering factor), such a fit yields the maximum possible intrinsic continuum luminosity for a given line-of-sight column density. The second corollary is that for a given line-of-sight column density, a distribution of matter with full covering (such as a spherically-symmetric distribution) will give the minimum possible intrinsic luminosity. In the Compton-thin limit, these minimum and maximum luminosities will of course be equal to each other because in that limit there is only the zeroth-order continuum regardless of covering factor. As the Compton depth of the matter distribution approaches unity (), the Compton-scattered continuum from a fully-covered source dominates over the zeroth-order continuum in the observed spectrum. As we will see, the two extremes give implied intrinsic luminosities that can differ by an order of magnitude or more. In all of the tables in which we will give the results of spectral fitting, we will give observed fluxes and luminosities in various energy bands. However, the intrinsic luminosities and their ratios with respect to the Eddington luminosity will not be discussed until all of the spectral fitting results have been presented. Discussion of the intrinsic luminosities and their implications will be presented in §8.

4.4 Procedure for NGC 4945

Our analysis procedure for NGC 4945 is then as follows.

We begin with the simplest and extreme scenario, namely that in which the spectrum of NGC 4945 above 10 keV consists only of the zeroth-order continuum.

(i)We examine all of the three data sets above 10 keV only (i.e. utilizing only HXD data for Suzaku, only PDS data for BeppoSAX, and the Swift BAT data). The model above 10 keV is very simple because no emission lines or soft X-ray emission components need to be included.
(ii) These spectral fits are described in §5, and we will find that, in addition to a simple power law, we need to consider intrinsic spectra that rollover in the instrument bandpasses. For this we use a thermally Comptonized intrinsic continuum (details in §3).

Obviously, the Compton-scattered continuum cannot be zero since there has to be a specific flux of this continuum that is associated with the fluorescent Fe K and Fe K emission lines. However, these extremal fits will be useful for four reasons:

(i) One is that the fits can guide spectral fitting with more complex models across the full instrumental bandpasses.
(ii) Another reason is that our results can be used to assess the limitations of deriving key physical parameters (such as column density and intrinsic luminosity) when a particular source only has Swift BAT data available. Even though the Suzaku and BeppoSAX observations are not contemporaneous with the Swift BAT data, the latter contain information about long-term variability spanning a period of over 5 years, and about the average spectrum over a similarly long time period.
(iii) A third reason is that the zeroth-order continuum fits will provide an indicator of the maximum possible intrinsic continuum luminosities.
(iv) A fourth reason is that this is the only model in which an arbitrary intrinsic continuum can be used, with any of the intrinsic continuum parameters allowed to be free (without having to generate grids of tables at finite parameter-value intervals).

We then proceed to obtain full solutions for the Suzaku data and BeppoSAX data, including the Fe K emission line and other model components in the fits.

(i) Spectral fitting is then divided into two classes of models, one in which the Compton-thick reprocessor has the zeroth-order and Compton-scattered continuum components “coupled” to each other, and one in which they are “decoupled.”
(ii) Only the mytorus model allows decoupling, and when used in this mode, one interpretation is that the model mimics a patchy (or clumpy) X-ray reprocessor in which the “holes” allow unobscured observation of some of the reflection and fluorescence from the far-side, inner surface of the structure. In this mode, the geometry is not necessarily strictly toroidal, and the global covering factor is unspecified because the spectrum is dominated by matter observed through the “holes” and by matter in the line of sight. Another scenario is that a subset of the decoupled models describes two distinct X-ray reprocessing regions, one that obscures the central X-ray source with less than full global covering, and another more extended reflection region, such as that which has been spatially resolved in NGC 4945 (Marinucci et al. 2012).
(iii) The decoupled mode of the mytorus model is in fact closest to the procedure that has been universally used in the literature for AGNs in general for over 15 years: a disk-reflection continuum modeled with pexrav or pexmon (or equivalent), combined with decoupled line-of-sight extinction modeled with cabs or just zphabs (absorption only). However, disk-reflection models assume an infinite column density for the material responsible for producing the Compton-scattered continuum so they cannot produce spectral features in the data that are characteristic of scattering in a finite column-density medium. Combined with the fact that the geometry of disk-reflection models may be inappropriate, the mytorus model, even in the decoupled mode, yields column densities and intrinsic continuum luminosities that have more straightforward physical interpretations. Also, the line-of-sight extinction in the mytorus model employs a fully relativistic Compton-scattering cross section.
(iv) The detailed setup and parameters of the coupled and decoupled modes of the mytorus model are given in §4.5. The results of fitting the coupled mytorus model are given in §6, and those obtained from fitting the decoupled mytorus model are given in §7. A particular feature of the decoupled model is that it allows a Compton-thick structure observed edge-on to produce a large fluorescent Fe K line EW whilst still allowing the zeroth-order continuum to dominate above 10 keV.
(v) We will also utilize the toroidal and fully-covering spherical models of BN11. Since the zeroth-order and Compton-scattered continua cannot be decoupled in these models, their application is described along with the other coupled models in §6.

4.5 The MYTORUS Model

The toroidal Compton-thick X-ray reprocessor model, mytorus, has been described in detail in MY09, and Yaqoob & Murphy (2011a). The geometry consists of a torus with a circular cross section, whose diameter is characterized by the equatorial column density, . The model is currently restricted to a configuration in which the global covering factor of the reprocessor is , corresponding to a solid angle subtended by the structure at the central X-ray source of . However, spectral fits with the zeroth-order continuum only (see §5) correspond to the limit of a negligible covering factor, and fits with the BN11 fully-covering spherical model (see §6) correspond to the other extremal limit in the covering factor. We will also utilize the toroidal model of BN11, which does allow the covering factor to vary between 0.1 and 0.9, but, like the BN11 spherical model, this model does not allow separation of the zeroth-order and Compton-scattered continua.

The practical implementation of the mytorus model allows free relative normalizations between different components of the model in order to accommodate differences in the actual geometry (compared to the specific model assumptions used in the original calculations), and time delays between direct, scattered, and fluorescent line photons 777See http://mytorus.com/manual/ for details. The zeroth-order component of the model is essentially an energy-dependent multiplicative factor that is independent of the geometry and independent of the intrinsic continuum. The multiplicative factor is then implemented with a single XSPEC table for all applications of the model (it is mytorus_Ezero_v00.fits). The Compton-scattered continuum is implemented as an XSPEC additive table model, utilizing different tables for a power-law input continuum and a Comptonized thermal (comptt) input continuum (see Titarchuk 1994). For the former, tables with a termination energy of 200 keV were used, and for the latter, each table has a unique, fixed value of the Comptonizing plasma temperature. Tables with different temperatures were utilized, and details will be given in the appropriate places in the descriptions of the data analysis procedures. The Fe K and Fe K line emission is implemented with another XSPEC additive table model that is selected from line tables made with a range of energy offsets for best-fitting the peak energies of the emission lines. Preliminary fitting showed that an offset of  eV is optimal for the NGC 4945 Suzaku data (this offset covers both instrumental energy offsets, as well as any intrinsic offset due to very mild ionization). Different sets of emission-line tables are used for the power-law and Comptonized thermal intrinsic continua (i.e. each Compton-scattered continuum table has a corresponding emission-line table for a given offset energy). Again, details of the actual tables used will be given at the appropriate places in the data analysis descriptions. The Fe K and Fe K lines are broadened by two Gaussian convolution model components (gsmooth in XSPEC). One of these accounts for the residual instrumental broadening that is not in the response matrix, and is normalized to the broadening of the calibration source data (see §2.1), with a dependence of the Gaussian width, and the other is the actual velocity broadening (Gaussian width proportional to line energy).

4.5.1 Default (Coupled) Model

In this mode of use (regardless of the form of the intrinsic continuum), the angle made by the axis of the torus with the observer’s line of sight () is coupled to the column density that is intercepted by the zeroth-order continuum. In other words, the effective geometry of the X-ray reprocessor is precisely that assumed in the original Monte Carlo calculations (MY09). We denote the relative normalization between the scattered continuum and the direct, or zeroth-order continuum, by , which has a value of 1.0 for the assumed geometry with the assumption that either the intrinsic X-ray continuum flux is constant, or, for a variable intrinsic X-ray continuum, that the X-ray reprocessor is compact enough for the Compton-scattered flux to respond to the intrinsic continuum on timescales much less than the integration time for the spectrum. It is important to note that is not simply related to the covering factor of the X-ray reprocessor because the detailed shape of the Compton-scattered continuum varies with covering factor. Analogously to , the parameter is the relative normalization of the Fe K line emission, with a value of 1.0 having a similar meaning to that for . In our analysis we will set unless otherwise stated.

For the sake of reproducibility, we give below the exact model expression that we used in XSPEC (for the case of an intrinsic power-law continuum). The numbered model components and model parameters are described in Table 2. This example is for a power-law intrinsic continuum with a termination energy, , of 200 keV, and an offset of  eV for the emission-line tables. Substitution of the scattered continuum and emission-line tables with corresponding tables for a different intrinsic continuum is straightforward (for example, see §4.5.2). In the case of the comptt model substituting for the power-law continuum, the photon index, , is replaced by the Comptonizing plasma optical depth () for a given table selected for the Comptonizing plasma temperature, (and the normalization, , replaced by ). The parameters , , and are instrumental cross-normalizations (clearly, one or more of these will be absent in the model if data from the corresponding instruments are not utilized). The value of was fixed at 1.12 (see appendix), was allowed to float unless stated otherwise, and was fixed at 0.85 (see §2.2). Hereafter, Compton-scattered continuum components in the mytorus model will be referred to generically by the label MYTS and any energy-dependent multiplicative factor that is used to obtain the zeroth-order continuum will be referred to generically by the label MYTZ.

Par. Comp. Symbol Units Status Description
1 1 , fixed PIN:XIS or PDS:MECS instrumental cross-normalization ratio.
2 1 free GSO:XIS instrumental cross-normalization ratio.
3 2 fixed (1.57) Galactic column density.
4 3,6,10,15 ph. free Intrinsic power-law normalization at 1 keV.
5 3,6,10,15 free Photon index of the power-law continuum.
6 4,6,10 free Equatorial column density of the torus.
7 4,6,10 degrees free Inclination angle of the torus.
8 5 free Scaling factor for the scattered continuum from the torus.
9 7 Scaling factor for the fluorescent line emission from the torus.
10 8 eV fixed (14) Line width accounting for XIS resolution degradation.
11 9 FWHM[Fe K,Fe K] fixed (100) Intrinsic width of the Fe K and Fe K emission lines.
12 11 keV free Gaussian centroid energy of the line emission at  keV.
13 11 FWHM[Fe xxv] free Intrinsic width of the line emission at  keV.
14 11 ph. free Flux of line emission at  keV.
15 12 keV free Gaussian centroid energy of the Ni K line.
16 10 FWHM[Ni K] fixed (100) Intrinsic width of the Ni K line.
17 12 ph. free Flux of the Ni K line emission.
18 13 free Scattering fraction due to optically-thin matter.
19 14 free Absorber covering optically-thin scattering zone.
20 16 free Absorber covering extended thermal emission zone.
21 17 ph. free Normalization of the apec model.
22 17 keV free Temperature of the apec model.

Parameter number. Model component(s) that the parameter appears in (corresponding to the model component numbers in the model expression shown in §4.5.1). Determined from fitting calibration source data (see §2.1). The Gaussian emission-line centroid energies, and the intrinsic width of the Fe xxv line were initially allowed to float but they were then frozen at their best-fitting values in order to obtain robust statistical errors on the other parameters of interest. A single intrinsic width is associated with the Fe K and Fe K lines, and this width, along with that of the Ni K line was fixed at  FWHM since the lines were found to be unresolved. Upper limits were derived by allowing the two line widths to float in turn (see §6 and §7).

Table 2: Parameters for the Baseline Coupled mytorus Model with a Power-law Intrinsic Continuum

4.5.2 Decoupled Model

A problem with all Monte-Carlo simulations of the Compton-scattered continuum from a toroidal structure observed edge-on is that the spectrum is extremely sensitive to the geometry of the “edges” of the structure. This is because the column density presented to incident continuum photons is small at the edges, and the Compton-scattered flux from these regions can easily dominate the entire spectrum if the equatorial part of the reprocessor is Compton-thick. This is not just a problem with the mytorus model but it is a general problem with similar models observed edge-on (e.g., the toroidal models of Ghisellini, Haardt, & Matt 1994, Ikeda, Awaki, & Terashima 2009, and BN11). In reality, the geometry of the toroidal structure, particularly at the edges, may not be well represented by the exact model geometry that is used. For example, a structure that is cylindrical should produce an edge-on Compton-scattered spectrum that is much weaker than that produced by the particular toroidal geometry of the mytorus model. Another problem is that the finite size of the inclination-angle bins means that even when the inclination angle is in the model, there is always some “leakage” contribution from photons with angles less than . We can mitigate these problems in the mytorus model by decoupling the zeroth-order continuum from the inclination angle (), fixing this angle at , and allowing the relative normalization of the Compton-scattered continuum to be free, and much less than 1.0 if necessary. In this context, we refer to the relative normalization as (it was just in the coupled model). Since the zeroth-order continuum is independent of geometry (being purely a line-of-sight quantity), the inclination angle associated with this component becomes a dummy parameter and it is fixed at so that the zeroth-order column density is literally equal to the value of for this model component. (In the coupled mode, the equatorial is not equal to the line-of-sight column density for general values of .) The column density associated with the zeroth-order continuum and the Compton-scattered continuum remain coupled to a single value in our implementation for NGC 4945, although they could be decoupled if we wanted to mimic a more complex structure for the reprocessor.

Yet another issue with a Compton-thick structure observed edge-on is that the zeroth-order and Compton-scattered continua could be so weak that even a small amount of patchiness or clumpiness could give rise to an observed spectrum that is actually dominated by a small amount of reflection of the intrinsic continuum by the far side of the structure. In other words, even if a few percent of the reflection from the inner far side of the reprocessor is unobscured by material on the near side of the structure, the observed spectrum may be dominated by the far-side reflection, at least below  keV, at energies relevant for the Fe K and Fe K line emission. We can mimic this far-side reflection spectrum with the face-on reflection spectrum in mytorus (and in fact the shape of the reflection spectrum from the inner faces of the torus is similar for all lines of sight that do not intercept the torus). In practice, to implement this, we simply add another Compton-scattered continuum table to the XSPEC model, but this time we fix the value of the inclination angle at for that component only. This component has its own normalization, which we call . Thus, we have two Compton-scattered continua and each can be varied independently relative to the zeroth-order continuum with the parameters and . Each component has its own Fe K and Fe K emission-line table, each of which has all of its parameters tied to the corresponding continuum model parameters.

Figure 2: Illustration of the physical scenario that is approximately emulated when the mytorus model is used in “decoupled mode” (as described in §4.5.2). The X-ray reprocessing material, represented as clouds, is in the form of a clumpy distribution with an arbitrary covering factor, and has an average, global radial column density denoted by . The X-ray continuum source, shown with radial lines ending in arrows, is smaller than any of the individual matter clumps. The spectrum from back-side reflection that reaches the observer without further interception by any absorbing matter is approximated using a MYTS component, and scattered emission that is not from back-side reflection is approximated using a MYTS component. The direct, zeroth-order continuum that reaches the observer after intercepting line-of-sight material is modeled with an MYTZ component ( is set to in order for the parameter to correspond directly to the line-of-sight column density). This latter component can have a different column density, , if for example, there is additional material in the line of sight, so that is different to the global average. This is useful for modeling variable sources in which matter can come into or out of the the line of sight. Multiple clumps in the line of sight, including those in the main distribution, can be modeled with a single MYTZ component.

The generalized geometrical setup that is approximated by the decoupled model is illustrated in Fig. 2. In addition to decoupling of the inclination angle, there is a provision for the line-of-sight column density () to be decoupled from the global average column density (), and this is particularly useful for modeling sources in which there is spectral variability due to matter moving in and out of the line sight. Only a single line-of-sight component needs to be utilized for a given observation, corresponding to the total line-of-sight column density. Individual clumps that move in and out of the line of sight are assumed to be too small to make a measurable difference to the Compton-scattered continuum and fluorescent line emission (if this is not the case, the differences would manifest themselves in the existing MYTS components).

Note that neither nor should be interpreted as covering factors. In a scenario in which the high-energy spectrum is dominated by the zeroth-order continuum, the global covering factor cannot be constrained even in principle. This is because any Compton-scattered and fluorescent line flux that is observed in the patchy reprocessor scenario would be dominated by back-side reflection from the inner far side of the X-ray reprocessor, through the unobscured patches. The amount of “leakage” due to these patches is not related to the bulk global covering factor. In fact, the parameter in this case would be more closely related to the fraction of the total solid angle subtended by the X-ray reprocessor that is punctured by “holes.” Alternatively, in a dual reprocessor scenario, the illumination pattern of the extended reprocessor by the central X-ray source and the exact geometry of circumnuclear material are uncertain so cannot be interpreted as a simple covering factor. It should also be remembered that both of the parameters and also include the effects of any time delays between the intrinsic continuum and the response of the reflection spectra.

The resulting decoupled mytorus model, as implemented in XSPEC, is written out in full below, and its parameters are summarized in Table 3. The intrinsic X-ray spectrum here is the comptt Comptonized thermal spectrum but could just as well be replaced by the power-law intrinsic continuum (as was used to illustrate the usage of the coupled mytorus model in §4.5.1). The specific XSPEC tables used in the example expression correspond to a Comptonizing plasma temperature of  keV, and an offset of  eV for the emission-line tables.

Par. Comp. Symbol Units Status Description
1 1 , fixed PIN:XIS or PDS:MECS cross-normalization ratio.
2 1 free GSO:XIS instrumental cross-normalization ratio.
3 2 fixed Galactic column density, fixed at 1.57.
4 3,6,8,12,14,19 ph. free Normalization of the intrinsic continuum (comptt).
5 3,6,8,12,14,19 keV fixed Temperature of the Comptonizing plasma.
6 3,6,8,12,14,19 free Optical depth of the Comptonizing plasma.
7 4,6,8,12,14 free Column density of all reprocessor components.
8 5 free Scaling factor for a face-on scattered continuum.
9 7 free Scaling factor for an edge-on scattered continuum.
10 9 eV fixed (eV) Line width accounting for XIS resolution degradation.
11 10 FWHM[Fe K ,Fe K] fixed (100) Intrinsic width of the Fe K and Fe K lines.
12 11 Scaling factor for fluorescent line emission.
12 13 Scaling factor for fluorescent line emission.
14 15 keV free Gaussian centroid energy of the line emission at  keV.
15 15 FWHM[Fe xxv] free Intrinsic width of the line emission at  keV.
16 15 ph. free Flux of line emission at  keV.
17 16 keV free Gaussian centroid energy of the Ni K line.
18 16 FWHM[Ni K ] fixed Intrinsic width of the Ni K line.
19 16 ph. free Flux of the Ni K line emission.
20 17 free Scattering fraction due to optically-thin matter.
21 18 free Absorber covering optically-thin scattering zone.
22 20 free Absorber covering extended thermal emission zone.
23 21 ph. free Normalization of the apec model.
24 21 keV free Temperature of the apec model.

Parameter number. Model component(s) that the parameter appears in (corresponding to the model component numbers in the model expression shown in §4.5.2). Determined from fitting calibration source data (see §2.1). The Gaussian emission-line centroid energies, and the intrinsic width of the Fe xxv line were initially allowed to float but they were then frozen at their best-fitting values in order to obtain robust statistical errors on the other parameters of interest. A single intrinsic width is associated with the Fe K and Fe K lines, and this width, along with that of the Ni K line was fixed at  FWHM since the lines were found to be unresolved. Upper limits were derived by allowing the two line widths to float in turn (see §6 and §7).

Table 3: Parameters for the Baseline Model with mytorus Used in Decoupled Mode with a thermal Comptonized Intrinsic Continuum

Although the decoupled mytorus model involves some ad hoc parameterization in order to account for the unknown details of the exact geometry of the X-ray reprocessor and its unknown clumpiness, the procedure is different to the current practice of using the inappropriate geometry of disk reflection (in which the disk has an infinite column density), plus zeroth-order continuum extinction that has incorrect physics, along with Fe K line emission that cannot be related to a physical reprocessor. The line-of-sight column density and intrinsic luminosity derived from the latter model may not have simple physical interpretations. Moreover, the proper use of a finite column density for the material responsible for the Compton-scattered continuum produces a rich variety of spectral shapes that cannot be produced by standard disk-reflection spectra. Residuals in spectral fits using the disk-reflection models might therefore be misinterpreted and erroneously identified with a different origin.

4.6 Other Models of the Compton-thick X-ray Reprocessor

We will also refer to spectral fits using the toroidal and spherical X-ray reprocessor models of BN11, implemented using the XSPEC tables torus1006.fits and sphere0708.fits respectively (see BN11 for details). The model parameter setup for the BN11 toroidal model is essentially similar to that of the mytorus model in Table 2, with two exceptions. One is that there are no parameters corresponding to and , because neither the Compton-scattered continuum nor the fluorescent line spectrum can be varied with respect to the zeroth-order continuum. The second difference is that there is an extra parameter in the BN11 torus model that corresponds to the half-opening angle of the toroidal structure, which therefore controls the global covering factor (which can be varied between 0.1 and 0.9). For the BN11 spherical model, the parameter setup is again similar to that for the BN11 toroidal model, except that the covering factor is effectively fixed at 1.0, and there is no inclination angle parameter because of the spherical symmetry. Two extra parameters allow element abundances to be free. The spherical model is currently the only Compton-thick reprocessor model available that allows element abundances to be free parameters. We call the two parameters and , where the former is the Fe abundance relative to the adopted solar value, and the latter is a single abundance multiplier for C, O, Ne, Mg, Si, S, Ar, Ca, Cr, and Ni relative to their respective solar values. The solar abundances adopted in the BN11 spherical model are the same as those used in the mytorus model (Anders & Grevesse 1989). The column density in the spherical model, , is the radial column density. A technical issue with the both of the BN11 models is that the energies of the fluorescent emission lines cannot be varied. This is problematic because the signal-to-noise ratio of the NGC 4945 Suzaku data is so high that instrumental calibration errors and/or mild ionization cannot be ignored. The spectral fitting is highly sensitive to offsets as small as 10 eV. To accommodate the inflexibility of the BN11 models, we first allowed the redshift parameter to float and let the Fe K line drive the spectral fits to the optimal redshift. The redshift was then frozen permanently at the best-fitting value before proceeding with the full spectral-fitting analysis.

4.7 Spectral Fitting

We used XSPEC (Arnaud 1996) v12.6888http://heasarc.gsfc.nasa.gov/docs/xanadu/xspec/ for spectral fitting (Arnaud 1996). Galactic absorption with a column density of (Heiles & Cleary 1979) was included in all of the models described hereafter and its inclusion will be implicitly assumed. For all absorption components including the Galactic one, we used photoelectric cross sections given by Verner et al. (1996). Element abundances from Anders & Grevesse (1989) were used throughout. All astrophysical model parameter values will be given in the rest frame of NGC 4945, unless otherwise stated. Due to the large number of spectral fits and the large variety of combinations of model components and parameters, for the sake of brevity, certain quantities and details pertaining to particular spectral fits will be given in the tables of results and not repeated again in the text, unless it is necessary. Specifically, we are referring to the number of free parameters in a fit, the number of interesting parameters, the number of degrees of freedom, the null hypothesis probability, and the criteria for the derivation of statistical errors. In most cases we give 68% confidence multiparameter errors, since these errors can be used in future statistical analyses of samples of AGN. However, in some cases, certain parameters have to be frozen for the sake of stability of a spectral fit, and in that case those parameters are allowed to be free, one parameter at a time, in order to derive statistical errors. For these, one-parameter, 90% confidence errors are given. Further details will be given on a case-by-case basis.

For each spectral fit we will give the observed fluxes, , and the observed (rest-frame) luminosities, , in various energy bands, in the tables of spectral-fitting results. These quantities are not corrected for absorption or Compton scattering in either the line-of-sight material, or in the circumnuclear material. These fluxes and luminosities will not be discussed until all of the spectral fits have been presented. At that point, in §8, we will present and discuss the calculated intrinsic continuum luminosities for all of the spectral fits, as well as the ratio of the luminosities to the Eddington luminosity, . For a black-hole mass of , . We use a standard cosmology of , , throughout the paper.

5 Spectral Fits with Only a Zeroth-Order Continuum

Figure 3: Spectra and data/model ratios for the Swift BAT 58-month data for NGC 4945 where the model consists of only the zeroth-order component of the mytorus model. Shown in (a) are the results for an intrinsic power-law continuum (the photon index and column density were free parameters). Shown in (b) are the results for a thermally Comptonized incident spectrum (the plasma temperature and column density were free parameters). The power-law incident continuum gives a poor fit. See Table 4 and §5 for details.

Figure 4: Confidence contours of the intrinsic continuum Comptonizing plasma temperature () versus column density of the X-ray reprocessor. The contours were obtained from spectral fits to NGC 4945 data where the model consisted only of the zeroth-order continuum for a thermally Comptonized spectrum incident on a Compton-thick X-ray reprocessor. For these fits only data above 10 keV were utilized because in that regime the Compton-scattered continuum in NGC 4945 may be negligible in some physical scenarios, such as a ring-like Compton-thick patchy X-ray reprocessor observed edge-on. The three sets of contours shown in (a), (b), and (c) correspond to spectral fits to data from the Swift BAT, BeppoSAX PDS, and Suzaku HXD (PIN and GSO) respectively. The red, blue, and black lines correspond to two-parameter, 68%, 90%, and 99% confidence levels respectively. See §5 for details.

Figure 5: Confidence contours obtained from spectral fits to the NGC 4945 PIN and GSO data using a thermally Comptonized spectrum incident on a Compton-thick reprocessor. Only the zeroth-order continuum component of the mytorus model was utilized, modeling physical scenarios in which the Compton-scattered continuum is negligible above 10 keV. The relative normalization factor for the PIN and GSO was a free parameter in the fits, and the contours show the value of this parameter versus the line-of-sight column density, , of the reprocessor (the Comptonizing plasma temperature, was also a free parameter). The dotted, dashed, and solid lines correspond to two-parameter, 68%, 90%, and 99% confidence levels respectively. It can be seen that is uncorrelated with the GSO:PIN normalization ratio. See §5 for details.

Figure 6: A demonstration of why an edge-on Compton-scattered spectrum forces a solution in which the magnitude of the zeroth-order continuum is substantially diminished compared to the Compton-scattered continuum. Shown in (a) is a mytorus model fit to the Suzaku data of NGC 4945 with a decoupled, edge-on scattered continuum. In this case, the contrast, , between the peak of the “Compton hump” and the scattered continuum in the Fe K band, is so large that in order to fit the Fe K line, the magnitude of the scattered continuum is forced to be much larger than the zeroth-order continuum. In (b) the edge-on scattered continuum is replaced by a decoupled face-on scattered continuum, and in this case the contrast, , is much less than , and the Fe K line flux is much larger, so a solution in which the zeroth-order continuum dominates is possible. Note that the black curves show the total spectra including all of the model components shown in Table 3, but not all of the individual components are shown separately for the sake of clarity. See §5 for details.

In this section we investigate spectral solutions in which the spectra above 10 keV are fitted only with the zeroth-order continuum. The Compton-scattered continuum cannot of course be zero because the model Fe K emission-line flux cannot be zero. However, if we are looking for solutions in which the Compton-scattered continuum is negligible compared to the zeroth-order continuum, we can work with the approximation of no Compton-scattered continuum and no fluorescent line emission when we are fitting data above 10 keV. We can even omit the optically-thin scattered continuum and we can certainly omit the soft X-ray thermal emission components (and any absorption only associated with those components). We can then use the results from these simplified fits as a guide for setting up the correct, full-bandpass model that will include the Compton-scattered continuum and fluorescent line emission. Moreover, since the zeroth-order continuum is obtained from the intrinsic X-ray continuum simply by multiplying by an energy-dependent factor, we can use an arbitrary incident continuum model with all of its key parameters allowed to float (as opposed to having to generate tables that only allow a restricted number of free parameters).

Parameter zeroth-order mytorus mytorus BN11 (torus) BN11 (sphere)
only (coupled) (coupled)
Intrinsic Continuum comptt power law comptt power law power law
Free Parameters 4 4 4 4 3
Interesting Parameters 3 3 3 3 2
Degrees of Freedom 4 4 4 4 5
Reduced 0.596 0.474 0.920
Null probability
criterion (68% confidence)
(degrees) (f) (f)
(degrees) (f) (f)
[10-100 keV] ()
[14-195 keV] ()
[10–100 keV] ()
[14–195 keV] ()

Results for the Swift BAT data for NGC 4945 from spectral-fitting with Compton-thick reprocessor models. Details can be found in §5 for the fit with only the zeroth-order continuum, and for the remaining fits in §6. The BN11 torus and spherical fits refer to the models of Brightman & Nandra (2011). All fluxes and luminosities are in the observed frame, uncorrected for absorption or Compton scattering. Torus opening half-angle (the maximum allowed for the BN11 model is degrees). Inclination angle of the observer with respect to the azimuthal symmetry axis of the torus.

Table 4: NGC 4945 Swift BAT Spectral-Fitting Results.

5.1 Zeroth-order Continuum Fits to the Swift BAT Data

We begin by first reporting the results of fitting the 58-month Swift BAT spectrum using a power-law incident continuum. There were only three free parameters, , , and (see §4.5) and 8 spectral channels in the spectrum (i.e., 5 degrees of freedom). It can be seen from Fig. 3(a) that the fit is very poor (the reduced value is 5.65), and the data/model residuals in Fig. 3(a) show significant deviations across the entire 14–195 keV band, but in particular show a high-energy rollover compared to a power-law. The probability of obtaining the measured value or higher is , meaning that the model can be formally rejected at greater than the level. We conclude that if the high-energy X-ray spectrum in NGC 4945 is to be dominated by the zeroth-order continuum, the intrinsic X-ray continuum cannot be a simple power law, and the spectrum has to start rolling over below  keV. Therefore, we replaced the power-law continuum with the Comptonized thermal continuum model, comptt (as described in §4.5.2). The model now had 4 free parameters, namely the overall normalization, plasma optical depth () and temperature (), and the line-of-sight column density (). An excellent fit was obtained, with for 4 degrees of freedom, as can be seen in Fig. 3(b), which shows the data, model, and data/model ratio. We obtained best-fitting parameters ,  keV, and (see Table 4). The best-fitting parameters are also given in Table 4, where they can be compared with parameters from other models that were fitted to the Swift BAT (to be described below). In Fig. 4(a) we show the two-parameter, 68%, 90%, and 99% confidence contours of versus . We see that the 99% confidence lower limit on is flat (at  keV) over most of the allowed range of , and the 99%, two-parameter upper limit on is  keV.

5.2 Zeroth-order Continuum Fits to the Suzaku and BeppoSAX Data

We repeated the exercise, this time fitting high-energy data from BeppoSAX and Suzaku, with the same simple model that includes only the zeroth-order continuum (for an intrinsic continuum modeled by comptt). Confidence contours of versus are shown in Fig. 4(b) and Fig. 4(c) for the BeppoSAX and Suzaku data respectively. Since we were explicitly examining the high-energy spectra, we used only the PDS data for BeppoSAX (see §2.2) and only the PIN and GSO data for Suzaku (see §2.1). All of the data sets gave a consistent, albeit large, range in and . The Suzaku data gave the tightest constraints on and , with best-fitting values of 22 keV and respectively. We do not give the exact parameters and statistical errors derived from the BeppoSAX and Suzaku fits because these parameters will change when they are derived from full model fits that will include the Compton-scattered continua and fluorescent lines (and the data below 10 keV). Since the mytorus Compton-scattered continuum tables have to be calculated for fixed values of , we will use the contours in Fig. 4 as a guide for the full-band spectral fits (see §7). We note that for the Suzaku confidence contours in Fig. 4, the GSO to XIS cross-normalization ratio was a free parameter in the spectral fit. Fig. 5 shows two-parameter, 68%, 90%, and 99% confidence contours for this cross-normalization versus , and we see that the ratio is uncorrelated with the derived column density. The range in the ratio is fairly large, but nevertheless consistent with the results for 3C 273 given in the appendix.

5.3 A Requirement of the Compton-scattered Continuum If the High-energy Spectrum is Dominated By the Zeroth-order Continuum

We now demonstrate that if we are looking for Compton-thick solutions in which the high-energy spectrum is dominated by the zeroth-order continuum, then the Compton-scattered continuum and Fe K line emission must be dominated by photons originating from back-illumination and then reaching the observer along paths that do not intercept the Compton-thick structure. In other words, the structure must be clumpy, allowing a reflection continuum to reach the observer either from the far inner side of a toroidal structure, or from an extended and dispersed distribution of matter (as in NGC 4945). The reason for this constraint is that the Fe K line emission and Compton-scattered continuum below 10 keV, relative to the Compton-hump peak flux in the  keV range, is much larger for unobstructed reflection than it is from reflection from matter intercepting the line of sight (e.g., see Yaqoob et al. 2010). If the reprocessor were not patchy, then raising the Fe K line flux high enough to account for the observed spectral data also raises the Compton-scattered flux so high that the Compton hump necessarily swamps the zeroth-order continuum. This is illustrated in Fig. 6, which shows model spectra in which the mytorus Compton-scattered continuum and fluorescent lines are decoupled from the zeroth-order continuum (see §4.5.2), comparing the two cases in which the reflection features are observed edge-on (Fig. 6(a)) and face-on (Fig. 6(b)). Both of these extreme cases fit the full-band (three-instrument) Suzaku data, but Fig. 6 shows that only the face-on case allows the zeroth-order continuum to dominate above 10 keV. The intrinsic continuum in Fig. 6 was the comptt model with  keV. We do not give the remaining model parameters here because detailed fits with variations on this decoupled mytorus model will be given below, in §7. The purpose of Fig. 6 is only to illustrate the need for a clumpy X-ray reprocessor if the hard X-ray continuum variability in NGC 4945 is to be produced by the zeroth-order continuum. In practice there is likely to be some contribution from both the far-side unobscured reflection, and the near-side emission from the obscuring material, but the former component must dominate over the latter component. Even when this condition is met, the Compton-scattered continuum spectrum cannot be too high, otherwise it would again dominate over the zeroth-order continuum and we are not looking for those solutions here (which will be discussed in §6).

6 Spectral Fits with Coupled Reprocessor Models

Figure 7: Results of spectral fitting to the NGC 4945 Suzaku data with the default mytorus X-ray reprocessor model (see §6 for details). In the default configuration, the zeroth-order continuum is linked to the scattered continuum (and fluorescent lines) by virtue of the specific geometry adopted for the mytorus model. In this configuration, the best fit gives a Compton-scattered continuum that dominates over the zeroth-order continuum below  keV. In this scenario, the X-ray reprocessor must be compact enough for the Compton-scattered continuum to respond to intrinsic continuum variability. (a) The counts spectra overlaid with the folded best-fitting model. The three data groups from left to right correspond to data from the XIS, HXD/PIN, and the HXD/GSO. The data from XIS0, 1, 2, and 3 are combined into a single spectrum. For clarity, for some energy ranges, the data shown in the plot are binned more coarsely than the binning used for the actual spectral fitting, For the GSO, the effect of a systematic error in the background model of and is shown in blue and brown respectively (see text). (b) The total best-fitting model photon spectrum (black), with the contribution from the Compton-scattered continuum and the zeroth-order continuum shown in red and blue, respectively. Other constituent components are not shown for clarity (but are included in the total spectrum). (c) The ratios of the data to the best-fitting model. Again, two additional ratios are shown for the GSO, corresponding to the background-subtraction systematic errors used in (a). (d) A close-up zoom of the Fe K region in panel (a). From left to right, the dotted lines correspond to the energies of Fe i K, Fe xxv (r), Fe i K, and the neutral Fe K edge. The bump above the Fe K edge is the Ni K line.

In this section we present the results of fitting the Suzaku, BeppoSAX, and Swift BAT spectra with coupled models of the Compton-thick X-ray reprocessor (see §4). We fitted three sets of models, using mytorus, the BN11 torus, and the BN11 sphere, for the Compton-thick reprocessor. We tried using both a simple power-law and Comptonized thermal intrinsic continuum in the case of the mytorus models. The BN11 models do not allow any other intrinsic continuum aside from a power law.

6.1 BN11 toroidal model

We found that we could not obtain an acceptable fit with the BN11 toroidal model to either the Suzaku data or the BeppoSAX data, even with all parameters of the model allowed to float, including the toroidal opening angle. (The other free parameters are the same as those of the mytorus model.) The best values of the reduced that could be obtained were and for the Suzaku and BeppoSAX data respectively. For the Suzaku fit, the probability for obtaining such a bad fit or worse, due to statistical fluctuations alone, is . For the BeppoSAX data, the null hypothesis probability is 10 orders of magnitude worse. One reason for the poor fits is that the geometry of the toroidal BN11 model is rather peculiar in that all rays from the intrinsic X-ray continuum are presented with the same zeroth-order column density, whereas in the mytorus model, rays incident at the equator are presented with a larger column density than those incident away from the equator. This results in very different emergent spectra from the BN11 model compared to the mytorus model. The shape of the  keV spectral hump in the BN11 model severely mismatches the data, and the Fe K line fluxes associated with the reprocessed continuum cannot match the data.

The Swift BAT data, having a lower statistical quality than the other data sets, did yield an acceptable fit, but the orientation of the torus had to be fixed at the highest inclination allowed by the model, and only a lower limit could be obtained on . The results for this fit are shown in Table 4.

6.2 Suzaku Fits with the Coupled mytorus Model

For the mytorus model, good fits were obtained for the Suzaku data with both intrinsic continuum models, and the results are shown in Table 5. The difference in between the two fits is not significant, bearing in mind the complexity of the models and systematic errors that we do not account for. Note that the parameter is free in both fits and the best-fitting values center around unity, which corresponds to the default, steady-state configuration of mytorus. The orientation of the torus is essentially edge-on for both intrinsic continua. We will discuss the column density after discussing the remaining fits.

The fit to the Suzaku data with the power-law intrinsic continuum is shown in Fig. 7. The folded model and counts spectra are shown in Fig. 7(a), the best-fitting photon spectrum is shown in Fig. 7(b), and the data/model ratios are shown in Fig. 7(c). It can be seen that an excellent fit is obtained over the whole bandpass. In this fit, the continuum above 10 keV is dominated by the Compton-scattered continuum, not the zeroth-order continuum. In order to assess the importance of the GSO background-subtraction systematics, we applied systematic offsets to the background spectrum of and (the extreme values for the advertised systematic errors in the GSO background model). The results are shown in Fig. 7, panels (a) and (c), from which it can be seen that the negative offset can result in an error in the background-subtracted spectrum of up to , and the positive offset can result in negative counts in the background-subtracted spectrum. The GSO:XIS fitted normalization parameter very likely includes some compensation for any background-subtraction systematic errors.

The folded model and counts spectrum zoomed in on the Fe K region is shown in Fig. 7(d), and it can be seen that the detailed fit is excellent. All four emission lines (Fe K, Fe xxv, Fe K, and Ni K), and the Fe K edge are very well modeled. The line emission at  keV must originate in a region that is distinct from the one that produces the Fe K, Fe K, and Ni K lines because these latter three lines, and the Fe K edge are modeled with neutral matter. It also appears that no Fe xxvi line emission is required: including an additional unresolved Gaussian emission-line component at 6.966 keV gives a two-parameter, 90% confidence upper limit on the EW of 34 eV.

6.3 BeppoSAX and Swift BAT Fits with the Coupled mytorus Model

Next, we describe the fits to the BeppoSAX data. In this case, we were not able to obtain an acceptable fit with a power-law intrinsic continuum and mytorus. The best value of the reduced that we obtained was , with a null probability of . However, when we used the Comptonized thermal model for the intrinsic continuum we did obtain an acceptable fit (see Table 5) but with one very important concession. That is, the parameter is required to be an order-of-magnitude smaller than unity (, ), which means that the Compton-scattered continuum is heavily suppressed (but the fluorescent line spectrum is still high enough to fit the Fe K line).

Spectral-fitting results to the Swift BAT spectrum with the mytorus model, using both intrinsic continuum models, are shown in Table 4, and acceptable fits were obtained in both cases. The parameter was fixed at in both cases.

6.4 Spectral Fits with a Spherical Model

Figure 8: Spectral fits to the Suzaku data for NGC 4945, showing the BN11 spherical model overlaid on the counts spectra for (a) solar abundances, and (b) the relative abundance parameters for Fe () and the other metals () free (see §6.4). In each case a zoomed view is shown of the spectral region containing the Fe K, Fe K, Ni K lines, and the Fe K absorption edge. The fit with solar abundances illustrates how the column density required to fit the  keV spectral peak underpredicts the Fe K emission line. This fit was performed by omitting the 6–8 keV data and finding the best fit, and then including the 6–8 keV data for the plot (after inserting the required Fe xxv emission line at  keV). Allowing the abundances to float then enables a good fit to both the Fe K line and the Compton hump, as shown in Fig. 8(b). See §6.4 and Table 5 for details.

Figure 9: Spectral fits to the BeppoSAX data for NGC 4945, showing two models overlaid on the unfolded spectra (top panels), and the data/model ratios (bottom panels). (a) A fit with the spherical model of Brightman and Nandra (2011). The model parameters are shown in Table 5 (see §6 for details). (b) A fit with the decoupled mytorus model (mimicking a patchy reprocessor). The incident, intrinsic continuum for the model fit for this fit has a thermally Comptonized spectrum with the plasma temperature, , fixed at  keV. The model parameters are shown in Table 3 (see §7 for details). For clarity, the data in some energy ranges is binned more coarsely than the binning used for the actual spectral fitting. Note that the unfolded spectra are for illustration purposes only and are by their nature model-dependent so should be interpreted with caution (the fitting is performed on the counts spectra not the unfolded spectra).

Figure 10: The best-fitting coupled mytorus model (red curve) with a power-law intrinsic continuum that was fitted to the NGC 4945 Suzaku data (taken in 2006, January), overlaid on the noncontemporaneous BeppoSAX data (black), and on the Swift BAT data (blue). The BeppoSAX data were taken in 1999, July, and the Swift BAT data are averaged over 58 months. The best-fitting Suzaku model is the same as the one shown in Fig. 7(b) and the model parameters are shown in Table 5 (see §6 for details). No corrections have been made for the different cross-normalizations of the different instruments for this plot. Also, the BeppoSAX and Swift BAT photon spectra were only crudely constructed by unfolding using only a simple power-law continuum with absorption, so they should be interpreted with caution. The purpose of the plot is only to show the approximate relative magnitudes of the different spectra in the Fe K band ( keV), and around the Compton hump (between  keV).

Finally, we fitted the BN11 spherical model to all the data sets (see §4.6 for details of this spherical model). We could not obtain an acceptable fit to the Suzaku with solar abundances. The best-fitting reduced value was , with a null hypothesis probability of . The poor fit is illustrated in Fig. 8(a), which shows that the shape of the Compton hump is not correctly reproduced and the Fe K line flux is not well-fitted. Essentially, the column density that is required to correctly fit the Compton hump, severely underpredicts the Fe K line flux, and this is shown in the zoomed-in panel in Fig. 8(a). However, when we allowed the relative Fe abundance, , to float, the best-fitting value dropped by 83.0 for the addition of a single free parameter, and a good fit was obtained. On the other hand, a reduction in of less than 4 was obtained by allowing the relative abundance of the other elements () to float (see §4.6 for details of the meaning of the abundance parameters). The data and model, including a zoomed view of the Fe K spectral region, are shown in Fig. 8(b), and the best-fitting parameters and statistical errors are shown in Table 5. It can be seen that the required enhancement of the Fe abundance relative to solar is very modest (), yet the difference in the goodness of fit is substantial. It is also important to realize that varying the Fe abundance in a Compton-thick medium has effects well beyond the Fe K spectral region because of the high absorption optical depth over a broad energy range, and the indirect effect on Compton scattering. The best-fitting relative abundance of the other elements, , was consistent with unity. The best-fitting value of for degrees of freedom indicates a marginally worse fit than the coupled mytorus model, and this is due to a small underprediction of the Fe K line flux, as can be seen in Fig. 8(b). However, less than full covering of the X-ray reprocessor (or equivalently, some patchiness) would alleviate the problem.

We have shown the spherical model solutions mainly in the interest of application to AGN other than NGC 4945. In the case of NGC 4945, in principle, the deficit in the Fe K line flux in the solar-abundance model could be made up by the Fe K line emission from the extended region spatially resolved by Chandra (and indeed this component should be included). However, none of the spherical model solutions are applicable to NGC 4945 because the continuum above 10 keV is dominated by the Compton-scattered continuum, overwhelming the zeroth-order continuum, and this is inconsistent with the variability of the high-energy continuum and the lack of simultaneous variability of the Fe K line flux (as reported in Marinucci et al. 2012). Note that when applying the spherical model to other sources, it should be remembered that it is not quite self-consistent because it is required that the X-ray reprocessor is patchy or has less than full covering, otherwise there would be no optically-thin scattered continuum, so that the X-ray continuum below  keV would be more suppressed than it actually is, and it would be decreasing in magnitude with decreasing energy.

We also obtained an acceptable fit with the spherical model to the BeppoSAX data, again with the relative Fe abundance allowed to float, but we had to fix the relative abundance of the other heavy elements at their solar values in order to obtain a stable spectral fit. The results are given in Table 5, and the data, model, and data/model ratios are shown in Fig. 9(b). The best-fitting relative Fe abundance is , and this is statistically consistent with the corresponding result obtained from the Suzaku data. The mytorus solution to the BeppoSAX data is physically very different to the spherical model solution. The former is dominated by the zeroth-order continuum, whereas the latter is dominated by the Compton-scattered continuum. However, the two solutions cannot be distinguished statistically (the -test shows that the probability of obtaining the slightly higher value, or higher, for the spherical model than the mytorus model is about 38%).

The BN11 spherical model gave an acceptable fit to the Swift BAT spectrum, and the results for solar abundances are shown in Table 4 (the abundance parameters could not be constrained).

6.5 Overview of the Parameters for the Coupled Models

In summary, we can say that for coupled models of the X-ray reprocessor, the Suzaku data for NGC 4945 prefer a spectrum in which the Compton-scattered continuum dominates over the zeroth-order continuum, and these data prefer a medium that has a substantial global covering factor (a few tenths to nearly full covering, or full covering with some patchiness). However, models in which the Compton-scattered continuum dominates are inconsistent with the continuum above 10 keV in NGC 4945 varying independently of the Fe K line (Marinucci et al. 2012). On the other hand, two very different degenerate solutions can describe the BeppoSAX data. One solution has the spectrum dominated by the zeroth-order continuum, consistent with a ring-like geometry in which the X-ray reprocessor has a small covering factor. The other solution instead has the Compton-scattered continuum dominate the spectrum over the zeroth-order continuum, achieved by the full covering of the spherical model. It is true to say that both the BeppoSAX and Suzaku data are consistent with a nearly fully-covering (or patchy) spherical model, in which case no changes in covering factor are required going from the BeppoSAX observation to the Suzaku observation, but such a scenario can be ruled out for NGC 4945 because of the variability constraints discussed earlier. In the interest of modeling other AGNs, this scenario would require a global decrease of the column density by between observations (see Table 5), and an Fe abundance up to higher than solar (for both observations). We shall also see in §8 that the spherical model has an intrinsic luminosity that is more than an order of magnitude less than the zeroth-order-dominated spectrum. We defer to §8 for further discussion (after presenting the decoupled model fits). In the remainder of this section, we summarize some of the other results in Table 4 (for the Swift BAT data) and Table 5 (for Suzaku and BeppoSAX). Statistical errors for all of the parameters can be found in Table 4 and Table 5 but are not always quoted in the text. To aid the comparison between the Suzaku, BeppoSAX, and Swift BAT spectra, we have overlaid the best-fitting mytorus model for the Suzaku spectra (with an intrinsic power-law continuum) on the BeppoSAX and Swift BAT photon spectra in Fig. 10.

Parameter Suzaku Suzaku Suzaku BeppoSAX BeppoSAX
Model mytorus mytorus B11 sphere mytorus BN11 sphere
Intrinsic Continuum power law comptt power law comptt power law
Free Parameters 13 14 13 8 7
Interesting Parameters 11 12 11 7 6
/ degrees of freedom 440.6/354 435.1/353 447.2/354 85.8/70 92.5/70
Reduced
Null Probability
criterion (68% confidence) 12.6 13.70 12.6 8.15 7.01
GSO:XIS normalization ratio

or
(keV) 80(f)

(degrees)
1.0(f) 1.0(f) 1.0(f)
1.0(f) 1.0(f) 1.0(f) 1.0(f)
FWHM [Fe K, Fe K] () (f) (f) (f) (f) (f)
()
EW (eV)
(keV) (f) (f)
FWHM [Fe xxv ] () (f) (f) (f)
()
EW (eV)
(keV) (f) (f)
FWHM [Ni K ] () (f) (f) (f)
()
EW (eV)
(optically-thin scattered fraction)

()
(f) (f)
(keV) (f) (f)
(f) (f)
[Intrinsic] ()
[0.7–2 keV] ()
[2–10 keV] ()
[10–100 keV] ()
[14–195 keV] ()
[0.7–2 keV] ()
[2–10 keV] ()
[10–100 keV] ()
[14–195 keV] ()

Spectral-fitting results obtained from fitting the NGC 4945 Suzaku and BeppoSAX data with various coupled models of the Compton-thick X-ray reprocessor, as described in §6. A parameter value that is followed by “(f)” indicates that the parameter was fixed during the fitting but the statistical errors were obtained by allowing the fixed parameter to be free only for obtaining the statistical errors. The FWHM values of the Fe K, Fe K, and Ni K lines were fixed at during the fitting. The criterion used for these fixed parameters, and for the GIS:XIS normalization ratio, was , corresponding to 90% confidence for interesting parameter. The statistical errors for the remaining free parameters used a criterion shown in the appropriate column of the table. No statistical errors are given for the Fe K line flux and EW because these emission-line parameters are determined completely by the other parameters of the mytorus model (but see §6 for an estimate of the statistical errors). The continuum fluxes () and luminosities () are all observed values and uncorrected for absorption and Compton scattering.

Table 5: NGC 4945 Spectral-Fitting Results with the Coupled Reprocessor Models

6.5.1 Continua

The temperature of the optically-thin thermal emission component is  keV for both Suzaku fits with the mytorus model (Table 5), so it is not sensitive to the different models for the intrinsic continuum. The same temperature is obtained with the spherical model, albeit with slightly different statistical errors. The intrinsic luminosity of the optically-thin thermal component is and this is not sensitive to the differences in any of the three coupled models fitted to the Suzaku data. The same is true for the column density associated with the region producing the thermal emission (), and is . This optically-thin thermal emission continuum component is below the bandpass of both the BeppoSAX and Swift BAT data so its parameters cannot be constrained by those data. In the case of the BeppoSAX fits, the parameters of this continuum component, along with , were fixed at the values obtained from the Suzaku fits. (For the Swift BAT fits, this continuum component was omitted altogether.)

In the case of the power-law model for the intrinsic continuum applied to the Suzaku data with the mytorus model, the photon index is . The power-law continuum is much flatter with the spherical reprocessor model (), but it is steeper when the spherical model is applied to the BeppoSAX data (). For the Comptonized thermal continuum we tried fits with mytorus tables for a range of values of that were consistent with the 99% confidence contours shown in Fig. 4, and found that  keV gave the best fit for the Suzaku data. The parameter was then allowed to be free, although strictly speaking it is only correct to do this for the zeroth-order continuum. However, the statistical error obtained in this way is sufficiently small ( keV), that the procedure is justified in the present application. Interestingly, the Swift BAT spectrum, which is averaged over 58 months, gave a consistent value of  keV for the mytorus coupled model fit (Table 4). However, the statistical errors are larger so should be regarded as only approximate. For the BeppoSAX data we found that fits with in the range 50–100 keV yielded insignificant differences in the best-fitting values of . In order to get stable fits, had to be frozen, so we performed fits for fixed at , ,  keV. For the sake of brevity, the full set of parameters and statistical errors are given in Table 5 only for the fit with  keV, but parameter values and luminosities for the broader range of will be given where appropriate. The plasma optical depth, , is for the Suzaku and Swift BAT data, and for the BeppoSAX data.

The percentage of the intrinsic continuum scattered into the line of sight by optically-thin circumnuclear material is highly model-dependent because the luminosity of the intrinsic continuum is highly model-dependent. However, models with similar intrinsic luminosities will give similar values of as is the case for the two models shown in Table 5 for the Suzaku data (). Both of these models are dominated by the Compton-scattered continuum so they have similar intrinsic continuum luminosities. On, the other hand, for the BeppoSAX data we get values of of and for the mytorus and spherical models respectively. The spherical model applied to the Suzaku data gives the highest value of . The smallest and largest values differ by nearly a factor of because the mytorus fit to the BeppoSAX data is dominated by the zeroth order continuum, whereas the spherical fit is dominated by the Compton-scattered continuum (see discussion in §6).

The column density associated with the optically-thin scattering region () is for the Suzaku fits, and for the BeppoSAX fits.

6.5.2 Column Density of the X-ray Reprocessor

The toroidal equatorial column density for the coupled mytorus fit to the Suzaku data with a power-law intrinsic continuum is . The mytorus Suzaku fit with a Comptonized thermal intrinsic continuum gave a consistent value of (see Table 5). On the other hand, the column density for the BeppoSAX fit with the coupled mytorus model is somewhat higher than the values from the Suzaku fits, at