Probing the Extent of Fe Kα Emission in Nearby Active Galactic Nuclei Using Multi-order Analysis of Chandra High Energy Transmission Grating Data

The Chandra HETG consists of two grating arrays, the high-energy grating (HEG) for 0.8–10.0 keV and the medium-energy grating (MEG) for 0.4–5.0 keV. Observations with the HETG are done in combination with the Advanced CCD Imaging Spectrometer (ACIS), which can determine the energy of detected photons. The CCD-determined energy from ACIS-S allows for order sorting to be performed to obtain high-resolution HETG spectra of multiple orders.

For this work, we analyzed the same sample of seven objects from Liu (2016), NGC 1068, NGC 3783, NGC 4151, NGC 4388, NGC 4507, Mrk 3, and the Circinus galaxy. These are the AGN in the Chandra data archive that have sufficient HETG spectral data to probe the line width of the Fe Kα line in second- and third-order spectra. While the second- and third-order spectra have higher resolution than the first-order spectrum, their effective areas are smaller by a factor of approximately 1/15 (Canizares et al. 2005). Thus, requiring high signal-to-noise ratio second- and third-order spectra limits the sample to bright, nearby AGN that have been extensively observed with the Chandra HETG. Table 1 summarizes the Chandra Observation IDs (ObsIDs) used for each source in this analysis. For Circinus, we do not include ObsID 374 in our analysis, as it was approximately 7 ks long, contributing negligibly to the total observation time and lacking sufficient data above the iron line to properly constrain the fit. For NGC 4151, we only utilize the first- and second-order data due to issues identified in the third-order data across different observations. Given that NGC 4151 has one of the strongest narrow Fe Kα features, and we only need two spectral widths to fully classify the velocity width, σ_v , and spatial extent, σ_θ , we only use the first- and second-order data in this object to avoid issues with the third-order spectrum.

HETG data were obtained from the Chandra archive and reprocessed using CIAOv4.11 (Fruscione et al. 2006) and CALDBv4.8.5. We followed the standard data reduction process for grating data with one exception. We decreased the width of the masks on the grating arms used to extract the spectra to 18 pixels (approximately half the default value), which decreases the overlap between the HEG and MEG arms and hence allows us to extend our HEG analysis to higher energies. First-, second-, and third-order spectra were extracted from each observation, and the positive and negative spectra for each order were combined to increase signal-to-noise ratio using combine_grating_spectra. These combined spectra were then grouped to have a minimum of 1 count per bin using the grppha tool from HEASOFTv6.26.1. This binning is required in order to correctly employ use of the C statistic during spectral fitting. Spectra were analyzed with the X-ray spectral fitting package, XSPECv12.10.1f (Arnaud 1996). Fits were completed using only HEG data, as it has a larger effective area and better resolution at 6.4 keV, the energy of the neutral Fe Kα line under investigation. All fits were performed in the 4–9 keV range and with the C statistic used for minimization, which is suitable for Poisson-distributed data (Cash 1979).

For each object in our sample, we model the 4–9 keV spectra with Galactic absorption, neutral absorption at the source, a power-law continuum, and the neutral Fe Kα emission line. All abundance values were adopted from Wilms et al. (2000). Galactic absorption was modeled with tbabs with column densities adopted from HI4PI Collaboration et al. (2016). We chose to model absorption at the source with the ztbabs model, which accounts for a single neutral absorber, redshifted to the source redshift. There are objects in our sample whose absorption has been studied extensively and found to be more complex than our simple model. For example, NGC 3783 has been shown to have complex ionized absorption (e.g., Reynolds 1997; Kaspi et al. 2002; Krongold et al. 2003; Netzer et al. 2003). However, complex absorption in the X-ray spectrum is far more prevalent at softer energies, below about 2 keV. Since we are fitting from 4 to 9 keV, we do not include such complex absorption models, as our fit is not sensitive to them. Our continuum power law and Fe Kα emission line are both redshifted to the source redshifts given in Table 1. To model the Fe Kα line, we use two Gaussian emission lines. The Fe Kα transition is a doublet due to a difference in energy released based on the spin of the electron involved in the transition. The two lines, Kα₁ and Kα₂, are at energies of 6.404 and 6.391 keV, respectively. The laboratory-observed flux ratio between the two transitions is 2:1 (Bearden 1967). Hence, we set the normalization of the Kα₁ line to be twice the Kα₂ normalization and set their widths to be the same.

When modeling the Fe Kα line as seen by the HETG, we write the observed width, σ_{E, measured}, directly in terms of the velocity width, σ_v , and spatial extent, σ_θ , outlined in Equation (1). The instrumental width, σ_i , is accounted for in the data reduction pipeline via the response matrix. Thus, we can write Equation (1) in terms of the observed energy width by applications of the grating equation and Doppler physics. Approximating the energy of the line to be much greater than the width yields

$$\begin{eqnarray}&&{\sigma }_{E,\ \mathrm{measured}}^{2}={\left(\displaystyle \frac{{E}_{0}}{c}\right)}^{2}{\sigma }_{v}^{2}+{\left(\displaystyle \frac{{\mathrm{FPE}}_{0}^{2}}{{hcmR}}\right)}^{2}{\sigma }_{\theta }^{2},\end{eqnarray} \tag{ 3 }$$

where E₀ is the energy of the line and the other quantities are as defined in Equation (1). We approximate E₀ as the average of the Kα₁ and Kα₂ energies. The advantage of writing the model this way is that we can obtain more accurate error estimates on σ_v and σ_θ , which would be difficult otherwise because of how close we are to the instrument resolution. This yields a final XSPEC model of tbabs(ztbabs(zpower + zgauss + zgauss)). In fitting, we fix the Galactic column density, redshift, and centroid energies of the Gaussian emission lines and fit for the source column density, power-law normalization, photon index, line normalization, velocity width, and spatial extent.

For each object, we fit simultaneously to first-, second-, and third-order spectra for each observation. We allow the source absorption column density, power-law normalization, power-law photon index, and line normalization to vary for every ObsID. This accounts for changes in the source obscuration over time and the intrinsic variability of the source. These same values are fixed across all three spectral orders for a given observation when fitting, as the normalizations are corrected for the effective area with response files. We fix the value of z for all model components to the values given in Table 1. Lastly, we fix σ_v and σ_θ to be the same for all observations and spectral orders of a given source. The difference in Fe Kα width that we are measuring then is accounted for in the dependence on the spectral order, m, in the spatial extent in Equation (3). For a constant σ_v and σ_θ , the velocity width contributes a constant amount across all orders, but the spatial width contribution decreases with increasing spectral order. This behavior should give the observed behavior of decreasing total line width with spectral order from Liu (2016) and permit independent measurements of σ_v and σ_θ .

We expect that the simple, one-dimensional grating equation used to obtain Equation (3) may be insufficient to describe the complexity of the HRMA-HETG geometry in detail. Hence, we use MARX (version 5.5.0) to calibrate our model by simulating Chandra observations and fitting these simulated observations with the methodology described previously. MARX is a Monte Carlo, ray-tracing program used to create simulated Chandra observations (Davis et al. 2012). We simulated a power-law source with point geometry, since the corona has been shown to be compact and quite close to the central SMBH. The Fe Kα emission, however, is spatially extended. Hence, we modeled the Fe Kα doublet with some intrinsic velocity width, σ_v , and extended the emission over a Gaussian source with width σ_θ . The two components, the corona and the line source, were concatenated to make a single simulated observation using marxcat and then processed in the standard way with MARX and CIAO tools.

Simulations were run for a range of σ_v and σ_θ values, spanning a range of reasonable narrow Fe Kα line widths, including cases where σ_v dominates σ_θ , σ_θ dominates σ_v , and the two contribute similarly. The left panel of Figure 1 shows an example of the fit that uses Equation (3) to relate the total line width in each order to σ_v and σ_θ for 10 simulations using input values of σ_v = 750 km s⁻¹ and σ_θ = 04. Each simulation was run for 10 Ms, giving us excellent data with which to test the model. Following the reprocessing of the data using standard CIAO tools, the first-, second-, and third-order spectra were fit using the same procedure as described in Section 2.1 and with the same model as described in Section 2.2. The 10 simulations were each fit individually and then fit simultaneously, with σ_v and σ_θ fixed across all simulations, similarly to how we fit simultaneously to all observations for a given object.

Zoom In Zoom Out Reset image size

The left panel of Figure 1 shows that while the model fits the velocity width accurately, the use of Equation (3) leads to a spatial width that is significantly underestimated. This trend also holds for the other combinations of σ_v and σ_θ that we tested. It is thus apparent that Equation (3) does not fully capture the response of the HETG to finite spatial extent. We adopt a calibration factor, f, to attain the true value of σ_θ when fitting. This is implemented by inserting this calibration factor f into the spatial width term of Equation (3), giving

$$\begin{eqnarray}&&{\sigma }_{E,\mathrm{measured}}^{2}={\left(\displaystyle \frac{{E}_{0}}{c}\right)}^{2}{\sigma }_{v}^{2}+{\left(f\displaystyle \frac{{\mathrm{FPE}}_{0}^{2}}{{hcmR}}\right)}^{2}{\sigma }_{\theta }^{2}.\end{eqnarray} \tag{ 4 }$$

The value of f is then determined by fixing σ_v and σ_θ to the input values and fitting the simulated data to f. The right panel of Figure 1 shows the result of fitting to f for the same simulations as in the left panel. We adopt the average value of the simultaneous fits for five different input combinations of σ_v and σ_θ , f = 0.73, for the analysis of the data.

We stress that this is a first-order correction to Equation (3). While the calibration factors show general consistency across a range of velocity and spatial widths, there is some hint of small deviations across different input values of σ_v and σ_θ . We suspect that there is a second-order correction due to a deviation from Gaussianity that is on the order of 10% of f and potentially dependent on σ_v , σ_θ , and the signal-to-noise ratio. For the purposes of this work, we simply adopt the first-order correction, f = 0.73, as these small, second-order corrections are a negligible source of uncertainty.

Adopting a calibration factor of f = 0.73, we performed fits to the spectral model described in Section 2.2 using the Markov Chain Monte Carlo (MCMC) method implemented in XSPEC. We utilized the Goodman–Weare algorithm (Goodman & Weare 2010), with five independent chains for each object, where each chain has 10⁶ steps and 500 walkers. For NGC 3783, NGC 4151, NGC 4388, NGC 4507, and Circinus, the MCMC chains were started based on the covariance matrix derived from the initial fit to the data. In the Circinus chains, the covariance matrix used to populate the initial distribution of walkers was scaled by 10⁻¹ to allow the walkers to fully explore parameter space. The burn-in length for these objects was 2 × 10⁵ chain steps. For NGC 1068 and Mrk 3, the MCMC chains were populated from a uniform distribution for all parameters across a wide range of reasonable values. This was done because the initial fit performed in XSPEC using C statistic minimization collapsed to essentially zero spatial extent, resulting in subsequent chains not fully exploring $\left({\sigma }_{v},{\sigma }_{\theta }\right)$ parameter space. These objects required a longer burn-in length of 10⁶ chain steps for convergence. For each object, all five chains are then combined into a single composite chain with a total of 5 × 10⁶ chain steps and used for analysis. Reported best-fit values are median values from the combined MCMC chains, and uncertainties are the 5th and 95th percentile chain values.

For each object, we checked convergence with the Geweke diagnostic (Geweke 1992) and the Gelman–Rubin scale reduction factor, $\hat{R}$ (Gelman & Rubin 1992). The Geweke diagnostic, which compares the mean of a given parameter at the beginning of the chain (first 10%) and at the end of the chain (last 50%), was found to be $\left|{z}_{G}\right|\lt 1$ for each fit parameter in each chain. The Gelman–Rubin scale reduction factor measures convergence across independent chains and satisfies $\hat{R}\lesssim 1.2$ for each fit parameter. Together, these two convergence factors indicate that the chains have converged to the posterior distribution.

For each object in the sample, we obtained a fit to σ_v and σ_θ with uncertainty determined using the MCMC posterior distributions. These fit values are given in Table 2, along with the line width in energy space for each order as calculated with Equation (4). The values and errors on the line width in each order are computed directly from the MCMC chains, taking σ_v and σ_θ for each chain step and converting these to a total energy width for each order. We find that the unexpected behavior from Liu (2016), in which first-order line widths are larger than their second- and third-order counterparts, can indeed be described by the intrinsic velocity width and spatial extent, as proposed in Marshall (2017).

Table 2. Fits to σ_v and σ_θ , Resulting Fe Kα Line Widths for Different Spectral Orders, and Fe Kα Equivalent Widths

Object	σv	vFWHM	rv	σθ	rθ	σ (±1)	σ (±2)	σ(±3)	EWunabs	C/dof
	(km s−1)	(km s−1)	(pc)	(arcsec)	(pc)	(eV)	(eV)	(eV)	(eV)
NGC 1068	${898}_{-432}^{+231}$	${2110}_{-1020}^{+540}$	${0.013}_{-0.005}^{+0.035}$	${0.31}_{-0.28}^{+0.41}$	${21.8}_{-19.6}^{+28.4}$	${21.6}_{-3.6}^{+4.0}$	${19.7}_{-6.1}^{+4.6}$	${19.4}_{-7.7}^{+4.8}$	10–510	2189.7/2617
NGC 3783	${592}_{-245}^{+177}$	${1390}_{-580}^{+420}$	${0.088}_{-0.036}^{+0.168}$	${0.30}_{-0.26}^{+0.25}$	${55.5}_{-49.0}^{+46.0}$	${15.5}_{-2.7}^{+2.9}$	${13.3}_{-3.4}^{+3.3}$	${12.9}_{-4.2}^{+3.6}$	${79.5}_{-23.9}^{+29.8}$	12331.4/13673
NGC 4151	${894}_{-359}^{+185}$	${2100}_{-850}^{+440}$	${0.059}_{-0.019}^{+0.106}$	${0.39}_{-0.34}^{+0.33}$	${30.3}_{-26.6}^{+25.5}$	${22.1}_{-2.3}^{+2.4}$	${19.8}_{-5.0}^{+3.4}$	${19.4}_{-6.4}^{+3.7}$	${108.6}_{-57.8}^{+55.2}$	7925.8/8501
NGC 4388	${619}_{-506}^{+413}$	${1460}_{-1190}^{+970}$	${0.023}_{-0.015}^{+0.672}$	${0.57}_{-0.49}^{+0.33}$	${49.9}_{-42.8}^{+29.2}$	${21.1}_{-5.3}^{+5.8}$	${15.5}_{-5.2}^{+7.0}$	${14.2}_{-6.7}^{+8.0}$	${101.3}_{-19.7}^{+20.4}$	2087.7/2367
NGC 4507	${561}_{-458}^{+379}$	${1320}_{-1080}^{+890}$	${0.806}_{-0.519}^{+22.844}$	${0.36}_{-0.33}^{+0.38}$	${89.1}_{-79.6}^{+94.1}$	${16.7}_{-6.0}^{+7.2}$	${13.3}_{-5.8}^{+7.3}$	${12.5}_{-6.8}^{+7.7}$	${45.5}_{-9.6}^{+10.8}$	1091.2/1117
Mrk 3	${976}_{-556}^{+259}$	${2300}_{-1310}^{+610}$	${0.485}_{-0.182}^{+2.142}$	${0.36}_{-0.33}^{+0.45}$	${101.0}_{-91.5}^{+126.3}$	${23.7}_{-3.9}^{+4.4}$	${21.4}_{-7.5}^{+5.2}$	${21.1}_{-9.7}^{+5.4}$	${157.9}_{-81.4}^{+103.8}$	2138.7/2824
Circinus	${341}_{-108}^{+106}$	${800}_{-260}^{+250}$	${0.015}_{-0.006}^{+0.017}$	${0.37}_{-0.10}^{+0.07}$	${7.5}_{-2.0}^{+1.4}$	${12.4}_{-1.1}^{+1.1}$	${8.9}_{-1.3}^{+1.5}$	${8.0}_{-1.7}^{+1.9}$	20–770	6452.9/7400

Note. Column (1): object name. Column (2): measured velocity width. Column (3): FWHM velocity. Column (4): distance from the SMBH measured from the FWHM velocity (Equation (5)). Column (5): measured spatial extent. Column (6): distance from the SMBH measured from the spatial extent (Equation (6)). Column (7): first-order Fe Kα line width. Column (8): second-order Fe Kα line width. Column (9): third-order Fe Kα line width. Column (10): Fe Kα equivalent width from first-order spectra corrected for absorption and averaged over all observations. Column (11): average value of the C statistic from MCMC chains and degrees of freedom.

Download table as:  ASCIITypeset image

First-, second-, and third-order spectra for all seven objects in our sample are shown in Figure 2. These spectra contain the combined data from all observations listed in Table 1. Each spectrum is plotted with error bars, and the model for each order containing fit parameters averaged over all observations is overplotted in bold. The first-order spectrum is reduced in normalization by a factor of 15 to roughly account for the difference in effective areas between the orders, and all spectra are binned for plotting purposes only. However, we stress that this is not how we performed the fits, as we fit each observation for each object to its own absorption, continuum parameters, and line normalization to account for variability (see Section 2.2 for details). This is simply a representation of the data we are working with and the features of the spectrum at 6.4 keV.

Zoom In Zoom Out Reset image size

We note that our errors on the second- and third-order line widths are significantly smaller than those in Liu (2016), which show that the measured line width in the combined higher-order spectrum is an upper limit for four of the seven sources. Our errors are smaller because we did not fit the second- and third-order data individually. Rather, we fit all three orders simultaneously and linked them through writing the line widths in terms of σ_v and σ_θ and tying these values across all three orders. Given that the first-order data have significantly higher signal-to-noise ratio than the second- and third-order data, our fit to σ_v and σ_θ is most sensitive to first-order data. Thesecond- and third-order data allow us to break the degeneracy between σ_v and σ_θ and estimate where in this parameter space each object lies.

However, we also see less spatial extent in NGC 1068 and Mrk 3 than would be expected given the fits from Liu (2016). That is, our second- and third-order line widths for these objects are significantly larger than those from Liu (2016), which are quite small (upper limits of ∼5–7 eV). We investigate this discrepancy by fitting the second- and third-order data of both of these objects individually and fixing the continuum parameters to those from our overall fit. In the third-order spectrum of NGC 1068, we find anomalously high and poorly constrained energy widths on the order of ∼100–400 eV, a consequence of the limited data quality in the third-order spectrum. In the second-order spectrum for NGC 1068 and in both second- and third-order spectra for Mrk 3, we find larger line widths than those from Liu (2016), on the order of ∼25–50 eV, albeit with quite large error bars ranging from ∼10 to 25 eV. With slightly different fitting methods and more recent calibration files implemented, we find no evidence for such small line widths in higher-order HETG data for NGC 1068 and Mrk 3.

Corner plots for each object in our sample are shown in Figure 3. In each corner plot, the two histograms show the posterior distributions of σ_v and σ_θ . The bottom left plot shows the density of chain steps in (σ_v , σ_θ ) space. Lines of constant total line width are overplotted, where the energy is equal to the values given in Table 2, the median σ_{E, measured} from Equation (4). The red dashed line, which shows constant first-order line width, tends to trace the shape of the distribution of (σ_v , σ_θ ) values quite well. This illustrates that our fitting is most sensitive to first-order data and is picking out a roughly constant first-order line width over the entire chain. The blue and green dashed lines show constant line width in second and third order, respectively. These values are breaking the degeneracy between σ_v and σ_θ that would not be possible with first-order data alone. From the plots, we can see that with increasing order, the effect of σ_θ decreases. In third order, the green dashed line is nearly vertical, indicating that the third-order data are relatively insensitive to the value of σ_θ compared to the first-order data.

Zoom In Zoom Out Reset image size

For each object and each observation, additional fit parameters from the MCMC analysis are given in Appendix A. These include the source absorption column density (N_H), photon index (Γ), power-law normalization (K_power), and line normalization (K_line). We note that for NGC 1068 and Circinus our source absorption column densities are significantly lower than those reported in the literature from more complex modeling of the absorption (e.g., Matt et al. 1997, 1999; Arévalo et al. 2014; Bauer et al. 2015; Zaino et al. 2020). These two sources are known Compton-thick AGN, whereby the obscuring material is optically thick to electron scattering (with N_H ≥ 1.5 × 10²⁴ cm⁻²). Similarly, Mrk 3 has been shown to be near the Compton-thick limit along the line of sight (e.g., Cappi et al. 1999; Yaqoob et al. 2015; Guainazzi et al. 2016). When the nucleus is this obscured, it can be difficult to obtain information about the intrinsic X-ray properties. This is addressed further in Section 4.2, where we discuss how this impacts our results and outline prior work that has been done in an attempt to unveil the nuclei of these objects and determine their intrinsic X-ray properties.

From both σ_v and σ_θ , we can estimate the distance of the gas from the black hole. Assuming that the motion is purely gravitational with the potential dominated by the SMBH and the emitting gas is far enough away from the black hole to ignore general relativistic effects, this is given by the simple Keplerian formula, r = GM_BH/〈v²〉. Adopting the assumption that the velocity dispersion is related to the FWHM velocity by $\langle {v}^{2}\rangle =\tfrac{3}{4}{v}_{\mathrm{FWHM}}^{2}$ (Netzer et al. 1990), the distance from the black hole is

$$\begin{eqnarray}&&{r}_{v}=\displaystyle \frac{4{{GM}}_{\mathrm{BH}}}{3{v}_{\mathrm{FWHM}}^{2}}.\end{eqnarray} \tag{ 5 }$$

We adopt black hole masses from the literature, given in Table 3. For our fit values to σ_v , this gives distances on the order of r_v ∼ 0.01–1 pc, or emission coming from the BLR or inner parts of the torus.

Table 3. Cold Gas Mass, Luminosity, and Mass Outflow Rates

Object	Mgas	${\dot{M}}_{\mathrm{out}}$	$\mathrm{log}{L}_{\mathrm{bol}}$	Reference	$\mathrm{log}{M}_{\mathrm{BH}}$	Reference	λEdd
	(107 M⊙)	(M⊙ yr−1)	(erg s−1)		(M⊙)
NGC 1068	0.06–5 a	20–2100 a	44.7	1	7.0	5	0.399
NGC 3783	${5.3}_{-5.2}^{+12.7}$	${500}_{-420}^{+480}$	44.2	2	7.47	6	0.042
NGC 4151	${1.8}_{-1.8}^{+5.3}$	${440}_{-380}^{+570}$	43.7	3	7.66	7	0.008
NGC 4388	${4.9}_{-4.7}^{+8.7}$	${460}_{-400}^{+620}$	43.7	2	6.93	8	0.047
NGC 4507	${6.3}_{-6.2}^{+23.8}$	${360}_{-300}^{+600}$	44.3	2	8.39	9	0.006
Mrk 3	${33.8}_{-33.6}^{+135.9}$ a	${2870}_{-2530}^{+3940}$ a	44.8	2	8.65	10	0.011
Circinus	0.02-0.9 a	10–410 a	43.6	4	6.23	11	0.186

Notes. Column (1): object name. Column (2): mass of Fe Kα emitting gas. Column (3): mass outflow rate, calculated using Equation (8). Column (4): bolometric luminosity. Column (5): reference for bolometric luminosity. Column (6): black hole mass. Column (7): reference for black hole mass. Column (8): Eddington ratio (λ_Edd = L_bol/L_Edd, where ${L}_{\mathrm{Edd}}=1.26\times {10}^{38}\left({M}_{\mathrm{BH}}/{M}_{\odot }\right)$ erg s⁻¹).

^a See Sections 3.3 and 4.2 for discussions on how our modeling impacts these measurements in sources that are close to or exceed the Compton-thick limit. References . (1) Lopez-Rodriguez et al. 2018; (2) Vasudevan et al. 2010; (3) Duras et al. 2020; (4) Moorwood et al. 1996; (5) Greenhill et al. 1996; (6) Peterson et al. 2004; (7) Bentz et al. 2006; (8) Kuo et al. 2011; (9) Winter et al. 2009; (10) Woo & Urry 2002; (11) Greenhill et al. 2003.

Download table as:  ASCIITypeset image

The spatial extent, σ_θ , provides another measurement for the distance of the material from the black hole. With the distance to the galaxy, D, the spatial extent in angular units is converted to a physical distance simply by

$$\begin{eqnarray}&&{r}_{\theta }=D{\sigma }_{\theta }.\end{eqnarray} \tag{ 6 }$$

The two most distant galaxies, NGC 4507 and Mrk 3, can be well described by Hubble flow distances, D = cz/H₀. For the remainder of the galaxies in our sample, we use distances determined from other measures in the literature, given in Table 1. For our fits to σ_θ , we obtain distances on the order of r_θ ∼ 5–100 pc, indicating that the emission is more extended than the typical BLR or inner torus.

These distances for each object are given in Table 2, and a comparison of the distances measured using the spatial extent and using the velocity width is shown in Figure 4. We find that distances measured with the velocity width are significantly smaller than the distances from spatial extent. Further discussion of how this informs our understanding of the origin of the narrow Fe Kα line follows in Section 4.1.

Zoom In Zoom Out Reset image size

Following the steps outlined in Hitomi Collaboration et al. (2018), which builds off of the equivalent width analysis originally presented in Reynolds et al. (2000), we estimate the mass of the X-ray irradiated gas. The average, unabsorbed equivalent width measured from the spectral model is used to calculate the quantity f_cov N_H via Equation (1) of Hitomi Collaboration et al. (2018),

$$\begin{eqnarray}&&{\mathrm{EW}}_{\mathrm{Fe}}\approx 65\,{f}_{\mathrm{cov}}\left(\displaystyle \frac{{Z}_{\mathrm{Fe}}}{{Z}_{\odot }}\right)\,\left(\displaystyle \frac{{N}_{{\rm{H}}}}{{10}^{23}\,{\mathrm{cm}}^{-2}}\right)\,\mathrm{eV}.\end{eqnarray} \tag{ 7 }$$

Here f_cov is the covering fraction of the material, allowing for a nonuniform, clumpy or patchy distribution of material, and N_H is the column density. This calculation stems from counting fluorescing iron atoms based on the photoionization probability, fluorescent yield, and incident flux and is scaled from the initial calculation of ${{EW}}_{\mathrm{Fe},\max }\approx 65\,\mathrm{eV}$ with Z_Fe = Z_⊙ and N_H = 10²³ cm⁻² for NGC 4258 from Reynolds et al. (2000). The details behind this calculation are given in full in Appendix B. Then, using the quantity f_cov N_H and assuming that the gas is located in a shell at radius r, the gas mass can be estimated using M_gas = 4π r² f_cov N_H μm_p , where μ is the mean molecular weight. We adopt μ = 1.3 for neutral, solar-metallicity material and Z_Fe = Z_⊙ for solar iron abundance, and we use the distance measured from our fit to the spatial extent, r_θ .

This calculation requires the total equivalent width of the Fe Kα line, which is found by adding the equivalent widths for the Kα₁ and Kα₂ transitions from the first-order spectrum and averaging over all observations for a given object. However, the equivalent width in Equation (7) is the unabsorbed equivalent width. To compute the unabsorbed equivalent width for gas mass estimates, we first fit to the model tbabs(zgauss + zgauss + ztbabs ∗ zpower), where only the continuum is being obscured at the source. Then, we remove the ztbabs component to compute the Fe Kα equivalent width measured against the unabsorbed incident X-ray flux. To fit this model, we fix the fit parameters N_H, Γ, K_power, σ_v , and σ_θ , leaving only the line normalization (K_line) free to vary, as we expect this to be the only affected parameter in changing the model. This assumption was explicitly verified for NGC 3783, NGC 4151, NGC 4388, and NGC 4507. The normalization of the Fe Kα line decreases in this new model because the line emission is no longer attenuated by the absorption. The amount of decrease in K_line is positively correlated with column density of the absorber, N_H, as expected.

These unabsorbed equivalent width values are given in Table 2. We report the Compton-thin equivalent widths with errors that account for the uncertainties in the original fit parameters, as well as those from the new fit to K_line. To assess these errors, we took 100 random draws from the MCMC chains for the fixed fit parameters and followed the above procedure to fit to K_line for each draw. Then, for each draw, we took 100 random draws for K_line from a Gaussian distribution centered at the fit value of K_line with standard deviation based on the fit error. This gives us a distribution of unabsorbed equivalent width values from which we compute uncertainties.

For the two Compton-thick sources in our sample (NGC 1068 and Circinus), accurately determining the intrinsic continuum is extremely difficult, as the majority of the observed emission in the 4–9 keV range is scattered and reprocessed emission. The intrinsic nuclear continuum is best determined by including hard X-ray data in the modeling, which contains more transmitted emission than the soft energy band. Such modeling is beyond the scope of this work, and hence, for the Compton-thick sources in our sample, we report a range of equivalent width values, which represent the extremes of possible equivalent width values depending on different assumptions about the continuum emission.

As an upper bound on the equivalent width, we assume that the observed continuum is the continuum that the Fe Kα emitting material sees. In reality, this is likely all scattered emission, but this provides a lower bound on the continuum flux and hence an upper bound on the equivalent width. To compute the lower bound for the equivalent width in our Compton-thick sources, we use the nuclear continuum estimated from detailed, broadband modeling including NuSTAR data from prior work (e.g., NGC 1068, Bauer et al. 2015; Marinucci et al. 2016, Circinus, Arévalo et al. 2014; Uematsu et al. 2021). In this scenario, the Fe Kα emitting material sees a much stronger continuum, leading to a lower equivalent width measurement. The picture is certainly more complicated than these two extremes, especially given that the Fe Kα emitting material likely emits at a range of radii, thus seeing different illuminating radiation and being obscured differently depending on the location of the emission. However, the ranges provided in Table 2 for the equivalent width of the Compton-thick sources capture the uncertainty in determining the intrinsic continuum that the Fe Kα emitting material sees and the location of the Fe Kα emitting material relative to the obscurer. We further discuss the uncertainty associated with modeling Compton-thick sources in Section 4.2.

Adopting the unabsorbed equivalent widths from Table 2, we compute the mass of the cold, X-ray irradiated gas. The masses and their uncertainties are given in Table 3. As with the equivalent widths, we report a range of gas masses corresponding to the equivalent width ranges for the Compton-thick sources in our sample. For the Compton-thin sources, the uncertainty in the gas masses includes the uncertainty in both the spatial extent and the unabsorbed equivalent width by using the distribution of unabsorbed equivalent width values and corresponding r_θ chain value from each equivalent width measurement. Most of our mass measurements are close to upper limits, with large uncertainty due to the large uncertainty on the spatial extent of the emitting material. It is important to also note that we assumed solar abundance for iron, as our fit does not constrain this value, but that the gas mass is proportional to ${Z}_{\mathrm{Fe}}^{-1}$. Having nonsolar abundances could change the result by a factor of a few, but we expect that our results are accurate to within an order of magnitude.

In Section 4.1, we explore two possibilities for the discrepancy between the distance measurements from Section 3.2, one of which is that the Fe Kα emitting material is outflowing. Using the mass measurements, we can thus estimate the mass outflow rates of the cold gas. Adopting the velocity width, σ_v , to be the characteristic outflow velocity of the gas and r_θ to be the distance of the emitting gas from the black hole, the mass outflow rate is given by

$$\begin{eqnarray}&&{\dot{M}}_{\mathrm{out}}=\displaystyle \frac{{M}_{\mathrm{gas}}{v}_{\mathrm{out}}}{r}\sim \displaystyle \frac{{M}_{\mathrm{gas}}{\sigma }_{v}}{{r}_{\theta }}.\end{eqnarray} \tag{ 8 }$$

The outflow rates for each object are given in Table 3. We note that, like the mass estimates from earlier in the section, many of these values are highly uncertain. The similarities between these outflow rates and molecular outflow rates are discussed further in Section 4.3.

We investigated trends between our results for σ_v and σ_θ and AGN properties such as X-ray luminosity, obscuration, and Eddington ratio. However, due to the large uncertainties on all objects except for Circinus and our relatively small sample size, we are unable to find any significant trends with AGN properties. Likewise, we are not able to draw any firm conclusions on the lack of correlations but suggest that this is best left as work that could be investigated with future X-ray missions, such as XRISM.

The origin of the narrow Fe Kα line has long been in debate, with the typical location thought to be in the outer accretion disk, BLR, or torus. Nearby AGN show a wide variety of measured line widths and no connection with the optical BLR as measured by the width of the Hβ line, which suggests no universal location for the narrow Fe Kα line (Yaqoob & Padmanabhan 2004; Nandra 2006; Shu et al. 2010). In our sample of seven nearby AGN, we use a new technique to probe the spatial extent of the emitting material, which provides an alternative measurement of the location of the narrow Fe Kα line. We find that distance estimates from measurements of the intrinsic velocity width suggest BLR or torus origin, but that these measurements consistently underestimate the inferred spatial extent of the emitting material.

Many of the sources in our sample have previously shown evidence for extended Fe Kα emission. Circinus, the closest object in our sample, shows Fe Kα emission (Marinucci et al. 2013; Arévalo et al. 2014) extending up to ∼3'' (∼60 pc) from the nucleus, which is anticorrelated with molecular gas in the circumnuclear environment (Kawamuro et al. 2019). In NGC 1068, Young et al. (2001) revealed spatially extended Fe Kα emission out to approximately 2.2 kpc from the nucleus, and Bauer et al. (2015) found that approximately 30% of the Fe Kα emission is extended on scales larger than ∼140 pc. These two sources were also recently found to have the most extended emission in a sample of many bright AGN, using a combination of variability and imaging analyses (Andonie et al. 2022a). Likewise, Guainazzi et al. (2012) found that the Fe Kα emitting material extended up to 300 pc from the nucleus in Mrk 3, another highly obscured AGN in our sample.

Extended emission is easier to detect in Compton-thick AGN because of the heavy obscuration of the nuclear emission, but it has also been detected in the Compton-thin AGN NGC 4388. Faint extended Fe Kα emission was first detected out as far as 2.5 kpc in one direction by Iwasawa et al. (2003), and more recently, additional observations have allowed for more detailed morphological studies of the extended Fe Kα emission on scales of ≲1 kpc (Yi et al. 2021). In NGC 4151, another Compton-thin AGN, the amount of extended Fe Kα emission has been debated, with first evidence coming early on in the Chandra mission (Ogle et al. 2000). However, later Wang et al. (2011) argued, with updated MARX PSF calculations, that the extended Fe Kα emission could only account for ∼5% of the total line emission. Likewise, Miller et al. (2018) and Szanecki et al. (2021) suggest that the narrow Fe Kα line is produced at several hundred gravitational radii through modeling of first-order HETG and Suzaku/NuSTAR spectra, respectively. Time delays also suggest a BLR origin, with Zoghbi et al. (2019) finding time delays between the Fe Kα line and the continuum in the XMM-Newton data on the order of ∼3 days.

We note also that recent studies focused on developing a consistent picture of the torus of Circinus have implemented similar analyses involving the first-, second-, and third-order Chandra HETG data (Uematsu et al. 2021; Andonie et al. 2022b). The analysis by Uematsu et al. (2021) revealed a spatial extent of ${\sigma }_{\theta }=0\buildrel{\prime\prime}\over{.} {66}_{-0.21}^{+0.33}$, which is slightly larger than our results for Circinus of ${\sigma }_{\theta }=0\buildrel{\prime\prime}\over{.} {37}_{-0.10}^{+0.07}$. We suspect that our value is lower because Uematsu et al. (2021) considered both point-like emission from closer to the black hole and extended emission. They found that roughly 20% of emission from the Fe Kα line is extended in Circinus. Thus, our smaller extent is likely because our methodology can be interpreted as providing a spatially averaged measurement of the extent of the Fe Kα emitting material.

Our analysis provides another measure of spatial extent, avoiding the issues of pileup and PSF contributions that must be corrected for and properly modeled in imaging analysis. Given that these issues greatly affect the nucleus in imaging data, our method is more sensitive to smaller extension than can be properly observed with imaging data. We find that the bulk of the Fe Kα emitting material is extended on scales of ∼5–100 pc across the seven sources in our sample, although with relatively large uncertainty due to the quality of the higher-order HETG spectra. However, in most of our objects there is a discrepancy between the spatial extent of the material measured by σ_θ and the location of the gas measured with the intrinsic velocity width, σ_v , assuming that motion is governed by the gravitational potential of the central SMBH. The intrinsic velocity of the gas indicates that the material is much closer to the black hole than we measure with the spatial extent. Here we present two possible explanations for the discrepancy between these distances.

Through modeling emission from both a point-like source and extended emission, Uematsu et al. (2021) found that extended emission in Circinus accounted for roughly 20% of the Fe Kα line emission. Our fitting method does not include these two features as separate model components and instead can be interpreted as a spatial average of the two in a single model component. It is thus possible that our fits are being driven by gas closer to the BLR for the velocity width and by gas in and beyond the torus for the spatial extent. This suggests that the Fe Kα emitting material responsible for the narrow Fe Kα line in nearby AGN is present at a range of radii, from the inner BLR out to and beyond the putative torus. This interpretation is consistent with recent findings that the variability and widths of the Fe Kα line in a sample of almost 40 nearby AGN do not show a universal picture for the location of the narrow Fe Kα line (Andonie et al. 2022a) and can help explain the discrepancy between different measurements of spatial extent.

Another possibility is that these large velocity widths are the result of nongravitational motions driving the intrinsic velocity width to larger values. We investigate the nature of possible nongravitational motions by allowing the redshift of the Fe Kα line to vary, finding that six of the seven sources prefer slightly redshifted emission at roughly the 1σ level. Assuming that the Fe Kα emitting material is Compton-thick so that our view is dominated by clouds on the far side of the nucleus, excess redshift would imply outflowing material. We note that this excess redshift could be the result of contamination from the Compton shoulder, which we have not included in our modeling. However, the intrinsic velocity widths we measure are much larger than the freefall velocities expected of inflowing gas in the galactic potential. Outflows can be driven to higher velocities via radiative, thermal, or magnetic launching mechanisms and have been observed in UV and X-ray spectra with velocities ranging from v ∼ hundreds of kilometers per second (warm absorbers and their UV counterparts; e.g., Reynolds 1997; Crenshaw et al. 1999) up to ≳0.1c (ultrafast outflows; e.g., Tombesi et al. 2010, 2011; Gofford et al. 2013; Tombesi et al. 2013). Outflows, with a variety of phases, scales, and velocities, have been detected in all seven objects in our sample (e.g., NGC 1068, Cecil et al. 1990; García-Burillo et al. 2014; NGC 3783, Kaspi et al. 2001; Mehdipour et al. 2017; NGC 4151, Crenshaw & Kraemer 2007; Storchi-Bergmann et al. 2010; NGC 4388, Rodríguez-Ardila et al.2017; Domínguez-Fernández et al. 2020; NGC 4507, Fischer et al. 2013; Mrk 3, Ruiz et al. 2001; Gnilka et al. 2020; Circinus, Greenhill et al. 2003; Zschaechner et al. 2016; Stalevski et al. 2019). Thus, we suggest that if the distance discrepancy is resolved by nongravitational motions driving the intrinsic velocity widths higher, then it is likely that the Fe Kα emitting material is outflowing from the central engine.

Two of the sources in our sample, NGC 1068 and Circinus, are well-known Compton-thick AGN (with N_H ≥ 1.5 × 10²⁴ cm⁻²), and Mrk 3 is close to the Compton-thick limit. Extracting the intrinsic X-ray properties from Compton-thick AGN is difficult because the amount of emission transmitted directly from the AGN is often quite low compared to the amount of reprocessed emission. The additional scattering component that must be included in the modeling of Compton-thick sources is strongly dependent on the geometry of the system, which introduces a large amount of uncertainty. The best treatment of Compton-thick AGN to date involves analyzing data over a wide energy range. In particular, including hard X-ray data from observatories such as NuSTAR and Swift BAT is important to accurately model Compton-thick AGN because almost all of the emission with energy ≲10 keV is scattered and reprocessed, leaving no intrinsic emission to detect in the soft X-ray band. Recent studies of NGC 1068 and Circinus have revealed estimates of the intrinsic AGN properties by fitting detailed models for various different geometries of the obscuring material to broadband X-ray data from many different observatories (Arévalo et al. 2014; Bauer et al. 2015; Marinucci et al. 2016; Uematsu et al. 2021).

Our simple absorption modeling of these sources fails to account for the additional scattering component and introduces some biases in the continuum parameter estimation. For NGC 1068 and Circinus, the column densities we find from our simple absorption model significantly underestimate those from the literature with a full model including both absorption and electron scattering (see Table 4). Thus, for these sources, we cannot properly estimate parameters like the equivalent width of the Fe Kα line using our simple continuum modeling of the relatively narrow 4–9 keV band.

Table 4. Fit Parameters for Each Object and ObsID

Object	ObsID	NH	Γ	Kpower	Kline
		(1022 cm−2)		(10−2 photons keV−1 cm−2 s−1)	(10−4 photons cm−2 s−1)
NGC 1068 a	332	${63.4}_{-16.7}^{+18.5}$	${2.41}_{-0.49}^{+0.39}$	${1.16}_{-0.73}^{+1.05}$	${0.85}_{-0.23}^{+0.31}$
	9148	${72.6}_{-15.6}^{+15.4}$	${2.29}_{-0.43}^{+0.35}$	${1.13}_{-0.66}^{+0.98}$	${0.61}_{-0.16}^{+0.20}$
	9149	${58.8}_{-13.8}^{+14.9}$	${2.30}_{-0.38}^{+0.39}$	${0.87}_{-0.47}^{+0.95}$	${0.70}_{-0.16}^{+0.19}$
	9150	${73.8}_{-21.0}^{+25.0}$	${2.33}_{-0.54}^{+0.47}$	${1.08}_{-0.73}^{+1.25}$	${0.52}_{-0.19}^{+0.30}$
	10815	${85.5}_{-35.6}^{+49.5}$	${2.33}_{-0.70}^{+0.67}$	${1.24}_{-0.89}^{+1.53}$	${0.94}_{-0.45}^{+0.84}$
	10816	${103.4}_{-47.3}^{+73.7}$	${2.07}_{-0.77}^{+0.72}$	${1.16}_{-0.88}^{+1.55}$	${0.81}_{-0.52}^{+1.21}$
	10817	${73.5}_{-21.0}^{+24.1}$	${2.26}_{-0.50}^{+0.42}$	${1.13}_{-0.69}^{+1.05}$	${0.92}_{-0.33}^{+0.46}$
	10823	${78.0}_{-19.7}^{+23.6}$	${2.24}_{-0.50}^{+0.41}$	${1.14}_{-0.72}^{+1.09}$	${0.78}_{-0.28}^{+0.40}$
	10829	${64.2}_{-20.8}^{+25.3}$	${2.49}_{-0.56}^{+0.49}$	${1.10}_{-0.73}^{+1.32}$	${0.55}_{-0.19}^{+0.30}$
	10830	${53.1}_{-18.1}^{+21.5}$	${2.57}_{-0.52}^{+0.45}$	${1.11}_{-0.71}^{+1.22}$	${0.64}_{-0.20}^{+0.29}$
NGC 3783	2090	${3.1}_{-2.2}^{+2.1}$	${1.67}_{-0.12}^{+0.11}$	${1.46}_{-0.30}^{+0.34}$	${0.38}_{-0.07}^{+0.07}$
	2091	${8.6}_{-2.2}^{+2.1}$	${1.97}_{-0.12}^{+0.11}$	${2.71}_{-0.56}^{+0.64}$	${0.40}_{-0.07}^{+0.08}$
	2092	${3.7}_{-2.2}^{+2.1}$	${1.75}_{-0.12}^{+0.11}$	${1.68}_{-0.35}^{+0.39}$	${0.43}_{-0.07}^{+0.07}$
	2093	${7.4}_{-1.9}^{+1.9}$	${2.03}_{-0.10}^{+0.10}$	${4.09}_{-0.77}^{+0.88}$	${0.47}_{-0.08}^{+0.08}$
	2094	${8.1}_{-2.0}^{+2.0}$	${1.99}_{-0.11}^{+0.10}$	${3.36}_{-0.67}^{+0.75}$	${0.38}_{-0.07}^{+0.08}$
	14991	${8.0}_{-3.7}^{+3.5}$	${1.89}_{-0.17}^{+0.15}$	${1.76}_{-0.51}^{+0.61}$	${0.42}_{-0.11}^{+0.12}$
	15626	${7.7}_{-3.1}^{+3.0}$	${1.73}_{-0.15}^{+0.13}$	${1.24}_{-0.32}^{+0.39}$	${0.36}_{-0.08}^{+0.09}$
	18192	${9.8}_{-3.2}^{+3.1}$	${2.07}_{-0.15}^{+0.14}$	${2.69}_{-0.73}^{+0.84}$	${0.39}_{-0.10}^{+0.12}$
	19694	${15.3}_{-3.6}^{+3.3}$	${2.24}_{-0.17}^{+0.15}$	${3.28}_{-0.95}^{+1.11}$	${0.37}_{-0.10}^{+0.11}$
NGC 4151	335	${22.9}_{-3.6}^{+3.4}$	${1.67}_{-0.17}^{+0.16}$	${2.89}_{-0.86}^{+1.08}$	${1.77}_{-0.27}^{+0.29}$
	3052	${8.3}_{-1.7}^{+1.6}$	${1.61}_{-0.09}^{+0.09}$	${4.74}_{-0.82}^{+0.91}$	${1.32}_{-0.15}^{+0.15}$
	3480	${9.1}_{-2.0}^{+2.0}$	${1.54}_{-0.11}^{+0.10}$	${4.37}_{-0.87}^{+0.99}$	${1.39}_{-0.20}^{+0.21}$
	7829	${20.6}_{-4.5}^{+4.3}$	${1.68}_{-0.21}^{+0.17}$	${1.51}_{-0.53}^{+0.62}$	${1.00}_{-0.19}^{+0.21}$
	7830	${14.6}_{-2.5}^{+2.3}$	${2.02}_{-0.13}^{+0.12}$	${11.51}_{-2.64}^{+3.07}$	${1.21}_{-0.26}^{+0.29}$
	16089	${24.7}_{-2.2}^{+2.2}$	${1.93}_{-0.11}^{+0.11}$	${4.79}_{-1.01}^{+1.15}$	${1.51}_{-0.14}^{+0.15}$
	16090	${24.4}_{-3.3}^{+3.1}$	${1.68}_{-0.16}^{+0.14}$	${2.84}_{-0.79}^{+0.95}$	${1.38}_{-0.20}^{+0.22}$
NGC 4388	9276	${37.2}_{-5.1}^{+4.8}$	${1.38}_{-0.25}^{+0.24}$	${0.75}_{-0.31}^{+0.48}$	${0.67}_{-0.10}^{+0.11}$
	9277	${38.5}_{-6.0}^{+5.7}$	${1.71}_{-0.30}^{+0.28}$	${1.62}_{-0.75}^{+1.28}$	${0.76}_{-0.14}^{+0.16}$
NGC 4507	2150	${64.7}_{-5.8}^{+5.8}$	${1.70}_{-0.27}^{+0.27}$	${2.61}_{-1.14}^{+1.99}$	${0.75}_{-0.14}^{+0.16}$
Mrk 3	873	${72.1}_{-10.4}^{+10.8}$	${2.03}_{-0.35}^{+0.33}$	${0.99}_{-0.51}^{+0.89}$	${0.85}_{-0.17}^{+0.20}$
	12874	${76.0}_{-11.6}^{+12.0}$	${1.98}_{-0.37}^{+0.31}$	${1.09}_{-0.59}^{+0.88}$	${0.86}_{-0.19}^{+0.23}$
	12875	${81.7}_{-18.4}^{+19.7}$	${1.94}_{-0.45}^{+0.40}$	${1.08}_{-0.65}^{+1.09}$	${0.81}_{-0.30}^{+0.41}$
	13254	${83.1}_{-19.1}^{+22.6}$	${1.98}_{-0.50}^{+0.39}$	${1.14}_{-0.72}^{+1.10}$	${0.76}_{-0.28}^{+0.42}$
	13261	${68.7}_{-20.8}^{+23.9}$	${2.22}_{-0.57}^{+0.46}$	${1.20}_{-0.81}^{+1.34}$	${0.58}_{-0.27}^{+0.40}$
	13263	${82.0}_{-24.9}^{+32.7}$	${1.98}_{-0.57}^{+0.51}$	${1.08}_{-0.73}^{+1.38}$	${1.03}_{-0.44}^{+0.69}$
	13264	${82.7}_{-16.1}^{+17.9}$	${1.89}_{-0.43}^{+0.37}$	${1.03}_{-0.60}^{+1.02}$	${0.59}_{-0.24}^{+0.32}$
	13406	${97.0}_{-25.0}^{+30.2}$	${1.85}_{-0.52}^{+0.44}$	${1.14}_{-0.74}^{+1.20}$	${1.42}_{-0.51}^{+0.76}$
	14331	${76.0}_{-15.5}^{+16.5}$	${1.86}_{-0.41}^{+0.38}$	${0.85}_{-0.49}^{+0.94}$	${0.83}_{-0.23}^{+0.29}$
Circinus a	10223	${51.4}_{-5.3}^{+5.4}$	${1.26}_{-0.17}^{+0.17}$	${0.41}_{-0.13}^{+0.15}$	${3.87}_{-0.33}^{+0.36}$
	10224	${50.4}_{-6.1}^{+6.4}$	${1.35}_{-0.20}^{+0.18}$	${0.46}_{-0.16}^{+0.18}$	${3.96}_{-0.38}^{+0.43}$
	10225	${58.1}_{-6.8}^{+7.0}$	${1.56}_{-0.21}^{+0.20}$	${0.72}_{-0.26}^{+0.31}$	${4.43}_{-0.47}^{+0.51}$
	10226	${79.5}_{-13.7}^{+15.3}$	${2.27}_{-0.33}^{+0.30}$	${3.66}_{-1.78}^{+2.35}$	${4.83}_{-0.96}^{+1.20}$
	10832	${46.8}_{-13.3}^{+14.3}$	${0.64}_{-0.33}^{+0.31}$	${0.11}_{-0.05}^{+0.07}$	${3.92}_{-0.74}^{+0.88}$
	10833	${59.1}_{-11.0}^{+11.6}$	${1.55}_{-0.29}^{+0.27}$	${0.77}_{-0.35}^{+0.44}$	${4.52}_{-0.73}^{+0.86}$
	10842	${73.8}_{-11.4}^{+12.4}$	${2.01}_{-0.28}^{+0.27}$	${1.94}_{-0.83}^{+1.12}$	${5.30}_{-0.82}^{+0.99}$
	10843	${54.2}_{-8.0}^{+8.5}$	${1.19}_{-0.23}^{+0.21}$	${0.35}_{-0.13}^{+0.16}$	${3.88}_{-0.47}^{+0.52}$
	10844	${56.4}_{-11.2}^{+11.7}$	${1.73}_{-0.29}^{+0.28}$	${0.90}_{-0.41}^{+0.50}$	${3.40}_{-0.60}^{+0.69}$
	10850	${53.0}_{-16.5}^{+18.4}$	${1.00}_{-0.36}^{+0.36}$	${0.25}_{-0.13}^{+0.18}$	${2.98}_{-0.75}^{+0.94}$
	10872	${75.9}_{-16.3}^{+17.6}$	${1.55}_{-0.34}^{+0.34}$	${0.98}_{-0.48}^{+0.64}$	${5.54}_{-1.22}^{+1.51}$
	10873	${67.4}_{-13.2}^{+15.2}$	${2.30}_{-0.35}^{+0.33}$	${2.88}_{-1.45}^{+1.87}$	${4.35}_{-0.86}^{+1.09}$
	62877	${63.3}_{-7.5}^{+7.7}$	${1.67}_{-0.23}^{+0.21}$	${0.98}_{-0.36}^{+0.44}$	${3.84}_{-0.46}^{+0.51}$
	4770	${64.6}_{-7.9}^{+8.2}$	${1.79}_{-0.23}^{+0.22}$	${1.19}_{-0.46}^{+0.56}$	${4.05}_{-0.49}^{+0.54}$
	4771	${70.4}_{-8.1}^{+8.6}$	${1.64}_{-0.23}^{+0.22}$	${0.98}_{-0.37}^{+0.46}$	${4.61}_{-0.56}^{+0.65}$

Notes. Column (1): object name. Column (2): Chandra ObsID. Column (3): column density of source absorption. Column (4): power-law photon index. Column (5): power-law normalization. Column (6): Gaussian line normalization.

^a The column densities (N_H) reported for NGC 1068 and Circinus underestimate the true column density along our line of sight as a result of our simple phenomenological modeling of absorption in a narrow energy band. See Section 4.2 for details on how this affects our estimates of various physical parameters.

Download table as:  ASCIITypeset image

Properly modeling the absorption and scattering in these Compton-thick sources is beyond the scope of this work. Hence, we quote a range of values for the properties that depend on the intrinsic continuum, including the equivalent width and the subsequent gas mass and mass outflow rate measurements, for the two truly Compton-thick AGN in our sample (NGC 1068 and Circinus). The range is determined based on two extreme continuum estimates and utilizing the nuclear emission estimates from past multiwavelength modeling, details of which are given in Section 3.3. For Mrk 3, we find an average column density of N_H ∼ 0.8 × 10²⁴ cm⁻², which is at the low end of the line-of-sight values typically found in the literature (e.g., Yaqoob et al. 2015; Guainazzi et al.2016) but is in line with the finding that Mrk 3 is close to, but does not exceed, the Compton-thick limit along our line of sight. Thus, we report values for Mrk 3, albeit with relatively high uncertainties, but urge caution in the interpretation of values that depend on the intrinsic continuum, such as the equivalent width, gas mass, and mass outflow rates, which may be overestimated as a result of our simple phenomenological modeling.

The Fe Kα emission line traces cold, neutral gas around AGN, regardless of whether the gas is in atomic or molecular form. Molecular gas around AGN can also be traced via specific line transitions at submillimeter and infrared wavelengths, which have the advantage of high spatial resolution and velocity map information from spatially resolved spectroscopy. Studies of the molecular gas around nearby AGN have probed the circumnuclear region around the black hole in great detail, revealing significant outflows, indications of inflowing material (see Storchi-Bergmann & Schnorr-Müller 2019, and references therein), and complexities of the molecular torus (e.g., García-Burillo et al. 2016; Imanishi et al. 2018; Combes et al. 2019). Molecular outflows can be quite massive, with mass outflow rates on the order of 100–1000 hundreds to thousands of solar masses per year (e.g., Feruglio et al. 2010; Sturm et al. 2011; Veilleux et al. 2013; Cicone et al. 2014; Tombesi et al. 2015), which are similar to our derived values from the Fe Kα emitting material.

Two of the objects in our sample, NGC 1068 and Circinus, have been extensively studied with ALMA, allowing us to directly compare our results to the molecular gas properties. ALMA observations of NGC 1068 reveal significant molecular gas outflows on a variety of scales and gas densities with various molecular line tracers (e.g., García-Burillo et al. 2014; Gallimore et al. 2016; García-Burillo et al. 2019; Impellizzeri et al. 2019; Imanishi et al. 2020). García-Burillo et al. (2014) found significant molecular outflows in the circumnuclear disk (CND). On these scales of approximately 100 pc, the projected outflow velocities were on the order of v ∼ 100 km s⁻¹ and the molecular outflow rate was ${\dot{M}}_{\mathrm{out}}\sim 63\,{M}_{\odot }$ yr⁻¹. This is consistent with, but falls on the low end of, our large range of mass outflow rates for the neutral Fe Kα emitting material in NGC 1068 (see Table 3). On smaller scales, similar to those traced by the neutral iron line in this study (∼20 pc), García-Burillo et al. (2019) showed that about half of the mass in the molecular torus is outflowing, although this portion of the outflow is significantly smaller in mass, momentum, and energy compared to the outflow in the CND. On even smaller scales of roughly a few parsecs, fast molecular outflows have been detected in both Gallimore et al. (2016) and Impellizzeri et al. (2019), with projected velocities on the order of v ∼ 400–450 km s⁻¹. Although with higher uncertainties, our results for NGC 1068 reveal similar mass outflow rates and higher velocities of the potentially outflowing Fe Kα emitting material compared to those traced by molecular line transitions with ALMA.

Previous ALMA observations of the Circinus galaxy have revealed molecular and atomic outflows, although the geometry of Circinus makes it difficult to distinguish between outflow and disk motions. Zschaechner et al. (2016) found that the molecular outflow in the central kiloparsec of Circinus had a consistent velocity with the ionized outflow (v ∼ 150 km s⁻¹; Veilleux & Bland-Hawthorn 1997). However, this molecular outflow has significantly lower energetics than some of the massive molecular outflows (e.g., Cicone et al. 2014), with an estimated mass outflow rate of ${\dot{M}}_{\mathrm{out}}\sim 0.35\mbox{--}12.3\,{M}_{\odot }$ (Zschaechner et al. 2016). Like in NGC 1068, this is on the low end of our reported range of mass outflow rates for the Fe Kα emitting material. On smaller scales, Izumi et al. (2018) found streaming motions indicative of an inflow to the AGN and an atomic outflow with a velocity on the order of v ∼ 60 km s⁻¹. This outflow is thought to give rise to the thickness of the diffuse atomic gas and provides evidence for a multiphase, dynamic torus in Circinus. Additionally, Kawamuro et al. (2019) found that the spatial extent of the molecular line emission in Circinus was anticorrelated with the Fe Kα emitting material but had similar extents in the central 100 pc of the galaxy.

This study opens the door for further work that can be done in tandem with future X-ray missions, such as XRISM, Athena, and Lynx. These missions will have microcalorimeters to perform nondispersive, high-resolution X-ray spectroscopy. The power of microcalorimeters in X-ray spectroscopy is evident from the Hitomi observations of NGC 1275 in the Perseus cluster, which provided the ability to resolve the narrow Fe Kα line in NGC 1275 for the first time (Hitomi Collaboration et al. 2018). In relation to this work, microcalorimeter spectroscopy will provide an independent measure of the intrinsic velocity width of the narrow Fe Kα line and avoid contributions from the spatial extent, an effect that we have just shown has increased the line widths in dispersed Chandra HETG spectra. In principle, the spatial extent of the emitting material can be extracted by comparing Chandra HETG first-order line widths with those from a microcalorimeter spectrum. This will be more prevalent in the future with X-ray missions, such as XRISM, Athena, and Lynx, but Reynolds et al. (2021) have already demonstrated the possibilities of this technique by estimating the extent of the Fe Kα emitting material in NGC 1275 with Hitomi SXS data and first-order Chandra HETG data.

The higher-order HETG spectra have significantly lower signal-to-noise ratio compared to the first-order spectrum due to their smaller effective areas and thus are the limiting factor in our analysis and the cause of the large uncertainty on the spatial extent reported in this work. Therefore, being able to disentangle the spatial extent and intrinsic velocity width solely with the first-order HETG spectrum and one from an X-ray microcalorimeter should greatly decrease the uncertainty in our current estimates of the spatial extent of the Fe Kα emitting material in these objects, most of which are close to upper limits. Likewise, requiring adequate signal-to-noise ratio in the higher-order HETG spectra restricts the sample of AGN for which this analysis can be done to bright, nearby sources with an extensive amount of observation. As already shown in Reynolds et al. (2021), it is possible to obtain constraints on the Fe Kα emitting material in NGC 1275, a difficult target because of the surrounding X-ray-emitting intracluster medium of the Perseus Cluster, by applying this technique to microcalorimeter and dispersive spectroscopy together. Thus, together with archival first-order Chandra HETG data, future X-ray microcalorimeter spectroscopy will also allow for this study to be extended to many more AGN.