A Long Look at MCG-5-23-16 with NuSTAR. I. Relativistic Reflection and Coronal Properties

We first attempt to check for column density variability using the Swift data alone. We fit an absorbed power law to all the Swift spectra and track their changes. The column density showed some changes. However, the strong degeneracy between column density and power-law index does not allow any firm conclusions to be drawn, and therefore analysis of all the spectral data is required.

To explore the changes in the iron line complex using a phenomenological approach, we show in Figure 3 the spectrum of the iron line from the highest and lowest flux NuSTAR observations (N2 and N4, respectively, which are separated by almost two years). The difference between the spectra is also shown. The spectrum in the iron line complex is clearly variable, and most of the variability is in the low energy wing of the line, not the core. The centroid energy for the N2 and N4 spectra are 6.30 ± 0.01 and 6.36 ± 0.01 keV, respectively, while the centroid from the difference spectrum is 6.17 ± 0.05 keV. It appears therefore that the strongest changes in the iron line are in the broad component and not the narrow component.

Zoom In Zoom Out Reset image size

To investigate this in a more systematic way, we fit the 1–10 keV band of the spectral groups using a power law plus a narrow and a broad Gaussian line. The width of the narrow line is fixed at the instrument resolution as neither NuSTAR nor Suzaku data are able to resolve it. Constraints to the column density for the NuSTAR data are provided by including Swift data, as discussed in Section 2. The resulting parameter changes are shown in Figure 4.

Zoom In Zoom Out Reset image size

NuSTAR observation N2 was simultaneous with Suzaku S2, but there are clear systematic differences between them, both in the absolute flux values and in the photon indices. These are due to absolute calibration uncertainties between the two detectors and the uncertain cross-calibration between the front- and back-illuminated detectors in Suzaku. The photon index differences are the main cause of the large difference in ${N}_{{\rm{H}}}$ between S2 and N2 (which are degenerate in the fits). Nonetheless, it is clear that most of the variability is in the power-law continuum flux and its photon index. The energy of the narrow component is consistent with a constant. In fact, a model where the line energy is fixed to the average is statistically preferred over a model where it is free to change.

We assess the significance of the parameter changes using the sample-corrected Akaike Information Criterion (cAIC; Akaike 1974; Burnham et al. 2011), where we compare models in which the parameter of interest is either fixed or allowed to change between observations. For the narrow line, we find that fixing the line flux between observations gives a lower cAIC than allowing it to change, with ${\rm{\Delta }}\mathrm{cAIC}=-2$ from each observation. This implies that the model with a fixed line flux is preferred. For the line energy, ${\rm{\Delta }}\mathrm{cAIC}\lt 0$ for the Suzaku-only data and ${\rm{\Delta }}\mathrm{cAIC}\gt 10$ when the NuSTAR data are included. In other words, the line appears to change only between different instruments but is constant within the same instrument. This suggests that the line flux is physically constant and the observed changes are caused by instrument absolute calibration. For the column density, there appears to be significant changes between observations, even when using the same instrument (${\rm{\Delta }}\mathrm{cAIC}\gt 15$, corresponding to a $\gt 3.3\sigma$ significance). Changes in the parameters of the broad component are significant at the $3\sigma$ level when the narrow component is assumed constant. Degeneracies between the two reflection components are addressed in Section 3.1.2 where we use full physical models.

The narrow Gaussian line is due to distant reflection from the broad-line region or the torus. To model it more physically, we replace the narrow Gaussian with the reflection model xillver (García et al. 2014). xillver self-consistently includes emission from Fe Kβ and allows for the reflection to be ionized. Using the xillver+powerlaw model accounts for most of the residuals around 6.4 keV, including the Fe Kβ line present in MCG-5-23-16, also seen in previous observations (Reeves et al. 2007). The xillver model provides a better fit compared to pexmon (Nandra et al. 2007), for example, with ${\rm{\Delta }}W\sim 28$ per observation for the same number of degrees of freedom as the Suzaku spectra where the Kβ line is most clearly seen. This corresponds to ${\rm{\Delta }}\mathrm{cAIC}=17$ and a significance of $\gt 3.5\sigma$. The best-fit ionization parameter of the reflector in this case is $\mathrm{log}(\xi )=0$, consistent with neutral reflection.¹⁴

Continuing the analysis of the spectra in the 1–10 keV band, we next model the broad component of the iron line with a full relativistic reflection model. We use the relxill model (version v0.4a) (Dauser et al. 2010; García et al. 2014). The reflection spectrum is a result of a hard X-ray source illuminating a constant density disk. The observer sees emission from both the illuminating source and the reflector. The reflection spectrum is convolved with a relativistic kernel to model the strong gravity effects of the black hole. As we will show, the inner radius of the disk is $\gt 10{r}_{g}$, and because the inner radius is degenerate with the black hole spin, we fix the latter at the maximum. The fact that the inner radius is $\gt 10{r}_{g}$ shows that the exact fixed spin value has little effect on the fits. We use a single power-law emissivity profile and assume that the directly observed component has the same spectral index as that illuminating the disk. The high energy cutoff is fixed at 300 keV, and it is modeled when fitting the whole NuSTAR band in Section 3.2. The abundance of the inner and outer reflectors are assumed to be the same. We fit all seven spectra independently, and the results are summarized in Table 2.

Table 2.  Fit Parameter for the relxill+xillver for the 1–10 keV fits for the Suzaku and NuSTAR Data Sets, and for 1–79 keV for the NuSTAR Data Sets

Obs	${N}_{{\rm{H}}}$	Γ	R	θ	${R}_{\mathrm{in}}$	q	$\mathrm{log}(\xi )$	${N}_{{\rm{r}}}$	${N}_{{\rm{x}}}$	Ec
Fits to Individual Spectra between 1 and 10 keV
S0	1.49(1)	1.84(3)	0.3(1)	57(7)	$\lt 28$	2(1)	2.6(1)	−3.25(1)	−3.38(6)	⋯
S1	1.41(1)	1.89(2)	0.2(1)	39(8)	$\lt 40$	3(1)	2.6(1)	−3.10(1)	−3.4(1)	⋯
S2	1.41(1)	1.90(1)	0.21(3)	47(7)	77(20)	$\gt 6$	2.70(5)	−3.19(1)	−3.4(1)	⋯
N2	1.24(5)	1.91(1)	0.29(8)	34(7)	41(18)	5(2)	2.3(1)	−3.18(1)	−3.6(1)	⋯
N4	1.26(5)	1.83(2)	0.5(1)	64(6)	$\lt 41$	$\lt 7$	2.5(9)	−3.34(1)	−3.5(1)	⋯
N6	1.46(5)	1.88(2)	0.4(2)	52(13)	$\lt 83$	2(1)	2.3(8)	−3.29(1)	−3.6(5)	⋯
N8	1.34(5)	1.84(1)	0.29(7)	45(8)	$\lt 33$	3(2)	2.3(8)	−3.26(1)	−3.5(1)	⋯
Fits to Individual Spectra between 1 and 79 keV
N2	1.39(1)	1.87(1)	0.2(1)	51	$\gt 50$	8(2)	2.5(5)	−3.23(1)	−3.45(1)	140(10)
N4	1.26(4)	1.77(1)	0.34(3)	⋯	$\lt 68$	1(1)	2.7(1)	−3.41(2)	−3.84(5)	120(8)
N6	1.41(5)	1.82(1)	0.25(7)	⋯	$\lt 59$	1(2)	2.5(1)	−3.33(1)	−3.7(1)	146(18)
N8	1.35(4)	1.77(1)	0.18(3)	⋯	$\lt 73$	0.2(7)	2.7(1)	−3.33(1)	−3.66(5)	124(7)
Joint Fit to All the Spectra between 1 and 79 keV
	${N}_{{\rm{H}}}$	Γ	Np	θ	${R}_{\mathrm{in}}$	q	$\mathrm{log}(\xi )$	${N}_{{\rm{r}}}$	${N}_{{\rm{x}}}$	Ec
N2	1.40(1)	1.85(1)	−1.47(1)	51	47(23)	1.6(6)	2.66(3)	−3.80(1)	−3.60(2)	152(8)
N4	1.25(4)	1.78(1)	−1.68(1)	⋯	⋯	⋯	⋯	−4.21(6)	⋯	107(7)
N6	1.45(4)	1.83(1)	−1.59(1)	⋯	⋯	⋯	⋯	−4.12(7)	⋯	149(14)
N8	1.41(4)	1.79(1)	−1.60(1)	⋯	⋯	⋯	⋯	−4.11(1)	⋯	130(6)

Note. The 1σ statistical uncertainty in the last significant figure is shown in brackets. N is the normalization in units of $\mathrm{log}$ (photons cm⁻² s⁻¹). Subscripts r, p, and x are for relxill, cutoffpl, and xillver, respectively. R is the reflection fraction measured as the ratio of direct to reflected fluxes between 20 and 40 keV. ${R}_{\mathrm{in}}$ is in units of gravitational radius r_g and the inclination θ is in degrees. q is the emissivity index, ξ is the ionization parameter, Γ is the photon index, and E_c is the cutoff energy. The observations in the first column are defined in Table 1.

Download table as:  ASCIITypeset image

The reflection parameters are generally better constrained in the Suzaku spectra. This is because the resolution of NuSTAR in the iron K band does not allow the narrow and broad components of the line to be unambiguously separated. One effect of this is that the values of the iron abundance are not consistent between Suzaku and NuSTAR. The three Suzaku spectra suggested a value of about 1, while it is around 0.5 (the model minimum) in the NuSTAR spectra. We therefore fixed the NuSTAR value at the Suzaku value. The uncertainties in Table 2 are calculated from Monte Carlo Markov Chains (MCMC) as the $1\sigma$ standard deviation of the chains. We found when exploring the likelihood space that it is multi-modal, with multiple parameter combinations having close likelihood values near the maximum. MCMC is therefore well suited to explore this multi-modality. All the chains reported here were generated using the affine invariant ensemble sampler (Goodman & Weare 2010). All the chains were run several times and long enough to ensure convergence. The convergence is assessed with both the autocorrelation of the chains and the stability of the chain variances.

Table 2 quotes only the average values. There are however two general solutions in the modeling with different values for the ionization parameter ξ of the relativistic reflection component ($\mathrm{log}(\xi )\sim 0$ and $\mathrm{log}(\xi )\sim 2.7$). This is illustrated in the top panel of Figure 5, where we plot the confidence contours for the best-fit parameters for (the log of) the ionization parameter versus the photon index for all of the observations. Although the best-fit value for the ionization parameter is $\mathrm{log}(\xi )\sim 2.3-2.7$, lower values ($\leqslant 1$) are also possible with a slightly higher value to Γ. Two parameters that are of interest are ${R}_{\mathrm{in}}$ and the emissivity index, which locate the emitting region relative to the central object. These two parameters are highly correlated in the modeling as shown by the middle panel of Figure 5. Although the best-fit values are at ${R}_{\mathrm{in}}\sim 20$ gravitational radii (${r}_{g}={GM}/{c}^{2}$) and $q\sim 3$, lower and higher values for ${R}_{\mathrm{in}}$ are also supported by the data.

Zoom In Zoom Out Reset image size

The confidence contours of the inclination θ and the normalization of the distant reflector ${N}_{{\rm{x}}}$ are shown in the bottom panel of Figure 5. The best-fit inclination value in this case is $\theta \sim 50^\circ$, but higher inclinations with stronger distant reflection are also supported by the data. The data in this case support either a low-inclination disk ($\theta \lt 60^\circ$) with a relatively weak distant reflector or a highly inclined disk ($\theta \sim 88^\circ$) and stronger reflection. Given that this object is seen through a Compton-thin rather than thick absorber, suggests an intermediate inclination, making the first solution more physically plausible. We note here that parameters reported in the analysis of the first NuSTAR observation (Baloković et al. 2015) are consistent with one of the local minima in the fit, with $\mathrm{log}(\xi )\sim 0$. Our best fit has a value of $\mathrm{log}(\xi )\sim 2.7$. Other parameters change accordingly, with reflection parameters not differing significantly (apart from the normalization).

Previous results on possible ${\rm{\Gamma }}\mbox{--}{E}_{c}$ correlations in samples of objects were not conclusive. Piro et al. (1999) first noted a possible ${\rm{\Gamma }}\mbox{--}{E}_{c}$ relation using two BeppoSAX observations of NGC 4151. Petrucci et al. (2001) found a weak relation with six Seyfert Galaxies, and a relatively stronger relation was found by Perola et al. (2002) using a slightly larger sample. Using INTEGRAL data, Molina et al. (2013) reported a weak relation while Malizia et al. (2014) reported no relation. It appears therefore that as far as a sample of AGNs is concerned, there is at most a weak relation between Γ and E_c.

The data for individual objects is less clear, mostly because of the difficulty of obtaining high quality data in single epoch observations, with low energy coverage. We note that from the INTEGRAL study of Molina et al. (2013), who analyzed separate observations of individual objects, in almost all cases of objects with multiple observations, flatter spectra are accompanied by small cutoff energies. The uncertainties in the parameters are, however, large. Using NuSTAR, Ballantyne et al. (2014) analyzed two observations of the radio galaxy 3C 382 in two flux intervals. The low flux observation had a flatter spectrum and a higher cutoff energy compared to the higher flux observation (i.e., opposite the trend seen in INTEGRAL data and seen here in MCG-5-23-16 ). Also using NuSTAR data, Keek & Ballantyne (2016) found a positive correlation between Γ and E_c in Mrk 335, although we note that both the photon indices and cutoff energies ($\lt 50$ keV) found there are small, differing substantially from other studies using the same data sets (Parker et al. 2014; Wilkins et al. 2015). The result we found here suggests a strong positive correlation with the photon index Γ, similar to Mrk 335.

Variability of the cutoff energy (or electron temperature) with flux or luminosity has not been explored in detail extensively in AGNs, unlike in black hole binaries. As we pointed out in Section 4.2.1, results from AGNs are not yet conclusive, where both a correlation and an anti-correlation of E_c and flux have been reported for 3C 382 and Mrk 335, respectively (Ballantyne et al. 2014; Keek & Ballantyne 2016).

For X-ray binaries, Cyg X-1 showed an increase in cutoff energy when the luminosity in the hard X-rays drops during the hard state (Gierlinski et al. 1997; Ibragimov et al. 2005). A strong anti-correlation of the cutoff energy and luminosity was also observed in GX 339-4 when the luminosity was above $\sim 10 \%$ of the Eddington luminosity, and it remained constant below that (Miyakawa et al. 2008). A similar result was found by Motta et al. (2009), who additionally observed the reverse trend when the source softened before transiting to the soft state. A similar behavior is seen in other objects, including V404 Cyg in its recent outburst as observed with Fermi (Jenke et al. 2016), and possibly also Cyg X-1 in the soft state from NuSTAR observations (Walton et al. 2016). We note that when E_c is correlated with luminosity, so is Γ, and when the spectra soften during the hard intermediate state, both Γ and E_c reverse their dependence on luminosity. The result we find for MCG-5-23-16 appears to match the behavior of black hole binaries not in the hard state, where E_c is anti-correlated with L, but in the intermediate state. A correlation between Γ and the flux is well-established in bright AGNs and Galactic black holes (e.g., Sobolewska & Papadakis 2009; Yang et al. 2015).

Before discussing the details of the plasma physics, it is worth mentioning the possibility that the changes in E_c may not be due to changes in the intrinsic election temperature, but rather due to changes in the gravitational redshift of a constant spectrum (e.g., Niedźwiecki et al. 2016). Such changes in the gravitational redshift of the emitted photons (due to changes in the size of the corona, for instance) could artificially introduce variations in E_c without the plasma properties changing. This, however, also produces changes in the reflection fraction, due to the focusing of light rays into and away from the disk. The fact that the observed reflection fraction is constant suggests that the geometry does not change significantly, strengthening the interpretation in which the E_c variations are intrinsic to the plasma. Also, the inner radius we measure is relatively large, so GR effects are present but not extreme, and therefore the discussion of relativistic modeling in Niedźwiecki et al. (2016) is not applicable in this work.

In the simplest considerations of a pure thermal plasma (Sunyaev & Titarchuk 1980) (no electron–positron pairs), an increase in the soft flux impinging on the corona leads to softer Comptonization spectra and lower temperatures as the electrons are cooled efficiently (e.g., Zdziarski et al. 2002). This picture cannot be applied directly here, first because pairs are not included and their effect could be important (Fabian et al. 2015), and second because the correlation we measure is in the hard flux (emitted by the corona) rather than the soft flux impinging on it. Therefore, we would like first to assess the importance of pair production given the measurements we have.

We start by comparing the observations to predictions of pair-dominated plasmas. The temperature of a plasma cannot be arbitrarily high for a given size. The key parameter that is often used is the compactness $l=4\pi ({m}_{p}/{m}_{e})({r}_{g}/r)(L/{L}_{\mathrm{edd}})$, which measures the luminosity to source size ratio. As the compactness increases, photon–photon interactions become important, and any extra heating goes into producing electron–positron pairs rather than heating the plasma, causing the temperature to saturate (Guilbert et al. 1983; Zdziarski 1985).

Following Zdziarski (1985) and Ghisellini & Haardt (1994), we calculate the spectral index α ($\alpha ={\rm{\Gamma }}-1$) and cutoff energy predicted from models in thermal and pair equilibria, for different values of the compactness l_h and ${l}_{h}/{l}_{s}$, where l_h is the compactness of the Comptonization plasma (i.e., the power heating the corona), and l_s is the compactness of the soft source producing the seed photons. We use the model eqpair (Coppi et al. 1999) to generate spectra for a grid of parameters for l_h (between 10 and 5 × 10⁴) and ${l}_{h}/{l}_{s}$ (between 1 and 100). We assume the soft source is a blackbody with a temperature of 10 eV and the plasma is spherical and contains no background electron plasma (${\tau }_{p}=0$). The generated spectra are then fitted with a cutoff power-law model to simulate the fitting procedure and obtain the energy spectral index α and E_c. The results are shown in the left panel of Figure 8. Contours of α and E_c are shown, and the $1\sigma$ measured values of α and E_c are shown with the green boxes. This plot shows that, first, the inferred compactness ratio ${l}_{h}/{l}_{s}\sim 5-6$, which is not atypical of AGNs. Second and more importantly, it shows that, if the plasma is dominated by pairs, then the inferred l_h is large (for reference, a source radiating at the Eddington limit that is 1 gravitational radius in size has l ∼ 10⁵). Therefore, based just on the measured α and E_c, if the plasma is dominated by pairs, the source has to be very compact, suggesting a small size and/or high luminosity.

Zoom In Zoom Out Reset image size

Further information is provided by including the source size measurement we have from the reflection spectrum and the observed luminosity. The results in this case are shown in the right panel of Figure 8, showing the temperature–l relations at the pair limit from the modeling of Stern et al. (1995) for three geometries of the corona. For a given compactness and geometry, a source cannot have a temperature above the lines shown. Below the lines, the effect of pairs decreases and the plasma contains only electrons. As we have discussed in Section 3, the reflection spectrum constrains the inner radius of the disk to be ${R}_{\mathrm{in}}=47\pm 23\,{r}_{g}$. If we assume the corona is of the same size (otherwise relativistic features in the reflection will be washed out), we obtain the green circles shown in Figure 8. We used the cutoff power-law flux in the range 0.1–200 keV to measure the luminosity assuming a standard cosmology (${{\rm{\Omega }}}_{m}=0.3,{\rm{\Lambda }}=0.7$) with ${H}_{0}=68\,\mathrm{km}\,{{\rm{s}}}^{-1}\,{\mathrm{Mpc}}^{-1}$, and a black hole mass of $M={10}^{7.9}\,{M}_{\odot }$ (Ponti et al. 2012).¹⁶ The red arrows show the upper limits on the observed l_h obtained by setting ${R}_{\mathrm{in}}=1.23{r}_{g}$, the innermost stable circular orbit for a maximally spinning black hole. The electron temperature is estimated as ${{kT}}_{e}\sim {E}_{c}/2$ (Petrucci et al. 2001).

We can see that all the measurements fall below the pair limit lines for the three geometries, indicating that the plasma in MCG-5-23-16 is not dominated by pairs and consists mostly of electrons. This is a robust statement given the small uncertainties in the cutoff measurements. Using the nthcomp (Zdziarski et al. 1996) model (as implemented in the reflection model relxillCp which calculates the reflection spectrum when illuminated by nthcomp; J. A. Garcia et al. 2017, in preparation) instead of the cutoffpl shifts the electron temperatures up only by $\sim 10 \%$, and our conclusion about the plasma content is not altered. The points can of course be shifted to the right (i.e increasing l_h) if the black hole mass is erroneous. We find that in order for the plasma to be in pair balance for the slab geometry, the black hole mass needs to be smaller by ∼ two orders of magnitude (i.e., $M\sim {10}^{6}\,{M}_{\odot }$). We note that the black hole mass in Ponti et al. (2012) is uncertain. A mass estimate using the fundamental plane of black hole activity (Gültekin et al. 2009) using the radio fluxes from (Mundell et al. 2009) and the X-ray fluxes from our observations suggest a lower mass of ${10}^{7}\,{M}_{\odot }$. Other estimates suggest similar smaller values (e.g., Zhou & Zhao 2010), but not low enough to alter our conclusions about the plasma content. Note also that the correlation between E_c and l_h is weaker than the ${E}_{c}\mbox{--}{F}_{p}$ correlation in Figure 7. That is because we use the wider energy range to calculated the flux and also because of the uncertainties in the radius measurements.

The additional information provided by the four measurements of the plasma properties provide further constraints. The cutoff energy in pair-dominated plasmas scales inversely with compactness (or with luminosity when the source size is constant, as in the case here where we measure a constant reflection fraction and reflection parameters): ${E}_{c}\propto {l}_{h}^{-1}$ (Svensson 1994). This comes from the fact that increasing l_h produces more pairs, and for balance to hold, the same energy is now distributed to more particles so that the energy per particle drops. This trend is not what we observe in MCG-5-23-16. Instead, we find that the cutoff energy is higher for higher fluxes, providing further evidence that the plasma is not dominated by pairs. In electron plasmas on the other hand, the electron temperature is not expected to depend on l_h for a given ratio ${l}_{h}/{l}_{s}$ and optical depth τ. This comes from the fact that although electrons gain energy when l_h increases, the constant ${l}_{h}/{l}_{s}$ means cooling also increases so to keep the temperature constant. The fact that the cutoff energy (or electron temperature) varies with l_h observationally means that either ${l}_{h}/{l}_{s}$ or τ is variable. The first is ruled out by virtue of Figure 8, left panel. We conclude, therefore, that the optical depth τ varies in such a way as to produce the E_c–flux relation in Figure 7.

We now turn to the ${E}_{c}\mbox{--}{\rm{\Gamma }}$ correlation. In pair-dominated plasma, and for temperatures below the rest energy of the electron (as observed here), E_c is expected to be either positively correlated or independent of Γ, depending on the temperature and the compactness l_h (Ghisellini & Haardt 1994; Zdziarski et al. 2002). In pair-free plasma on the other hand, an ${E}_{c}\mbox{--}{\rm{\Gamma }}$ anti-correlation is expected for a fixed l_h. However, as we have already established observationally, l_h is not constant, which implies a variable optical depth τ. To investigate the variable τ possibility further in pair-free plasma, we employ a similar method to that used to produce Figure 8 and discussed in Section 4.2.3, but now we use the model compps (Poutanen & Svensson 1996) and use a grid of T_e and τ. The results are shown in Figure 9 for a slab geometry (geometry parameter in compps set to 1). We find that the optical depth τ varies significantly with T_e, being lower for higher temperature. The exact values of τ depend on the assumed geometry (e.g., τ varies between 1.3 and 1.9 if we assumed a spherical geometry instead of the slab geometry shown in Figure 9).

Zoom In Zoom Out Reset image size

The conclusion here is that in order to explain the ${E}_{c}\mbox{--}{\rm{\Gamma }}$ and ${E}_{c}\mbox{--}{F}_{p}$ correlations with the plasma, it needs to be pair-free and its optical depth needs to change as shown in Figure 9. This could possibly be accompanied by geometry changes, but it has to be small enough for the inner radius and R measurements to remain constant within the observational uncertainty.

One additional observation that can be noted from Figure 8, left panel, is that the ratio of heating to cooling in the corona changes very little between observations. The observed changing coronal flux therefore suggests that the photon flux cooling the corona changes, too, and in the same direction. This could be achieved if the UV photons of the disk vary with the X-rays. The UV flux from the source measured with the Swift UVOT camera, however, shows little variations compared to the X-rays (the fractional rms variation in X-rays is 24 ± 2%, while in the UV, it is 10 ± 4% in the W2 filter and no more than 5% in other bands redward of 2000 Å). The soft flux reaching the corona could in principle change if only the disk temperature changes, so the flux in the UVOT filters is not affected. This however would suggest that the inner radius changes, which is not observed. The constant heating over cooling we find implies that there is feedback between the hot corona and the disk photons cooling it (e.g., Haardt & Maraschi 1991), suggesting that a significant portion of photons cooling the corona are due to reprocessing in the disk.

Comparing our results with Fabian et al. (2015) indicates that AGN coronae are not always pair dominated, or that some sources are in that regime and others are not. Mrk 335 appears to show behavior similar to that reported here for MCG-5-23-16 (Keek & Ballantyne 2016), so it, too, is unlikely to be pair dominated. The presence or absence of reflection close to the black hole is unlikely to be the reason for the difference, and neither is the Eddington ratio (Mrk 335 is accreting close to the Eddington limit while MCG-5-23-16 accretes at the few percent level). Studies of other sources with NuSTAR in the near future will help address the issue.