The X-Ray Coronae in NuSTAR Bright Active Galactic Nuclei

• 1.  
  NGC 5506, Sy 1.9, E_cut > 424 keV (pexrav, this work, hereafter the same for the rest 9 sources). Consistently, Matt et al. (2015) reported an E_cut = ${720}_{-190}^{+130}$ keV and a 3σ lower limit of 350 keV, Sun et al. (2018) reported an E_cut = ${500}_{-240}^{+100}$ keV, and Panagiotou & Walter (2020) reported a 1σ lower limit of 8400 keV. The only exception came from Baloković et al. (2020), who reported an E_cut = 110 ± 10 keV with contemporaneous Swift/BAT data. Baloković et al. (2020) claimed in their appendix that the BAT spectrum shows a much smaller cutoff than the NuSTAR one. E_cut variation and background subtraction may have played a role.
• 2.  
  NGC 1566, Sy 1.5, E_cut > 434 keV. Akylas & Georgantopoulos (2021) reported an E_cut = ${336}_{-140}^{+646}$ keV, while Parker et al. (2019) reported an incompatible result of E_cut = 167 ± 3 keV. A possible reason is that Parker et al. (2019) used quasi-simultaneous XMM-Newton data, which have a photon index Γ_pn ∼ 1.43, quite different from our result (Γ ∼ 1.84). Besides, the reflection fraction R_relxill is ∼0.09, smaller than that in this work (R_relxill ∼0.25). The data are actually barely simultaneous, considering a start time offset of ∼10 ks and the fact that NuSTAR exposure is 57 ks while PN exposure is 100 ks. Meanwhile, the inter-instrument calibration issue and the pileup effect in PN data may also have played a part here.
• 3.  
  NGC 5273, Sy 1.5, E_cut > 467 keV. Panagiotou & Walter (2020) reported a 1σ lower limit of 1967 keV. Meanwhile, both Panagiotou & Walter (2020) and this work get Γ ∼ 1.9. Pahari et al. (2017) reported an E_cut = ${143}_{-40}^{+96}$ keV and Γ ∼ 1.8. Note Pahari et al. (2017) employed the quasi-simultaneous Swift-XRT data (6.5 ks XRT exposure, while 21 ks of NuSTAR) and adopted a quite complex model, which may explain the discrepancy. Akylas & Georgantopoulos (2021) reported an E_cut =${115}_{-37}^{+95}$ keV, Γ ∼ 1.6, and R_pexmon ∼ 0.74. The reason behind the discrepancy between Akylas & Georgantopoulos (2021) and our result (both fitting only NuSTAR spectra) remains unclear, and we cannot reproduce their result following the same process with the same model as them (the same for NGC 3516 and Ark 120 below).
• 4.  
  NGC 3516, Sy 1.2, E_cut > 476 keV. Panagiotou & Walter (2020) reported a 1σ lower limit of 4940 keV. Akylas & Georgantopoulos (2021) reported an inconsistent E_cut =${89}_{-48}^{+24}$ keV and a R_pexmon ∼ 1.29.
• 5.  
  WKK 1263 (IGR J12415–5750), Sy 1.5, E_cut > 530 keV. Kamraj et al. (2018), Panagiotou & Walter (2020), and Akylas & Georgantopoulos (2021) reported lower limits of 224 keV, 1826 keV, and 282 keV, respectively, and all three works derive Γ ∼ 1.8, similar to our results. Molina et al. (2019) reported an E_cut = ${123}_{-47}^{+54}$ keV, Γ ∼ 1.6, and a similar R_pexrav < 0.23. The involvement of the quasi-simultaneous Swift-XRT data (5.7 ks XRT exposure, while 16 ks of NuSTAR) in Molina et al. (2019) may account for such discrepancy.
• 6.  
  Mrk 279, Sy 1.5, E_cut > 542 keV. Not reported elsewhere.
• 7.  
  MCG-06-30-015, Sy 1.9, E_cut > 707 keV. Panagiotou & Walter (2020) reported a 1σ lower limit of 12000 keV.
• 8.  
  Ark 120, Sy 1, E_cut > 744 keV. Consistently, Panagiotou & Walter (2020) reported a 1σ lower limit of 1631 keV, Hinkle & Mushotzky (2021) reported an E_cut = ${506}_{-200}^{+814}$ keV, Nandi et al. (2021) reported an T_e= ${222}_{-107}^{+105}$ keV, and Marinucci et al. (2019) reported an T_e = ${155}_{-55}^{+350}$ keV. The only statistically inconsistent result comes from Akylas & Georgantopoulos (2021), who reported E_cut = ${233}_{-67}^{+147}$ keV.
• 9.  
  NGC 4593, Sy 1, E_cut > 800 keV. Zhang et al. (2018), Panagiotou & Walter (2020), and Akylas & Georgantopoulos (2021) reported E_cut lower limits of 450 keV, 6972 keV, and 220 keV, respectively. Ursini et al. (2016) reported E_cut = ${470}_{-150}^{+430}$ keV.
• 10.  
  NGC 4051, Sy 1.5, E_cut > 800 keV. Akylas & Georgantopoulos (2021) reported E_cut lower limits of 846 keV.

In general, our large lower limits on E_cut are consistent with most of those from the literature. Discrepancies do exist in some sources, mostly due to the inclusion of the data from other missions in some literature studies. In this work, the E_cut/T_e of the radio-loud and radio-quiet samples are measured with solely NuSTAR spectra, uniformly processed and analyzed. We therefore anticipate the comparison between two samples in this work is unbiased, though the specific measurement of E_cut in individual sources could be altered if including quasi-simultaneous observations or using a more complex model. The spectra and the best-fit data-to-model residuals of these 10 sources (as shown in the Appendix) have been visually examined and no clear systematical residuals could be identified.

The large E_cut lower limits reported in this work, and the generally consistent results from literature studies, appear to contradict our intuition as such large E_cut lower limits are far beyond the NuSTAR spectral coverage (3–78 keV). For instance, the correcting factor of an 800 keV exponential cutoff to a single power law is only ≈e^−0.1 (around 10%) at 78 keV, making the measurements of large E_cut only possible in a few brightest sources with sufficiently high NuSTAR spectral S/N at the high-energy end. However, as García et al. (2015) pointed out, the reflection component, which is sensitive to the spectral shape of the hardest coronal radiation, may assist the measurements of high E_cut with NuSTAR spectra. Based on the relxill model, they showed that E_cut can be constrained to as high as 1 MeV for bright sources. Below we also demonstrate the effect of the reflection component in model pexrav with spectral simulations. Using the NuSTAR spectra of NGC 4051 as input, with E_cut set at 10⁶ keV and other parameters at the best-fit values, we generate artificial spectra assuming different R in pexrav using fakeit. Fitting the artificial spectra following the same process we apply to the real spectra, we successfully constrain the E_cut lower limit to be above 800 keV in 0.2%, 23%, and 40% of the mock spectra, for R = 0, 1, and 2, respectively. This clearly shows that large E_cut can be better constrained in spectra with a stronger reflection component.

We also check other factors that may affect the reliability of the high E_cut lower limits. The NuSTAR images have been visually double-checked and confirmed to be normal. Moreover, using the traditional method of background subtraction instead of employing NUSKYBGD, i.e., extracting the background within a region close to the source, would not alter the main results here.

In Figure 3 we plot E_cut versus the 50–78 keV S/N and E_cut versus the 50–78 keV background fraction for our sample. Although in a considerable fraction (32%) of our sources, their NuSTAR spectra appear background dominated at >50 keV (i.e., with 50–78 keV background fraction >50%), in all but one source is the net 50–78 keV (FPMA) S/N > 3. This indicates our spectral fitting results are unlikely biased by poor spectral quality or high background level at high energies. From Figure 3 we also see that E_cut lower limits increase with 50–78 keV S/N and decrease with 50–78 keV background fraction. In other words, these high E_cut lower limits (>400 keV) can only be obtained at relatively higher 50–78 keV S/N and lower 50–78 keV background fraction. This confirms these high E_cut lower limits are not due to strong background or poor spectral quality at the highest energies.

Zoom In Zoom Out Reset image size

Besides, we note a complex parameter degeneracy may exist between E_cut and other parameters (e.g., Hinkle & Mushotzky 2021). We hence review the fitting results in individual sources using two parameter contours, among which six sources with E_cut lower limits >400 keV but controversial E_cut detections ⁶ reported in the literature are presented in Figure 4. For these six sources, the degeneracies between E_cut, Γ, and R are found to be weak, with a 2σ E_cut lower limit ∼300 keV obtained even using two parameter confidence contours. In addition we also demonstrate how the low E_cut detections reported in the literature (see Section 4.1) deteriorate the spectral fitting in the lower panel for each source of Figure 4. We conclude our results are robust in the sense of fitting statistics. See Sections 4.3 and 4.4 for further discussion on the effect of parameter degeneracy.

Zoom In Zoom Out Reset image size

Finally, the three models we adopted in this work ensure the main results are model independent. As shown in Table 2, the E_cut measurements of pexrav generally agree with those of relxill, particularly for those sources with large E_cut lower limits. As for the Comptonization model, T_e is often harder to constrain (more lower limits, fewer detections) than the E_cut, and the lower limits to T_e are smaller than 1/3 E_cut (Petrucci et al. 2001) in some sources. This is likely because the e-folded power law produces a smoother break (thus extending to a lower energy range and could be better constrained in the case of large T_e/E_cut) than Comptonization models (Zdziarski et al. 2003; Fabian et al. 2015). However, the overall results from the three models are accordant, i.e., sources with extremely large E_cut lower limits do have relatively high T_e, especially compared with radio-loud sources (see next section). We hence rule out the possibility that the large E_cut/T_e lower limits we obtained are due to unknown faults of certain models.

We have shown that our radio-quiet sample has a considerably larger mean T_e/E_cut compared with the radio-loud one. To explore the statistical reliability of the difference, we need to explore various biases behind the E_cut measurements which might be significant here. The first is the complex degeneracies between the spectral parameters; although we have shown above an example that the degeneracies appear weak in individual sources, we need to quantitatively explore whether such effects could be responsible for the different E_cut between two samples. The second fact is the radio-loud sample is known to have prominently flatter spectra and weaker reflection component than the radio-quiet one (see Figure 6), while flatter spectra imply relatively more photons at the high-energy end, facilitating the E_cut measurement, the weaker reflection could, in contrast, make it hard to constrain high E_cut. The measurements of E_cut also rely on the spectral S/N as shown in Figure 1, the effect of which could vary from source to source. Lastly, but might be most important, the Kaplan–Meier estimator itself can be sensitive to the size of the sample, the fraction of the censored data (lower limits), and the extremely large lower limits. As shown in Figure 1 and especially in the right panel of Figure 2, the mean values, even calculated in the logarithm space, are severely biased toward those large lower limits. ⁷

To address the overall complicated biases, we employ fakeit within XSPEC to create simulated spectra for each source using the best-fit results from pexrav ⁸ but manually assigning a set of E_cut as input. We repeat the spectral fitting to the mock spectra and then the measurement of mean E_cut for the mock samples with the Kaplan–Meier estimator to examine whether our overall procedures could well recover the input E_cut or produce artificially different mean E_cut between two samples. As shown in Figure 5, while the simulations could recover the input E_cut in case of low E_cut values, high input E_cut values (400 keV and above) are clearly underestimated because of the limited bandwidth of NuSTAR and because we have manually fixed the larger E_cut lower limit to 800 keV. Because a considerable fraction of radio-quiet sources have rather large intrinsic E_cut while none of the radio-loud sources do, this indicates we may have underestimated the mean E_cut for our real radio-quiet sample, further strengthening the difference between the two samples we have observed. However, no statistical difference is found between the mock radio-loud and radio-quiet samples. We therefore conclude the biases aforementioned put together are unable to account for the difference in the E_cut distribution between the two samples.

Zoom In Zoom Out Reset image size

The larger average E_cut in radio-quiet sources is however surprising, as we would anticipate a larger observed E_cut in the radio-loud sample due to potential jet contamination (Madsen et al. 2015b) or the stronger Doppler boosting of an outflowing corona in radio AGNs (e.g., Beloborodov 1999; Liu et al. 2014; Kang et al. 2020), even if two populations have the same intrinsic coronal temperature. ⁹ The key underlying reason might be the different Γ distributions of the two samples. In Figure 6 we plot E_cut versus Γ and the reflection strength R from pexrav for the two samples. We find that E_cut is positively correlated with Γ and those large E_cut lower limits are mainly detected in sources with steep spectra. Besides, we find no difference in E_cut between two populations at comparable Γ. Therefore, the difference in E_cut between two populations could dominantly be attributed to the fact that E_cut correlates with the photon index Γ while the radio-loud sample is dominated by sources with flat spectra. Meanwhile, E_cut exhibits no clear correlation with R, while radio-quiet AGNs do show larger E_cut compared with radio-loud ones at a given R, which could be attributed to the effect of Γ. We note that Kang et al. (2020) found the E_cut distribution of their radio-loud sample is indistinguishable from that of a radio-quiet sample from Rani et al. (2019). This is likely because the sample of Rani et al. (2019) is incomplete, as they only collected from literature sources with well-constrained E_cut and most lower limits were excluded. In fact, if we drop lower limits from our samples in this work, we would find no difference either in mean E_cut between the two populations. Meanwhile, Gilli et al. (2007) has shown an average E_cut of above 300 keV can saturate the X-ray background at 100 keV. The fact that large E_cut mainly exists in steeper spectra also renders our large mean value of E_cut in radio-quiet AGNs compatible with that of Gilli et al. (2007), as sources with steep X-ray spectra make little contribution to the high-energy X-ray background even with a large E_cut.

Zoom In Zoom Out Reset image size

A tentative positive correlation between E_cut and Γ has been reported in other studies with NuSTAR (e.g., Kamraj et al. 2018; Molina et al. 2019; Hinkle & Mushotzky 2021) and previously with BeppoSAX data (e.g., Petrucci et al. 2001); however, it was not as pronounced as we have found, likely because of smaller sample size or the domination by poorly constrained lower limits. For instance, the sample in Kamraj et al. (2018) consists of 46 sources, whereas E_cut can be well constrained in only two of them. The samples in Molina et al. (2019) and Hinkle & Mushotzky (2021) consist of 18 and 33 sources, respectively, considerably smaller than the one presented in this work; meanwhile, the inclusion of XRT and XMM-Newton data in those two works may have disturbed the measurements of E_cut and Γ as already discussed above.

The tentative E_cut–Γ correlation reported in the literature had often been attributed to the parameter degeneracy between E_cut and Γ. In this work, the correlation between E_cut and Γ is rather strong, and Γ is well constrained, thanks to the high-quality NuSTAR spectra. We thus expect the effect of such degeneracy to be insignificant. We perform simulations to quantify such an effect in our sample. Utilizing E_cut = 400 keV as input and other best-fit spectral parameters from pexrav, we simulate mock spectra for each source. We then examine the correlation between the output E_cut and output Γ for the mock sample. As shown in Figure 6, while the parameter degeneracy does yield a weak artificial correlation between the output E_cut and Γ, it is much weaker and negligible compared with the observed one.

The positive correlation between E_cut and Γ found in this work indicates sources with steeper X-ray spectra tend to hold hotter coronae. Subsequently, to produce the steeper spectra, the hotter coronae need to have lower opacity. The negative link between coronal temperature and opacity could partly be attributed to the fact that the cooling is more efficient in coronae with higher opacity, i.e., sustainable hotter coronae are only possible with lower opacity. However, while lower opacity could lead to steeper spectra, higher temperature alters the spectral slope toward the opposite direction. While it is yet unclear what drives the positive E_cut–Γ correlation reported in this work, it is intriguing to compare it with how E_cut varies with Γ in individual AGNs. E_cut variabilities detected in several individual AGNs show a common trend that when an individual source brightens in X-ray flux, its power-law spectrum gets softer and E_cut increases, also revealing a positive E_cut–Γ correlation (hotter when softer/brighter; e.g., Zhang et al. 2018; Kang et al. 2021). However, the similarity between the two types of positive E_cut–Γ correlation (intrinsic: in individual AGNs, versus global: in a large sample of AGNs) does not necessarily imply common underlying mechanisms. This is because, while the intrinsic E_cut–Γ correlation, which could be accompanied with dynamical/geometrical changes of the coronae such as inflation/contraction (Wu et al. 2020), reflects variations in the innermost region of individual AGNs, the global E_cut–Γ correlation we find in a sample of AGNs shall mainly reflect the differences in their physical properties, including SMBH mass, accretion rate, and other unknown parameters. Kang et al. (2021) also found a tentative trend that E_cut reversely decreases with Γ at Γ > 2.05 in one individual source, yielding a Λ shape in the E_cut–Γ diagram. Such trend however is not seen in the global E_cut–Γ relation.

The positive global E_cut–Γ correlation also implies a potential positive correlation between E_cut and Eddington ratio λ_edd, as sources with a higher accretion rate tend to have steeper spectra (e.g., Shemmer et al. 2006; Risaliti et al. 2009; Yang et al. 2015). However, we find no significant correlation between λ_edd and Γ, or between λ_edd and E_cut in our sample (see Figure 7), consistent with the results of Molina et al. (2019), Hinkle & Mushotzky (2021), and Kamraj et al. (2022). This is likely because the uncertainties in the measurements of λ_edd are large, or the E_cut–Γ correlation we find is not driven by the Eddington ratio. However, our results disagree with those of Ricci et al. (2018), who claimed a negative correlation between E_cut and λ_edd based on SWIFT BAT spectra. Note, however, that a dominant fraction (144 out of 212) of the E_cut measurements reported in Ricci et al. (2018) are lower limits. ¹⁰

Zoom In Zoom Out Reset image size

We note a couple of individual local sources with high Eddington ratios (>1) have been reported with NuSTAR spectra to have low E_cut/T_e in the literature (e.g., Ark 564 and IRAS 04416+1215; Kara et al. 2017; Tortosa et al. 2022), seeming to suggest lower coronal temperatures at higher Eddington ratio. While the NuSTAR spectral quality of Ark 564 is rather high (10–78 keV FPMA S/N = 88), it is not in the 105 month SWIFT/BAT catalog, and thus not included in this work. The NuSTAR spectral quality of IRAS 04416+1215 (with a 10–78 keV S/N of 10) is much poorer compared with the sample presented in this work, and our independent fitting to its NuSTAR spectra alone could only yield poorly constrained lower limits to its E_cut or T_e. Utilizing XMM-Newton and NuSTAR data, low E_cut/T_e is also detected in a high-redshift source with Eddington ratio >1 (PG 1247+267; Lanzuisi et al. 2016). However, its NuSTAR spectra also have poor S/N (∼20 in the rest frame 10–78 keV). Meanwhile, simply collecting positive detections of E_cut/T_e from the literature could lead to significant publication bias.

We finally plot the samples on the well-known compactness–temperature (l–Θ) diagram. Fabian et al. (2015) has shown that the AGN coronae are located near the boundary of the forbidden region in the l–Θ diagram, suggesting the coronal temperature is governed and limited by runaway pair production. Following Fabian et al. (2015), we calculate the compactness, l = 4π(m_p /m_e )(r_g /r)(L/L_edd), and dimensionless temperature, Θ = kT_e /m_e c². We assume r = 10r_g , adopt the unabsorbed 0.1–200 keV primary continuum luminosity extrapolated by the best-fit pexrav model to NuSTAR spectra (listed in Table 1), and calculate L_edd using the SMBH mass in Table 1. ¹¹ For pexrav and relxill, the T_e is approximated by E_cut/3 (Petrucci et al. 2001), while for relxillcp the measured T_e is directly used. The l–Θ diagrams of the three models are shown in Figure 8, with the boundaries of runaway pair production of the three geometries (Stern et al. 1995; Svensson 1996) over-plotted. Apparently, the sources in this work have a wider Θ range compared with that of Fabian et al. (2015), likely because of the large sample size of this work. On the one hand, there are many sources lying clearly to the left of the slab pair line, particularly sources in the upper-left corner in the l–Θ diagram. They appear to support the existence of hybrid plasma in the coronae as hybrid plasma would shift the pair line to the left and the shift is more prominent at the top of the line (see Figure 6 in Fabian et al. 2017). On the other hand, both the directly measured and conservatively estimated T_e (1/3 E_cut here, while it is 1/2 in Fabian et al. 2015) of a considerable fraction of sources lie beyond (to the right of) the slab pair line, consistent with Kamraj et al. (2022), favoring the sphere or hemisphere geometry. Considering the E_cut–Γ relation shown above, it is implied that the coronal geometry might be spectral slope dependent, i.e., flatter shape for harder spectra, and rounder for softer spectra. Furthermore, there are several sources with lower limits of Θ lying even beyond the boundaries of all three geometries, which suggest their coronae could be more extended than the 10 r_g we have assumed.

Zoom In Zoom Out Reset image size