Distinct High Energy Cutoff Variation Patterns in Two Seyfert Galaxies
MMNRAS , 1–8 (2020) Preprint 6 January 2021 Compiled using MNRAS L A TEX style file v3.0
Distinct High Energy Cutoff Variation Patterns in Two Seyfert Galaxies
Jia-Lai Kang, , ★ Jun-Xian Wang, , † Wen-Yong Kang , CAS Key Laboratory for Research in Galaxies and Cosmology, Department of Astronomy, University of Science and Technology of China, Hefei, Anhui 230026, China School of Astronomy and Space Science, University of Science and Technology of China, Hefei 230026, China
Accepted 2021 January 4. Received 2020 December 22; in original form 2020 September 29
ABSTRACT
Investigating how the cutoff energy 𝐸 cut varies with X-ray flux and photon index Γ in individual AGNs opens a new windowto probe the yet unclear coronal physics. So far 𝐸 cut variations have only been detected in several AGNs but different patternshave been reported. Here we report new detections of 𝐸 cut variations in two Seyfert galaxies with multiple NuSTAR exposures.While in NGC 3227 𝐸 cut monotonically increases with Γ , the 𝐸 cut – Γ relation exhibits a Λ shape in SWIFT J2127.4+5654 ( 𝐸 cut increasing with Γ at Γ (cid:46) Γ (cid:38) 𝐸 cut variations ever reported with NuSTAR observations in the 𝐸 cut – Γ diagram, we find they could beunified with the Λ pattern. Although the sample is small and SWIFT J2127.4+5654 is the only source with Γ varying across thebreak point thus the only one exhibiting the complete Λ pattern in a single source, the discoveries shed new light on the coronalphysics in AGNs. Possible underlying physical mechanisms are discussed. Key words:
Galaxies: active – Galaxies: nuclei – X-rays: galaxies
In the standard disc-corona paradigm the hard X-ray emission ofactive galactic nuclei (AGNs) is produced in a hot and compactregion, the so called corona (e.g. Haardt & Maraschi 1991; Haardtet al. 1994), through the inverse Compton scattering of the seedphotons from the accretion disk. This process could produce theobserved power law continuum with a high-energy cutoff. Such acutoff has been detected in a number of AGNs (Zdziarski et al.2000; Molina et al. 2013), particularly with the high-quality hardX-ray spectra of NuSTAR (e.g., Matt et al. 2015; Tortosa et al. 2018;Molina et al. 2019; Kang et al. 2020), providing key constraints onthe yet unclear coronal physics (e.g. Fabian et al. 2015).The Nuclear Spectroscopic Telescope Array (NuSTAR Harrisonet al. 2013) also enables the detection of 𝐸 cut (or coronal temperature 𝑇 𝑒 ) variations in individual AGNs with multiple exposures, includ-ing 3C 382 (Ballantyne et al. 2014), NGC 5548 (Ursini et al. 2015),Mrk 335 (Keek & Ballantyne 2016), NGC 4593 (Ursini et al. 2016;Middei et al. 2019a), MCG–5–23–16 (Zoghbi et al. 2017), and 4C74.26 (Zhang et al. 2018). Zhang et al. (2018) also revisited the firstfive sources mentioned above using the spectra ratio technique theydeveloped. They confirmed the claimed 𝐸 cut variations in 3 of them,but disproved those in NGC 4593 and MCG–5–23–16. Despite thelimited number of sources, these studies have opened a new win-dow to probe the coronal physics. Remarkably, Zhang et al. (2018)found that all the 4 AGNs with 𝐸 cut variations confirmed tend tohave larger 𝐸 cut (thus hotter corona) when they brighten and softenin X-ray. In other words, they show a “hotter-when-brighter” behav- ★ [email protected] † [email protected] ior along with the conventional “softer-when-brighter” pattern (e.g.,Markowitz et al. 2003; Sobolewska & Papadakis 2009). Possible un-derlying mechanisms have been discussed in Zhang et al. (2018) andWu et al. (2020), including geometrical changes of the corona andpair production. Do Seyfert galaxies universally follow this “hotter-when-softer/brighter” pattern? A possible counter-example is thenarrow line Seyfert 1 galaxy (NLS1) Ark 564, for which Barua et al.(2020) found cooler corona (though statistically marginal) during thesofter and brighter phases within a 200 ks NuSTAR observation.In this letter we report new detections of 𝐸 cut variations in twoSeyfert galaxies, NGC 3227 and SWIFT J2127.4+5654, and a Λ shaped 𝐸 cut – Γ relation for the first time. §2 presents the NuSTAR ob-servations and data reduction. In §3 we describe the spectral modelsand deliver the fitting results. In §4 we discuss the spectral variabil-ities and the underlying mechanisms for AGNs with reported 𝐸 cut variations. NGC 3227 is a radio-quiet Seyfert 1.5 galaxy (Véron-Cetty & Véron2006) at z = 0.0039 . In Tab. 1 we list the seven archival NuS-TAR observations of NGC 3227. NGC 3227 shows highly variableX-ray emission and its absorption feature have been extensively in-vestigated in literature. As an example, based on the NuSTAR andXMM-Newton observations, Turner et al. (2018) found a rapid oc-cultation event in NGC 3227 between two exposures of NuSTAR(60202002010 and 60202002012), with several absorber zones in- The radio types and the redshifts are from NED: http://ned.ipac.caltech.edu © a r X i v : . [ a s t r o - ph . H E ] J a n Jia-Lai Kang et al.
Figure 1.
NuSTAR light curves (with a bin size of 4 ks) in 3 – 10 keV, 10 – 78 keV bands and the 10 – 78 keV / 3 – 10 keV hardness ratios. The observations,sorted and numbered by observation date (see Tab. 2), are color coded. The vertical dashed lines mark the positions where the x-axis is discontinuous becauseof long intervals between exposures.
Figure 2.
The 10 – 78 keV / 3 – 10 keV hardness ratio versus 3 – 78 keV count rate. The black lines show simple linear fits to the data points. The observationsare color coded as in Fig. 1.MNRAS , 1–8 (2020) he High Energy Cutoff Variations L3 Table 1.
NuSTAR Observation Logs.
Source ID and No. Obs. time Exposure Flux − (ks) ( − 𝑒𝑟𝑔 / 𝑐𝑚 / 𝑠 ) NGC 3227 60202002002 (1) 2016–11–09 49.8 1.2660202002004 (2) 2016–11–25 42.5 1.0560202002006 (3) 2016–11–29 39.7 1.1660202002008 (4) 2016–12–01 41.8 1.3760202002010 (5) 2016–12–05 40.9 1.3860202002012 (6) 2016–12–09 39.3 1.3560202002014 (7) 2017–01–21 47.6 1.8SWIFT J2127.4+5654 60001110002 (1) 2012–11–04 49.2 0.5860001110003 (2) 2012–11–05 28.8 0.7160001110005 (3) 2012–11–06 74.6 0.7760001110007 (4) 2012–11–08 42.1 0.8260402008004 (5) 2018–07–16 71.6 0.8360402008006 (6) 2018–07–30 72.1 0.8560402008008 (7) 2018–09–14 72.9 0.6660402008010 (8) 2018–12–30 74.2 0.76 ★ : For convenience, the observations for each source were sorted and numbered (in parenthesis) bytime. volved. However, as further shown in §3, our study on the high-energycutoff in this work is barely influenced by these complex absorbers.Meanwhile, SWIFT J2127.4+5654, a radio-quiet NLS1 (Mal-izia et al. 2008) at z = 0.0144, has been observed by NuSTAR intwo campaigns, with four exposures in 2012 and five in 2018. Wedropped the observation 60402008002 (not listed in Tab. 1) of SWIFTJ2127.4+5654, which has an issue flag = 1, indicating possible con-tamination from solar activity or other unexpected issues. Marinucciet al. (2014) performed a joint spectral fitting of the four 2012 obser-vations with (quasi-)simultaneous XMM-Newton data and an aver-age 𝐸 cut = 108 + − keV was reported. Besides, using XMM-Newtondata only, Sanfrutos et al. (2013) reported a partial covering absorberin SWIFT J2127.4+5654 with 𝑁 H = × 𝑐𝑚 − and a coveringfraction ∼ nupipeline . We first extract thelight curves using nuproducts , adopting a circular source region witha radius of 60 (cid:48)(cid:48) centered on each source, and an annulus from 120 (cid:48)(cid:48) to 200 (cid:48)(cid:48) for background extraction. The light curves from FPMA andFPMB, with the livetime, PSF/EXPOSURE and vignetting correc-tions applied, are then combined using lcmath . The 3 – 10 keV and10 – 78 keV light curves, along with the 10 – 78 keV/ 3 – 10 keVhardness ratios, are plotted in Fig. 1. Both sources show clear varia-tions in flux (count rate) and spectra shape (hardness ratio), not onlybetween but also within the individual exposures. In the plot of hard-ness ratio (HR) versus count rate (Fig. 2) both sources clearly exhibitthe “softer-when-brighter” pattern. However different individual ex-posures appear to follow different “softer-when-brighter” tracks. Forinstance, Obs. ID 60202002014 (No. 7) of NGC 3227 clearly deviatefrom other exposures in Fig. 2. See also exposures No. 1 and No. 2,No. 5 and No. 6 of SWIFT J2127.4+5654. Such variations could bedue to the physical or structural changes in the corona which may leadto different “softer-when-brighter" tracks (e.g., Sarma et al. 2015),stopping us from merging data from different exposures accordingto the count rate or hardness ratio. In this work we focus on the anal-yses of spectra integrated over individual exposures and investigatethe 𝐸 cut variations between these exposures. Though rapid hardnessratio variations within individual exposures are seen, due to limitedphoton counts we are yet unable to explore more rapid 𝐸 cut variationsin two sources. Source spectra are extracted from the same circular regions as thelight curves, using the nuproducts . As for background extraction,we use NUSKYBGD developed by Wik et al. (2014) to handle thespatially variable background of NuSTAR observations (see alsoKang et al. 2020, for an example). NuSTAR observations generallydo not suffer from pile-up . Meanwhile, we find the low-energyeffective area issue for FPMA (Madsen et al. 2020) to be insignificantin all the observations and no low energy excess in FPMA spectra isfound (see Fig. A1). As a final step, the source spectra are rebinnedto achieve a minimum of 50 counts bin − using grppha .We notice there are (quasi-)simultaneous XMM-Newton obser-vations for both sources (six of NGC 3227 and three of SWIFTJ2127.4+5654). However, we find slightly different photon indicesbetween most XMM-Newton and NuSTAR exposures for bothsources. Such discrepancy, likely due to the inter-instrument cali-bration, is widely found in literature (e.g. Cappi et al. 2016; Pontiet al. 2018; Middei et al. 2019b). Additionally, the fact that XMM-Newton and NuSTAR exposures are not perfectly simultaneous mayalso have played a role due to the intrinsic spectral variation. How-ever requiring perfect simultaneity would yield significant loss of thevaluable NuSTAR exposure time. Since 𝐸 cut measurement is sensi-tive to the photon index (e.g., Molina et al. 2019; Kang et al. 2020)and not all NuSTAR exposures have corresponding XMM-Newtonobservations, in this work we do not include those XMM-Newtonexposures but provide uniform spectral fitting to NuSTAR spectraalone. Zhang et al. (2018) developed the spectral ratio technique, analo-gous to the difference-imaging technique in astronomy, to assist thestudy of 𝐸 cut variations. Briefly, if the 𝐸 cut is invariable within twoobservations, the ratio of two spectra (primarily exponentially cutoffpower law) is supposed to be a straight line in log-log space in thespectra ratio plot. So we can notice potential 𝐸 cut variations directlyby looking for deviations from the straight line at the high energyend (see Zhang et al. 2018, for details). We applied this technique toAGNs with multiple archival NuSTAR exposures and took notice ofNGC 3227 and SWIFT J2127.4+5654, of which the spectral ratiosindicate clear and prominent 𝐸 cut variations as shown in Fig. 3. Inthis section, we perform spectral fitting to quantify the 𝐸 cut variationsin both sources.Spectral fitting is performed in the 3–78 keV band within XSPEC(Arnaud 1996), using 𝜒 statistics and the relative element abun-dances given by Anders & Grevesse (1989). All errors along withthe upper/lower limits reported throughout the letter are calculatedusing Δ 𝜒 = 2.71 criterion (90% confidence range). For each obser-vation, the spectra obtained by the two NuSTAR modules (FPMAand FPMB) are fitted simultaneously, with a cross-normalizationdifference typically less than 5% (Madsen et al. 2015).We employ pexrav (Magdziarz & Zdziarski 1995) to describethe exponentially cutoff power law plus the reflection component.For simplicity, the solar element abundance for the reflector and aninclination of 𝑐𝑜𝑠𝑖 = .
45 are adopted (as default of this model) . https://heasarc.gsfc.nasa.gov/docs/nustar/nustar_faq.html These two parameters are poorly constrained with NuSTAR spectra ifallowed free to vary, thus are commonly fixed at the default values in manystudies on NuSTAR spectra (e.g. Zhang et al. 2018; Molina et al. 2019;Panagiotou & Walter 2020).Through joint fitting XMM-Newton and NuSTARspectra of SWIFT J2127.4+5654, Marinucci et al. (2014) reported an ironMNRAS000
45 are adopted (as default of this model) . https://heasarc.gsfc.nasa.gov/docs/nustar/nustar_faq.html These two parameters are poorly constrained with NuSTAR spectra ifallowed free to vary, thus are commonly fixed at the default values in manystudies on NuSTAR spectra (e.g. Zhang et al. 2018; Molina et al. 2019;Panagiotou & Walter 2020).Through joint fitting XMM-Newton and NuSTARspectra of SWIFT J2127.4+5654, Marinucci et al. (2014) reported an ironMNRAS000 , 1–8 (2020) Jia-Lai Kang et al.
Table 2.
Spectral Fitting Results.
ID and No. N H Γ 𝑅 EW 𝐸 pexrav 𝜒 𝜈 (pexrav) 𝐸 pexriv 𝜒 𝜈 (pexriv) 𝐸 relxill 𝜒 𝜈 (relxill) 𝑘𝑇 xillverCp 𝜒 𝜈 (xillverCp) 𝑘𝑇 relxillCp 𝜒 𝜈 (relxillCp)( 𝑐𝑚 − ) (eV) (keV) (keV) (keV) (keV) (keV)NGC 322760202002002 (1) . + . − . . + . − . . + . − . + − + − + − + − + − + − . + . − . . + . − . . + . − . + − ★ + − + − + − + − + − . + . − . . + . − . . + . − . + − > > + − > > . + . − . . + . − . . + . − . + − > > > > > . + . − . . + . − . . + . − . + − > > > > > . + . − . . + . − . . + . − . + − > > > > > . + . − . . + . − . . + . − . + − + − > + − > > < . . + . − . . + . − . + − ★ + − + − + − + − + − . + . − . . + . − . . + . − . + − + − + − + − + − + − . + . − . . + . − . . + . − . + − + − + − + − + − + − . + . − . . + . − . . + . − . + − + − + − + − + − + − . + . − . . + . − . . + . − . + − + − + − + − + − + − . + . − . . + . − . . + . − . + − ★ + − + − + − + − + − . + . − . . + . − . . + . − . + − ★ + − + − + − + − + − . + . − . . + . − . . + . − . + − + − + − + − + − + − ★ : In some observations a broad Fe K 𝛼 line is statistically needed, with the corresponding EW marked with ★ . NGC 3227: 60202002004, 𝜎 = . + . − . keV. SWIFT J2127.4+5654: 60001110002, 𝜎 = . + . − . keV; 60402008006, 𝜎 = . + . − . keV; 60402008008, 𝜎 = . + . − . keV. no r m li s e d c oun t s s k e V Energy ( keV ) S p ec t r a l r a ti o modeldata no r m li s e d c oun t s s k e V Energy ( keV ) S p ec t r a l r a ti o modeldata Figure 3.
The rebinned FPMA spectra and spectral ratio (always the ratio of a brighter spectrum to a fainter one) of NGC 3227 (the left panel) and SWIFTJ2127.4+5654 (the middle and right panels). Following Zhang et al. (2018), we adopt a single power law to fit each spectrum and derive the correspondingunfolded spectra for the calculation of spectra ratio. As approved in Zhang et al. (2018), the spectra ratio plot is insensitive to the adopted spectral model, exceptfor in the spectral range of Fe K 𝛼 line (which is dropped from the plot). For NGC 3227 we plot the ratio of the two observations showing the most prominent 𝐸 cut variation. The upward curvature in the lower left panel (deviation from a straight line at high energies) demonstrates clear “hotter-when-brighter” pattern inNGC 3227. For SWIFT J2127.4+5654 we plot the ratios of two observation pairs, showing both “cooler-when-brighter” (the downward high energy curvaturein the lower middle panel) and “hotter-when-brighter” (the lower right panel) patterns. In the lower panels , the ratios of best-fit models presented in this workare over-plotted, illustrating the 𝐸 cut variations have been properly accounted in the spectral models. We let the photon index Γ , 𝐸 cut and the reflection fraction 𝑅 free tovary. In addition, zphabs is used to model the intrinsic absorption, abundance A Fe of 0.71 and an inclination angle of 49 ◦ , slightly differentfrom the default values we adopted. Generally, larger A Fe (inclination angle)would yield slightly higher (higher) reflection fraction R, smaller (larger)photon index Γ and lower (higher) cutoff energy 𝐸 cut . However adoptingdifferent values of A Fe or inclination angle would not alter the main resultsof this work. with the Galactic absorption ignored due to its negligible impact onNuSTAR spectra. Replacing the 𝑧𝑝ℎ𝑎𝑏𝑠 component with 𝑧𝑥𝑖𝑝𝑐 𝑓 toaccount for the partial covering reported in both sources (Turner et al.2018; Sanfrutos et al. 2013) does not affect our 𝐸 cut measurements,as such absorbers have negligible influence on NuSTAR spectra.As for the Fe K emission lines, several lines have been previouslyfound in both sources with XMM-Newton spectra (e.g. Markowitzet al. 2009; Marinucci et al. 2014), whereas some of them are insignif-icant in NuSTAR spectra, likely due to the limited spectral resolution MNRAS , 1–8 (2020) he High Energy Cutoff Variations L5 ( ∼ zgauss component at 6.4 keV (rest frame)with its width fixed at 19 eV (the mean Fe K 𝛼 line width in AGNsmeasured with Chandra HETG, Shu et al. 2010) to describe a neutraland narrow Fe K 𝛼 line. Since the Fe K 𝛼 line could be relativisticallybroadened, we allow the width to vary freely. If a free width can sig-nificantly improve the fit ( Δ 𝜒 > 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 × 𝑧𝑝ℎ𝑎𝑏𝑠 × ( 𝑝𝑒𝑥𝑟𝑎𝑣 + 𝑧𝑔𝑎𝑢𝑠𝑠 ) .The spectra and the best-fit models are shown in Fig. A1.Besides, we adopt different models to check the results. Firstly wereplace the 𝑝𝑒𝑥𝑟𝑎𝑣 component with 𝑝𝑒𝑥𝑟𝑖𝑣 (Magdziarz & Zdziarski1995) to take account of potential ionized reflection. As shown inTab. 2, the results of the two models ( 𝑝𝑒𝑥𝑟𝑎𝑣 and 𝑝𝑒𝑥𝑟𝑖𝑣 ) are veryclose. Furthermore, we employ relxill (Dauser et al. 2010; Garcíaet al. 2014) which models the spectra with a cutoff power law andrelativistic ionized reflection from the accretion disc. For SWIFTJ2127.4+5654 we fix its spin 𝑎 = .
58 referring to Marinucci et al.(2014), while for NGC 3227 𝑎 is tied among the observations dur-ing fitting, with 𝑙𝑜𝑔𝜉 and 𝐴 Fe tied among observations for bothsources. In this way, we derive 𝑎 = − . + . − . , 𝑙𝑜𝑔𝜉 = . + . − . and 𝐴 Fe = . + . − . for NGC 3227, and 𝑙𝑜𝑔𝜉 = . + . − . , 𝐴 Fe = . + . − . for SWIFT J2127.4+5654. We let photon index Γ , reflection fraction and 𝐸 cut vary freely, and set other parametersincluding inclination and disk radii as default. As shown in Tab.2, while the 𝐸 cut results from two models are generally consistentwithin statistical uncertainties, the relxill model yields systematicallysmaller 𝐸 cut for NGC 3227 and larger 𝐸 cut for SWIFT J2127.4+5654compared with the 𝑝𝑒𝑥𝑟𝑎𝑣 model. Nevertheless, the yielded 𝐸 cut variation trends from two models, as the focus of this work, aresimilar. Moreover, we adopt comptonized models 𝑥𝑖𝑙𝑙𝑣𝑒𝑟𝐶 𝑝 and 𝑟𝑒𝑙𝑥𝑖𝑙𝑙𝐶 𝑝 (Dauser et al. 2010; García et al. 2014, for the normaland relativistic reflection components respectively) to directly mea-sure the coronal temperature 𝑇 e . The derived coronal temperatures 𝑘𝑇 relxillCp and 𝑘𝑇 xillverCp (see Tab. 2) for SWIFT J2127.4+5654 aregenerally consistent with 1/3 of the measured 𝐸 pexrav (e.g. Petrucciet al. 2001), but systematically smaller than 1/3 of the best-fit 𝐸 pexrav for NGC 3227.From Tab. 2 we can see that 𝑝𝑒𝑥𝑟𝑎𝑣 and 𝑝𝑒𝑥𝑟𝑖𝑣 yield similarlysmaller reduced 𝜒 compared with other models, while 𝑝𝑒𝑥𝑟𝑖𝑣 hasone more free parameter than 𝑝𝑒𝑥𝑟𝑎𝑣 . As 𝑝𝑒𝑥𝑟𝑎𝑣 is widely adoptedin literature to measure 𝐸 cut in literature (e.g. Zhang et al. 2018;Molina et al. 2019; Panagiotou & Walter 2020), to directly comparewith those studies, hereafter we simply adopt the best-fit resultsfrom 𝑝𝑒𝑥𝑟𝑎𝑣 . Utilizing results from the other models however wouldnot alter the conclusions of this work. Further note that in 𝑟𝑒𝑙𝑥𝑖𝑙𝑙 , 𝑟𝑒𝑙𝑥𝑖𝑙𝑙𝐶 𝑝 and 𝑥𝑖𝑙𝑙𝑣𝑒𝑟𝐶 𝑝 , the reflection component and the Fe linesare coupled under certain assumptions, which may bias the 𝐸 cut (or 𝑇 e ) measurements in some sources (e.g., Zhang et al. 2018; Kanget al. 2020).We plot the 𝐸 cut vs. Γ contours in Fig. 4 to illustrate the 𝐸 cut variation patterns in two sources. A clear positive correlation between 𝐸 cut and Γ is seen in NGC 3227. However the 𝐸 cut – Γ plot of SWIFTJ2127.4+5654 exhibits a distinct Λ shape: 𝐸 cut increases with Γ at Γ (cid:46) Γ (cid:38) 𝐸 cut and Γ , the rising part of the Λ shape is lesssignificant comparing with the declining part, the overall variationtrend in SWIFT J2127.4+5654 clearly deviates from a monotonousfunction. Meanwhile, the common “softer-when-brighter” trend inSeyfert galaxies is clear in both sources (Fig. 4). To quantifying the significance of the Λ shape, we perform Spear-man rank-order correlation analyses on the rising (obs. No. 1, 2, 3,4, 7) and descending (obs. No. 2, 3, 5, 6, 8) branches of the Λ shape.We find a positive correlation between 𝐸 cut and Γ ( 𝜌 = .
87 witha p-value = 0.054) for the rising branch, and a negative correlationfor the descending branch (a 𝜌 = − .
90 with a p-value = 0.037).We also perform linear regression to measure the slopes of the twobranches of the Λ shape ( 𝛽 =
220 for the left and 𝛽 = −
240 for theright). However, the Spearman’s correlation could be unreliable whenthe sample size is small (e.g., n < 10), and random fluctuation canproduce strong correlation/anti-correlation in small samples. Mean-while, the measurement errors and the degeneracy of the parametersshould also be taken into account. We perform simulations to addressthese issues. Assuming there is no intrinsic 𝐸 cut variation in SWIFTJ2127.4+5654, we jointly fit all eight observations and derive a 𝐸 cut of 80 keV. Starting from 𝐸 cut = 80 keV and other best-fit spectral pa-rameters (derived with 𝐸 cut tied) for each observation, we create oneartificial spectrum for each exposure using 𝑓 𝑎𝑘𝑒𝑖𝑡 . We then performspectral fitting to those faked spectra to measure the simulated 𝐸 cut and Γ and perform Spearman rank and linear regression analyses.We repeat the process 1000 times, and find only 26 runs out of themshow stronger Spearman’s correlation and steeper linear regressionslope (compared with the observed values) for the left side of the Λ shape, while only 2 runs out of 1000 for the right one. This indicatethe rising and descending of the Λ pattern have statistical confidencelevel of 97.4% and 99.8% respectively, showing statistical fluctua-tions of the parameters and the degeneracy between Γ and 𝐸 cut areunlikely able to reproduce the observed Λ pattern. In Fig. 5 we plot 𝐸 cut – Γ for both our sources together with thoseintroduced in §1. For Ark 564 we convert the corona temperature 𝑘𝑇 e given by Barua et al. (2020) into 𝐸 cut , assuming an opticallythick corona and 𝑘𝑇 𝑒 ∼ 𝐸 cut / 𝐸 cut – Γ variation patterns. Interestingly, it appears that allseven sources could be unified with the Λ shaped pattern seen inSWIFT J2127.4+5654, e.g., “hotter-when-softer/brighter” at Γ (cid:46) Γ (cid:38) Γ varying across the breakpoint, thus the only one showing the complete Λ pattern in a singlesource.The common “softer-when-brighter” trend in Seyfert galaxieswas generally attributed to presumbly cooler corona during brighterphases due to more effective cooling by more seed photons. How-ever, such scenario clearly contradicts the discovery of “hotter-when-brighter” pattern detected in AGNs (e.g. Keek & Ballantyne 2016;Zhang et al. 2018). Geometry changes of the corona are required toreproduce the “softer-when-brighter” trend (e.g. Keek & Ballantyne2016; Zhang et al. 2018; Wu et al. 2020). Specifically, the coronacould be heated to a higher temperature and simultaneously drivento inflate during X-ray brighter phases (Wu et al. 2020), leading toa smaller opacity and thus softer spectra, and reproducing the ob-served “hotter-when-softer/brighter” pattern (the rising part of the Λ pattern). The inflation could be primarily vertical, as there areevidences that suggest the corona is vertically outflowing (e.g. Liuet al. 2014) and the corona could reach higher heights during brighterphases (Wilkins & Gallo 2015; Alston et al. 2020). Note in case of MNRAS000
240 for theright). However, the Spearman’s correlation could be unreliable whenthe sample size is small (e.g., n < 10), and random fluctuation canproduce strong correlation/anti-correlation in small samples. Mean-while, the measurement errors and the degeneracy of the parametersshould also be taken into account. We perform simulations to addressthese issues. Assuming there is no intrinsic 𝐸 cut variation in SWIFTJ2127.4+5654, we jointly fit all eight observations and derive a 𝐸 cut of 80 keV. Starting from 𝐸 cut = 80 keV and other best-fit spectral pa-rameters (derived with 𝐸 cut tied) for each observation, we create oneartificial spectrum for each exposure using 𝑓 𝑎𝑘𝑒𝑖𝑡 . We then performspectral fitting to those faked spectra to measure the simulated 𝐸 cut and Γ and perform Spearman rank and linear regression analyses.We repeat the process 1000 times, and find only 26 runs out of themshow stronger Spearman’s correlation and steeper linear regressionslope (compared with the observed values) for the left side of the Λ shape, while only 2 runs out of 1000 for the right one. This indicatethe rising and descending of the Λ pattern have statistical confidencelevel of 97.4% and 99.8% respectively, showing statistical fluctua-tions of the parameters and the degeneracy between Γ and 𝐸 cut areunlikely able to reproduce the observed Λ pattern. In Fig. 5 we plot 𝐸 cut – Γ for both our sources together with thoseintroduced in §1. For Ark 564 we convert the corona temperature 𝑘𝑇 e given by Barua et al. (2020) into 𝐸 cut , assuming an opticallythick corona and 𝑘𝑇 𝑒 ∼ 𝐸 cut / 𝐸 cut – Γ variation patterns. Interestingly, it appears that allseven sources could be unified with the Λ shaped pattern seen inSWIFT J2127.4+5654, e.g., “hotter-when-softer/brighter” at Γ (cid:46) Γ (cid:38) Γ varying across the breakpoint, thus the only one showing the complete Λ pattern in a singlesource.The common “softer-when-brighter” trend in Seyfert galaxieswas generally attributed to presumbly cooler corona during brighterphases due to more effective cooling by more seed photons. How-ever, such scenario clearly contradicts the discovery of “hotter-when-brighter” pattern detected in AGNs (e.g. Keek & Ballantyne 2016;Zhang et al. 2018). Geometry changes of the corona are required toreproduce the “softer-when-brighter” trend (e.g. Keek & Ballantyne2016; Zhang et al. 2018; Wu et al. 2020). Specifically, the coronacould be heated to a higher temperature and simultaneously drivento inflate during X-ray brighter phases (Wu et al. 2020), leading toa smaller opacity and thus softer spectra, and reproducing the ob-served “hotter-when-softer/brighter” pattern (the rising part of the Λ pattern). The inflation could be primarily vertical, as there areevidences that suggest the corona is vertically outflowing (e.g. Liuet al. 2014) and the corona could reach higher heights during brighterphases (Wilkins & Gallo 2015; Alston et al. 2020). Note in case of MNRAS000 , 1–8 (2020) Jia-Lai Kang et al.
NGC 3227 + + + + + Г E c u t ( k e V ) E c u t ( k e V ) Г SWIFT J2127.4+5654 + + + + + + + + Figure 4.
Contour plots (at 1 𝜎 and 90% confidence levels) of Γ vs. 𝐸 cut ( Γ and 𝐸 pexrav from Tab. 2), and the Γ vs. 3 – 78 keV flux variabilities. The observationsare sorted and numbered by observation date (see Tab. 2). outflowing corona, if the outflowing velocity is higher during X-raybrighter phases, higher 𝐸 cut is also expected due to stronger Dopplershift.As the X-ray flux brightening, spectrum softening and corona infla-tion continue, more seed photons from the disk could be intercepted,leading to higher cooling efficiency. Moreover, the cooling efficiencycould be further boosted if the steeper X-ray spectrum is accompaniedby a stronger soft X-ray excess component from the presumed warmcorona (e.g. Petrucci et al. 2013) which could also contribute as seedphotons. The latter mechanism may be essential, that the Comptoncooling effect begins to dominate beyond a certain Γ , yielding thedeclining part of the Λ pattern (“cooler-when-brighter”). However, asSWIFT J2127.4+5654 is yet the only individual source showing a Λ pattern, it is unclear whether the break point of Γ ∼ Γ for electron temperature 𝑘𝑇 𝑒 < 𝑚 𝑒 𝑐 . Therefore positivecorrelations between X-ray flux and 𝐸 cut and between Γ and 𝐸 cut areexpected in pair-dominated corona.It is known that the NLS1 Ark 564 lies well below the thermal pair-production limit (Kara et al. 2017), meanwhile 3C 382, 4C 74.26,NGC 5548 and Mrk 335 lie close to the limit (e.g. Zhang et al.2018). Following Fabian et al. (2015) we calculate the compactness, 𝑙 = 𝜋 ( 𝑚 𝑝 / 𝑚 𝑒 )( 𝑟 𝑔 / 𝑟 )( 𝐿 / 𝐿 edd ) , and dimensionless temperature, Θ = 𝑘𝑇 𝑒 / 𝑚 𝑒 𝑐 , for the two sources reported in this work, where 𝑘𝑇 𝑒 ≈ 𝐸 cut / . We adopt 𝑟 = 𝑟 𝑔 and the 0.1–200 keV luminosity, 𝑀 = . × 𝑀 (cid:12) for NGC 3227 (Graham 2008), and 𝑀 = . × 𝑀 (cid:12) for SWIFT J2127.4+5654 (Malizia et al. 2008). Comparingthe results with the runaway pair production boundary in Stern et al.(1995), we find while NGC 3227 lies close to or on the boundary, We adopt 𝑘𝑇 𝑒 ≈ 𝐸 cut / 𝑘𝑇 relxillCp or 𝑘𝑇 xillverCp we derived,or assuming 𝑘𝑇 𝑒 ≈ 𝐸 cut / E c u t ( k e V )
3C 3824C 74.26NGC 5548Mrk 335 NGC 3227SWIFT J2127.4+5654Ark 564
Figure 5.
The Γ – 𝐸 cut variation patterns of our two sources and those reportedin literature. To avoid confusion, no error bars or contours are given, and wedrop those exposures in which 𝐸 cut are non-detected. Besides, we droppedthe data of 60002044006, NGC 5548, to avoid the potential photon indexdiscrepancy issue, caused by XMM-Newton data as discussed in §2. A singlebest-fit direct line is over-plotted to demonstrate the overall variation trendof each source, except that for SWIFT J2127.4+5654 we plot two lines toillustrate the Λ shape. The vertical dotted line marks the transition to the left(right) of which 𝐸 cut positively (negatively) correlates with Γ . the NLS1 SWIFT J2127.4+5654 also lie clearly below the boundary(though closer to the boundary compared with Ark 564, Fig. 6).It is remarkable to note that there also likely exists a link be-tween 𝐸 cut variation patterns and pair-dominance: pair-dominatedcoronae (those lying close to or on the pair limit in the 𝑙 – Θ di-agram) only exhibit “hotter-when-softer/brighter” trend, while a“cooler-when-softer/brighter” or Λ shape is only possible in coro-nae which are not pair-dominated. In this case the pair productioncould counter against the higher cooling efficiency of an expandedand less compact corona in many AGNs. Consequently the “cooler-when-softer/brighter” trend or the Λ pattern only exists in sources MNRAS , 1–8 (2020) he High Energy Cutoff Variations L7
3C 3824C 74.26NGC 5548Mrk 335NGC 3227SWIFT J2127.4+5654Ark 564 slabhemispheresphere at 0.5h
Figure 6.
The 𝑙 – Θ diagram of all seven sources. The results of Ark 564in Kara et al. (2017) as well as the four sources in Zhang et al. (2018) aresimply taken and plotted. The maximum temperature that can be reached by aplasma dominated by the runaway pair production for three geometries (Sternet al. 1995) are over-plotted as lines. For the four sources from Zhang et al.(2018) we take the data points from its Fig. 13 (the data point with the higher Θ for each source). For NGC 3227 and SWIFT J2127.4+5654 we plot theobservation with the highest detected 𝐸 cut . For simplicity, no uncertainties to 𝑙 are given. lacking strong pair production, like the NLS1 SWIFT J2127.4+5654and Ark 564. We note that Fabian et al. (2017) proposed that thecoronae lying well below the pair limit (such as in Ark 564) couldalso be pair dominated if containing both thermal and non-thermalparticles. However, if the possible link aforementioned does exist,it suggests the pair production in the cool coronae of Ark 564 andSWIFT J2127.4+5654 is indeed weak.Though the sample discussed above is small, the discoveries pre-sented in this work shed new light on the coronal physics in AGNs.Future observations of 𝐸 cut variations in a larger sample of AGNsare desired to testify the universality of the Λ pattern, confirm thepotential link between 𝐸 cut variation pattern and pair production, andindependently probe the coronal physics. ACKNOWLEDGEMENTS
This research has made use of the NuSTAR Data Analysis Software(NuSTARDAS) jointly developed by the ASI Science Data Center(ASDC, Italy) and the California Institute of Technology (USA). Thework is supported by National Natural Science Foundation of China(grants No. 11421303, 11890693 & 12033006) and CAS FrontierScience Key Research Program (QYZDJ-SSW-SLH006).
DATA AVAILABILITY
The data underlying this article are available in the article and in itsonline supplementary material.
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APPENDIX A: NUSTAR SPECTRA
This paper has been typeset from a TEX/L A TEX file prepared by the author.MNRAS , 1–8 (2020) he High Energy Cutoff Variations L9 −4 −3 no r m a li z ed c oun t s s − k e V − NGC 3227_60202002002
105 20 5011.5 r a t i o Energy (keV) 10 −4 −3 no r m a li z ed c oun t s s − k e V − NGC 3227_60202002004
105 20 5011.52 r a t i o Energy (keV) −4 −3 no r m a li z ed c oun t s s − k e V − NGC 3227_60202002006
105 20 500.811.21.4 r a t i o Energy (keV)10 −4 −3 no r m a li z ed c oun t s s − k e V − NGC 3227_60202002008
105 20 500.811.21.4 r a t i o Energy (keV) 10 −4 −3 no r m a li z ed c oun t s s − k e V − NGC 3227_60202002010
105 20 500.811.21.4 r a t i o Energy (keV) −4 −3 no r m a li z ed c oun t s s − k e V − NGC 3227_60202002012
105 20 5011.5 r a t i o Energy (keV)10 −4 −3 no r m a li z ed c oun t s s − k e V − NGC 3227_60202002014
105 20 5011.5 r a t i o Energy (keV) 10 −4 −3 no r m a li z ed c oun t s s − k e V − SWIFT J2127.4+5654_60001110002
105 20 5011.52 r a t i o Energy (keV) −4 −3 no r m a li z ed c oun t s s − k e V − SWIFT J2127.4+5654_60001110003
105 20 500.811.21.4 r a t i o Energy (keV) −5 −4 −3 no r m a li z ed c oun t s s − k e V − SWIFT J2127.4+5654_60001110005
105 20 500.511.52 r a t i o Energy (keV) 10 −5 −4 −3 no r m a li z ed c oun t s s − k e V − SWIFT J2127.4+5654_60001110007
105 20 5011.5 r a t i o Energy (keV) 10 −5 −4 −3 no r m a li z ed c oun t s s − k e V − SWIFT J2127.4+5654_60402008004
105 20 500.511.52 r a t i o Energy (keV)10 −5 −4 −3 no r m a li z ed c oun t s s − k e V − SWIFT J2127.4+5654_60402008006
105 20 50123 r a t i o Energy (keV) 10 −5 −4 −3 no r m a li z ed c oun t s s − k e V − SWIFT J2127.4+5654_60402008008
105 20 500.511.5 r a t i o Energy (keV) 10 −4 −3 no r m a li z ed c oun t s s − k e V − SWIFT J2127.4+5654_60402008010
105 20 5011.5 r a t i o Energy (keV)
Figure A1.
NuSTAR spectra, best-fit models ( pexrav ) and the residual data-to-model ratios. Spectra from both FPMA (black) and FPMB (red) modules aregiven. The best-fit spectral parameters are given in Tab. 2. MNRAS000