On the Observational Difference Between the Accretion Disk-Corona Connections among Super- and Sub-Eddington Accreting Active Galactic Nuclei
Hezhen Liu, B. Luo, W. N. Brandt, Michael S. Brotherton, S. C. Gallagher, Q. Ni, Ohad Shemmer, J. D. Timlin III
aa r X i v : . [ a s t r o - ph . GA ] F e b D RAFT VERSION F EBRUARY
8, 2021Typeset using L A TEX twocolumn style in AASTeX63
On the Observational Difference Between the Accretion Disk-Corona Connections among Super- and Sub-EddingtonAccreting Active Galactic Nuclei H EZHEN L IU ,
1, 2, 3
B. L UO ,
1, 3
W. N. B
RANDT ,
2, 4, 5 M ICHAEL
S. B
ROTHERTON , S. C. G
ALLAGHER , Q. N I ,
2, 4 O HAD S HEMMER , AND
J. D. T
IMLIN
III
2, 41
School of Astronomy and Space Science, Nanjing University, Nanjing, Jiangsu 210093, China; [email protected] Department of Astronomy & Astrophysics, 525 Davey Lab, The Pennsylvania State University, University Park, PA 16802, USA Key Laboratory of Modern Astronomy and Astrophysics (Nanjing University), Ministry of Education, Nanjing 210093, China Institute for Gravitation and the Cosmos, The Pennsylvania State University, University Park, PA 16802, USA Department of Physics, 104 Davey Lab, The Pennsylvania State University, University Park, PA 16802, USA Department of Physics and Astronomy, University of Wyoming, Laramie, WY 82071, USA Department of Physics & Astronomy and Institute for Earth and Space Exploration, The University of Western Ontario, London, ON, N6A 3K7, Canada Department of Physics, University of North Texas, Denton, TX 76203, USA
ABSTRACTWe present a systematic X-ray and multiwavelength study of a sample of 47 active galactic nuclei(AGNs) with reverberation-mapping measurements. This sample includes 21 super-Eddington accretingAGNs and 26 sub-Eddington accreting AGNs. Using high-state observations with simultaneous X-ray andUV/optical measurements, we investigate whether super-Eddington accreting AGNs exhibit different accretiondisk-corona connections compared to sub-Eddington accreting AGNs. We find tight correlations between theX-ray-to-UV/optical spectral slope parameter ( α OX ) and the monochromatic luminosity at 2500 Å ( L )for both the super- and sub-Eddington subsamples. The best-fit α OX – L relations are consistent over-all, indicating that super-Eddington accreting AGNs are not particularly X-ray weak in general comparedto sub-Eddington accreting AGNs. We find dependences of α OX on both the Eddington ratio ( L Bol / L Edd )and black hole mass ( M BH ) parameters for our full sample. A multi-variate linear regression analysis yields α OX = − . L Bol / L Edd ) − . M BH − .
69, with a scatter similar to that of the α OX – L relation. Thehard (rest-frame > Γ ) is strongly correlated with L Bol / L Edd for the full sample andthe super-Eddington subsample, but these two parameters are not significantly correlated for the sub-Eddingtonsubsample. A fraction of super-Eddington accreting AGNs show strong X-ray variability, probably due tosmall-scale gas absorption, and we highlight the importance of employing high-state (intrinsic) X-ray radiationto study the accretion disk-corona connections in AGNs. INTRODUCTIONActive galactic nuclei (AGNs) are powered by accretiononto central massive black holes (BHs). The inflowing gasnaturally forms an accretion disk, producing luminous emis-sion mainly in the optical and UV bands. Evidence indicatesthat the primary AGN X-ray emission is produced via Comp-ton up-scattering of the accretion-disk UV/optical photons byenergetic electrons in a compact corona surrounding the BH(e.g., Sunyaev & Titarchuk 1980; Haardt & Maraschi 1993).The emitted X-ray photon spectrum is well described with apower-law continuum with a form of N ( E ) ∝ E − Γ . The pho-ton index ( Γ ) of the spectrum is expected to depend on coro-nal parameters such as the electron temperature and opticaldepth (e.g., Rybicki & Lightman 1986; Haardt & Maraschi1991, 1993).As would be expected from the paradigm describedabove, observations have revealed evidence that the accre-tion disk and X-ray corona are connected. First, there is a strong correlation between AGN UV/optical and X-rayluminosities, which is often parameterized as a relationbetween the optical-to-X-ray power-law slope parameter α OX1 and L across a broad range in UV luminos-ity (e.g., Avni & Tananbaum 1982, 1986; Kriss & Canizares1985; Wilkes et al. 1994; Vignali et al. 2003; Strateva et al.2005; Steffen et al. 2006; Just et al. 2007; Gibson et al.2008; Green et al. 2009; Lusso et al. 2010; Grupe et al.2010; Jin et al. 2012; Laha et al. 2018; Chiaraluce et al.2018). This correlation can also be described as thedependence of L on L (e.g., Tananbaum et al.1979; Avni & Tananbaum 1982, 1986; Wilkes et al. 1994;Strateva et al. 2005; Steffen et al. 2006; Just et al. 2007;Lusso et al. 2010; Lusso & Risaliti 2016; Chiaraluce et al. α OX is defined as α OX = 0 . L / L ), where L and L are the monochromatic luminosities at rest-frame 2 keV and2500 Å, respectively. α OX – L or L – L relation can be used to identify AGNs emittingunusually weak or strong X-ray emission, relative to their UVluminosities (e.g., Gibson et al. 2008; Miller et al. 2011). Awell-calibrated L – L relation can also be used to es-timate cosmological parameters (e.g., Lusso & Risaliti 2016,2017; Bisogni et al. 2017).Another remarkable piece of evidence showing thedisk-corona connection is the significant positive correla-tion between the hard X-ray photon index and Eddington ra-tio ( L Bol / L Edd , where L Bol is the bolometric luminosity and L Edd is the Eddington luminosity; e.g., Shemmer et al. 2006,2008; Jin et al. 2012; Risaliti et al. 2009; Brightman et al.2013; Trakhtenbrot et al. 2017). A possible interpretationof this relationship is that in a higher L Bol / L Edd system theenhanced UV/optical emission from the accretion disk re-sults in more effective Compton cooling of the corona, de-creasing its temperature and/or optical depth, which leadsto the softening of the X-ray spectrum (a larger value of Γ ; e.g., Haardt & Maraschi 1991, 1993; Pounds et al. 1995;Fabian et al. 2015; Cheng et al. 2020).The AGN accretion-disk properties likely depend onthe accretion rate (usually represented by L Bol / L Edd ).Typical AGNs with 0 . . L Bol / L Edd . . L Bol / L Edd & . ∼ α OX ( L )– L and Γ – L Bol / L Edd relations.Previous studies of these relations usually targeted sam-ples including both super- and sub-Eddington accretingAGNs, and the two groups were not separated. Therehave been some suggestions that super-Eddington accretingAGNs may show relatively weak X-ray emission, deviat-ing from the α OX ( L )– L relation for sub-Eddingtonaccreting AGNs. For example, X-ray investigations ofintermediate-mass BH (IMBH) candidates with high Edding-ton ratios suggested that a number of IMBHs appear tohave suppressed X-ray emission (e.g., Greene & Ho 2007;Dong et al. 2012). However, weak X-ray emission observedfrom super-Eddington accreting AGNs might not be intrin-sic, and it may instead be caused by X-ray absorption. Somenarrow-line Seyfert 1 (NLS1) galaxies and quasars with highaccretion rates have been found to show extreme (by factorsof >
10) X-ray variability without coordinated UV/opticalvariability, and they are significantly X-ray weak in the lowX-ray states; their extreme X-ray weakness is probably re-lated to the shielding of the corona by a thick inner accre-tion disk and its associated outflow (e.g., Liu et al. 2019;Ni et al. 2020, and references therein). In addition, althoughthere have been some studies of the Γ – L Bol / L Edd relationfor AGNs with high Eddington ratios (e.g., Ai et al. 2011;Kamizasa et al. 2012), they have not compared systemati-cally the difference between the relations among super- andsub-Eddington accreting AGNs.In this work, we utilize an AGN sample with reverber-ation mapping (RM) measurements to investigate system-atically the observational difference between the accretiondisk-corona connections among super- and sub-Eddingtonaccreting AGNs. The RM technique is considered to pro-vide the most accurate measurements of BH masses forbroad emission-line AGNs (e.g., Blandford & McKee 1982;Peterson 1993). Successful RM studies have been car-ried out for nearly 200 AGNs (e.g., Peterson et al. 1998,2002, 2004; Kaspi et al. 2000, 2007; Bentz et al. 2008, 2009;Denney et al. 2009; Barth et al. 2013, 2015; Rafter et al.2011, 2013; Du et al. 2014, 2015, 2016, 2018; Wang et al.2014b; Shen et al. 2016; Jiang et al. 2016; Fausnaugh et al.2017; Grier et al. 2012, 2017, 2019). Most of these cam-paigns do not target super-Eddington accreting AGNs. Arecent campaign targeting super-Eddington accreting mas-sive black holes (SEAMBHs) has identified about 24candidates, which increases significantly the number ofsuper-Eddington accreting AGNs with RM measurements(Du et al. 2014, 2015, 2016, 2018; Wang et al. 2014b). Themajority of reported RM AGNs are nearby bright sources thathave sensitive X-ray coverage from archival
XMM-Newton (Jansen et al. 2001),
Chandra (Weisskopf et al. 1996), and
Swift (Gehrels et al. 2004) observations. For
XMM-Newton and
Swift observations, simultaneous UV/optical measure-ments by the same satellites are available.The paper is organized as follows. In Section 2, wedescribe the sample-selection procedure, the observationaldata, and the methods of data reduction and analysis. InSection 3, we present the statistical analysis of the corre-lations between α OX ( L ) and L , Γ and L Bol / L Edd ,for our super- and sub-Eddington accreting AGN subsam-ples. In Section 4, we discuss the implications of the corre-lations, and we explore the dependence of α OX on both M BH and L Bol / L Edd . We summarize and present future prospects inSection 5. Throughout this paper, we use J2000 coordinatesand a cosmology with H = 67 . − Mpc − , Ω M = 0 . Ω Λ = 0 .
686 (Planck Collaboration et al. 2020). All errorsare quoted at a 68% (1 σ ) confidence level. SAMPLE PROPERTIES AND DATA ANALYSIS2.1.
Sample Selection
Our RM AGN sample was selected from the RMAGNs compiled by the SEAMBH collaboration (Du et al.2015, 2016, 2018), which contains 25 targets (includ-ing 24 super-Eddington accreting AGN candidates) in theSEAMBH campaign and 50 AGNs studied in previous RMwork. We selected sample objects from these 75 AGNs basedon the following considerations:(1) We selected radio-quiet AGNs, since radio-loud AGNsmay have excess X-ray emission linked to the radio jetsand other processes (e.g., Miller et al. 2011; Zhu et al. 2020).We searched for radio information from the literature (e.g.,Kellermann et al. 1989; Wadadekar 2004; Sikora et al. 2007)and the NASA/IPAC Extragalactic Database (NED), and wediscarded five radio-loud AGNs.(2) Since we aim to explore the intrinsic X-ray andUV/optical properties of our sample, objects affected byheavy absorption in the X-ray and UV/optical bands wereexcluded. We discarded 11 objects in total, nine ofwhich are well-studied objects (PG 1700 + https://ned.ipac.caltech.edu. super-Eddington accreting AGN, Mrk 202, shows an unusu-ally flat 2–10 keV spectrum and an absorption feature promi-nent in the < XMM-Newton observation of NGC 5548 revealed that it was obscuredby clumpy gas not seen before, which blocks a large frac-tion of its soft X-ray emission and causes UV BALs (e.g.,Kaastra et al. 2014; Cappi et al. 2016). We checked itshigh-state X-ray and UV/optical data obtained from the 2002
XMM-Newton observation, and we found that the simulta-neous X-ray and UV/optical fluxes are free from absorp-tion. Its 2002 UV spectrum also shows no absorption fea-tures (e.g., Kaastra et al. 2014). We thus also retained thisobject in our study and analyzed its 2002
XMM-Newton observation. Moreover, a super-Eddington accreting AGN,IRAS F12397 + XMM-Newton , Chandra , or
Swift coverage. Since we focused on thehard (rest-frame > > XMM-Newton data have the high-est priority since they have high-quality X-ray spectral dataand simultaneous UV/optical data. For AGNs without
XMM-Newton data, we used
Chandra observations if avail-able, otherwise,
Swift observations are used. There are sixAGNs without archival X-ray data, of which four are SloanDigital Sky Survey Release 7 (SDSS-DR7) quasars in theSEAMBH campaign. In addition, there are six SDSS quasarsin the SEAMBH campaign serendipitously detected by
Swift with low S/N ratios. We thus discarded these 12 AGNs.Our final sample consists of 47 RM AGNs, which are re-ferred to as the full sample. From these objects we identified21 super-Eddington accreting AGNs that were classified onthe basis of normalized accretion rate of ˙ M ≥
3, followingthe approach of the SEAMBH campaign (Wang et al. 2014b;Du et al. 2015). The normalized accretion rate is defined as ˙ M = ˙ Mc / L Edd , where ˙ M is the mass accretion rate. We mea-sured ˙ M based on the Shakura & Sunyaev (1973) standardthin disk model (see Section 2.6). For super-Eddington ac-creting AGNs, ˙ M may be a better indicator of the accretionrate, rather than L Bol / L Edd , because their bolometric lumi-nosities may be saturated due to the photon-trapping effect(e.g., Wang et al. 2014b). The criterion of ˙ M ≥ L Bol / L Edd ≥ . η = 0 .
1. We refer to the 21 super-Eddington accreting AGNsas the super-Eddington subsample. The remaining 26 objectsconstitute the sub-Eddington subsample.Table 1 lists the basic properties of our sample AGNs in-cluding 5100 Å luminosities, H β FWHMs, and BH masses( M BH ) and associated measurement uncertainties, whichwere adopted from Du et al. (2015, 2016); Du & Wang(2019). We note that there may be considerable systematicuncertainties on the RM BH masses (see Section 4.3 belowfor discussion), which are difficult to quantify. We thus onlytake into account the measurement uncertainties in the fol-lowing analyses. For the full sample, the measurement un-certainties on M BH range from 0.03 to 0.40 dex, with a me-dian value of 0.13 dex. Figure 1 shows the distribution of oursample AGNs in the redshift versus 2500 Å luminosity plane.For all sample objects (except SDSS J085946 + + + z l o g ( L ) | = Å ( e r g s ) N u m b e r o f S o u r c e s Number of Sources
Figure 1.
Redshift vs. 2500 Å luminosity for the super-Eddingtonsubsample (blue circles) and the sub-Eddington subsample (greensquares). The right panel shows the distribution of 2500 Å lumi-nosity, and the upper panel shows the distribution of redshift. Thesuper-Eddington (sub-Eddington) subsample is represented by thehatched blue (filled green) histograms. preparation; see details in Appendix). They have undergonechanges in their optical spectral types and UV/optical andX-ray fluxes. We used their observational data in the histori-cal high states, when they exhibit strong broad optical emis-sion lines and the brightest X-ray and UV/optical luminosi-ties. A list of the X-ray observations used in this study ispresented in Table 2.2.2.
XMM-Newton ObservationsXMM-Newton data are available for 37 sample AGNs.Except for one AGN, SBS 1116+583A, all these AGNswere targets of the corresponding
XMM-Newton observa-tions. Simultaneous X-ray and UV/optical data were ob-tained from the European Photon Imaging Camera (EPIC)PN (Strüder et al. 2001) and MOS (Turner et al. 2001) detec-tors, and the Optical Monitor (OM; Mason et al. 2001). Weprocessed the data using the
XMM-Newton
Science AnalysisSystem (SAS v.16.0.0), and the latest calibration files wereapplied. For the X-ray analysis, we only used the EPIC PNdata. The task epproc was first used to reduce the PN data andcreate the calibrated event lists. Bad or hot pixels were re-moved from the event lists, and high-background flares werechecked and filtered according to the standard criteria. Onlysingle and double events (PATTERN ≤ ′′ wasused to extract the source spectrum. Each data set was in-spected for pile-up by running the task epatplot . For ninesources with detected pile-up (see Table 2), an inner circularregion with a radius of 5–10 ′′ was discarded from the sourceextraction region. These are bright X-ray sources, and the ex-tracted spectra still have high quality, allowing robust spec-tral fitting. The background spectrum was extracted from anearby source-free circular region with a radius of 50–100 ′′ on the same CCD chip. The response matrix and ancillary re-sponse function files were created using the tasks rmfgen and arfgen , which account for the point spread function correc-tion of the source-extraction region. The final PN spectrumwas grouped with a minimum number of one count per binusing the task specgroup .We analyzed OM data mainly for deriving flux densitiesat the rest-frame 2500 Å band. OM imaging data are avail-able for all sample objects, except for Mrk 335 with onlyUV grism data in its selected observation. There are six OMfilters, including three optical filters (V, B, U with centralwavelengths of 5430 Å, 4500 Å, 3440 Å) and three UV fil-ters (UVW1, UVM2, UVW2 with central wavelengths of2910 Å, 2320 Å, 2110 Å). We processed the OM filterdata using the pipeline omchian . Point sources and extendedsources were automatically identified as part of the pipeline.Source fluxes and magnitudes were extracted from the SWS-RLI files, and we adopted the mean magnitudes and fluxesof all the exposure segments for each filter. For Mrk 335,the OM UV grism data were processed with the pipeline omghian . The pipeline generated 24 calibrated spectra, andthe spectra cover a wavelength range of 1800–3600 Å. Thefluxes of the OM filters and the mean grism spectra were thencorrected for Galactic extinction using the extinction law ofCardelli et al. (1989). Table 1 lists the mean values of Galac-tic extinction E B − V (Schlegel et al. 1998) that were obtainedfrom the NASA/IPAC Infrared (IR) Science Archive. We utilized the OM UV-filter flux densities to derivethe 2500 Å flux densities. Our sample objects are bright,and at least in the UV-filter images, they were identifiedas point sources. Therefore, host-galaxy contamination inthe UV-filter fluxes should be mild (see Grupe et al. 2010for discussion regarding the
Swift
UV/optical photometricdata), and we did not correct the source fluxes and mag-nitudes for any host-galaxy contamination. Eleven out ofthe 36 objects with OM imaging data were observed withthree UV filters, and another 14 objects were observed withtwo filters. We derived their 2500 Å flux densities by fit-ting a power-law model to the observed data. For eightobjects observed with only one UV filter, the 2500 Å fluxdensities were extrapolated assuming a power-law slope of https://irsa.ipac.caltech.edu/applications/DUST/. α ν = − .
44 (e.g., Vanden Berk et al. 2001). For three otherobjects without UV-filter data, NGC 5548, NGC 6814 andPG 0844 + α ν = − .
44. Finally, the 2500 Å flux densityof Mrk 335 was measured from the mean grism spectrum.The UV-filter information and the derived L values arelisted in Table 2.2.3. Chandra Observations
We used
Chandra data for only one object,SDSS J085946 + Chandra
Interactive Analysis of Observations (CIAO;v4.11) tools. A new level 2 event file was generated usingthe
CHANDRA _ REPRO script, and high-background flareswere filtered by running the
DEFLARE script with an iterative3 σ clipping algorithm. A 0.5–7 keV image was then con-structed by running the DMCOPY script. The
SPECEXTRACT tool was used to extract and group spectra (with at least onecount per bin), and to generate the response matrix and an-cillary response function files. The source-extraction regionis a circular region with a radius of 3 ′′ , centered on the X-raysource position detected by the automated source-detectiontool WAVDETECT . An annulus region centered on the X-raysource position with a 10 ′′ inner radius and a 30 ′′ outer ra-dius was chosen as the background-extraction region. Theextracted source spectrum was grouped with a minimumnumber of one count per bin.There are no simultaneous UV/optical data availablefor this Chandra object. We interpolated its Near-UV(NUV) flux density, observed on 2006 February 18, from
Galaxy Evolution Explorer ( GALEX ; Martin et al. 2005) andSDSS u -band flux density, observed on 2004 April 17, to de-rive the 2500 Å flux density.2.4. Swift Observations
We used
Swift data for nine AGNs. Simultaneous X-rayand UV/optical data are available from the X-ray Telescope(XRT; Burrows et al. 2005) and the UV-Optical Telescope(UVOT; Roming et al. 2005). For all observations, the XRTwas operated in the Photon Counting (PC) mode (Hill et al.2004). The data were reduced with the task xrtpipeline ver-sion 0.13.4, which is included in the HEASOFT package6.25. The XRT data were not affected by photon pipe-upgiven the low count rates (0 . .
14 counts s − ) of these nineAGNs. For each source, the source photons were extractedusing the task xselect version 2.4, from a circular region witha radius of 47 ′′ . The background spectrum was extractedfrom a nearby source-free circular region with a radius of100 ′′ . The ancillary response function file was generated by xrtmkarf , and the standard photon redistribution matrix filewas obtained from the CALDB. We grouped the spectra us-ing grppha such that each bin contains at least one photon.The UVOT has a similar set of filters (V, B, U, UVW1,UVM2, UVW2 with central wavelengths of 5468 Å, 4392 Å,3465 Å, 2600 Å, 2246 Å, and 1928 Å) to the OM. Simi-larly, we used mainly the UV-filter data to derive the 2500 Åflux densities. Among these nine Swift
AGNs, six were ob-served with one UV filter, one was observed with two UVfilters, and two were observed with three UV filters. Thedata from each segment in each filter were co-added usingthe task uvotimsum after aspect correction. Source countswere selected from a circular region with a radius of 5 ′′ , cen-tered on the source position determined by the task uvotdetect Freeman et al. (2002). A nearby source-free region with a ra-dius of 20 ′′ was used to extract background counts. Sourcemagnitudes and fluxes in each UVOT filter were then com-puted using the task uvotsource , and these data were cor-rected for Galactic extinction. We derived the 2500 Å fluxdensities following the same procedure as used for the OMphotometric data.2.5. X-ray Spectral Analysis
X-ray spectral analysis was performed with XSPEC(v12.10.1; Arnaud 1996). All spectra were grouped with atleast one count per bin, and the Cash statistic (CSTAT; Cash1979) was applied in parameter estimation; the W statisticwas actually used because the background spectrum was in-cluded in the spectral fitting. Since the aim of this study isto obtain properties of the intrinsic coronal X-ray radiation,we focused only on the rest-frame > < PHABS * ZPOWERLW ) to fit the rest-frame > / (1 + z )–10 keV spectra for XMM-Newton and
Swift observationsand the observed-frame 2 / (1 + z )–7 keV spectra for the Chan-dra observation. We visually inspected whether there arestrong iron K lines in the spectra. For 25 AGNs in which theiron K lines were detected, the rest-frame 5 . . https://heasarc.gsfc.nasa.gov/xanadu/xspec/imanualXSappendixStatistics.html. N u m b e r o f S o u r c e s Figure 2.
Distribution of the X-ray spectral photon indices forthe super-Eddington (hatched blue histograms) and sub-Eddington(filled green histograms) subsamples. The two points with er-ror bars on the top show the mean values and 1 σ deviations forthe two subsamples. The two subsamples are clearly distinct,with super-Eddington accreting AGNs showing steeper (softer) hardX-ray spectra. and the fitting residuals are distributed close to zero withoutany apparent systematic excesses/deficiencies. As shown inFigure 2, the photon indices ( Γ ) of the full sample span arange of 1 . .
46 with a median value of 1.94. In general,the super-Eddington subsample has larger (softer) photon in-dices than the sub-Eddington subsample.Since we have discarded X-ray and UV/optical absorbedAGNs from our sample, and the high-state data for objectswith multiple observations were used, it is likely that intrinsicabsorption has little impact on the derived X-ray propertiesof our sample. To confirm this, we checked for the presenceof intrinsic absorption in each object by adding an intrinsicneutral absorption component (
ZPHABS model in XSPEC)to the fitting model. For each object, the best-fit statisticdid not change significantly, and the resulting column den-sity is consistent with zero; an F test also indicated thatthe absorption component is likely not required. Moreover,we extrapolated the data-to-model ratios of the best-fit sim-ple power-law model (not including the intrinsic absorptioncomponent) to the entire spectral energy range (0.3–10 keVfor
XMM-Newton and
Swift observations and 0.5–7 keV forthe
Chandra observation) to inspect whether absorption ispresent at rest-frame < + ≈ > > + f ) were thencomputed based on the best-fit models. The best-fit modelparameters and fitting statistics are presented in Table 2.2.6. Estimation of Normalized Accretion Rates
The Shakura & Sunyaev (1973) standard thin disk modelpredicts a power-law SED in the form of F ν ∝ ν / from op-tical to NUV, and the monochromatic luminosity at a givenwavelength depends on the BH mass and accretion rate (e.g.,Equation 5 of Davis & Laor 2011). Given the observed SEDand the BH mass, the accretion rate ( ˙ M or ˙ M ) can be com-puted (e.g., Davis & Laor 2011; Netzer 2013; Wang et al.2014b). We used the monochromatic luminosity at 2500 Åto calculate ˙ M following the expression: ˙ M = 4 . ℓ / cos i ) / m − , (1)where ℓ = ν L / erg s − is the 2500 Å luminosityin units of 10 erg s − , m = M BH / M ⊙ , and i is the incli-nation angle of the disk. For Type 1 AGNs, the dependenceof ˙ M on cos i is weak, and thus we adopted a median cos i value of 0.75. We adopted the 2500 Å luminosity insteadof the 5100 Å luminosity that is often used to calculate ˙ M in previous studies, because the emission around 2500 Å isless affected by host-galaxy contamination that is significantfor nearby moderate-luminosity AGNs. Moreover, for mostsample objects, the 2500 Å luminosities were derived fromthe UV/optical data that were observed simultaneously withthe X-ray data, and thus the accretion-disk corona connec-tions explored below are free from any variability effects. Forthe full sample, the ˙ M values span a range of 0 .
012 to 530,with a median value of 0 .
83. The uncertainties on ˙ M arepropagated from the measurement uncertainties on M BH andthe 2500 Å luminosities. Table 1 lists the log ˙ M values andtheir uncertainties.We note that Equation 1 likely also holds forsuper-Eddington accreting AGNs (e.g., Du et al. 2016;Huang et al. 2020), where the accretion disks are expected tobe geometrically thick. Based on the self-similar solution ofthe slim disk model (Wang & Zhou 1999; Wang et al. 1999),the radius of the disk region emitting 2500 Å photons is larger According to the unified model, Type 1 AGNs are observed at relativelysmall inclination angles ( i ). For a typical i range of 0–60 ◦ , cos i onlyvaries by a factor of two (0 . i = 0 .
75 (see alsodiscussions in Du et al. 2014, 2016; Wang et al. 2014b). than the photon-trapping radius for our sample objects. Observationally, studies of the SEDs of super-Eddingtonaccreting AGNs revealed that their UV/optical SEDs arewell-fitted by the thin disk model, and the characteris-tics of the thick-disk emission likely emerge in the EUV(e.g., Castelló-Mor et al. 2016; Kubota & Done 2018). Itis also supported by our finding that the high-luminositysuper-Eddington accreting AGNs in our sample showUV/optical SEDs consistent with those of typical quasars(see Section 3.4). Furthermore, a recent accretion-diskreverberation mapping on a super-Eddington accretingAGN, Mrk 142, found that the UV/optical (rest-frame ≈ τ ( λ ) ∝ λ / , as expected from a thin disk (Cackett et al.2020); this result also supports the idea that the emission at2500 Å likely comes from a thin disk.2.7. Bolometric Luminosities and Eddington Ratios
Considering that most objects in our sample are nearbymoderate-luminosity AGNs, for which the IR-to-UV SEDsmay have significant contamination from the host galaxies,we used an IR-to-UV quasar SED template scaled to the2500 Å luminosity plus the observed X-ray SED to esti-mate the bolometric luminosity for each object. An ex-ample of such an IR-to-X-ray SED (for PG 0844 + ν L ν ) | λ =2500 Å ≤ .
41; mid luminosity: 45 . ≤ log( ν L ν ) | λ =2500 Å ≤ . ∼ µ m) radiation is likely reprocessed emission from the“dusty torus”, which should not be included in the computa-tion of the bolometric luminosity (e.g., Krawczyk et al. 2013,and references therein). We thus replaced the 1–30 µ m SEDtemplate with an α ν = 1 / > Using the self-similar solution of the slim disk model (Wang & Zhou 1999;Wang et al. 1999) and Wien’s law, we estimated the radius of the disk re-gion emitting 2500 Å photons to be R / R g ≈ . × m − / , andthe photon-trapping radius is given by R trap / R g ≈
450 ( ˙ M / R g = GM BH / c (see Du et al. 2016; Cackett et al. 2020). Equation 1 holdsprovided that R > R trap (i.e., ˙ M . . × m − / ), and this conditionis met for all the objects in our sample. sample objects when extrapolating the hard X-ray power-lawmodels to rest-frame < . / (1 + z ) keV for XMM-Newton and
Swift observations and 0.5 keV to 2 / (1 + z ) keV for the Chandra observation). The procedure is described as follows: (1) Wefirst attempted to fit the soft X-ray spectra with a power-law model modified by Galactic absorption. This model fitswell the spectra for 24 objects. (2) For the other 23 ob-jects, their soft X-ray spectra are not described well by thepower-law model with substantial residuals shown in the datavs. model plots. Therefore, we fitted the soft X-ray spec-tra with a thermal-Comptonization component (
COMPTT inXSPEC) plus a power-law model, where the power-law com-ponent accounts for the coronal emission and was fixed tothat constrained from the rest-frame > + ZXIPCF ) into the fitting to ac-count for weak absorption in the soft X-rays; such absorptiondoes not affect significantly the rest-frame > . µ m–10 keV) SEDs, we obtained the bolometric lumi-nosities for our sample, which span a range of 1 . × to2 . × erg s − . We used the uncertainties on L andthe 0.2–10 keV X-ray luminosities to compute the measure-ment uncertainties on L Bol . Given the L Bol and M BH values,we derived L Bol / L Edd for our sample, which range from6 . × − to 5 .
5, with a median value of 0 .
14. The uncer-tainties on L Bol / L Edd are propagated from the measurementuncertainties on L Bol and M BH . The uncertainty on L Bol / L Edd is dominated by the M BH uncertainty, and the contributionfrom the L Bol uncertainty is negligible. We note that thereare potential systematic uncertainties on both M BH and L Bol that may introduce additional uncertainties for the L Bol / L Edd estimates (see discussion in Section 4.3 below). Table 1
13 14 15 16 17 18 log(ν (est ) (Hz) l o g ( L )( e ( g ) − ) PG 0844+349α ν = 1/3 power lawKrawczyk et al. (2013) quasar SEDX-ray SED from spectral fitting2500 Å luminosity Figure 3.
An example of the SED used to estimate the bolometricluminosity. The gray dots show the observed UV/optical photomet-ric data points (see Section 3.4 for details). The purple symbols rep-resent the X-ray spectral data points that have been corrected for theGalactic absorption; the 5.5–7.5 keV spectrum was discarded due tostrong iron K emission. The IR-to-UV SED template is normalizedto the 2500 Å luminosity that is extrapolated from the UV photo-metric data. The 912 Å–0 . . ZPOWERLW model plus a 2–10 keV
ZPOWERLW model; see Tables 2 and 3). lists the log( L Bol ) and log( L Bol / L Edd ) values and associateduncertainties. RESULTS3.1. α OX versus L Correlation
Figure 4 displays α OX versus log( L ) for oursuper-Eddington and sub-Eddington subsamples. The twoparameters are highly correlated for both subsamples. Forthe super-Eddington (sub-Eddington) subsample, the Spear-man rank correlation test gives a correlation coefficient of r s = − .
84 ( r s = − .
77) and a p -value of p = 2 . × − ( p = 2 . × − ). The p -value indicates the probability ofobtaining a correlation coefficient r s at least as high as theobserved one, under the null hypothesis that the two sets ofdata are uncorrelated.We performed linear regression analysis on the α OX ver-sus log( L ) relations, using the LINMIX_ERR method(Kelly 2007). This is a Bayesian method that accounts formeasurement uncertainties. For the super-Eddington sub-sample, the best-fit regression equation with the 1 σ uncer-tainty on each parameter is α OX = ( − . ± . L ) + (1 . ± . , (2)
27 28 29 30 31 log L (erg s −1 Hz −1 ) −1.6−1.4−1.2−1.0 α O X Super-EddingtonSub-Eddington
Figure 4.
X-ray-to-optical power-law slope ( α OX ) vs. 2500 Å lu-minosity for the super-Eddington subsample (blue circles) and thesub-Eddington subsample (green squares). The blue dashed (greendot-dashed) line shows the best-fit relation for the super-Eddington(sub-Eddington) subsample, given by Equation 2 (Equation 3). Forcomparison, the best-fit relation of Steffen et al. (2006) is denotedwith the black dotted line. OX N u m b e r o f S o u r c e s Figure 5.
Distribution of ∆ α OX for the super-Eddington (hatchedblue histograms) and sub-Eddington (filled green histograms) sub-samples. ∆ α OX is defined as the difference between the observed α OX value and the one expected from the Steffen et al. (2006) rela-tion (shown as the black dotted line in Figure 4). The two pointswith error bars on the top show the mean values and 1 σ deviationsfor the two subsamples. The two subsamples are consistent in the ∆ α OX distribution. with a scatter of 0.06. For the sub-Eddington subsample, thebest-fit relation is α OX = ( − . ± . L ) + (1 . ± . , (3)with a scatter of 0.08. The relations (slopes and intercepts)for the two subsamples are consistent within their 1 σ uncer-tainties.We then performed linear regression on the full sample,and the best-fit relation is α OX = ( − . ± . L ) + (1 . ± . , (4)with a scatter of 0.07. The relation slope is consistent withinthe 1 σ uncertainties with those for the super-Eddingtonand sub-Eddington subsamples. Compared to previous re-sults, our slope for the full sample is flatter than the slopesof − .
14 to − .
22 reported in most of the previous stud-ies (Strateva et al. 2005; Steffen et al. 2006; Just et al. 2007;Gibson et al. 2008; Lusso et al. 2010; Chiaraluce et al. 2018;Timlin et al. 2020), but it is steeper than the slopes of − . − .
07 found by Green et al. (2009); Jin et al. (2012).Steffen et al. (2006) have suggested that the power-law slopeof the α OX – L relation may be L dependent, and itappears to be steeper towards higher L . Studies of thisrelation for high-luminosity quasars did find steeper slopes(e.g., Gibson et al. 2008; Timlin et al. 2020). Therefore, theflat slope for our sample may be due to the generally lowerUV luminosities. The best-fit relations for the two subsam-ples are plotted in Figure 4. For comparison, we also plottedin Figure 4 the relation of Steffen et al. (2006) with a dottedline.We further investigated the distribution of the ∆ α OX pa-rameter, defined as the difference between the observed α OX value and the one expected from the α OX – L re-lation for typical AGNs. Considering that our full sam-ple may be biased toward super-Eddington accreting AGNs,we adopted the Steffen et al. (2006) α OX – L relation, α OX = − . × log( L ) + . α OX values. The parameter ∆ α OX is an indicatorof the level of X-ray weakness. As shown in Figure 5, the ∆ α OX distributions for the two subsamples span the samerange of − .
15 to 0.15, which is within the rms scatter of theSteffen et al. (2006) α OX – L relation. The mean and rmsof the ∆ α OX values for the super-Eddington (sub-Eddington)subsample are − .
024 (0 . .
062 (0 . ≈
23% lower) X-ray emission comparedto the sub-Eddington subsample, but the significance of thedifference is only 0 . σ . A Kolmogorov-Smirnov (KS) teston the ∆ α OX distributions for the two subsamples yielded d = 0 .
328 and p = 0 . α OX – L re-lation (Equation 4) for our full sample to compute the ex-pected α OX values. These results suggest that both the super-and sub-Eddington subsamples show generally normal X-rayemission, when the high-state data are considered.3.2. L versus L Correlation
We also investigated the correlations between L and L for our sample, shown in Figure 6. The correlationsfor both the super- and sub-Eddington subsamples are highlysignificant with Spearman coefficients of r s = 0 .
91 and r s =0 .
93, respectively. We performed regression analysis withthe LINMIX_ERR method on the two sets of parameters. Forthe super-Eddington subsample, the best-fit relation islog( L ) = (0 . ± . L ) + (4 . ± . , (5)with a scatter of 0.17. For the sub-Eddington subsample, thebest-fit relation islog( L ) = (0 . ± . L ) + (5 . ± . , (6)with a scatter of 0.22. The slopes and intercepts of the re-lations for the two subsamples are consistent within the 1 σ uncertainties. The best-fit relation for the full sample islog( L ) = (0 . ± . L ) + (5 . ± . , (7)with a scatter of 0.19. The slope of the relation for thefull sample is consistent with those ( ≈ α OX is defined as the ratio between L and L .3.3. Correlation between Γ and accretion rate Figure 7 plots Γ versus log( L Bol / L Edd ) for our sampleobjects. For the full sample, a highly significant correla-tion is present, and the Spearman rank correlation test re-sulted in a correlation coefficient of r s = 0 .
72 with a p -valueof p = 1 . × − . The correlation is significant for thesuper-Eddington subsample ( r s = 0 .
60 and p = 0 . Γ and log( L Bol / L Edd ) for the sub-Eddington subsample ( r s =0 .
21 and p = 0 . Γ and L Bol / L Edd in the fitting.The best-fit relation for the super-Eddington subsample is Γ = (0 . ± . L Bol / L Edd ) + (2 . ± . , (8)with a scatter of 0.14. For the full sample, we obtained abest-fit relation: Γ = (0 . ± . L Bol / L Edd ) + (2 . ± . , (9)
27 28 29 30 31 log L (erg s −1 Hz −1 ) l o g L k e V ( e r g s − H z − ) Super-EddingtonSub-Eddington
Figure 6.
Rest-frame 2 keV monochromatic luminosityvs. rest-frame 2500 Å monochromatic luminosity for thesuper-Eddington subsample (blue circles) and the sub-Eddingtonsubsample (green squares). The blue dashed (green dot-dashed) lineshows the best-fit relation for the super-Eddington (sub-Eddington)subsample, given by Equation 5 (Equation 6). For comparison,the best-fit relation of Steffen et al. (2006) is shown with the blackdoted line, which follows very closely with the blue-dashed line thatdenotes the relation for the super-Eddington subsample. with a scatter of 0.14. Our relation slope for the full sam-ple is consistent with the slope (0 . ± .
01) reported inShemmer et al. (2008) for their high-redshift quasars withBH masses determined based on the H β emission lines us-ing the single-epoch virial mass method. A similar slope(0 . ± .
05) was found by Brightman et al. (2013) fortheir sample with BH masses obtained from either H β orMg II -based single-epoch estimators. However, Risaliti et al.(2009) reported a steeper slope (0 . ± .
11) for their sub-sample with H β -based single-epoch BH masses. A steepslope ( ≈ .
57) was also found by Jin et al. (2012), fortheir AGN sample with Γ and L Bol / L Edd estimated from theUV/optical-to-X-ray SED fitting.We also investigated the correlations between Γ and nor-malized accretion rate ( ˙ M ; see Figure 8). Similar to thetrends between Γ and L Bol / L Edd , Γ and ˙ M are highly cor-related for the full sample ( r s = 0 .
70 and p = 5 . × − )or the super-Eddington subsample ( r s = 0 .
63 and p = 0 . r s = 0 .
14 and p = 0 . Γ = (0 . ± . ˙ M + (1 . ± . , (10)with a scatter of 0.14. For the full sample, the best-fit relationobtained from the linear regression analysis is Γ = (0 . ± . ˙ M + (1 . ± . . (11)1 −2.0 −1.5 −1.0 −0.5 0.0 0.5log L Bol /L Edd Γ Super-EddingtonSub-Eddington
Figure 7.
Hard X-ray photon index vs. L Bol / L Edd for thesuper-Eddington subsample (blue circles) and the sub-Eddingtonsubsample (green squares). The two subsamples overlap slightlyin the L Bol / L Edd values, because they are classified on the basis of ˙ M instead of L Bol / L Edd . The blue dashed (orange solid) line showsthe best-fit relation for the super-Eddington subsample (full sam-ple), given by Equation 8 (Equation 9).
The similar dependences of Γ on L Bol / L Edd and ˙ M indi-cate that L Bol / L Edd and ˙ M are likely correlated. A Spear-man rank correlation test indicates a highly significant cor-relation ( r s = 0 .
97 and p = 4 . × − ) between L Bol / L Edd and ˙ M . Our linear regression analysis on log( L Bol / L Edd ) andlog ˙ M resulted in a slope of 0 .
53. Such a tight L Bol / L Edd – ˙ M relation has also been reported in Huang et al. (2020) fortheir quasar sample, where they found a power-law slope of0 .
52. This relation can be naturally explained by the depen-dence of the two parameters on M BH : ˙ M mainly dependson M − (see Section 2.6), and L Bol / L Edd is proportional to M − . Therefore, L Bol / L Edd and ˙ M are related in the form of L Bol / L Edd ∝ ˙ M . , with some scatter associated with the dis-tributions of L Bol and L for the sample AGNs. Given thesimilarities of the Γ – L Bol / L Edd and Γ – ˙ M relations, we focuson the Γ – L Bol / L Edd relations in the following discussion.3.4.
Spectral Energy Distributions of Super-EddingtonAccreting AGNs
We constructed IR-to-X-ray SEDs for ten super-Eddingtonaccreting AGNs with UV luminosities ( ν L ν | λ =2500 Å ) exceed-ing 10 . erg s − . This selection is based on the considerationthat the contamination from host galaxies should be small inluminous AGNs. The photometric data were collected fromthe Wide-field Infrared Survey Explorer ( WISE ; Wright et al.2010), Two Micron All Sky Survey (2MASS; Skrutskie et al.2006), SDSS, and
GALEX public catalogs. The UV/opticaldata were corrected for Galactic extinction using the ex-tinction law of Cardelli et al. (1989). The SEDs are shown −2 −1 0 1 2 3log ̇1.01.52.02.5 Γ SupeṙEddingtonSuḃEddington
Figure 8.
Hard X-ray photon index vs. normalized accretionrate for the super-Eddington subsample (blue circles) and thesub-Eddington subsample (green squares). The blue dashed (or-ange solid) line shows the best-fit relation for the super-Eddingtonsubsample (full sample), given by Equation 10 (Equation 11). in Figure 9. We added the OM or UVOT data and the2 keV and 10 keV luminosities. For comparison, the meanSED of typical SDSS quasars from Krawczyk et al. (2013),scaled to the 2500 Å luminosity of each object, is plotted ineach panel of Figure 9. The IR-to-X-ray SEDs of most ob-jects are consistent with those of typical quasars, except forthree objects (SDSS J081441 + + + WISE )bands.The weak IR emission of PG 0844 +
349 and PG 0953 +
414 has been reported in Lyu et al. (2017). PG 0953 +
414 was identified as a warm-dust-deficient quasar, andPG 0844 +
349 was an ambiguous case but likely ahot-dust-deficient quasar. The IR weakness of these threeobjects may be related to their super-Eddington accre-tion rates. As suggested by Kawakatu & Ohsuga (2011),super-Eddington accreting AGNs may tend to show weakIR emission due to the self-occultation effect of the thickaccretion disk, which reduces the illumination of the torus.However, these three IR weak objects do not show extremeproperties (e.g., M BH , L Bol / L Edd ) compared to the other sevenobjects, and they also exhibit typical optical-to-X-ray SEDs.PG 0844 +
349 has been found to show extreme X-ray vari-ability (e.g., Gallagher et al. 2001; Gallo et al. 2011), but theother extremely X-ray variable AGN among these ten ob-jects, PG 1211 + Figure 9.
IR-to-X-ray SEDs for the ten super-Eddington accretingAGNs with log( ν L ν ) | λ =2500 Å ≥ .
5. The IR-to-UV photometricdata points were gathered from the
WISE (magenta), 2MASS (gray),SDSS (orange), and
GALEX (blue) catalogs. The UVOT and OMphotometric data are shown as red points, and the luminosities at2 keV and 10 keV are shown as purple points. The dashed line ineach panel shows the mean SED of SDSS quasars (Krawczyk et al.2013), which is scaled to the mean 2500 Å luminosity extrapolatedfrom the UV photometric data of each object. The SEDs may beaffected by variability due to non-simultaneous multi-band observa-tions (e.g., SDSS J074352 + + DISCUSSION4.1.
X-ray Emission Strength of Super-Eddington AccretingAGNs
We examined the correlations between α OX and L forthe super- and sub-Eddington subsamples, in order to de-termine whether super-Eddington accreting AGNs show dif- ferent X-ray emission strength relative to UV/optical emis-sion, compared to sub-Eddington accreting AGNs. Sig-nificant α OX – L correlations were confirmed for bothsubsamples. Compared to the sub-Eddington subsample,the best-fit relation between α OX and log( L ) for thesuper-Eddington subsample has a slightly flatter slope anda smaller intercept, but the parameters are consistent consid-ering the 1 σ uncertainties. The two subsamples also showsimilar ∆ α OX distributions (see Figure 5), with the rangeswithin the rms scatter of the Steffen et al. (2006) α OX – L relation. These results suggest that super-Eddington accret-ing AGNs show normal X-ray emission strength and followa similar α OX – L relation as sub-Eddington accretingAGNs or typical AGNs, when their high-state X-ray data areconsidered.A few studies of IMBH candidates with high Eddington ra-tios have revealed that a large fraction of IMBHs deviate sig-nificantly (with ∆ α OX . − .
25; corresponding to & σ devi-ations) from the α OX – L relation for typical AGNs (e.g.,Greene & Ho 2007; Dong et al. 2012). We consider that theX-ray weakness of these IMBHs may be caused by X-rayabsorption, as some objects show unusually flat X-ray spec-tra. Our investigation shows that super-Eddington accretingAGNs tend to show strong X-ray variability, likely relatedto shielding by the thick accretion disk and/or its associatedoutflow in the low states (see discussion in Section 4.4 bel-low). In this study, we have intentionally selected high-stateobservational data to probe the intrinsic X-ray properties ofour sample. Mixing high- and low-state data could reveal afraction of objects deviating from the expected α OX – L relation, showing different levels of X-ray weakness.Equivalent to the α OX – L correlations, strong and con-sistent correlations between L and L for the super-and sub-Eddington subsamples were also found. Althoughthe L – L and α OX – L relations are strong,the scatters of the two relations are large, as also notedin previous studies (e.g., Vignali et al. 2003; Strateva et al.2005; Steffen et al. 2006; Just et al. 2007; Lusso et al. 2010;Lusso & Risaliti 2016). The scatters may be caused byfactors such as measurement uncertainties, X-ray absorp-tion, host-galaxy contamination, and intrinsic scatter re-lated to differences in AGN physical properties (e.g.,Lusso & Risaliti 2016). There are only slight ( < σ ) dif-ferences between the power-law slopes and intercepts of the α OX – L ( L – L ) relation for the two subsamples,suggesting that the different accretion physics in super- andsub-Eddington accreting AGNs likely contributes little to theintrinsic scatter of these relations.The α OX – L or L – L relation indicates thatthe fraction of accretion-disk radiation (or equivalently theaccretion power in the radiatively-efficient case) dissipatedvia the corona has a strong dependence on the UV lumi-3nosity. More optically luminous AGNs are observed toproduce relatively weaker X-ray emission from their coro-nae. There is still no clear understanding of the physics be-hind this empirical disk-corona connection. Simple quali-tative explanations usually involve how the accretion powerdissipation formula or the coronal size/structure changeswith accretion rate (e.g., Merloni 2003; Wang et al. 2004;Yang et al. 2007; Lusso & Risaliti 2017; Kubota & Done2018; Wang et al. 2019; Jiang et al. 2019; Arcodia et al.2019; see more discussion in Section 4.2). Nevertheless,our finding here that super-Eddington accreting AGNs fol-low basically the same α OX – L ( L – L ) relationas that for typical AGNs suggests that super-Eddington ac-creting AGNs, regardless of their geometrically thick accre-tion disks and the potential photon-trapping effects, likelyshare the same relation when dissipating the accretion powerbetween the accretion disk and corona as sub-Eddington ac-creting AGNs. Alternatively, our finding may suggest thatsuper-Eddington accreting AGNs, or at least the AGNs inour super-Eddington subsample, probably do not have dis-tinctive accretion physics (e.g., no thick disks) compared tosub-Eddington accreting AGNs.Our finding indicates that typical AGNs with log( L )in the range of ∼ . . − Hz − ) all follow the same α OX – L relation. After accounting for the scatter, thisrelation may indeed be used to estimate the intrinsic X-rayluminosity for an AGN/quasar given its UV/optical luminos-ity, and then to identify X-ray weak AGNs (e.g., Gibson et al.2008; Pu et al. 2020) or to measure enhanced X-ray emissionin radio-loud AGNs (e.g., Miller et al. 2011; Zhu et al. 2020).4.2. A More Fundamental α OX versus L Bol / L Edd plus M BH Relation?
Our carefully constructed sample of AGNs with the bestavailable BH-mass measurements provides a good oppor-tunity for seeking a physical explanation of the observed α OX – L relation. In this section, we explore the possi-bility that the α OX – L relation is physically driven bythe dependences of α OX on the two fundamental parameters, L Bol / L Edd and M BH (e.g., Shemmer et al. 2008).One promising explanation for the formation of thecorona is that the magnetic field amplified by themagneto-rotational instability (MRI) saturates due tovertical buoyancy, and it extends outside the accre-tion disk and forms a magnetically dominated coro-nal region (e.g., Stella & Rosner 1984; Tout & Pringle1992; Svensson & Zdziarski 1994; Miller & Stone 2000;Merloni & Fabian 2002; Blackman & Pessah 2009;Jiang et al. 2014). A fraction ( f X ) of the accretionpower carried away by the magnetic buoyancy is releasedvia magnetic reconnection, thereby heating the corona(e.g., Galeev et al. 1979; Di Matteo 1998; Liu et al. 2002; Uzdensky & Goodman 2008). Based on these descrip-tions and the basic theory of the standard accretion disk(Shakura & Sunyaev 1973), analytic models of the accre-tion disk-corona system (e.g., Merloni 2003; Wang et al.2004; Yang et al. 2007; Cao 2009; Lusso & Risaliti 2017;Kubota & Done 2018; Wang et al. 2019; Arcodia et al. 2019;Cheng et al. 2020) predict a smaller energy dissipation frac-tion f X for an accretion disk with a higher L Bol / L Edd , asthe accretion disk becomes more radiation-pressure domi-nated and the MRI grows less rapidly. Besides, the radiationmagneto-hydrodynamic (MHD) simulations by Jiang et al.(2014, 2019) also suggest a weaker (smaller f X ) and morecompact corona when the accretion rate increases. A similar,albeit weaker, trend between f X and M BH is also expected(e.g., Figure 5 of Yang et al. 2007), as the gas pressure de-creases more rapidly than the radiation pressure when M BH increases and the disk is again more radiation-pressure dom-inated with relatively weaker MRI.The parameter α OX , as an indicator of the coronal X-rayemission strength relative to accretion-disk UV/optical emis-sion, is likely dependent on the fraction of accretion en-ergy released in the corona. As discussed above, an AGNwith higher L Bol / L Edd and/or M BH has a smaller f X , andthus the corona is relatively weaker, leading to a smaller(steeper) α OX . Therefore, α OX is expected to be inverselycorrelated with L Bol / L Edd or M BH when the other parameteris fixed. We thus investigated whether these expected cor-relations exist for our sample. It is shown in Figure 10(a)that α OX is anti-correlated with L Bol / L Edd , and the correla-tion appears more significant when breaking the full sam-ple into the high- M BH and low- M BH subsamples. Moreover,at a fixed L Bol / L Edd , objects with higher M BH systematicallyhave lower α OX , which implies a dependence of α OX on M BH .Such an anti-correlation does exist, as shown in Figure 10(b).The correlation appears more significant when limiting tothe super-Eddington or sub-Eddington subsample. We per-formed partial correlation analysis using the R package pp-cor (Kim 2015) on α OX versus L Bol / L Edd ( M BH ), control-ling for M BH ( L Bol / L Edd ). The α OX – L Bol / L Edd ( α OX – M BH )correlation is highly significant when controlling for M BH ( L Bol / L Edd ), with a Spearman correlation coefficient of − . − .
69) and a p -value of 3 . × − (1 . × − ). The de-pendence of α OX on L Bol / L Edd or M BH has been discussed inprevious studies. Some authors found a significant correla-tion between α OX and L Bol / L Edd (e.g., Shemmer et al. 2008;Grupe et al. 2010; Lusso et al. 2010; Wu et al. 2012; Jin et al.2012; Chiaraluce et al. 2018), while some found no signifi-cant correlation (e.g., Vasudevan & Fabian 2007; Done et al.2012). Some authors found a significant correlation between α OX and M BH (e.g., Done et al. 2012; Chiaraluce et al. 2018).Our results above suggest that α OX likely depends on both4 Figure 10.
X-ray-to-optical power-law slope ( α OX ) vs. (a) L Bol / L Edd and (b) M BH . In Panel (a), the orange circles represent high- M BH objectswith BH masses larger than the median value (10 . M ⊙ ) of the full sample, and the purple squares represent the low- M BH objects. The best-fitrelations for the high- M BH objects (orange dashed line) and low- M BH objects (purple dot-dashed line) are plotted to guide the eye. In Panel (b),the super-Eddington (sub-Eddington) subsample is shown as blue circles (green squares), with the best-fit relation shown as the blue dashed(green dot-dashed) line. L Bol / L Edd and M BH . Thus the scatter of the correlation withsolely L Bol / L Edd or M BH is considerable.We performed multi-variate linear regression on therelation α OX = β log( L Bol / L Edd ) + γ log M BH + δ using thePython package emcee (Foreman-Mackey et al. 2013), whichis a Python implementation of Goodman & Weare’saffine-invariant Markov chain Monte Carlo (MCMC) ensem-ble sampler. The measurement uncertainties on the three pa-rameters are included in the fitting. The best-fit relation is α OX = ( − . ± . L Bol / L Edd ) − (0 . ± . M BH − (0 . ± .
09) (12)with a scatter of 0.07. An edge-on view of the α OX – L Bol / L Edd – M BH three-dimensional plane is shown inFigure 11(a). The α OX – L Bol / L Edd – M BH relation may bethe physical origin of the observed α OX – L relation,as L Bol / L Edd × M BH ∝ L Bol ∝ L . For comparison, weplotted the α OX versus log( L ) relation for our fullsample in Figure 11(b). We note that the scatter of the α OX – L Bol / L Edd – M BH relation is comparable to that of the α OX – L relation, which is probably due to the large un-certainties on both L Bol / L Edd and M BH . It could also be dueto the dependence of α OX on a third parameter, the ratio ofthe gas plus radiation pressure to the magnetic pressure, asthis ratio may work together with L Bol / L Edd and M BH to de-termine the broad-band AGN SED (e.g., Cheng et al. 2020).We note that it is difficult to determine if the relation be-tween α OX and L Bol / L Edd plus M BH is more fundamental thanthe α OX – L relation, or if it is a secondary manifestationof the observed α OX – L relation. There is a tight lin-ear correlation ( r s ≈
1) between L Bol ( ∝ L Bol / L Edd × M BH ) and L for our sample objects. Therefore, from the α OX – L relation (equivalently an α OX – L Bol relation), asignificant partial correlation between α OX and L Bol / L Edd or M BH when controlling for the other parameter is expected.We performed a test through creating mock sets of parame-ter K to replace M BH . In each realization, the K values arerandomly distributed in the same range as that of M BH forour sample, and we then analyzed the partial correlation be-tween α OX and L / K when controlling for K . A num-ber of realizations with different K values generated correla-tion coefficients of − . − . p -values of 10 − –10 − .These correlation significance levels are similar to those of α OX against L Bol / L Edd or M BH . Plots of α OX versus L / K are also similar to the α OX – L Bol / L Edd relation presented inFigure 10 (a). Therefore, we cannot determine whether the α OX versus L Bol / L Edd plus M BH correlation is fundamental,although physically this is an appealing explanation. A pos-sible method to resolve this issue is to investigate these cor-relations for individual AGNs, such as changing-look AGNsvarying in accretion rate. Without the complication from M BH , we may constrain better the dependence of α OX on L Bol / L Edd . 4.3.
Relation between Γ and L Bol / L Edd
A strong correlation between Γ and L Bol / L Edd ( ˙ M ) wasconfirmed for our full sample and super-Eddington sub-sample. However, such a correlation is not statisticallysignificant for the sub-Eddington subsample. We cautionthat large uncertainties associated with the measurements of L Bol / L Edd and Γ may introduce considerable uncertaintiesfor the Γ –log( L Bol / L Edd ) relation. The BH masses of our5 −1.6−1.4−1.2−1.0 α O X (a) Super-EddingtonSub-Eddington −0.8 −0.7 −0.6 −0.5 −0.13 log L
Bol /L Edd − 0.10 log M BH /M ⊙ −0.20.00.2 F i tt i n g R e s i d u a l (b) Super-EddingtonSub-Eddington
27 28 29 30 31 log L (erg s −1 Hz −1 ) Figure 11. (a) α OX – L Bol / L Edd – M BH plane seen edge-on. The red solid line shows the best-fit relation given by Equation 12. (b) α OX vs. 2500Åluminosity. The red solid line shows the best-fit relation given by Equation 4. The bottom panels show the fitting residuals, defined as thedifferences between the observed α OX values and the expectations from the corresponding best-fit relation. The two relations show comparablescatters. sample were obtained from the RM method, which is ar-guably the most reliable method for AGN BH-mass measure-ments. However, the RM method is based on the assump-tion of virial gas motions in the broad-line regions (BLRs),which may not be valid for super-Eddington accreting sys-tems due to the impact of the large radiation pressure andthe anisotropy of the ionizing radiation (e.g., Marconi et al.2008, 2009; Netzer & Marziani 2010; Krause et al. 2011;Pancoast et al. 2014; Li et al. 2018). In addition, there arepotential uncertainties associated with the measurements of L Bol . The approach we used to obtain L Bol is similar tothe estimation through the use of bolometric corrections,which employ approximations to the mean properties of typ-ical quasars. The main improvement in our study is thatthe X-ray spectral shapes for individual objects were takeninto account. Additional uncertainties on L Bol may comefrom the UV-to-X-ray SED which was set to a simple powerlaw. Super-Eddington accreting AGNs are expected to emitexcess EUV radiation compared to sub-Eddington accret-ing AGNs (e.g., Castelló-Mor et al. 2016; Kubota & Done2018), although there is still no clear observational evidencedue to the lack of EUV data. Moreover, the criterion of L Bol / L Edd (or ˙ M ) for identifying super-Eddington accret-ing AGNs is also rather uncertain (e.g., Laor & Netzer 1989;Sa¸dowski et al. 2011; Sa¸dowski & Narayan 2016).The choice of X-ray energy band in spectral fitting mayalso introduce uncertainties on the derived photon indices.The X-ray energy band investigated in this study is the rest-frame > Γ – L Bol / L Edd relation for the full sample. Comparedto similar relations reported in previous studies (see Sec-tion 3.3), there are notable discrepancies in the power-lawslopes. These discrepancies might be due to the differentsamples, different M BH ( L Bol / L Edd ) estimation methods, ordifferent statistical methods used in these studies (also seeSection 4.3 of Brandt & Alexander 2015). A large unbi-ased sample with reliable parameter measurements and cov-ering a wide range of L Bol / L Edd is required to establish the Γ – L Bol / L Edd relation for general AGNs. The X-ray photonindex could then, if confirmed, serve as an Eddington-ratioindicator, provided that the large scatter of the Γ – L Bol / L Edd relation is understood and taken into account.There is not a significant Γ – L Bol / L Edd correlation for thesub-Eddington subsample. The best-fit relation for thesuper-Eddington subsample does not appear to differ sig-nificantly from that for the full sample either. Therefore,we cannot constrain any difference between the super- andsub-Eddington accreting AGNs in terms of the Γ – L Bol / L Edd relation. However, a few recent studies have reportedthat super-Eddington accreting AGNs have even steeperX-ray photon indices in excess of those expected fromthe Γ – L Bol / L Edd relation for sub-Eddington accreting AGNs6(e.g., Gliozzi & Williams 2020; Huang et al. 2020). If such afinding is real, any physical explanations must involve the ex-pected properties of super-Eddington accretion disks, whilemaintaining basically the same accretion power dissipationrelation for the accretion disk-corona system (see the discus-sion in Section 4.1). A possible physical explanation is thatin the thick disk of a super-Eddington AGN, more radiation isemitted from the inner region of the disk due to the longer dif-fusion timescale for photons to escape from the disk surfaceand the stronger magnetic buoyancy in the inner region (e.g.,Jiang et al. 2014); this effect increases the UV/optical emis-sion received by the compact corona, reduces its temperatureand optical depth, and leads to an even steeper X-ray spec-trum. Nevertheless, a larger sample of sub-Eddington accret-ing AGNs with RM measurements is required to allow fur-ther investigations of any difference between the Γ – L Bol / L Edd correlations for super- and sub-Eddington accreting AGNs.4.4.
The Impact of X-ray Variability
Our study suggests that super-Eddington accreting AGNsexhibit normal X-ray emission and generally follow the same α OX – L ( L – L ) relation as sub-Eddington ac-creting AGNs, as long as their intrinsic X-ray emission isconsidered. However, a fraction of super-Eddington accret-ing AGNs tend to show extreme large-amplitude (factors of >
10) X-ray variability (e.g., 1H 0707 − − . + .
1: Liu et al. 2019). Threesuper-Eddington accreting AGNs (Mrk 335, PG 1211 + + α OX – L ( L – L ) relation. Their lowX-ray states can be explained by a partial-covering absorp-tion scenario, where the geometrically inner thick accretiondisk and its associated outflow play the role of the absorber(see Luo et al. 2015; Liu et al. 2019; Ni et al. 2020, and ref-erences therein). Analyses of their low-state spectra some-times cannot detect any absorption, perhaps because they ex-hibit soft ≈ . . + . ∼ ≈
14% (3/21) among the super-Eddington subsample, which is gen-erally consistent with that reported in Liu et al. (2019).Moreover, a number of our super-Eddington accreting AGNs,mostly the SDSS quasars, have limited numbers (one or two)of X-ray observations, and thus their X-ray variability behav-ior is not well constrained. It is thus possible that the actualnumber of extremely X-ray variable AGNs among our sam-ple is larger, resulting in a more significant impact of X-rayvariability on the study of the α OX – L ( L – L )and Γ – L Bol / L Edd relations for super-Eddington accretingAGNs. We therefore emphasize the importance of usinghigh-state X-ray data to probe the intrinsic accretion disk-corona connections in AGNs, especially for objects with highaccretion rates. Multiple X-ray observations are required tocollect the variability information for every sample object, inorder to construct an unbiased sample for such studies. SUMMARY AND FUTURE PROSPECTSIn this study, we constructed a sample of 47 AGNs withRM measurements, to systematically study the observationaldifferences between the coronae and accretion disk-coronaconnections in super- and sub-Eddington accreting AGNs.All our sample objects have sensitive X-ray coverage fromarchival
XMM-Newton , Chandra , or
Swift observations, andwe have selected high-state data for objects with multiple ob-servations to probe their intrinsic X-ray emission. All thesample objects, except one, have simultaneous UV/opticaldata. Our full sample was divided into the super-Eddingtonsubsample with ˙ M ≥ ˙ M <
3, and we performed detailed statistical analysis onthe α OX ( L )– L and Γ – L Bol / L Edd ( ˙ M ) correlationsfor the two subsamples. Our main results are as follows:1. We found a strong correlation between α OX and L for both the super- and sub-Eddington sub-samples. The linear regression analysis on α OX ver-sus log L reveals a slope of − . ± .
019 forthe super-Eddington subsample, which is slightly flat-ter than, but still consistent within 1 σ with the slopeof − . ± .
019 for the sub-Eddington subsample.The best-fit intercepts are also consistent within 1 σ .A strong correlation between L and L forboth the super- and sub-Eddington subsamples wasalso found. The best-fit log( L )–log( L ) rela-tions for the two subsamples are also consistent con-sidering the 1 σ uncertainties. See Section 3.1.2. A statistically significant correlation was foundbetween the hard (rest-frame > Γ ) and L Bol / L Edd for thesuper-Eddington subsample and the full sample. How-ever, there is no significant correlation between Γ and L Bol / L Edd for the sub-Eddington subsample. The7slope of the best-fit Γ –log( L Bol / L Edd ) relation for thesuper-Eddington subsample is 0 . ± .
13. See Sec-tion 3.3.3. We constructed IR-to-X-ray SEDs for tensuper-Eddington accreting AGNs with 2500 Å lu-minosities exceeding 10 . erg s − . The SEDs of mostobjects are largely consistent with those of typicalquasars, except for three objects that show weakermid-IR emission. See Section 3.4.4. Super- and sub-Eddington accreting AGNs follow thesame α OX – L ( L – L ) relation, indicatingthat super-Eddington accreting AGNs are not signifi-cantly X-ray weak compared to sub-Eddington accret-ing AGNs, as long as their intrinsic X-ray emission isconsidered. These two groups likely share the sameaccretion power dissipation relation for the accretiondisk-corona system. See Section 4.1.5. We discuss the possibility that the α OX versus L Bol / L Edd plus M BH relation serves as the physicaldriver for the observed α OX – L relation. Signif-icant dependences of α OX on both L Bol / L Edd and M BH are confirmed for our sample. A multi-variate lin-ear regression revealed the relation: α OX = ( − . ± . L Bol / L Edd ) − (0 . ± . M BH − (0 . ± . Γ and L Bol / L Edd for the sub-Eddington subsample, probably due to the smallsample size. We thus cannot constrain the difference betweenthe Γ – L Bol / L Edd relations for the two subsamples. Fromour parent sample, we excluded another six objects withoutX-ray observations and six objects with low-S/N observa-tions. Five of them have new
Chandra observations, whichwill provide constraints on their X-ray properties in the nearfuture. If targeted observations with
XMM-Newton or Chan-dra are obtained for the other objects, we will have a largersample after adding these 12 objects.We may also consider a larger sample from some ongo-ing or upcoming AGN RM projects. For example, the on-going SDSS-RM project is the first dedicated multi-objectRM program, executed with the SDSS-III Baryon OscillationSpectroscopic Survey (BOSS) spectrograph (e.g., Shen et al.2015). The primary goal of this project is to obtain RMmeasurements for &
100 quasars, which cover a wider lu-minosity and redshift range compared to previous RM AGNsamples (e.g., Shen et al. 2016; Grier et al. 2017, 2019).This program is accompanied by a large
XMM-Newton pro-gram (XMM-RM) that completes the X-ray coverage of thesame field (Liu et al. 2020). However, we note that this
XMM-Newton program has a limited number of observations with limited exposure times, and some quasars are not de-tected. These X-ray observations cannot provide tight con-straints on the X-ray properties, and they might also be bi-ased against X-ray weak/undetected objects. Targeted obser-vations with higher-quality data are still required.There are some upcoming multi-object RM campaigns.The SDSS-V Black Hole Mapper (BHM) will further ex-tend the number of RM AGNs to an "industrial scale"(Kollmeier et al. 2017). It will perform RM campaigns in anumber of fields including three of the four Deep-DrillingFields (DDFs; XMM-LSS, CDF-S, and COSMOS) of theVera C. Rubin Observatory Legacy Survey of Space andTime (LSST), and the total number of RM AGNs is expectedto be > XMM-Newton and
Chandra observations (e.g., Chen et al. 2018; Ni Q. et al. in prepa-ration). Therefore, these programs will provide promisingRM AGN samples with high-quality multiwavelength datato study the accretion disk-corona connections in AGNs.Some issues related to the multiwavelength properties ofsuper-Eddington accreting AGNs remain unclear. TheseAGNs are expected to have different SEDs compared tosub-Eddington accreting AGNs, with the primary differencesarising in the EUV band (e.g., Castelló-Mor et al. 2016;Kubota & Done 2018). The upcoming Chinese Space Sta-tion Optical survey (CSS-OS; e.g., Zhan 2018) will performa deep NUV to optical imaging survey utilizing the Multi-Channel Imager. It will provide rest-frame EUV photometricobservations for a large sample of high-redshift AGNs, whichare valuable for studying the difference between the SEDs ofsuper- and sub-Eddington accreting AGNs.Our investigation has suggested that super-Eddington ac-creting AGNs tend to show extreme X-ray variability. Itis thus important to obtain the high-state or intrinsic X-raydata for super-Eddington accreting AGNs when studyingthe disk-corona connection in these systems. The na-ture of extreme X-ray variability in super-Eddington accret-ing AGNs is still not well understood. With the ongoingeROSITA (Merloni et al. 2012; Predehl 2017) X-ray surveyof AGNs, we will obtain more variability information for thesuper-Eddington accreting AGNs that have limited numbersof X-ray observations now. We will likely discover moresources with extreme X-ray variability. Nearby luminousAGNs with high-quality mulitwavelength data are optimalsamples for examining the physical scenario for such ex-8treme behavior (e.g., Liu et al. 2019). Moreover, a system-atic monitoring program of a uniform AGN sample selectedfrom the RM campaigns discussed above, is required to con-strain better the occurrence rate of extreme X-ray variabilityin super-Eddington accreting AGNs.We thank the referee, Belinda Wilkes, for helpful suggestionsand detailed comments. We thank Pu Du, Chen Hu, Jian-Min Wang, Qiusheng Gu, Yong Shi, and Zhiyuan Li for help-ful discussions. H.L. and B.L. acknowledge financial sup- port from the National Natural Science Foundation of Chinagrants 11991053 and 11673010 and National Key R&D Pro-gram of China grant 2016YFA0400702. H.L. acknowledgesfinancial support from the program of China ScholarshipsCouncil (No. 201906190104) for her visit to the Pennsylva-nia State University. W.N.B. and J.D.T acknowledge supportfrom NASA ADP grant 80NSSC18K0878. S.C.G. thanksthe Natural Science and Engineering Research Council ofCanada for support.REFERENCES
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30 compared to the 2000 and 2006
XMM-Newton fluxes (Grupe et al. 2007). Since then, it has been continuously monitored by
Swift , but it has never fully recovered to the previousbright state (e.g., Grupe et al. 2008, 2012; Gallo et al. 2018). Compared to the 2000
XMM-Newton observation, the 2–10 keVX-ray flux of the 2006
XMM-Newton observation is slightly larger, and the exposure time is much longer (Grupe et al. 2008). Wethus used the 2006
XMM-Newton data of Mrk 335 for our study. B. IRAS F12397 + + XMM-Newton in two consecutive revolutions during2005 June 20 and 23, and the X-ray flux varied mildly between these two segments. The observations reveal that it was affectedby ionized absorption mainly in the soft (rest-frame < > Γ = 2 . ± .
02, consistent with that reported in Dou et al. (2016).It has a
Chandra observation in 2000 (Observation ID: 3000). The rest-frame 2–7 keV
Chandra spectrum is well modeled bya flatter power law with Γ = 1 . ± .
06. The 2–10 keV flux of the
Chandra observation is slightly smaller than those of the
XMM-Newton observations, and the 0.5–2 keV flux is about half of the
XMM-Newton fluxes. Therefore, the ionized absorptionduring the
Chandra observation is likely stronger. We thus used the high-state
XMM-Newton observation in our study.The UV/optical spectrum of IRAS F12397 + α/ H β = 5 .
71 and 6.14 for the broad and narrow lines, respectively (e.g., Du et al. 2014). We found an unusual flattening ofthe optical/UV spectral slope at shorter wavelengths for the OM UV/optical fluxes, which also indicates intrinsic reddening. Inorder to correct for the intrinsic reddening, we converted the Balmer decrement of the broad lines to E B − V assuming an intrinsicH α/ H β = 3 .
06 (Dong et al. 2008) and a Galactic extinction curve (Cardelli et al. 1989). The estimated E B − V value is 0.59. Wenote that the extinction does not affect the hard X-ray emission of IRAS F12397 + C. MRK 382Mrk 382, a super-Eddington accreting AGN, was observed by
Chandra for 4.9 ks on 2010 December 6 (Observation ID:13008). The rest-frame 2–7 keV
Chandra spectrum is well described by a Galactic absorption modified power law with Γ =1 . ± .
16. The extrapolation of this power law to the 0.5–7 keV energy range reveals a small excess below 2 keV. In comparison,the rest-frame > XMM-Newton spectrum (observed on 2011 November 2) is much steeper ( Γ = 2 . ± . Chandra observation. The 0 . / (1 + z ) keV XMM-Newton spectrum can be wellfitted with a single power-law model ( Γ s = 2 . ± .
01) modified by Galactic absorption. The 0.5–2 keV flux was measured to be4 . × − erg cm − s − , larger than the Chandra . × − erg cm − s − ) by a factor of about eight. Moreover,we have analyzed two archival Swift observations (2009 February 6 and 2011 September 12, respectively), which reveal fluxesbetween those in the
Chandra and
XMM-Newton observations. We thus considered the 2011
XMM-Newton observation as thehigh-state observation. D. MRK 493Mrk 493 is a super-Eddington accreting AGN. Bonson et al. (2018) has reported that the flux of Mrk 493 observed in the2015
XMM-Newton observation is about half of that of the 2003
XMM-Newton observation. Mrk 493 also has one
Chandra observation (2010 February 7; Dong et al. 2012), during which the flux and spectral photon index are consistent with those of the2003
XMM-Newton observation. We thus used the 2003
XMM-Newton observation in our analysis. E. PG 1211 + + XMM-Newton and
Swift archival observations that have not been reported in the literature, and compared the derived X-ray fluxes with those4reported in the aforementioned studies. We finally selected the highest-state observation (Observation ID: 0745110601) of thecontinuous
XMM-Newton observations in 2014 (see e.g., Lobban et al. 2016). F. PG 0844 + +
349 is a super-Eddington accreting AGN showing extreme X-ray variability by a factor of larger than 10, andits long-term X-ray light curve was presented in Gallo et al. (2011). The observation used in this study is its 2001 high-state
XMM-Newton observation. G. MRK 1310Mrk 1310 is a sub-Eddington accreting AGN that has been observed multiple times by
XMM-Newton and
Swift from 2006to 2019. Its X-ray flux showed extreme variability with a maximum amplitude of ∼
30. Meanwhile, coordinated variability inUV/optical and IR fluxes was also observed, with smaller variability amplitudes toward longer wavelengths. Its optical spectraltype has also changed, which makes it a changing-look AGN. The detailed analysis on this source will be reported in Luo B. etal. (in preparation). In this study, we used its 2016
Swift observation when it exhibited the brightest multiwavelengh fluxes. H. NGC 2617NGC 2617 is a sub-Eddington accreting AGN that underwent a dramatic X-ray outburst from 2013 April to May, duringwhich its X-ray flux increased by an order of magnitude, followed by an increase of the UV/ optical flux by almost an order ofmagnitude (e.g., Shappee et al. 2014; Giustini et al. 2017). Its optical spectral type switched from Seyfert 1.8 to Seyfert 1.0 dueto the appearance of broad optical emission lines. It was observed by
XMM-Newton on 2013 May 24 when its X-ray flux was atthe peak level (see Figure 4 of Shappee et al. 2014). We thus used this observation in our study. I. ARP 151Arp 151 is a sub-Eddington accreting AGN that showed normal X-ray emission in its 2009 February 15
Swift observation. The0.3–10 keV spectrum can be well fitted by a single power-law model modified by Galactic absorption with Γ = 1 . ± .
09, andthe 0.5–2 keV flux was measured to be 4 . × − erg cm − s − . It was observed by Chandra on 2011 December 4 (ObservationID: 12871), when it exhibited a flatter 0.5–7 keV spectrum with Γ = 1 . ± .
02. The 0.5–2 keV flux (1 . × − erg cm − s − )decreased by a factor of ≈
3, compared to the
Swift flux. We thus used the
Swift observation in our study.5
Table 1 . BH Masses, Accretion Rates, and Optical PropertiesObject z E B − V N H , gal log L FWHM(H β ) log( M BH / M ⊙ ) log ˙ M log L Bol log L Bol / L Edd (10 cm − ) (erg s − ) (km s − ) (erg s − )(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)Super-Eddington Subsample ( ˙ M ≥ .
026 0 .
035 3 .
48 43 .
76 1707 6 . + . − . . + . − . . − . + . − . Mrk 1044 0 .
016 0 .
033 3 .
10 43 .
10 1178 6 . + . − . . + . − . . − . + . − . IRAS 04416 + .
089 0 .
436 12 .
43 44 .
47 1522 6 . + . − . . + . − . .
52 0 . + . − . SDSS J074352 . + . .
252 0 .
045 4 .
69 45 .
37 3156 7 . + . − . . + . − . .
32 0 . + . − . Mrk 382 0 .
034 0 .
048 4 .
81 43 .
12 1462 6 . + . − . . + . − . . − . + . − . SDSS J080101 . + . .
140 0 .
032 2 .
53 44 .
27 1930 6 . + . − . . + . − . .
31 0 . + . − . SDSS J081441 . + . .
163 0 .
039 3 .
50 43 .
96 1729 7 . + . − . . + . − . . − . + . − . PG 0844 +
349 0 .
064 0 .
036 2 .
79 44 .
22 2694 7 . + . − . . + . − . . − . + . − . SDSS J085946 . + . .
244 0 .
032 2 .
51 44 .
41 1718 7 . + . − . . + . − . . − . + . − . Mrk 110 0 .
035 0 .
013 1 .
32 43 .
66 1633 7 . + . − . . + . − . . − . + . − . SDSS J093922 . + . .
186 0 .
014 1 .
19 44 .
07 1209 6 . + . − . . + . − . .
16 0 . + . − . PG 0953 +
414 0 .
234 0 .
012 1 .
25 45 .
19 3070 8 . + . − . . + . − . . − . + . − . SDSS J100402 . + . .
329 0 .
022 1 .
77 45 .
52 2088 7 . + . − . . + . − . .
34 0 . + . − . Mrk 142 0 .
045 0 .
016 1 .
28 43 .
59 1462 6 . + . − . . + . − . . − . + . − . UGC 6728 0 .
007 0 .
100 4 .
37 41 .
86 1641 5 . + . − . . + . − . . − . + . − . PG 1211 +
143 0 .
081 0 .
033 2 .
92 44 .
73 2012 7 . + . − . . + . − . . − . + . − . IRASF 12397 + .
043 0 .
019 1 .
42 44 .
23 1802 6 . + . − . . + . − . .
97 0 . + . − . NGC 4748 0 .
015 0 .
051 3 .
50 42 .
56 1947 6 . + . − . . + . − . . − . + . − . Mrk 493 0 .
031 0 .
025 2 .
09 43 .
11 778 6 . + . − . . + . − . .
35 0 . + . − . KA 1858 + .
079 0 .
054 4 .
28 43 .
43 1820 6 . + . − . . + . − . . − . + . − . PG 2130 +
099 0 .
062 0 .
043 3 .
80 44 .
20 2450 7 . + . − . . + . − . .
44 0 . + . − . Sub-Eddington Subsample ( ˙ M < +
129 0 .
142 0 .
072 4 .
56 44 .
97 2543 8 . + . − . . + . − . . − . + . − . PG 0052 +
251 0 .
154 0 .
046 4 .
40 44 .
81 5007 8 . + . − . − . + . − . . − . + . − . Fairall 9 0 .
047 0 .
025 3 .
22 43 .
98 5998 8 . + . − . − . + . − . . − . + . − . Ark 120 0 .
033 0 .
128 9 .
70 43 .
87 6077 8 . + . − . − . + . − . . − . + . − . MCG + − −
011 0 .
020 0 .
214 18 .
48 43 .
33 4138 7 . + . − . − . + . − . . − . + . − . Mrk 374 0 .
043 0 .
052 5 .
16 43 .
77 4980 7 . + . − . − . + . − . . − . + . − . Mrk 79 0 .
022 0 .
071 5 .
06 43 .
68 4793 7 . + . − . − . + . − . . − . + . − . PG 0804 +
761 0 .
064 0 .
035 3 .
29 44 .
91 3052 8 . + . − . − . + . − . . − . + . − . NGC 2617 0 .
014 0 .
034 3 .
52 42 .
67 8026 7 . + . − . − . + . − . . − . + . − . SBS 1116 + A .
028 0 .
011 0 .
75 42 .
14 3668 6 . + . − . − . + . − . . − . + . − . Arp 151 0 .
021 0 .
014 1 .
03 42 .
55 3098 6 . + . − . − . + . − . . − . + . − . MCG + − −
012 0 .
033 0 .
019 1 .
93 42 .
67 1334 6 . + . − . − . + . − . . − . + . − . Mrk 1310 0 .
020 0 .
031 2 .
50 42 .
29 2409 6 . + . − . . + . − . . − . + . − . Table 1 continued Table 1 (continued)
Object z E B − V N H , gal log L FWHM(H β ) log( M BH / M ⊙ ) log ˙ M log L Bol log L Bol / L Edd (10 cm − ) (erg s − ) (km s − ) (erg s − )(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)Mrk 766 0 .
013 0 .
020 1 .
86 42 .
57 1609 6 . + . − . − . + . − . . − . + . − . Ark 374 0 .
063 0 .
027 2 .
82 43 .
70 3827 8 . + . − . − . + . − . . − . + . − . NGC 4593 0 .
009 0 .
025 1 .
87 42 .
62 5141 7 . + . − . − . + . − . . − . + . − . PG 1307 +
085 0 .
155 0 .
034 2 .
26 44 .
85 5058 8 . + . − . − . + . − . . − . + . − . Mrk 279 0 .
030 0 .
016 1 .
67 43 .
71 5354 7 . + . − . − . + . − . . − . + . − . NGC 5548 0 .
017 0 .
020 1 .
65 43 .
29 7241 8 . + . − . − . + . − . . − . + . − . PG 1426 +
015 0 .
087 0 .
032 2 .
58 44 .
63 7112 8 . + . − . − . + . − . . − . + . − . Mrk 817 0 .
031 0 .
007 1 .
16 43 .
74 5347 7 . + . − . − . + . − . . − . + . − . Mrk 290 0 .
030 0 .
014 1 .
55 43 .
17 4542 7 . + . − . − . + . − . . − . + . − . Mrk 876 0 .
139 0 .
027 2 .
42 44 .
77 9073 8 . + . − . − . + . − . . − . + . − . NGC 6814 0 .
005 0 .
184 9 .
08 42 .
12 3323 7 . + . − . − . + . − . . − . + . − . Mrk 509 0 .
034 0 .
057 4 .
17 44 .
19 3014 8 . + . − . − . + . − . . − . + . − . NGC 7469 0 .
016 0 .
070 4 .
17 43 .
51 4369 7 . + . − . − . + . − . . − . + . − . N OTE —Columns (1), (2): object name and redshift. Column (3): Galactic extinction from Schlegel et al. (1998). Column (4): Galactic neutralhydrogen column density from Dickey & Lockman (1990). Columns (5)–(7): 5100 Å luminosity, H β FWHM, and BH mass, adopted fromDu et al. (2015, 2016); Du & Wang (2019). Column (8): normalized accretion rate calculated using ˙ M = 4 . ℓ / cos i ) / m − (cos i =0 .
75 adopted). Column (9): bolometric luminosity, measured through integrating the IR-to-X-ray SED (see Section 2.7 for details). Theuncertainties on the bolometric luminosities range from 0.001–0.09 dex, with a median value of 0.01 dex. Column (10): Eddington ratio. Table 2 . X-ray Observation Log and Hard X-ray Spectral Fitting ResultsObject Observatory Observation Exposure Source Γ log f log L W-stat/dof N UV log L α OX ∆ α OX ID Time (ks) Counts (erg cm − s − Hz − ) (erg s − ) (erg s − Hz − )(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)Super-Eddington Subsample ( ˙ M ≥ b X 0306870101 89.7 179984 2 . + . − . − .
60 43 .
44 1526 . / − . − .
33 0 . . + . − . − .
63 42 .
96 1395 . / . − . − . + . + . − . − .
37 43 .
63 106 . /
99 1 29 . − . − . . + . . + . − . − .
63 44 .
44 66 . /
66 1 30 . − . − . a X 0670040101 25.8 12318 2 . + . − . − .
25 43 .
00 1292 . / . − . − . . + . . + . − . − .
86 43 .
59 681 . /
864 3 29 . − . − . . + . . + . − . − .
89 43 .
75 854 . / . − .
37 0 . + a , b X 0103660201 5.9 3507 2 . + . − . − .
11 43 .
68 691 . / − . − . − . . + . . + . − . − .
36 43 .
77 71 . /
100 0 29 . − . − . . + . − . − .
50 43 .
92 1339 . / . − .
22 0 . . + . . + . − . − .
29 43 .
39 144 . /
175 1 29 . − . − . +
414 X 0111290201 10.6 5618 2 . + . − . − .
30 44 .
72 1015 . / . − .
45 0 . . + . . + . − . − .
94 44 .
29 803 . /
809 2 30 . − . − . . + . − . − .
59 42 .
93 122 . /
140 3 28 . − . − . . + . − . − .
88 42 .
12 342 . /
384 1 27 . − . − . + b X 0745110501 50.9 25632 2 . + . − . − .
21 43 .
84 1136 . / . − . − . + a X 0202180201 55.0 32163 2 . + . − . − .
13 43 .
34 1156 . / . − . − . a X 0723100401 26.3 14909 2 . + . − . − .
95 42 .
60 960 . / . − . − . a X 0112600801 12.2 6120 2 . + . − . − .
23 42 .
95 1191 . / . − . − . + . + . − . − .
62 43 .
47 36 . /
42 1 28 . − .
27 0 . +
099 X 0744370201 21.7 1843 2 . + . − . − .
17 43 .
66 598 . /
664 2 29 . − . − . M < +
129 X 0783270201 5.7 2779 1 . + . − . − .
32 44 .
35 728 . /
794 2 29 . − .
39 0 . + a X 0301450401 13.7 7193 1 . + . − . − .
10 44 .
64 1057 . / . − .
35 0 . Table 2 continued Table 2 (continued)
Object Observatory Observation Exposure Source Γ log f log L W-stat/dof N UV log L α OX ∆ α OX ID Time (ks) Counts (erg cm − s − Hz − ) (erg s − ) (erg s − Hz − )(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)Fairall 9 X 0741330101 5.2 8484 1 . + . − . − .
55 44 .
08 913 . / . − .
29 0 . . + . − . − .
31 43 .
98 1752 . / . − .
35 0 . + − −
011 X 0201930201 26.4 109848 1 . + . − . − .
36 43 .
64 1317 . / . − .
20 0 . . + . − . − .
29 43 .
28 266 . /
321 1 28 . − . − . . + . − . − .
56 43 .
42 1190 . / . − .
19 0 . +
761 X 0605110101 16.2 11784 2 . + . − . − .
87 43 .
97 987 . / . − . − . . + . − . − .
29 43 .
35 1286 . / . − .
16 0 . + a X 0821871801 18.7 3104 1 . + . − . − .
71 42 .
53 892 . / . − . − . . + . − . − .
02 43 .
01 347 . /
400 3 28 . − .
19 0 . + − −
012 S 00040821003 4.8 98 1 . + . − . − .
57 42 .
73 80 . /
84 1 28 . − . − . . + . − . − .
03 42 .
85 156 . /
185 2 28 . − . − . . + . − . − .
72 42 .
77 1175 . / . − .
05 0 . . + . − . − .
38 43 .
50 1063 . / . − . − . . + . − . − .
66 42 .
61 1254 . / . − . − . +
085 X 0110950401 9.9 1583 1 . + . − . − .
78 44 .
06 631 . /
811 2 30 . − . − . . + . − . − .
52 43 .
76 1299 . / . − .
24 0 . . + . − . − .
42 43 .
43 1300 . / − . − .
20 0 . + a X 0102040501 5.3 5945 1 . + . − . − .
95 44 .
20 927 . / . − .
47 0 . a X 0601781401 5.0 8127 2 . + . − . − .
75 43 .
48 1172 . / . − . − . . + . − . − .
07 43 .
30 1435 . / . − . − . . + . − . − .
34 44 .
36 765 . /
814 2 30 . − . − . . + . − . − .
66 42 .
14 1086 . / − . − . − . . + . − . − .
32 44 .
08 1512 . / . − .
38 0 . . + . − . − .
47 43 .
24 1500 . / . − . − . Table 2 continued Table 2 (continued)
Object Observatory Observation Exposure Source Γ log f log L W-stat/dof N UV log L α OX ∆ α OX ID Time (ks) Counts (erg cm − s − Hz − ) (erg s − ) (erg s − Hz − )(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)N OTE — Column (1): object name. Column (2): X-ray Observatory. X:
XMM-Newton ; C:
Chandra ; S:
Swift . Column (3): observation ID.Column (4): cleaned exposure time after filtering for high-background flares. Column (5): number of rest-frame > > −
2” denotes that only grism spectral data are available. “ −
1” denotes that UV-filter data are not available and U-filterdata were used for calculating the flux density at 2500 Å. “0” denotes that there are no simultaneous UV/optical data for the only
Chandra object, SDSS J085946 . + .
8, for which the flux density at 2500 Å was interpolated from its
GALEX
NUV and SDSS u -band fluxdensities. Column (11): logarithm of the rest-frame 2500 Å monochromatic luminosity. Columns (12), (13): observed α OX value, and thedifference between the observed α OX and the expected value derived from the Steffen et al. (2006) α OX – L relation.a X-ray sources affected by pile-up.b Objects that have shown extreme X-ray variability by factors of larger than 10. Table 3 . Soft X-ray Spectral Fitting ResultsObject Model Γ s COMPTT ZXIPCF log L . T seed (eV) kT (keV) τ N H (10 cm − ) log ξ f cov (erg s − )(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)Super-Eddington Subsample ( ˙ M ≥ ± . + . − . . + . − . ... ... ... . + − . + . − . . + . − . ... ... ... . + . + . − . ... ... ... ... ... ... 43 . . + . . + . − . ... ... ... ... ... ... 44 . . + . − . ... ... ... ... ... ... 43 . . + . + − . + . − . + − ... ... ... . . + . + − . + . − . + − ... ... ... . +
349 A 2 . + . − . ... ... ... ... ... ... 44 . . + . . + . − . ... ... ... ... ... ... 43 . . + . − . ... ... ... ... ... ... 44 . . + . + − . + . − . ± ... ... ... . +
414 B 2.02 82 ± . + . − . . + . − . ... ... ... . . + . ± . + . − . + − ... ... ... . . + . − . ... ... ... ... ... ... 43 . . + . − . ... ... ... ... ... ... 41 . +
143 B 2.07 80 ± . + . − . . + . − . ... ... ... . + .
15 229 + − . + . − . + − . + . − . . + . − . . + . − . . . + . − . ... ... ... ... ... ... 42 . + − . ± .
02 14 ± ... ... ... . + . + . − . ... ... ... ... ... ... 43 . +
099 A 2 . + . − . ... ... ... ... ... ... 43 . M < +
129 B 1.75 76 + − . + . − . ± ... ... ... . +
251 B 1.75 228 + − . + . − . + − ... ... ... . Table 3 continued Table 3 (continued)
Object Model Γ s COMPTT ZXIPCF log L . T seed (eV) kT (keV) τ N H (10 cm − ) log ξ f cov (erg s − )(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)Fairall 9 A 2 . + . − . ... ... ... ... ... ... 44 . ± . + . − . ± ... ... ... . + − −
011 A 1 . + . − . ... ... ... ... ... ... 43 . . + . − . ... ... ... ... ... ... 43 . ± . + . − . + − ... ... ... . +
761 B 2.08 60 + − . + . − . ± ... ... ... . . + . − . ... ... ... ... ... ... 43 . + A B 1.72 74 + − . + . − . . + . − . ... ... ... . . + . − . ... ... ... ... ... ... 42 . + − −
012 A 2 . + . − . ... ... ... ... ... ... 42 . . + . − . ... ... ... ... ... ... 42 . ± . + . − . . + . − . . + . − . . + . − . . + . − . . . + . − . ... ... ... ... ... ... 43 . + − . + . − . + − ... ... ... . +
085 A 2 . + . − . ... ... ... ... ... ... 43 . + − . + . − . . + . − . ... ... ... . ± . + . − . + − . + . − . . + . − . . + . − . . +
015 A 2 . + . − . ... ... ... ... ... ... 44 . . + . − . ... ... ... ... ... ... 43 . ± . + . − . . + . − . . + . − . . ± . . + . − . . . + . − . ... ... ... ... ... ... 44 . . + . − . ... ... ... ... ... ... 42 . ± . + . − . . + . − . ... ... ... . ± . ± .
03 9 . + . − . . + . − . . + . − . . OTE —Column (1): object name. Column (2):
XSPEC spectral fitting model. A:
PHABS * ZPOWERLW ; B:
PHABS *( COMPTT + ZPOWERLW ); C:
PHABS * ZXIPCF *( COMPTT + ZPOWERLW ). In Model B or C, the
ZPOWERLW component is fixed to that constrained from the rest-frame > Γ value in Table 2 for Model B or C. Columns (4)–(6):parameters of the COMPTT component (Model B or C), including the temperature of seed photons, temperature of electrons in the warmcorona, and optical depth of the warm corona. Columns (7)–(9): column density, ionization state, and covering factor of the partial-coveringionized absorption component (