A statistical relation between the X-ray spectral index and Eddington ratio of active galactic nuclei in deep surveys
M. Brightman, J. D. Silverman, V. Mainieri, Y. Ueda, M. Schramm, K. Matsuoka, T. Nagao, C. Steinhardt, J. Kartaltepe, D. B. Sanders, E. Treister, O. Shemmer, W. N. Brandt, M. Brusa, A. Comastri, L. C. Ho, G. Lanzuisi, E. Lusso, K. Nandra, M. Salvato, G. Zamorani, M. Akiyama, D. M. Alexander, A. Bongiorno, P. Capak, F. Civano, A. Del Moro, A. Doi, M. Elvis, G. Hasinger, E. S. Laird, D. Masters, M. Mignoli, K. Ohta, K. Schawinski, Y. Taniguchi
MMon. Not. R. Astron. Soc. , 000–000 (0000) Printed 29 October 2018 (MN L A TEX style file v2.2)
A statistical relation between the X-ray spectral index andEddington ratio of active galactic nuclei in deep surveys
M. Brightman (cid:63) , J. D. Silverman , V. Mainieri , Y. Ueda , M. Schramm , K. Matsuoka , T. Nagao , , C. Steinhardt , J. Kartaltepe , D. B. Sanders , E. Treister , O. Shemmer W. N. Brandt , M. Brusa , , , A. Comastri , L. C. Ho , G. Lanzuisi , E. Lusso K. Nandra , M. Salvato , G. Zamorani , M. Akiyama , D. M. Alexander , A. Bongiorno , P. Capak , F. Civano , A. Del Moro , A. Doi , M. Elvis , G. Hasinger , E. S. Laird D. Masters , M. Mignoli , K. Ohta , K. Schawinski , Y. Taniguchi Max-Planck-Institut f¨ur extraterrestrische Physik, Giessenbachstrasse 1, D-85748, Garching bei M¨unchen, Germany Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study, the University of Tokyo European Southern Observatory, Karl-Schwarzschild-Strasse 2, 85748 Garching bei M¨unchen, Germany Department of Astronomy, Kyoto University, Kitashirakawa-Oiwake- cho, Sakyo-ku, Kyoto 606-8502, Japan Department of Physics and Astronomy, Seoul National University, 599 Gwanak-ro, Gwanak-gu, Seoul 151-742, Republic of Korea Research Center for Space and Cosmic Evolution, Ehime University, 2-5 Bunkyo-cho, Matsuyama 790-8577, Japan The Hakubi Center for Advanced Research, Kyoto University, Yoshida- Ushinomiya-cho, Sakyo-ku, Kyoto 606-8302, Japan National Optical Astronomy Observatory, 950 North Cherry Aveue, Tucson, AZ 85719, USA Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA Departamento de Astronom´ıa, Universidad de Concepci´on, Casilla 160- C, Concepci´on, Chile Department of Physics, University of North Texas, Denton, TX 76203, USA Department of Astronomy and Astrophysics, The Pennsylvania State University, University Park, PA 16802, USA Dipartimento di Fisica e Astronomia, Universit´a degli Studi di Bologna, viale Berti Pichat 6/2, 40127 Bologna, Italy INAF Osservatorio Astronomico di Bologna, Via Ranzani 1, 40127 Bologna, Italy The Observatories of the Carnegie Institution for Science, 813 Santa Barbara Street, Pasadena, CA 91101, USA Max Planck Institut f¨ur Astronomie, K¨onigstuhl 17 D-69117 Heidelberg, Germany Astronomical Institute, Tohoku University, 6-3 Aramaki, Aoba-ku, Sendai 980-8578, Japan Department of Physics, Durham University, South Road, Durham DH1 3LE, UK INAF Osservatorio Astronomico di Roma, Via di Frascati 33, 00040 Monte Porzio Catone, Italy NASA/JPL Spitzer Science center, California Institute of Technology, 1200 East California Boulevard, Pasadena, CA 91125, USA Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA The Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Chuou-ku, Sagamihara, Kanagawa 252-5210, Japan Astrophysics Group, Imperial College London, Blackett Laboratory, Prince Consort Road, London SW7 2AZ, UK Department of Physics, Yale University, New Haven, CT 06520, USA
29 October 2018 © a r X i v : . [ a s t r o - ph . H E ] M a y M. Brightman, et al.
ABSTRACT
We present an investigation into how well the properties of the accretion flow onto asupermassive black hole may be coupled to those of the overlying hot corona. To doso, we specifically measure the characteristic spectral index, Γ, of a power-law energydistribution, over an energy range of 2 to 10 keV, for X-ray selected, broad-linedradio-quiet active galactic nuclei (AGN) up to z ∼ ii and H α emission lines with the later afforded by recent nearinfrared spectroscopic observations using Subaru/FMOS. We calculate the Eddingtonratios, λ Edd , for sources where a bolometric luminosity ( L Bol ) has been presented inthe literature, based on SED fitting, or, for sources where these data do not exist, wecalculate L Bol using a bolometric correction to the X-ray luminosity, derived from arelationship between the bolometric correction, and L X / L . From a sample of 69X-ray bright sources ( >
250 counts), where Γ can be measured with greatest precision,with an estimate of L Bol , we find a statistically significant correlation between Γ and λ Edd , which is highly significant with a chance probability of 6.59 × − . A statisticallysignificant correlation between Γ and the FWHM of the optical lines is confirmed,but at lower significance than with λ Edd indicating that λ Edd is the key parameterdriving conditions in the corona. Linear regression analysis reveals that Γ = (0 . ± . λ Edd +(2 . ± .
06) and Γ = ( − . ± . (FWHM/km s − )+(4 . ± . λ Edd are in very good agreement with previous results. Whilethe Γ- λ Edd relationship means that X-ray spectroscopy may be used to estimate blackhole accretion rate, considerable dispersion in the correlation does not make this viablefor single sources, however could be valuable however for large X-ray spectral samples,such as those to be produced by eROSITA . X-ray emission from AGN is ubiquitous (Tananbaum et al.1979), and is often used itself as an indicator of black holeaccretion activity. The hard X-ray ( > F γ = AE − Γ (photons cm − s − ). The X-rayemission is thought to be produced by the Compton up-scattering of seed optical/UV photons, produced by ther-mal emission from the accretion disc (Shakura & Sunyaev1973). This is believed to be done by hot electrons forminga corona in proximity to the disc (e.g. Sunyaev & Titarchuk1980). Investigations into the X-ray emission can yield im-portant insights into the accretion process and constrain ac-cretion models (e.g. Haardt & Maraschi 1991, 1993). How-ever, many details regarding this process remain unclear,for example the geometry of the corona, its heating and theenergy transfer between the two phases.The discovery of the intrinsic power-law index measuredto be Γ ∼ . e and optical depth to electron scattering, τ es , upon whichΓ depends (Rybicki & Lightman 1986).The temperature, and thus emission spectrum of a stan-dard Shakura & Sunyaev accretion disc depends on the massaccretion rate, ˙ m , (Shakura & Sunyaev 1973). The lumi-nosity of the system is thus related to ˙ m via the accretionefficiency, L Bol = η ˙ mc , which is often parametrised as afraction of the Eddington luminosity, L Edd , by the Edding-ton ratio, λ Edd = L Bol /L Edd . L Edd is the theoretical maximal luminosity achieved via accretion when accounting for ra-diation pressure and is dependent on the black hole mass( L Edd = 4 π G M BH m p c/σ T (cid:39) . × M BH erg s − ,where M BH is the black hole mass in solar masses). Due tothe dependance of the accretion disc spectrum on these pa-rameters, several works have investigated how the coronalX-ray emission is coupled. It has been shown that Γ is wellcorrelated with the full width at half maximum (FWHM) ofthe broad optical emission lines, specifically H β (e.g. Bolleret al. 1996; Brandt et al. 1997), giving some indication thatthe gravitational potential, i.e. black hole mass, is key. Sub-sequently λ Edd was shown to be strongly correlated withΓ (Lu & Yu 1999; Wang et al. 2004; Shemmer et al. 2006).However a known degeneracy exists between the H β FWHMand λ Edd of the system (Boroson & Green 1992), makingit difficult to determine the fundamental parameter behindthese relationships. Shemmer et al. (2006)(S06) were able tobreak this degeneracy by adding highly luminous quasars totheir analysis, concluding that λ Edd is the primary param-eter driving the conditions in the corona, giving rise to Γ.Shemmer et al. (2008) (S08) followed up the work of S06 byadding further luminous quasars, increasing the significanceof the previous result.Follow up studies have confirmed this relationship us-ing larger samples and extending the range of parametersprobed (e.g. Risaliti et al. 2009; Jin et al. 2012; Fanali et al.2013). Furthermore, works into the possible dependence ofΓ on X-ray luminosity ( L X ) have reported a positive corre-lation between these quantities in high redshift sources (Daiet al. 2004; Saez et al. 2008), but not seen in the local uni-verse (George et al. 2000; Brightman & Nandra 2011), andan evolution of this correlation was also reported in Saezet al. (2008). One interpretation of this correlation, how-ever, was that it is driven fundamentally by changes in ˙ m .It has been shown that ˙ m can also be estimated from X- ©000
06) and Γ = ( − . ± . (FWHM/km s − )+(4 . ± . λ Edd are in very good agreement with previous results. Whilethe Γ- λ Edd relationship means that X-ray spectroscopy may be used to estimate blackhole accretion rate, considerable dispersion in the correlation does not make this viablefor single sources, however could be valuable however for large X-ray spectral samples,such as those to be produced by eROSITA . X-ray emission from AGN is ubiquitous (Tananbaum et al.1979), and is often used itself as an indicator of black holeaccretion activity. The hard X-ray ( > F γ = AE − Γ (photons cm − s − ). The X-rayemission is thought to be produced by the Compton up-scattering of seed optical/UV photons, produced by ther-mal emission from the accretion disc (Shakura & Sunyaev1973). This is believed to be done by hot electrons forminga corona in proximity to the disc (e.g. Sunyaev & Titarchuk1980). Investigations into the X-ray emission can yield im-portant insights into the accretion process and constrain ac-cretion models (e.g. Haardt & Maraschi 1991, 1993). How-ever, many details regarding this process remain unclear,for example the geometry of the corona, its heating and theenergy transfer between the two phases.The discovery of the intrinsic power-law index measuredto be Γ ∼ . e and optical depth to electron scattering, τ es , upon whichΓ depends (Rybicki & Lightman 1986).The temperature, and thus emission spectrum of a stan-dard Shakura & Sunyaev accretion disc depends on the massaccretion rate, ˙ m , (Shakura & Sunyaev 1973). The lumi-nosity of the system is thus related to ˙ m via the accretionefficiency, L Bol = η ˙ mc , which is often parametrised as afraction of the Eddington luminosity, L Edd , by the Edding-ton ratio, λ Edd = L Bol /L Edd . L Edd is the theoretical maximal luminosity achieved via accretion when accounting for ra-diation pressure and is dependent on the black hole mass( L Edd = 4 π G M BH m p c/σ T (cid:39) . × M BH erg s − ,where M BH is the black hole mass in solar masses). Due tothe dependance of the accretion disc spectrum on these pa-rameters, several works have investigated how the coronalX-ray emission is coupled. It has been shown that Γ is wellcorrelated with the full width at half maximum (FWHM) ofthe broad optical emission lines, specifically H β (e.g. Bolleret al. 1996; Brandt et al. 1997), giving some indication thatthe gravitational potential, i.e. black hole mass, is key. Sub-sequently λ Edd was shown to be strongly correlated withΓ (Lu & Yu 1999; Wang et al. 2004; Shemmer et al. 2006).However a known degeneracy exists between the H β FWHMand λ Edd of the system (Boroson & Green 1992), makingit difficult to determine the fundamental parameter behindthese relationships. Shemmer et al. (2006)(S06) were able tobreak this degeneracy by adding highly luminous quasars totheir analysis, concluding that λ Edd is the primary param-eter driving the conditions in the corona, giving rise to Γ.Shemmer et al. (2008) (S08) followed up the work of S06 byadding further luminous quasars, increasing the significanceof the previous result.Follow up studies have confirmed this relationship us-ing larger samples and extending the range of parametersprobed (e.g. Risaliti et al. 2009; Jin et al. 2012; Fanali et al.2013). Furthermore, works into the possible dependence ofΓ on X-ray luminosity ( L X ) have reported a positive corre-lation between these quantities in high redshift sources (Daiet al. 2004; Saez et al. 2008), but not seen in the local uni-verse (George et al. 2000; Brightman & Nandra 2011), andan evolution of this correlation was also reported in Saezet al. (2008). One interpretation of this correlation, how-ever, was that it is driven fundamentally by changes in ˙ m .It has been shown that ˙ m can also be estimated from X- ©000 , 000–000 ray variability analysis (e.g. McHardy et al. 2006), where ˙ m is correlated with the break timescale in the power densityspectrum. Papadakis et al. (2009) used this result when con-ducting a joint X-ray spectral and timing analysis of nearbySeyfert galaxies to show in an independent manner that Γcorrelates with ˙ m . Furthermore, in a study of the X-rayvariability in primarily local AGN, Ponti et al. (2012) finda significant correlation between the excess variance, σ ,and Γ, which when considering the correlation between σ and ˙ m that they find, is indirect evidence for the dependanceof Γ on ˙ m .The strong correlation between Γ and accretion rate isinterpreted as enhanced emission from the accretion discin higher accretion rate systems more effectively coolingthe corona, leading to a steepening of the X-ray emission(Pounds et al. 1995).Not only is the Γ- λ Edd correlation significant with re-spect to constraining accretion models, but as pointed outby S06, it allows an independent measurement of the blackhole growth activity in galaxies from X-ray spectroscopyalone, and with a measurement of the bolometric luminos-ity, a black hole mass can be determined. This would beespecially useful for moderately obscured AGN, where virialblack hole mass estimates are not possible, but X-rays canpenetrate the obscuration.The aim of this work is to extend previous analyseson correlations with Γ for the first time to the deep ex-tragalactic surveys and in doing so, extending the range ofparameters explored, breaking degeneracies between param-eters where possible. By the use of survey data, we benefitfrom uniform X-ray data, where previous studies have re-lied on non-uniform archival data. In order to use Γ as anEddington ratio indicator, the dispersion in the relationshipmust be well parametrised, which we aim to do with thelarge range in parameters explored and our uniform X-raycoverage.In addition, our black hole mass estimates are based ontwo optical lines, H α and Mg ii . Risaliti et al. (2009) (R09)showed that there was a stronger correlation with λ Edd formeasurements made with H β compared to Mg ii and C iv ,suggesting that this line is the best black hole mass indicatorof the three. The H α data used here were specifically pursuedpartly in order to investigate the Γ correlations with H α data for the first time at high redshifts, facilitated by near-infrared (NIR) spectroscopy. The parameters we explore inthis work are L UV , L X , FWHM, M BH and λ Edd .In this work we assume a flat cosmological model with H =70 km s − Mpc − and Ω Λ =0.70. For measurement un-certainties on our spectral fit parameters we present the90% confidence limits given two interesting parameters (∆c-stat=4.61). Our sample is based on two major extragalactic surveys,the extended
Chandra
Deep Field-South (E-CDF-S Lehmeret al. 2005), inclusive of the ultra-deep central area (Giacconiet al. 2002; Luo et al. 2008; Xue et al. 2011), and COSMOS surveys (Cappelluti et al. 2009; Elvis et al. 2009), where deepX-ray coverage with high optical spectroscopic completenessexists in both fields. The sample selection is as follows: • We select sources with a black hole mass estimatesbased on H α or Mg ii from a black hole mass catalogueto be presented in Silverman, et al (in preparation). Mg ii line measurements were made from extensive existing op-tical spectra, primarily from zCOSMOS, Magellan/IMACS,Keck/Deimos and SDSS. Measurements of H α up to z ∼ . Chandra
X-ray selected AGN in COSMOS (Elvis et al. 2009) andE-CDF-S (Lehmer et al. 2005) with an already known spec-troscopic redshift and detection of a broad emission line(FWHM > − ). A subset of the optical and NIRspectroscopic data analysis has already been presented inMatsuoka et al. (2013). • In COSMOS we select Chandra sources also detected byXMM-Newton (see discussion in Brusa et al. 2010), due tothe higher throughput capability of this observatory with re-spect to Chandra. For the E-CDF-S, we use the deep Chan-dra data available.Combining these surveys and the selection criteria aboveyields a sample of 260 sources with both a black hole massestimate and X-ray data, however, the main goal of this workis to investigate the detailed relationship between the coro-nal X-ray emission, characterised by the power-law index, Γ,and the parameters of the accretion, the observed quantitiesbeing luminosity and FWHM, and the derived quantitiesbeing M BH and λ Edd . We therefore make the following cutsto the above sample as follows: • We take sources where there are at least 250 sourcecounts in the X-ray spectrum in order to get an accuratemeasurement of Γ. We describe this further in section 2.5. • For analysis with λ Edd , a bolometric luminosity is re-quired which we take from Lusso et al. (2012) (L12), whichare derived from spectral energy distribution (SED) fitting.As these data do not exist for E-CDF-S sources, we use abolometric correction to the X-ray luminosity, derived from L X / L , which we describe in section 2.6. There are 44which have an L Bol from L12, all of which are in COSMOS,and 31 of which have L Bol calculated using L X / L , all ofwhich are in the E-CDF-S. • As we wish to study the properties of the coronal emis-sion, responsible for the majority of X-ray emission in radioquiet AGN, we exclude radio loud sources. For this we makea cut of R < M BH and 69 sources for analysis with λ Edd .Fig 1 shows how our final sample spans the redshift-luminosity plane, and how it compares to the sample ofR09 which is derived from the
SDSS/XMM-Newton quasarsurvey of Young et al. (2009). Our combination of wideand deep survey data allows us to span a larger luminosityrange than done previously, and better sample to luminosity-redshift plane. © , 000–000 M. Brightman, et al.
Figure 1.
Plot of the redshift and X-ray luminosity distributionin our combined sample, where large red data points are fromthe E-CDF-S and the large black data points are from COSMOS.The sample covers redshifts up to ∼ . . (cid:46) log L X /erg s − (cid:46) .
5. The dots show thesample of R09, which is derived from the
SDSS/XMM-Newton quasar survey of Young, et al (2009).
The first step in our analysis is to determine the accretionparameters, the velocity dispersion of the material aroundthe black hole, characterised by the FWHM of the opticallines and M BH , which we derive from single-epoch opticalspectral line fitting. A full description of the target selection,data analysis, including spectral line fitting, and results onvirial black hole mass is presented in Matsuoka et al. (2013),which we briefly describe here.Mg ii line measurements were made from optical spec-tra obtained primarily from zCOSMOS, Magellan/IMACSand SDSS. Fitting of the Mg ii line was carried out usinga power-law to characterise the continuum, and one to twoGaussians used for the line. A broad Fe emission componentis also included, which is based on the empirical template ofVestergaard & Wilkes (2001).The H α measurements used here were the result of acampaign to make Balmer line observations of AGN out-side the optical window at z > . λ/λ (cid:39) µ m)and H (1.43-1.77 µ m) bands, yielding a velocity resolutionof FWHM ∼
500 km s − at λ = 1 . µ m. The target selectionwas such that the continuum around H α could be accuratelydetermined and fit by a power-law. The H α line was fit by2 to 3 Gaussians, while the neighbouring [NII] λ M BH M (cid:12) = a + b log λL λ or L line erg s − + c log FWHMkms − (1)where a=1.221, b=0.550 and c=2.060 for H α from Greene& Ho (2005) and a=0.505, b=0.620 and c=2.000 for Mg ii from McLure & Jarvis (2002). For H α , the line luminosity isused in the calculation, whereas for Mg ii the monochromaticluminosity at 3000 ˚A is used.In Matsuoka et al. (2013) a comparison of virial blackhole mass estimates from H α and Mg ii is presented. Theyfind a tight correlation between L H α and L and a closeone-to-one relationship between the FWHM of H α andMg ii , therefore leading to good agreements between themass estimates from these lines. While H β detections withFMOS do exist for this sample, measurements with this lineis to be presented in a forthcoming publication (Silverman,et al. in preparation). In the E-CDF-S, the targets of the FMOS observations werethe optical counterparts of type 1 AGN detected in the E-CDF-S survey described by Lehmer et al. (2005). The E-CDF-S consists of nine individual observations with fourdifferent central pointing positions, to a depth of 250 ks.The central region of the E-CDF-S survey is the location ofthe ultra deep 4 Ms E-CDF-S survey, which is described byXue et al. (2011) and consists of 52 individual observationswith a single central pointing position. We utilise all the
Chandra data in this region. The data were screened forhot pixels and cosmic afterglows as described in Laird et al.(2009), astrometric corrections made as described in Rangelet al. (2013) and the source spectra were extracted using the acis extract (AE) software package (Broos et al. 2010),using the positions of the E-CDF-S sources. AE extractsspectral information for each source from each individualobservation ID (obsID) based on the shape of the local pointspread function (PSF) for that particular position on thedetector. We choose to use regions where 90% of the PSF hasbeen enclosed at 1.5 keV. Background spectra are extractedfrom an events list which has been masked of all detectedpoint sources in Xue et al. (2011) and Lehmer et al. (2005),using regions which contain at least 100 counts. AE alsoconstructs response matrix files (RMF) and auxiliary matrixfiles (ARF). The data from each obsID are then merged tocreate a single source spectrum, background spectrum, RMFand ARF for each source. The rest-frame 2-10 keV signal-to-noise ratios in this field range from 2.5 to 500. In the COSMOS survey, the targets of the FMOS observa-tions were the optical counterparts of type 1 AGN detectedin the
Chandra -COSMOS survey (Elvis et al. 2009; Civanoet al. 2012). However, as medium-depth ( ∼ XMM-Newton data exist in this field, we take advantage of thehigh throughput of this satellite to obtain X-ray spectral The acis extract © , 000–000 data. The XMM-COSMOS data are described in Cappellutiet al. (2009) and the procedure adopted to extract sourcesand background spectra in Mainieri et al. (2007). We brieflyrecall the main steps here. The task region of the XMM-Newton
Science Analysis System (SAS) software has beenused to generate the source and background extraction re-gions. The source region is defined as a circle with radiusr s that varies according to the signal-to-noise and the off-axis angle of the detection to optimise the quality of thefinal spectrum. The radii of these regions are reduced bythe task to avoid overlapping with the extraction regions ofnearby sources. All source regions are further excised fromthe area used for the background measurement. The task es-pecget has been used to extract from the event file the sourceand background spectra for each object. The same task gen-erates the calibration matrices (i.e. arf and rmf) for eachspectrum and determines the size of the source and back-ground areas while updating the keyword BACKSCAL inthe header of the spectra appropriately . The single point-ing spectra have been combined with mathpha to generatethe spectrum of the whole observation. The rest-frame 2-10keV signal-to-noise ratios in this field range from 2.5 to 16.
The goal of the X-ray spectral analysis is to uniformly mea-sure Γ and L X in the rest-frame 2-10 keV range for all 260sources with black hole mass estimates. For both Chandra and
XMM-Newton data, we lightly bin the spectral datawith at least one count per bin using the heasarc tool grppha . We use xspec version 12.6.0q to carry out X-rayspectral fitting, and the Cash statistic (cstat, Cash 1979)as the fit statistic. We fit the rest-frame 2-10 keV spectrawith a power-law model, neglecting the rest-frame 5.5-7.5keV data where the iron K complex is emitted. We use all260 sources for analysis with L X , however, measurement ofΓ requires higher quality spectral data in order to obtaingood constraints. Fig. 2 shows how the uncertainty on Γ de-creases as the number of counts in the spectrum increases.We restrict analysis with Γ to 79 sources where there aregreater than 250 counts in the X-ray spectrum, which areneeded in order to measure Γ to ∆Γ < .
5. In the spectralfit, we include a local absorption component, wabs , to ac-count for Galactic absorption, with N H =7 × cm − forthe E-CDF-S and N H =1 . × cm − for the COSMOS.By restricting our analysis to rest frame energies above 2keV, we are insensitive to N H values below ∼ cm − .As we are studying broad-lined type 1 AGN, absorption in-trinsic to the source is not generally expected above this,however, we assess this by adding an absorption componentin the spectral fit ( zwabs in xspec ), and noting any im-provement in the fit statistic. Based on an F-test, we findevidence at >
90% confidence for absorption in three sources, http://xmm.vilspa.esa.es/external/xmm sw cal/sas frame.shtml The header keyword BACKSCAL is set to 1 for the sourcespectrum while for the background spectrum it is fixed to theratio between the background to source areas. We note that all the XMM-Newton observations in the COS-MOS field have been performed with the thin filter for the pn camera. Figure 2.
Plot of the uncertainty of Γ as a function of the num-ber of source counts in the X-ray spectrum. We cut the sample tosources with greater than 250 counts in order to include sourcesfor which ∆Γ < .
5. Red data points show where the data comefrom the E-CDF-S , while black data points come from COS-MOS. The points lying above the main relation are those whereabsorption has been included in the fit. for which we use the measurements carried out with the ad-dition of the absorption component. These are E-CDF-S IDs367 ( N H = 1 . × cm − ) and 391 ( N H = 6 . × cm − )and XMM-COSMOS ID 57 ( N H = 2 . × cm − ). Forthe remaining sources, spectral fits were carried out with asimple power-law component. Recent work by Lanzuisi et al.(2013) (L13) have presented spectral analysis of bright X-raysources ( >
70 counts) in
Chandra -COSMOS, however utilis-ing the full 0.5-7 keV
Chandra bandpass. We compare ourresults to theirs in a later section. λ Edd
The primary goal of this study is to investigate the relation-ship between Γ and λ Edd , which requires a measurementof the bolometric luminosity. For 207 COSMOS sources, wetake bolometric luminosities presented in L12, which are de-rived from spectral energy distribution (SED) fitting, fromobserved 160 µ m to hard X-rays. Bolometric luminositiesfor type 1 AGN are calculated in the rest frame 1 µ m to200 keV. These data do not exist for our E-CDF-S sourceshowever. For these sources we use a bolometric correctionto the 2-10 keV X-ray luminosity ( κ − ) to estimate L Bol .Lusso et al. (2010) showed that this can be done reliablyusing κ − derived from the X-ray to optical spectral in-dex, α OX . α OX is normally calculated using the monochro-matic luminosities at 2500 ˚A and 2 keV, however, we utilisethe 3000 ˚A luminosity we already have at hand from theline measurements, measured from the optical spectra, andthe 2-10 keV luminosity measured in the X-ray spectra and © , 000–000 M. Brightman, et al. calibrate a relationship between κ − and L X / L , us-ing sources with known L Bol in COSMOS. We utilise 32sources with L measured from FMOS and where L X and L Bol are available for this analysis. Figure 3 shows that κ − and L X / L are indeed tightly correlated. We per-form a linear regression analysis on these data, finding thatlog κ − = − . ( L X / L )+0.84. We then calcu-late L Bol for the E-CDF-S sources using this relationship.Figure 3 also shows the comparison between L Bol calculatedin this manner and L Bol from L12 with good agreement be-tween the two. For our sample of X-ray bright AGN to whichwe restrict our analysis with Γ, 44 have L Bol from L12 and31 have L Bol calculated using κ − . As the subject of this study is to probe the X-ray emissionfrom the corona, we must account for other sources of X-rayemission intrinsic to the AGN. Radio loud AGN constitute ∼
10% of the AGN population, the fraction of which mayvary with luminosity and redshift (e.g. Jiang et al. 2007)and are known to exhibit X-ray emission attributable to syn-chrotron or synchro-Compton emission from a jet (Zamoraniet al. 1981). As such we must exclude radio loud AGN fromour study. We compile radio data on our sample, specif-ically to exclude radio loud sources from our analysis, butalso to investigate the radio properties. Deep ( ∼ µ Jy rms)VLA 1.4 GHz observations of both COSMOS and the E-CDF-S exist (Schinnerer et al. 2007; Miller et al. 2013). InCOSMOS, we match the
XMM-Newton sources to the radiosources, and in E-CDF-S, we take the matches from Bonziniet al. (2012). For 21 sources with a radio detection, wecalculate the radio loudness parameter (Kellermann et al.1989), R, which is defined as f /f . We extrapolatethe observed 1.4 GHz flux density to rest-frame 5 GHz us-ing a power-law slope of -0.8. For the 4400˚A flux density,we extrapolate the observed R band flux density to rest-frame 4400˚A using a power-law slope of -0.5. R band mag-nitudes were taken from Brusa et al. (2010) and Lehmeret al. (2005) for COSMOS and E-CDF-S respectively. Forradio undetected sources, we calculate an upper limit on Rassuming a 10 µ Jy sensitivity in both fields. Figure 4 showsthe distribution of R in the sample. We find six radio loud(R > It is understood that the characteristic shape of the X-ray spectrum produced in the corona, parametrised by Γ,depends on the electron temperature, T e , and the opticaldepth to electron scattering, τ es , but it is unknown howthese conditions arise, and how they relate to the accretionflow. We explore the dependence of Γ on the various accre-tion parameters in an attempt to understand what bringsabout the physical conditions of the corona. The parame-ters we explore in this work are L UV , L X , FWHM, M BH and λ Edd . Figure 4.
Distribution of radio loudness parameter, R, forsources with radio detections (empty histograms), where the solidhistogram is for E-CDF-S sources. The hatched histogram showsupper limits on the sources with no radio detection, assuming10 µ Jy sensitivity. L X and redshift In order to investigate the relationships between Γ andFWHM, M BH and λ Edd , we first check for any dependen-cies on L X and redshift in our sample in order to rule outdegeneracies, as correlations with L X and redshift have beenreported previously (Dai et al. 2004; Saez et al. 2008). Fig-ure 5 plots these relationships. A Spearman rank correla-tion analysis shows that there are no significant correlationspresent between Γ and L X or Γ and redshift within thissample. We do note however that at the lowest X-ray lumi-nosities ( L X < × erg s − ) that Γ is systematically lowerthan at higher luminosities. While these are only 7 sources,we consider what affect if any they have on our results in alater section. L UV , FWHM, M BH and λ Edd
We next investigate the dependence on the observed quan-tities, the 3000 ˚A UV luminosity and FWHM of the linesand those derived quantities, black hole mass and λ Edd . TheUV luminosity traces the accretion disc luminosity, and isthus related to the mass accretion rate, ˙ m ( L acc = η ˙ mc ),whereas FWHM traces the gravitational potential. Further-more, L and FWHM are the ingredients in the black holemass calculation, which in turn is used in the determinationof λ Edd . In Fig. 6, we show how Γ depends on these fourquantities.Here we are using a combined sample of Mg ii and H α measurements for FWHM, M BH and λ Edd . In the figure wedistinguish between the two line measurements with differ-ent colouring. When considering the combined sample, if a © , 000–000 Figure 3.
Left - κ − vs. L X / L for 32 sources in COSMOS with L X , L and L Bol measured with SED fitting from L12. Theline plotted through the data shows the results of a linear regression analysis. Right - Comparison of L Bol calculated from SED fittingin L12 to L Bol calculated using L X and κ − derived from the relationship between κ − and L X / L . The line shows the one toone relationship. Figure 5.
Plot of Γ vs L X and redshift, where top panels show in-dividual measurements and bottom panels show binned averages.Spearman rank correlation coefficients and p-values are displayed,showing there are no significant correlations with either L X orredshift, however, the lowest luminosity bin shows systematicallylower Γ values than the higher luminosity bins. source has a measurement from both lines, we use the H α measurement over the Mg ii measurement. For λ Edd , we alsodifferentiate between cases where L Bol has been determinedusing SED fitting (filled squares), or where it has been de-termined from L X / L (open squares).A strong correlation with L is seen, which breaksat low luminosities ( L ∼ erg s − ) and a strong anti-correlation with FWHM can be seen. These then cancel outhere to give no dependence of Γ on M BH . A strong correla-tion is then seen with λ Edd . The Spearman rank correlationtest shows that there is a significant correlation between Γand L ( r S = 0 .
57 and p = 1 . × − , where r S is theSpearman rank correlation coefficient and p is the probabil-ity of obtaining the absolute value of r S at least as high asobserved, under the assumption of the null hypothesis of zero correlation.), a significant anti-correlation ( p =2.71 × − )between Γ and the FWHM ( r S = -0.41) and a highly sig-nificant correlation ( p =6.59 × − ) between Γ and λ Edd ( r S =0.60).Despite the several ingredients used to derive λ Edd , thisis by far the strongest correlation seen, stronger than withthe observed quantities L and FWHM. This further con-firms λ Edd as the primary parameter influencing the physicalconditions of the corona responsible for the shape of the X-ray spectrum, being the electron temperature and electronscattering optical depth. Furthermore, as the relationshipwith L , which is linked to the mass accretion rate, showsa break at low luminosities, which is not evident in the re-lationship with λ Edd , which is related to the mass accretionrate scaled by the black hole mass, this implies that theEddington rate is more important than mass accretion rate.Also shown on these plots are the Γ − λ Edd correlationspreviously reported by S08 and R09. Our results are con-sistent with S08 in the two highest bins of λ Edd , howeverour results diverge at lower values of λ Edd , with a flatterΓ − λ Edd relationship. Our results are systematically higherthan those reported in R09. We explore these differencesfurther in section 4.2.2.For the two relationships between Γ and FWHM and Γand λ Edd where emission line measurements were used, wefurther the investigation in different subsamples: in two dif-ferent redshift bins (0 . < z < . . < z < . α and Mg ii separately. Table 1 presents theresults of Spearman rank and linear regression analysis ofthe Γ vs. FWHM relationship for these different subsamples.The correlation is most significant in the full redshift rangewhen using only the Mg ii measurements ( p =1.32 × − ),however the correlation is not significant ( p > .
1) whenconsidering only H α measurements, though this may be dueto small number statistics. For the whole sample, we findthat Γ = (0 . ± . λ Edd + (2 . ± .
06) (2) © , 000–000 M. Brightman, et al.
Figure 6.
Plots of Γ versus UV luminosity ( λ =3000˚A), FWHM (km s − ), black hole mass ( M (cid:12) ) and λ Edd . Top panels show individualmeasurements, where red data points are measurements from the H α line, and green from the Mg ii line. For λ Edd , filed squares are dataderived using L Bol from SED fitting, whereas empty squares are data derived using L Bol from L X / L . Bottom panels show binnedaverages. The Spearman-rank correlation coefficient, r S , and the p-value are shown for each relationship. The black and red dotted linesare previous correlations reported on Γ- λ Edd from S08 and R09 respectively.
Figure 7.
Plots of Γ vs the FWHM of the emission lines in foursubsamples: two redshift bins, 0 . < z < . . < z < . α and Mg ii separately (bottom panels). Taking the two line measurements separately gives Γ =( − . ± . (FWHM/km s − )+(3 . ± .
53) from H α and Γ = ( − . ± . (FWHM/km s − )+(5 . ± . ii . The slopes are significantly different, at > σ .Fig. 7 shows the sample in the two redshift bins and for thetwo line measurements separately, along with the best fitlines.We also carry out Spearman rank correlation analysisand linear regression analysis on the Γ vs. λ Edd relationshipfor the different subsamples. The results are presented in Table 2. The correlation is most significant in the full red-shift range when using the two line measurements together( p =6.59 × − ). The correlation is significant ( p < .
1) inall redshift bins, however, not for measurements made withH α in the highest redshift bin. This is again likely due tosmall number statistics. For the whole sample we find thatΓ = ( − . ± . (FWHM / kms − )+(4 . ± .
42) (3)The slope of the correlations for H α and Mg ii agree verywell with each other with Γ = (0 . ± . λ Edd +(2 . ± .
09) for H α and Γ = (0 . ± . λ Edd +(2 . ± . ii and for all redshift bins. This supports the claimby Matsuoka et al. (2013) that the two line measurementsgive consistent black hole mass estimates. We plot Γ versus λ Edd in the two redshift bins and for the two lines separatelyin Figure 8, along with the best fit lines.
In section 2.7, we investigated the radio properties of thesample, finding six sources which are radio loud (R > λ Edd relationship found inthe previous section, here with only sources with radio de-tections. We colour code the data points by radio loudness.We find that radio loud sources are generally consistent withthis trend, with the exception of two sources with high Ed-dington ratios ( λ Edd > . © , 000–000 Table 1.
Table of Spearman rank correlation and linear regression analysis for Γ vs.log FWHM for sources with a measurement fromMg ii or H α and with greater than 250 source counts in the X-ray spectrum. In the combined sample of Mg ii and H α measurements,if both exist for one source, the H α measurement is used over the Mg ii measurement. Column (1) is the redshift range used; (2) is theemission lines used for the FWHM; (3) is the total number of sources within each subsample; (4) is the Spearman rank coefficient; (5)is the null hypothesis probability; (6) is the gradient coefficient in the linear regression analysis, where Γ =m log FWHM+c; and (7) isthe constant in this relationship.redshift range lines used number in subsample R S p m c(1) (2) (3) (4) (5) (6) (7)0.5- 2.1 H α & MgII 73 -0.41 2.71 × − -0.69 ± ± α
25 -0.24 2.54 × − -0.49 ± ± × − -1.02 ± ± α & MgII 34 -0.49 3.53 × − -0.86 ± ± α
12 -0.25 4.30 × − -0.71 ± ± × − -1.23 ± ± α & MgII 39 -0.36 2.52 × − -0.43 ± ± α
13 -0.20 5.17 × − -0.01 ± ± × − -0.61 ± ± Table 2.
Table of Spearman rank correlation and linear regression analysis for Γ vs. log λ Edd , for sources with M BH from Mg ii or H α ,an estimate of the bolometric luminosity and those with greater than 250 source counts in the X-ray spectrum. In the combined sampleof Mg ii and H α measurements, if both exist for one source, the H α measurement is used over the Mg ii measurement. Column (1) is theredshift range used; (2) is the emission lines used for the estimation of the black hole mass; (3) is the total number of sources withineach subsample; (4) is the Spearman rank coefficient; (5) is the null hypothesis probability; (6) is the gradient coefficient in the linearregression analysis, where Γ=m log λ Edd +c; and (7) is the constant in this relationship.redshift range lines used number in subsample R S p m c(1) (2) (3) (4) (5) (6) (7)0.5- 2.1 H α & MgII 69 0.60 6.59 × − ± ± α
22 0.60 2.94 × − ± ± × − ± ± α & MgII 33 0.74 8.82 × − ± ± α
11 0.67 2.33 × − ± ± × − ± ± α & MgII 36 0.53 8.38 × − ± ± α
11 0.50 1.17 × − ± ± × − ± ± L X sources We noted in section 3.1 that at low X-ray luminosities( L X < × erg s − ), Γ is systematically lower. Whilethere are only 7 sources at these low luminosities, and aSpearman rank correlation test tells us there is a lack ofa significant correlation between Γ and L X in our sam-ple, we check the effects on our results when excludingthese sources at low L X . When doing this, we find that asignificant correlation between Γ and λ Edd persists, with p = 7 . × − . Linear regression analysis of this subsam-ple gives Γ = (0 . ± . λ Edd +(2 . ± . When it was reported by Boller et al. (1996) and Laor et al.(1997) that the soft X-ray (0.2-2 keV) power-law index cor- related well with the FWHM of the H β line, also interpretedas a dependence on accretion rate, it was thought that thismay have been related to the soft X-ray excess seen in un-obscured AGN (e.g. Arnaud et al. 1985; Turner & Pounds1989). This feature is strong in narrow line Seyfert 1s (Bolleret al. 1996), which have low FWHMs (Osterbrock & Pogge1985), and as such a strong soft excess could cause a steep-ening of the X-ray spectrum leading to higher values of Γfor low FWHM sources. Brandt et al. (1997) later reported acorrelation between Γ in the 2-10 keV band and the FWHMof the H β line, where this band is less affected by the softexcess, leading to the conclusion that both the soft excessand the power-law are affected by the accretion rate. Weattempt to further rule out the effect of the soft excess onthe power-law by considering the 4-10 keV rest-frame bandwhere the X-ray spectrum should be completely indepen-dent of the soft excess. We rerun our analysis described insection 2.5 with this restriction, however, in doing this wedecrease the number of spectral counts. We therefore lowerthe count cut that we make using the 2-10 keV spectrum of250 counts to 100 counts in the 4-10 keV band. Despite this © , 000–000 M. Brightman, et al.
Figure 8.
Plots of Γ vs λ Edd for four subsamples: two redshiftbins, 0 . < z < . . < z < . α line, and green from theMg ii line. Filled symbols are data derived using L Bol from SEDfitting, whereas empty symbols are data derived using L Bol from L X / L . The bottom panels show the measurements from H α and Mg ii separately in the full redshift range. The black and reddotted lines are previous correlations reported on Γ- λ Edd fromS08 and R09.
Figure 9.
Γ vs. λ Edd for sources with radio detections only, wherecolour corresponds to radio loudness, parametrised by R. Thesolid line is the best fit line to the full sample found in the previoussection, when excluding radio loud sources. We find that radioloud sources are generally consistent with this trend, with theexception of sources with high Eddington ratios ( λ Edd > . we still find a significant correlation between Γ and λ Edd with a p-value of 0.002. This confirms that the soft excessdoes not substantially contribute to the Γ- λ Edd relationship.We next consider the relationship between FWHM and λ Edd (Boroson & Green 1992), and the degeneracy it mayintroduce in our work. As our aim here is to rule out de-generacies where possible, we investigate the effect of mak- ing a cut in FWHM. We note that the correlation of Γ vs.FWHM appears to be driven by sources with FWHM < − , and thus we investigate the Γ- λ Edd relationship forsources with FWHM > − in our sample. In doingso, however, we still find a significant correlation betweenΓ and λ Edd with a p-value of 0.005, which effectively rulesout a bias from low FWHM sources, and rules out degen-eracy with FWHM. A linear regression analysis finds thatΓ = (0 . ± . λ Edd +(1 . ± . It is important to consider what effects reflection of X-rays,from either the accretion disc or the circumnuclear torusmay have on our results. In our X-ray spectral fitting weuse a simple power-law to characterise the spectrum, how-ever in reality reflection features are present. As the geome-try of the torus is expected to change with X-ray luminosityand redshift (e.g. Lawrence 1991; Ueda et al. 2003; Hasinger2008; Brightman & Ueda 2012), this component should notbe neglected. In order to account for this, we utilise the X-ray spectral torus models of Brightman & Nandra (2011),which describe the X-ray spectra of AGN surrounded bya torus of spherical geometry. In order to explain the de-crease in the AGN obscured fraction with increasing X-rayluminosity, and the increase with redshift, new work fromUeda, et al (in preparation) have calculated the dependenceof the torus opening angle on these parameters. Essentiallythe torus opening angle increases with increasing X-ray lu-minosity and decreases with increasing redshift. The effectof this on the observed Γ is for Γ to decrease towards smalleropening angles, and hence greater covering factors, due togreater reflection from the torus which has a flat spectrum.We use this prescription when fitting our spectra with thistorus model, where the viewing angle is set such that thesource is unobscured, the N H through the torus is set to10 cm − and the opening angle depends on the X-ray lu-minosity and redshift. We follow the same spectral fittingtechnique as described in section 2.5, and study the results.We find that the correlation between Γ and λ Edd remainshighly significant with a p-value of 2 . × − . We note thatthe observed Γ produced by this torus model changes by amaximum of 0.06 in the 2-10 keV range for the extremesof the parameter space, while we observe changes of greaterthan 0.2. It is therefore unlikely that reflection affects ourresults. S08 also investigated the effects of reflection in theiranalysis, finding only two sources where a reflection compo-nent was significantly detected. This low detection rate isexpected due to the high luminosity nature of the sourcesat high redshifts. We briefly check if X-ray variability has an effect on ourresults, specifically if the outliers in our relationships maybe explained by this. Lanzuisi, et al (in preparation) haveconducted an investigation into AGN variability for XMM-COSMOS sources. They find that 6 of the sources in oursample are variable in X-rays through the detection of ex-cess variance. We find however, that these sources lie consis-tently on the best fit relations found here, leading us to the © , 000–000 conclusion that variability is not likely to affect our results.Papadakis et al. (2009) directly investigated the relation-ship between Γ and AGN variability, finding that Γ corre-lates with the characteristic frequency in the power spec-trum when normalised by the black hole mass. They thenused the result of McHardy et al. (2006), which showed thatthis normalised characteristic frequency is correlated to theaccretion rate, to also show in an independent manner towhat we have shown here, that Γ is correlated with accre-tion rate. Their result held true even when using the meanspectral slope of their data. This result is relevant here, aswe have used time averaged spectra, which Papadakis et al.(2009) have shown produces consistent results to time re-solved spectroscopy. We use both
Chandra and
XMM-Newton data in our analy-sis, with
XMM-Newton data in COSMOS and
Chandra datain the E-CDF-S . However, it has been found that a sys-tematic difference between measurements made by the twoobservatories of the same source exists (L13). Most rele-vant to our work is a systematic difference of up to 20%in Γ, which may seriously bias our results. We investigatethis issue by performing our analysis using the
Chandra data available in COSMOS. We extract the
Chandra spec-tra as described in section 2.3 for the E-CDF-S sourcesand analyse the data in the same way. While the samplesize is reduced to 44 sources with Γ and λ Edd due to thesmaller coverage of the
Chandra observations in COSMOSand the lower number of source counts per spectrum, ourmain result is maintained. For Γ vs. λ Edd , the Spearmanrank correlation analysis reveals a significant correlationwith p = 2 . × − and linear regression analysis findsthat Γ = (0 . ± . λ Edd +(2 . ± . Chandra / XMM-Newton analysis. These data are plotted with the best fitting trendline in Fig. 10.
Recent work by L13 has presented a spectral analysis ofbright
Chandra -COSMOS sources, the aim of which was todetermine the intrinsic absorption in the spectrum, as well asΓ. Their work also presents analysis of
XMM-Newton spec-tra of the
Chandra counterparts. Their analysis differs fromour own as they utilise the fuller 0.5-7 keV band pass andsources with greater than 70 net counts, whereas we limitourselves to analysis in the rest-frame 2-10 keV band andspectra with at least 250 counts. We investigate the differ-ences in these methods by comparing the results for 129common sources, in particular with respect to absorption.As we restrict ourselves to rest-frame energies greater than2 keV, we are not sensitive to N H (cid:46) cm − , whereas L13utilise a fuller band pass and as such are thus sensitive tolower levels of absorption. While we only detect absorptionin one source from our COSMOS sample, this is not a com-mon source with L13. From the common sources, they detectabsorption in six sources (XMM-IDs 28, 30, 34, 38, 66 and71), however the measured N H is < × cm − in all Figure 10.
Plots of Γ vs λ Edd when excluding sources withFWHM < − (top) and sources with L X < . erg s − (middle) in order to break any degeneracy with these parameters.The lowest panel shows Γ vs λ Edd when using
Chandra data inCOSMOS instead of
XMM-Newton data in order to investigatethe effect of the cross-normalisation between these telescopes. of these, and thus will have no affect on our measurementof Γ. When comparing Γ measurements between the twoanalyses, there is good agreement, with the difference beingwithin our measurement error and there being no systematicoffsets. © , 000–000 M. Brightman, et al. Γ - λ Edd correlation
In Figs. 6 & 8, we have compared our results on the Γ- λ Edd correlation with two previous works by S08 and R09.We found that for the whole sample, our binned averageswere consistent with the results of S08 in the highest λ Edd bins, while overall systematically higher than those of R09.At lower λ Edd values our Γ measurements lie above theseprevious correlations.The results from S08 were based on a sample of 35moderate- to high-luminosity radio quiet AGN having highquality optical and X-ray spectra, based on individual ob-servations, and including nearby sources and those up toz=3.2. The black hole masses were estimated from the H β line. The results of R09 are based on 403 sources from the SDSS/XMM-Newton quasar survey of Young et al. (2009),which span a wide range in X-ray luminosity (10 01) and R09 findthat Γ = (0 . ± . λ Edd +(1 . ± . λ Edd correlation is in excellent agreement withthese two previous works. The constant in the relationshipis higher than both studies by 3- σ . This may be due todiffering methods of X-ray spectral fitting. Here we useCash statistics in our analysis, whereas previous workshave used χ , the two being known to produce systematicdifferences in Γ (Tozzi et al. 2006).Furthermore, R09 reported significantly differing slopesfor Γ − λ Edd (H β ) and Γ − λ Edd (Mg ii ), where the H β slopewas steeper. We also compared our slopes for H α and Mg ii ,but found no such difference. We make a comparison to theresults from S08 and R09 considering the different lines sep-arately in Table 3. For the Mg ii line, only R09 have pre-sented results and we find that our results are consistentwith these within 2- σ . We present here for the first timeresults based on H α alone, however, our H α results are invery good agreement with the H β results in S08, though thedifference between these results and the H β results in R09is 3- σ .The differing results between H β and Mg ii reported inR09 were attributed to uncertainties in the measurement ofMg ii . However, Matsuoka et al. (2013), which describes themeasurements of H α and Mg ii used in this sample find verygood agreements between these lines, which subsequentlyhas lead to the good agreement we find between them here. We have confirmed previous results that λ Edd , rather than L UV , L X , FWHM or M BH , is the parameter which moststrongly correlates with the X-ray spectral index, Γ, andhence is responsible for driving the physical conditions ofthe corona responsible for the shape of the X-ray spectrum,being the electron temperature and electron scattering op-tical depth. This result enables models of accretion physics Table 3. A summary of the results of the best fit line to theΓ- λ Edd correlation from this work and those of S08 and R09, forline measurements made from H α , H β and Mg ii . Column (1) isthe sample used, column (2) is the lines used, column (3) is theslope of the relationship and column (4) is the interceptSample Lines m c(1) (2) (3) (4)This work H α & Mg ii . ± . 05 2 . ± . β , Mg ii & C iv . ± . 06 1 . ± . ii . ± . 05 2 . ± . ii . ± . 05 1 . ± . α . ± . 07 2 . ± . β . ± . 01 2 . ± . β . ± . 11 1 . ± . in AGN to be constrained. As this correlation is strongerthan the Γ- L correlation, where L is related to themass accretion rate, ˙ m and λ Edd is related to the mass accre-tion rate scaled by M BH , then the coronal conditions mustdepend on both mass accretion rate and black hole mass, de-spite there being no correlation with black hole mass itself. Apossible interpretation of the correlation between Γ and λ Edd is that as λ Edd increases, the accretion disc becomes hotter,with enhanced emission. This enhanced emission cools theelectron corona more effectively, leading to a lower electiontemperature, electron scattering optical depth, or both. Γthus increases as these quantities decrease.As pointed out by previous authors on this subject, astatistically significant relationship between Γ and λ Edd al-lows for an independent estimate of λ Edd for AGN from theirX-ray spectra alone. While the dispersion in this relation-ship means that this is not viable for single sources, it couldbe used on large samples, for example those produced by eROSITA . eROSITA is due for launch in 2014 and will de-tect up to 3 million AGN with X-ray spectral coverage upto 10 keV. These results could be valuable in placing esti-mates on the accretion history of the universe using thesenew data. We have presented an X-ray spectral analysis of broad-linedradio-quiet AGN in the extended Chandra Deep Field Southand COSMOS surveys with black hole mass estimates. Theresults are as follows: • We confirm a statistically significant correlation be-tween the rest-frame 2-10 keV photon index, Γ, and theFWHM of the optical broad emission lines, found previouslyby Brandt et al. (1997). A linear regression analysis revealsthat Γ = ( − . ± . (FWHM/km s − )+(4 . ± . • A statistically signifiant correlation between Γ and λ Edd is also confirmed, as previously reported in S06, S08 andR09. The relationship between Γ and λ Edd is highly signifi-cant with a chance probability of 6.59 × − . A linear regres-sion analysis reveals that Γ = (0 . ± . λ Edd +(2 . ± . λ Edd is the strongest of all parameters testedagainst Γ, indicating that it is the Eddington rate, which is ©000 Deep Field Southand COSMOS surveys with black hole mass estimates. Theresults are as follows: • We confirm a statistically significant correlation be-tween the rest-frame 2-10 keV photon index, Γ, and theFWHM of the optical broad emission lines, found previouslyby Brandt et al. (1997). A linear regression analysis revealsthat Γ = ( − . ± . (FWHM/km s − )+(4 . ± . • A statistically signifiant correlation between Γ and λ Edd is also confirmed, as previously reported in S06, S08 andR09. The relationship between Γ and λ Edd is highly signifi-cant with a chance probability of 6.59 × − . A linear regres-sion analysis reveals that Γ = (0 . ± . λ Edd +(2 . ± . λ Edd is the strongest of all parameters testedagainst Γ, indicating that it is the Eddington rate, which is ©000 , 000–000 related to the mass accretion rate scaled by the black holemass, that drives the physical conditions of the corona re-sponsible for the X-ray emission. 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