Mon.Not.R.Astron.Soc.000,1–5(2002) Printed6January2015 (MNLATEXstylefilev2.2) A direct comparison of X-ray spectral models for tori in active galactic nuclei 5 Yuan Liu1⋆ and Xiaobo Li1† 1 0 1Key Laboratory of Particle Astrophysics, Institute of HighEnergy Physics 2 Chinese Academy of Sciences, P.O.Box 918-3, Beijing 100049, China n a J 3 ] ABSTRACT E SeveralX-rayspectralmodelsfortoriinactivegalacticnuclei(AGNs)areavailableto H constrain the properties of tori; however, the accuracy of these models has not been . verified. We recently construct a code for the torus using Geant4, which can easily h handle differentgeometries(Liu & Li2014).Thus,weadoptthe sameassumptionsas p - Murphy & Yaqoob(2009,hereafterMY09)andBrightman & Nandra(2011,hereafter o BN11) and try to reproduce their spectra. As a result, we can reproduce well the tr reflection spectra and the strength of the Fe Kα line of MY09, for both NH = 1024 s and1025 cm−2.However,wecannotproducethestrongreflectioncomponentofBN11 a inthe low-energyband.Theoriginofthis componentisthe reflectionfromthe visible [ innerwallofthe torus,anditshouldbeveryweakintheedge-ondirectionsunderthe 1 geometry of BN11. Therefore, the behaviour of the reflection spectra in BN11 is not v consistentwiththeirgeometry.ThestrengthoftheFeKαlineofBN11isalsodifferent 7 from our results and the analytical result in the optically thin case. The limitation of 5 the spectral model will bias the parameters from X-ray spectral fitting. 5 0 Key words: radiative transfer – galaxies: active – X-rays: galaxies. 0 . 1 0 5 1 INTRODUCTION sources(Singh et al.2012;Yaqoob2012;Ar´evaloet al.2014; 1 Gandhiet al.2014).Withasurveysample,thesemodelsare : Under the unification scheme of active galactic nuclei v helpful for finding Compton thick AGNs and determining i (AGNs), a toroidal structure referred as “the torus” pro- how the tori evolve with the properties of AGNs, such as X vides anisotropic obscuration and can explain the diversity the correlation between the covering factor and luminos- r of optical and X-ray spectra of AGNs (Antonucci 1993). a ity (Brightman & Nandra 2012; Brightman & Ueda 2012; ThetorusabsorbstheintrinsicX-rayspectraofAGNs(usu- Brightman et al. 2014; Buchneret al. 2014; Ricci et al. ally modelled as an absorbed power law) and also scatters 2014).Inspiteofthesuccessoftheapplicationofsuchmod- the X-ray photons to produce a Compton hump at ∼20 els, theaccuracy and validityof suchmodels havenot been keV. The abundant and high quality data from recent X- independently verified. The parameters from these models ray satellites enable us to investigate the X-ray properties willbebiasediftherearesomelimitationsorerrorsinthese of AGNs in unprecedented detail. The structure of the tori models. We recently constructed an X-ray spectral model in AGNs can be constrained if an X-ray spectral model of for the tori in AGNs using Geant4, which can handle the thetoriisspecified.Compared withthemodelsforthedisk smooth and clumpy tori by the same code. Thus, if we geometry, e.g. pexrav and pexmon (Magdziarz & Zdziarski adoptthesameassumptionsusedbyMY09,BN11andIK09 1995; Nandraet al. 2007), several more physical and real- (e.g. geometries, cross sections and element abundances), istic models have been recently constructed to model the ourGeant4codeshould reproducetheirresult,in principle. X-rayspectrumfromthetorus,whichadoptatoroidalstruc- In Section 2, we present the quantitative comparison with ture and self-consistently include fluorescent lines (Ikeda the public models in MY09 and BN11. Because the results et al 2009, hereafter IK09; Murphy & Yaqoob 2009, here- of IK09 are not public, we just use the general trend pre- after MY09; Brightman & Nandra 2011, hereafter BN11). sented in IK09 as a reference. In Section 3, we discuss the These models have been applied to individual AGNs to difference found in the comparison, and we show our main derive the covering factor and column density of the conclusions in Section 4. ⋆ E-mail:[email protected] † E-mail:[email protected] 2 Yuan Liu and Xiaobo Li 2 SIMULATIONS FOR COMPARISON The details of our simulation method are pr esented in Liu & Li (2014). We have included several physical pro- cessesinourcode,e.g.photoelectriceffect,Comptonscatter- ing, Rayleigh scattering, γ conversion, fluorescent lines and Auger process. Similar physical processes have been con- sidered in the simulations of MY09 and BN11. Thus, it is convenient to modify our code to simulate their cases. Our codeandthesimulationsbyMY09andBN11haveincluded multi-scatterings,e.g. Figure7inLiu & Li(2014).Wethen Figure1.GeometryofMY09.Theredandbluearrowsindicate use the same assumptions adopted by BN11 and MY09 re- thepossibletrajectoriesoflow-energyscatteredphotonsthatcan spectively to try to reproduce their results1. The incident escapetoface-onandedge-ondirections,respectively.Theyellow flux is 5×108 photons (1-500 keV) for all simulations pre- arrows indicate the trajectories of low-energy scattered photons sented in this paper. that will be absorbed by the near side of the torus for edge-on directions. 2.1 Results under the assumptions of MY09 The geometry of MY09 is shown in Figure 1. The half- ◦ opening angle of thetorus is 60 . Usingthesamegeometry,crosssections,elementabun- dances and incident spectra (a single power law with the photon index Γ=1.8), we can well reproduce MY09’s con- tinua, for both NH =1024 and 1025 cm−2 (Figure 2, where θin is the inclination angle relative to an observer). The di- rect component is not shown for clarity. Since the shape of thescatteredcomponentisdeterminedbyboththescatter- ing and absorption processes (e.g. Fe K absorption edge at 7 keV),these results verify the accuracy of MY09’s simula- Figure 3.GeometryofBN11.Theredandbluearrowsindicate tions. thepossibletrajectoriesoflow-energyscatteredphotonsthatcan We have further compared the equivalent width (EW) escapetoface-onandedge-ondirections,respectively.Theyellow of the Fe Kα line of our simulations with that in Fig- arrows indicate the trajectories of low-energy scattered photons ure 8 of Murphy & Yaqoob (2011), which is the erratum that will be absorbed by the near side of the torus for edge-on of MY09. The photon index Γ is 1.9 in these simulations. directions. For NH = 1024 and 1025 cm−2, the difference of EWs be- tween our simulations and MY09’s model is smaller than Althoughthecontinuaoftheface-ondirectionsarecon- 1% for most of the directions. The maximum deviation is ∼2%forNH =1024 cm−2 andcosθin=0.3−0.4.Thissmall sistentwitheachother,thespectraoftheedge-ondirections, especially for low-energy band,are significantly different.It deviation could be due to the different simulation method seemsthereisan“additional”componentatthelow-energy adopted by MY09. The accuracy of this model is sufficient, band in the simulations of BN11. since the statistical error of EW(Fe Kα) in observed X-ray We have further compared EW(Fe Kα) of our simula- spectraislargerthan10%inmostcases(Liu & Wang2010; tionswith that in Figure3 of BN11. Thephoton index Γ is Shu,Yaqoob,& Wang2011). 2.0inthesesimulations.Fortheface-ondirection(θtor =60◦ and θin = 0−37◦), EW(Fe Kα) of BN11 is lower than our 2.2 Results under the assumptions of BN11 simulation results by30% and 35% for NH =1024 and 1025 cm−2,respectively.Fortheedge-ondirection(θtor =60◦and The geometry of BN11 is shown in F◦igure 3. The half- θin=78−90◦),theirEW(FeKα)ishigherthanourresults opening angle of thetorus is fixed at 60 . by 60% for NH =1024 cm−2. Due to the large deviation of The inner radius of the torus is assumed to be zero in thecontinuumoftheedge-ondirectionforNH =1025 cm−2, BN11’s model. The comparison between the BN11’s model we havenot compared the EW(FeKα) in this case. and our results is shown in Figure 4 (Γ=1.8). The total Weexplorethesediscrepanciesindetailinthenextsec- spectra are shown, i.e. direct+ scattered components, since tion. BN11’s model only provides the total spectra. The fluores- centlines(includingtheCompton shoulders) inthespectra of our simulations are not shown for clarity, because it is 3 DISCUSSION not easy to directly compare the strength of such a quasi-δ function in the figure. Under the NH discussed in Figure 2 and 4, the direct com- ponentishighlyabsorbedinthelow-energyband.Thus,the 1 The model file of MY09 is downloaded from low-energyspectraaredominatedbythereflectionfromthe http://mytorus.com/model-files-mytorus-downloads.html visible inner wall of the torus for a given inclination angle, The model file of BN11 is downloaded from which is referred to as the‘reflection component 2’ in IK09 http://www.mpe.mpg.de/∼mbright/data/torus1006.fits (theFigure 2 in IK09 illustrates its geometry and origin). X-ray models for tori in AGNs 3 105 104 V e k s/ on103 hot cosθ =0−0.1 P in cosθ =0.9−1.0 102 MY cinosθ =0−0.1 in MY cosθ =0.9−1.0 in 101 100 101 102 100 101 102 E (keV) E (keV) Figure 2. Spectra under MY09’s assumptions with NH = 1024 (left) and 1025 cm−2 (right). Only scattered continua are shown for clarity.Thescattered fluorescentphotons aretreatedastheportionofemissionlinesandnotshownhere. 108 cosθ =0−0.1 in 107 cosθin=0.9−1.0 BN cosθ =0−0.1 in V106 BN cosθin=0.9−1V.0 e e k k ns/105 ns/ o o ot ot h h P104 P 103 102 100 101 102 100 101 102 E (keV) E (keV) Figure 4. Spectra under BN11’s assumptions with NH =1024 (left) and 1025 cm−2 (right). The total spectra (scattered+direct) are shown, but the fluorescent lines (includingthe Compton shoulders) inour simulationarenot shownforclarity. Thehalf-opening angle isassumedtobe60◦. The strength of this component depends on the geom- ure6),thoughthevariationisnotasdramaticasthatinthe etry of the torus, i.e. the location and shape of the surface, Figure 9 in IK09. We will explain this later. The spectrum ◦ andshouldalsodependontheinclinationangles.Therefore, at1keVwithinclinationangleθin =65 ishigherthanthat tojudgewhethertheresultsofBN11’smodelinFigure4are with θin=85◦ bymore than one order. reasonable, we investigate the variation of this component However,thestrengthofthislow-energyreflectioncom- with inclination angles in different models. ponentinBN11’smodelonlyweaklydependsontheinclina- Because rin/rout = 0.01 adopted in the simulations of tionangles(Figure7).Thespectrumat1keVwithθin=65◦ IK09 is small, IK09’s geometry is actually very similar to is only higher than that with θin=85◦ by a factor of two. thatofBN11,i.e.theNH distributionisalmostconstantfor Thestrengthofthislow-energy componentdependson different inclination angles. We plot the distribution of NH the visibility of the inner wall of the torus at different in- using equation (3) in IK09 toshow this (Figure 5). clination angles. Under the geometry of MY09, since the As shown in the Figure 9 in IK09, the ‘reflection com- centralpartofthetorusisempty,thewholeinnersurfaceof ponent 2’ significantly decreases with increasing inclination thetorus is directly illuminated by thecentral source. As a angles, i.e. it is very weak in theedge-on directions. result, a considerable part of the inner wall is visible when Asimilar trendis alsoobserved inMY09’s model(Fig- theinclination angle isslightly largerthanthehalf-opening 4 Yuan Liu and Xiaobo Li angleofthetorus(thebluearrowsinFigure1);evenforthe edge-oncase,therimoftheinnerwallisstillvisiblebutthe 1 majorityofreflectioninlow-energybandisabsorbedbythe nearsideofthetorus(theblueand yellowarrows in Figure 0.8 1). This can explain thetrend observed in Figure 6. H 0.6 N To further support the above explanation, in Figure 8 NH/sl0.4 we also plot thepositions of thescatterings of theobserved photons in 1-2 keV, i.e. the photons have experienced scat- 0.2 terings and finally escaped to the observer. The distribu- tions of the positions of the scatterings for two directions 0 are shown. The scatterings of low-energy photons can only 60 65 70 75 80 85 90 θ (°) occur at the skin of the torus; otherwise, they will be ab- in sorbed in the body of the torus. As the inclination angle Figure 5. Ratio between the column density along the line of moves to the edge-on direction, the visible part also moves sightandthemaximumNHinIK09(half-openingangle=60◦and to the rim. If the scattered photons intend to escape from rin/rout=0.01).Itisalmostconstant exceptfortheanglesnear the edge-on direction, the scatterings should occur at the theedgeofthetorus. rim of the torus; otherwise, they will be absorbed by the near side of the torus. θ =65° FortheBN11geometry,thetorusextendstothecentre 10−4 θin=75° in and the column densities are the same for different incli- θ =85° in nation angles. As a result, if the low-energy photons are V e scattered and can escape to the observer, they can only be s/k10−5 n scattered very near to the centre; otherwise, they will be o ot absorbed before reaching a large radius. Therefore, the re- Ph flection component is only visible when the inclination is 10−6 slightly larger than the half-opening angle (a few degrees). Thepossibletrajectoryofthescatteredphotonsisindicated bythearrowsinFigure3.Fortheedge-oncase,thescattered 10 0 101 102 region is obscured bythenear sideof thetorus. Ifthescat- E (keV) teredphotonsintendtoescapetotheedge-ondirection,they Figure 6. The scattered component is significantly suppressed shouldbescatteredatalargeradiusandfollowthewayindi- intheedge-ondirectionunderMY09’sgeometry. catedbythebluearrowsinFigure3.However,suchphotons should be rare, since most of them will be absorbed before reachingthelargeradius.Thisisalsothereasonforthesig- 10−2 nificantdecreasefoundintheFigure9inIK09.Weplotthe θ =65° positions of the scatterings in Figure 9, which are indeed in cisonvceernytsrmataeldl cinomtphaerecdenwtriatlhptahretoouftetrheratdoiruuss.(2Tphce)roefgtiohne 10−3 θθin==7855°° in torus. Therefore, this reflection component in the edge-on eV MY (total) θ =85° k in direction should be very weak underthe geometry of BN11 ns/10−4 and IK09, as shown byour simulations in Figure 4. oto h P 10−5 AsmentionedinSection2.2,theEW(FeKα)ofBN11is also different from our simulations. For optically thin case, EW(FeKα)canbeanalytically calculated,e.g.byequation 10−6 (5) in MY09, and nearly isotropic. Thus, we take this ana- 100 101 102 103 E (keV) lyticalresultasthebenchmarktestofBN11’smodelandour simulations.UndertheassumptioninFigure3ofBN11,the Figure 7. The scattered component only weakly depends on ◦ analyticalEW(FeKα)is3.7eVforΓ=2.0,θtor =60 ,and theinclinationangels inBN11’smodel.Thestrengthofthelow- NH =1022 cm−2. The EW(Fe Kα) of our simulation under energycomponent inedge-ondirectionismuchhigherthanthat thesameassumptioniswellconsistentwith3.7eV(atbetter producedbyMY09’smodel(scatteredanddirectioncomponents than1%level).However,theEWofBN11’s modelisabout areadded). 4.4eVforthesamecase.Sincetheircontinuaat6.4keVare consistent with our results at 1% level even for theedge-on case of NH =1024 cm−2, there should be some problems in thetransportationofFeKαphotons,whichmightberelated to the problem inducing the overestimate of the reflection component. X-ray models for tori in AGNs 5 1 0.15 0.5 0.1 c) 0.05 z (p 0 pc) 0 z ( −0.5 −0.05 −1 −0.1 0 0.5 1 1.5 2 2.5 3 (x2+y2)1/2 (pc) −0.15 0 0.05 0.1 0.15 0.2 0.25 (x2+y2)1/2 (pc) 1 0.15 0.5 0.1 c) p 0 z ( 0.05 −0.5 pc) 0 z ( −0.05 −1 0 0.5 1 1.5 2 2.5 3 (x2+y2)1/2 (pc) −0.1 −0.15 Figure 8. Positions of the scatterings of the photons (1-2 keV) 0 0.05 0.1 0.15 0.2 0.25 escapedtocosθin=0−0.2(top)andcosθin=0.4−0.5(bottom) (x2+y2)1/2 (pc) under MY09’sgeometry. The3-D positions areprojected onto a planeto show thedistributionmoreclearly. Thebluelineshows Figure 9. Positions of the scatterings of the photons (1-2 keV) theboundaryofthetorusandthecentralX-raysourceislocated escapedtocosθin=0−0.49(top)andcosθin=0.49−0.5(bot- attheorigin. tom)underBN11’sgeometry.Theintervalsofcosθinaredifferent fromthatinFigure8,sincethenumberofthescatteredphotons under BN’sgeometry rapidlydecreases whenthe inclinationan- 4 CONCLUSIONS gle is larger than the half-opening angle of the torus by a few degrees. The 3-D positions are projected onto a plane to show With thecodeconstructed using Geant4, wecan reproduce the distribution more clearly. The inner radius of the torus is 0 well thecontinuaandthestrength of FeKαlineof MY09’s pcandtheouterradiusis2pc(notshown).Thebluelineshows model.However,thereflectioncomponentinthelow-energy theboundaryofthetorusandthecentralX-raysourceislocated band is much lower than that of BN11’s model. We have attheorigin. discussed theorigin ofthisreflection componentandshown that the scattered region is concentrated in the centre and Brightman M., UedaY., 2012, MNRAS,423, 702 invisible in the edge-on directions under the BN11’s geom- BuchnerJ., et al., 2014, A&A,564, A125 etry.Therefore, it seems thestrength of thereflection com- Gandhi P., et al., 2014, arXiv, arXiv:1407.1844 ponentisoverestimated inBN11fortheedge-ondirections. IkedaS., Awaki H., Terashima Y.,2009, ApJ, 692, 608 ThestrengthofFeKαlineofBN11’smodelisalsodifferent Liu T., Wang J.-X., 2010, ApJ,725, 2381 from our results and the analytical result in the optically Liu Y., LiX., 2014, ApJ,787, 52 thin case, which is likely to be due to the problem in the Magdziarz P., Zdziarski A.A., 1995, MNRAS,273, 837 transportationofFeKαphotons.Theaccuracyofthemodel Murphy K.D., Yaqoob T., 2009, MNRAS,397, 1549 is crucial to any conclusions from thespectral fitting. Murphy K.D., Yaqoob T., 2011, MNRAS,415, 3962 NandraK.,O’NeillP.M.,GeorgeI.M.,ReevesJ.N.,2007, MNRAS,382, 194 ACKNOWLEDGMENTS Ricci C., Ueda Y., Ichikawa K., Paltani S., Boissay R., This work is supported by the National Natural Science GandhiP.,StalevskiM.,AwakiH.,2014,A&A,567,A142 Foundation of Chinaundergrant Nos.11103019, 11303027, Shu X.W., Yaqoob T., Wang J. X., 2011, ApJ,738, 147 11133002, and 11103022. SinghV.,RisalitiG.,BraitoV.,ShastriP.,2012,MNRAS, 419, 2089 Yaqoob T., 2012, MNRAS,423, 3360 REFERENCES ThispaperhasbeentypesetfromaTEX/LATEXfileprepared AntonucciR., 1993, ARA&A,31, 473 bythe author. Ar´evalo P., et al., 2014, ApJ, 791, 81 Brightman M., Nandra K., 2012, MNRAS,422, 1166 Brightman M., Nandra K., 2011, MNRAS,413, 1206 Brightman M.,NandraK.,SalvatoM.,HsuL.-T.,AirdJ., Rangel C., 2014, MNRAS,443, 1999